Georgia Standards Alignment Grades One through Twelve

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Georgia Standards Alignment

Standards List with Aligned Product Skills

The Standards List with Aligned Product Skills Report is a standards-oriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product.

Note to Educator .....................................................iii

Grade 1 ..................................................... 1

Grade 2 ....................................................10

Grade 3 ....................................................18

Grade 4 ....................................................28

Grade 5 ....................................................38

Grade 6 ....................................................47

Grade 7 ....................................................58

Grade 8 ....................................................67

Mathematics I: Algebra .............................................76

Accelerated Mathematics 1 .........................................85

Mathematics III ....................................................96

Accelerated Mathematics 2 .......................................107

Mathematics I: Geometry .........................................120

Accelerated Mathematics 3 .......................................129

Mathematics 4 ..................................................138

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Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) 338-4204. Sincerely, Renaissance Sales and Funding Staff

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Agency Tag Set NameGeorgia, Math, 2004, Grade 1, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will understand how to represent numbers, and be able to add and subtract small numbers.

GA M1N1 - Students will estimate, model, compare, order, and represent whole numbers up to 100.

Topic 1 - Numbers and Operations

Obj. 27 - Compare whole numbers to 100 using words

GA M1N1.a - Represent numbers up to 100 using a variety of models, diagrams, and number sentences. Represent numbers larger than 10 in terms of tens and ones using manipulatives and pictures.


Obj. 19 - Count objects grouped in tens and ones

Obj. 20 - Model a number to 100 using tens and onesObj. 21 - Recognize a number from a model of tens and ones to 100

Obj. 32 - Relate a picture model to a basic addition factObj. 33 - Determine the basic addition fact shown by a picture modelObj. 36 - Relate a picture model to a basic subtraction factObj. 37 - Determine the basic subtraction fact shown by a picture modelObj. 45 - Determine equivalent addition or subtraction expressions involving words or symbols

GA M1N1.b - Correctly count and represent the number of objects in a set using numerals.


Obj. 5 - Count objects to 20

Obj. 19 - Count objects grouped in tens and onesObj. 21 - Recognize a number from a model of tens and ones to 100

GA M1N1.c - Compare small sets using the terms greater than, less than, and equal to.


Obj. 26 - Compare sets of objects using words

GA M1N1.d - Understand the magnitude and order of numbers up to 100 by making ordered sequences and representing them on a number line.


Obj. 6 - Count on by ones from a number less than 100

Obj. 7 - Count back by ones from a number less than 20

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Grade 1

Accelerated Math Grade 1

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Agency Tag Set NameGeorgia, Math, 2004, Grade 1, Performance Standards, State Department of EducationStandard Topic Description Objective Description


Obj. 8 - Count back by ones from a number between 20 and 100Obj. 9 - Identify a number to 20 represented by a point on a number lineObj. 10 - Locate a number to 20 on a number lineObj. 28 - Order whole numbers to 100 in ascending orderObj. 29 - Order whole numbers to 100 in descending order

GA M1N1.e - Exchange equivalent quantities of coins by making fair trades involving combinations of pennies, nickels, dimes, and quarters up to one dollar; count out a combination of coins needed to purchase items up to one dollar.


Obj. 17 - Determine the value of a collection of like coins

Obj. 18 - Determine the value of a collection of mixed coins

GA M1N1.f - Identify bills ($1, $5, $10, $20) by name and value and exchange equivalent quantities by making fair trades involving combinations of bills; count out a combination of bills needed to purchase items that total up to twenty dollars.GA M1N2 - Students will understand place value notation for the numbers 1 to 99. (Discussions may allude to 3-digit numbers to assist in understanding place value.)

GA M1N2.a - Determine to which ten a given number is closest using tools such as a sequential number line or chart.GA M1N2.b - Represent collections of less than 30 objects with 2-digit numbers and understand the meaning of place value.

GA M1N2.c - Decompose numbers from 10 to 99 as the appropriate number of tens and ones.GA M1N3 - Students will add and subtract numbers less than 100, as well as understand and use the inverse relationship between addition and subtraction.


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GA M1N3.a - Identify one more than, one less than, 10 more than, and 10 less than a given number.


Obj. 11 - Determine one more than or one less than a given number

Obj. 12 - Determine ten more than or ten less than a given number

GA M1N3.b - Skip-count by 2s, 5s, and 10s, forward and backwards; to and from numbers up to 100.


Obj. 13 - Count by 2s to 50 starting from a multiple of 2

Obj. 14 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively

GA M1N3.c - Compose/decompose numbers up to 10 (e. g. 3+5=8, 8=5+2+1).


Obj. 30 - Determine equivalent forms of a number, up to 10

Topic 2 - Algebraic Thinking Obj. 62 - Determine equivalent addition or subtraction expressions involving 1-digit numbers

GA M1N3.d - Understand a variety of situations to which subtraction may apply: taking away from a set, comparing two sets, and determining how many more or how many less.


Obj. 31 - Determine the missing portion in a partially screened (hidden) collection of up to 10 objects

Obj. 36 - Relate a picture model to a basic subtraction factObj. 37 - Determine the basic subtraction fact shown by a picture model

GA M1N3.e - Understand addition and subtraction number combinations using strategies such as counting on, counting back, doubles and making tens.


Obj. 34 - Relate a number-line model to a basic addition fact

Obj. 35 - Determine the basic addition fact shown by a number-line modelObj. 38 - Determine the basic subtraction fact shown by a number-line modelObj. 39 - Relate a number-line model to a basic subtraction factObj. 40 - Apply the relationship between addition and counting onObj. 41 - Apply the relationship between subtraction and counting back


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GA M1N3.f - Know the single-digit addition facts to 18 and corresponding subtraction facts with understanding and fluency. (Use strategies such as relating to facts already known, applying the commutative property, and grouping facts into families.)


Obj. 42 - Know basic addition facts to 10 plus 10

Obj. 43 - Know basic subtraction facts to 20 minus 10Obj. 47 - Complete an addition and subtraction fact family

Topic 2 - Algebraic Thinking Obj. 62 - Determine equivalent addition or subtraction expressions involving 1-digit numbers

GA M1N3.g - Apply addition and subtraction to 2 digit numbers without regrouping (e.g.15 + 4, 80 - 60, 56 + 10, 100 - 30, 52 + 5).


Obj. 44 - Add three 1-digit numbers

Obj. 49 - Add multiples of 10, sums to 90Obj. 50 - Subtract multiples of 10 up to 90Obj. 51 - Add zero to any number less than 100Obj. 52 - Subtract zero from any number less than 100Obj. 53 - Add a 2-digit and a 1-digit number without regroupingObj. 54 - Add two 2-digit numbers without regroupingObj. 55 - Subtract a 1-digit number from a 2-digit number without regroupingObj. 56 - Subtract a 2-digit number from a 2-digit number without regroupingObj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

GA M1N3.h - Solve and create word problems involving addition and subtraction to 100 without regrouping. Use words, pictures and concrete models to interpret story problems and reflect the combining of sets as addition and taking away or comparing elements of sets as subtraction.


Obj. 46 - WP: Use basic addition or subtraction facts to solve problems


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Obj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

Topic 2 - Algebraic Thinking Obj. 65 - WP: Determine a basic addition- or subtraction-fact number sentence for a given situation

GA M1N4 - Students will count collections of up to 100 objects by dividing them into equal parts and represent the results using words, pictures, or diagrams.GA M1N4.a - Use informal strategies to share objects equally between two to five people.GA M1N4.b - Build number patterns, including concepts of even and odd, using various concrete representations. (Examples of concrete representations include a hundreds chart, ten grid frame, place value chart, number line, counters, or other objects.).

Topic 2 - Algebraic Thinking Obj. 69 - Complete a pattern on a 1 to 100 chart

GA M1N4.c - Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of objects or a whole using pictures and models.GA M1N4.d - Understand halves and fourths as representations of equal parts of a whole. - Students will measure basic quantitative attributes of concrete objects.GA M1M1 - Students will compare and/or order the length, weight, or capacity of two or more objects by using direct comparison or a nonstandard unit.GA M1M1.a - Directly compare and/or order length, height, weight, and capacity of concrete objects.

Topic 3 - Geometry and Measurement

Obj. 70 - Compare objects using the vocabulary of measurement

Obj. 71 - Compare and order objects by attributes of height or length

GA M1M1.b - Estimate and measure using a non-standard unit that is smaller than the object to be measured.


Obj. 74 - Estimate length in nonstandard units


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GA M1M1.c - Measure with a tool by creating a "ruled" stick, tape, or container by marking off ten segments of the repeated single unit.

GA M1M2 - Students will develop an understanding of the measurement of time.GA M1M2.a - Tell time to the nearest hour and half hour and understand the movement of the minute hand and how it relates to the hour hand.


Obj. 76 - Tell time to the hour

Obj. 77 - Tell time to the half hourGA M1M2.b - Begin to understand the relationship of calendar time by knowing the number of days in a week and months in a year.GA M1M2.c - Compare and/or order the sequence or duration of events (e.g., shorter/longer and before/after).


Obj. 78 - Order events by time

- Students will understand the concepts of basic geometric shapes and spatial relationships of concrete objects.GA M1G1 - Students will study and create various two and three-dimensional figures and identify basic figures (squares, circles, triangles, and rectangles) within them.

GA M1G1.a - Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.


Obj. 81 - Identify a circle, a triangle, a square, or a rectangle

GA M1G1.b - Build, represent, name, and describe cylinders, cones, and rectangular prisms.GA M1G1.c - Create pictures and designs using shapes, including overlapping shapes.GA M1G2 - Students will compare, contrast, and/or classify geometric shapes by the common attributes of position, shape, size, number of sides, and number of corners.


Obj. 82 - Determine the common attributes in a set of geometric shapes

Obj. 83 - Determine the group in which a geometric shape belongsObj. 84 - Determine the rule used to sort geometric shapes


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GA M1G3 - Students will arrange and describe objects in space by proximity, position, and direction (near, far, below, above, up, down, behind, in front of, next to, and left or right of).


Obj. 72 - Apply the vocabulary of position or direction

- Students will pose questions, collect, organize and interpret data about themselves and their surroundings.GA M1D1 - Students will create simple tables and graphs and interpret them.GA M1D1.a - Interpret tally marks, picture graphs, and bar graphs.

Topic 4 - Data Analysis and Statistics

Obj. 88 - Read a 2-category tally chartObj. 90 - Answer a question using information from a 2-category tally chartObj. 91 - Read a picture graphObj. 93 - Answer a question using information from a picture graphObj. 94 - Read a pictograph (1 symbol = 1 object)Obj. 96 - Answer a question using information from a pictograph (1 symbol = 1 object)Obj. 97 - Read a bar graphObj. 99 - Answer a question using information from a bar graph

GA M1D1.b - Pose questions, collect, sort, organize and record data using objects, pictures, tally marks, picture graphs, and bar graphs.


Obj. 89 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)

Obj. 92 - Use a picture graph to represent groups of objects (1 symbol = 1 object)Obj. 95 - Use a pictograph to represent groups of objects (1 symbol = 1 object)

- Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.

GA M1P1 - Students will solve problems (using appropriate technology).GA M1P1.a - Build new mathematical knowledge through problem solving.


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GA M1P1.b - Solve problems that arise in mathematics and in other contexts.


Obj. 46 - WP: Use basic addition or subtraction facts to solve problems

Obj. 57 - WP: Add or subtract a 1- and 2-digit number without regroupingObj. 58 - WP: Add or subtract two 2-digit numbers without regrouping

GA M1P1.c - Apply and adapt a variety of appropriate strategies to solve problems.GA M1P1.d - Monitor and reflect on the process of mathematical problem solving.GA M1P2 - Students will reason and evaluate mathematical arguments.

GA M1P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.GA M1P2.b - Make and investigate mathematical conjectures.GA M1P2.c - Develop and evaluate mathematical arguments and proofs.

GA M1P2.d - Select and use various types of reasoning and methods of proof.GA M1P3 - Students will communicate mathematically.GA M1P3.a - Organize and consolidate their mathematical thinking through communication.GA M1P3.b - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

GA M1P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA M1P3.d - Use the language of mathematics to express mathematical ideas precisely.


Obj. 45 - Determine equivalent addition or subtraction expressions involving words or symbols

GA M1P4 - Students will make connections among mathematical ideas and to other disciplines.GA M1P4.a - Recognize and use connections among mathematical ideas.


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GA M1P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M1P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M1P5 - Students will represent mathematics in multiple ways.GA M1P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA M1P5.b - Select, apply, and translate among mathematical representations to solve problems.GA M1P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


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Agency Tag Set NameGeorgia, Math, 2004, Grade 2, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will further develop their understanding of numbers (including fractions) and how to represent them. The students will understand and apply addition, subtraction and multiplication through concrete manipulation and perform basic calculations.

GA M2N1 - Students will use multiple representation of numbers to connect symbols to quantities.

Topic 1 - Number Sense and Operations

Obj. 2 - Determine the word form of a whole number to 1,000

GA M2N1.a - Represent numbers using a variety of models, diagrams, and number sentences (e.g., 4703 represented as 4,000 + 700 + 3, and units, 47 hundreds + 3, or 4,500 + 203).


Obj. 12 - Model a number using hundreds, tens, and ones to 1,000

Obj. 13 - Recognize a number from a model of hundreds, tens, and ones to 1,000Obj. 14 - Represent a 3-digit number as hundreds, tens, and ones

Obj. 15 - Determine the 3-digit number represented as hundreds, tens, and onesObj. 16 - Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones

GA M2N1.b - Understand the relative magnitudes of numbers using 10 as a unit, 100 as a unit, or 1000 as a unit. Represent 2-digit numbers with drawings of tens and ones and 3-digit numbers with drawings of hundreds, tens, and ones.


Obj. 9 - Determine the value of a digit in a 3-digit number

Obj. 10 - Determine which digit is in a specified place in a 3-digit whole numberObj. 12 - Model a number using hundreds, tens, and ones to 1,000Obj. 13 - Recognize a number from a model of hundreds, tens, and ones to 1,000

GA M2N1.c - Use money as a medium of exchange. Make change and use decimal notation and the dollar and cent symbols to represent the collection of coins and currency.


Obj. 17 - Determine the value of a collection of bills and coins



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GA M2N2 - Students will build fluency with multi-digit addition and subtraction.GA M2N2.a - Correctly add and subtract two whole numbers up to three digits each with regrouping.


Obj. 24 - Determine a number pair that totals 100

Obj. 25 - Determine a number pair that totals 1,000Obj. 28 - Add two 3-digit numbers without regroupingObj. 29 - Add two 2-digit numbers with regrouping, given a modelObj. 30 - Add money values using cents or dollars with regroupingObj. 31 - Add a 2-digit number to a 1-digit number with regroupingObj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100Obj. 34 - Add 2- and 3-digit numbers with no more than one regrouping

Obj. 35 - Add two 3-digit numbers with one regroupingObj. 36 - Subtract a 3-digit number from a 3-digit number without regroupingObj. 37 - Subtract money values using cents or dollars with one regroupingObj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingObj. 39 - Subtract a 1- or 2-digit number from a 3-digit number with one regroupingObj. 40 - Subtract a 3-digit number from a 3-digit number with one regroupingObj. 41 - WP: Add or subtract numbers without regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

GA M2N2.b - Understand and use the inverse relation between addition and subtraction to solve problems and check solutions.


Obj. 43 - Apply the inverse relationship between addition and subtraction with 2- and 3-digit numbers


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Topic 2 - Algebraic Thinking Obj. 65 - Determine a missing addend in a number sentence involving 2-digit numbersObj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbersObj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers

Obj. 69 - WP: Use an open sentence to represent a given situation

GA M2N2.c - Use mental math strategies such as benchmark numbers to solve problems.GA M2N2.d - Use basic properties of addition (commutative, associative, and identity) to simplify problems (e.g. 98 + 17 by taking two from 17 and adding it to the 98 to make 100 and replacing the original problem by the sum 100 + 15).

GA M2N2.e - Estimate to determine if solutions are reasonable for addition and subtraction.


Obj. 44 - Estimate the sum of two 2-digit numbers

Obj. 45 - Estimate the difference of two 2-digit numbers

GA M2N3 - Students will understand multiplication, multiply numbers, and verify results.GA M2N3.a - Understand multiplication as repeated addition.


Obj. 47 - Use a repeated addition sentence to represent the sum of equal groupsObj. 49 - Represent repeated addition as multiplication

GA M2N3.b - Use repeated addition, arrays, and counting by multiples (skip counting) to correctly multiply 1-digit numbers and construct the multiplication table.


Obj. 46 - Determine the sum of equal groups using pictures

Obj. 50 - Relate a multiplication sentence to an array model

GA M2N3.c - Use the multiplication table (grid) to determine a product of two numbers.


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GA M2N3.d - Use repeated subtraction, equal sharing, and forming equal groups to divide large collections of objects and determine factors for multiplication.


Obj. 53 - Recognize the number of equal groups using pictures

Obj. 54 - Divide objects into equal groups using picturesObj. 55 - Determine the remainder when dividing objects into equal groupsObj. 56 - Determine the number of equal groups of objects excluding the remainderObj. 57 - WP: Divide objects into equal groups by sharing

GA M2N4 - Students will understand and compare fractions.GA M2N4.a - Model, identify, label, and compare fractions (thirds, sixths, eighths, tenths) as a representation of equal parts of a whole or of a set.


Obj. 58 - Identify a unit fraction as part of a whole

Obj. 59 - Identify a unit fraction as part of a set of objectsObj. 60 - Identify a fraction as part of a set of objectsObj. 61 - Identify a fraction as part of a wholeObj. 63 - Compare unit fractions using pictorial models

GA M2N4.b - Know that when all fractional parts are included, such as three thirds, the result is equal to the whole.


Obj. 62 - Relate a fraction equal to a whole to a pictorial model

GA M2N5 - Students will represent and interpret quantities and relationships using mathematical expressions including equality and inequality signs (=,>,<, not equal to).


Obj. 21 - Compare whole numbers to 1,000 using the symbols <, >, and =

GA M2N5.a - Include the use of boxes or ___ to represent a missing value.

Topic 2 - Algebraic Thinking Obj. 67 - Determine equivalent addition expressions involving 2-digit numbersObj. 69 - WP: Use an open sentence to represent a given situation

GA M2N5.b - Represent problem solving situations where addition, subtraction or multiplication may be applied using mathematical expressions.

Topic 2 - Algebraic Thinking Obj. 69 - WP: Use an open sentence to represent a given situation


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- Students will understand length, time, and temperature and choose an appropriate tool to measure them.GA M2M1 - Students will know the standard units of inch, foot, yard, and metric units of centimeter and meter and measure length to the nearest inch or centimeter.


Obj. 76 - Measure length in inches

Obj. 77 - Measure length in centimeters

GA M2M1.a - Compare the relationship of one unit to another by measuring objects twice using different units each time.GA M2M1.b - Estimate lengths, and then measure to determine if estimations were reasonable.GA M2M1.c - Determine an appropriate tool and unit for measuring.GA M2M2 - Students will tell time to the nearest five minutes and know relationships of time such as the number of seconds in a minute, minutes in an hour and hours in a day.


Obj. 78 - Tell time to the quarter hour

Obj. 79 - Tell time to 5-minute intervals

GA M2M3 - Students will explore temperature.GA M2M3.a - Determine a reasonable temperature for a given situation.GA M2M3.b - Read a thermometer. Topic 3 - Geometry and

MeasurementObj. 81 - Read a thermometer in degrees CelsiusObj. 82 - Read a thermometer in degrees Fahrenheit

- Students will understand basic and compound geometric shapes together with the elements from which they are composed.

GA M2G1 - Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of sides and vertices and the sizes of angles (right angle, obtuse, acute).


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GA M2G2 - Students will describe and classify solid geometric figures (prisms, pyramids, cylinders, cones, and spheres) according to such things as the number of edges and vertices and the number and shape of faces and angles.GA M2G2.a - Recognize the (plane) shapes of the faces of a geometric solid and count the number of faces of each type.GA M2G2.b - Recognize the shape of an angle as a right angle, an obtuse, or acute angle.GA M2G3 - Students will describe the change in attributes as two and three-dimensional shapes are cut and rearranged.


Obj. 86 - Decompose a plane shape composed of three or more simpler shapes

- Students will pose questions, collect, organize, and interpret data about themselves and their surroundings.GA M2D1 - Students will create simple tables and graphs and interpret their meaning.GA M2D1.a - Create, organize and display data using pictographs, Venn diagrams, bar graphs, picture graphs, simple charts, and tables to record results with scales of 1, 2 and 5.


Obj. 91 - Use a tally chart to represent data

Obj. 97 - Use a bar graph with a y-axis scale by 2s to represent data

GA M2D1.b - Know how to interpret picture graphs, Venn diagrams, and bar graphs.


Obj. 96 - Read a bar graph with a y-axis scale by 2s

Obj. 98 - Answer a question using information from a bar graph with a y-axis scale by 2s




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Obj. 41 - WP: Add or subtract numbers without regrouping

Obj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

Topic 2 - Algebraic Thinking Obj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers





Topic 2 - Algebraic Thinking Obj. 69 - WP: Use an open sentence to represent a given situation

GA M2P4 - Students will make connections among mathematical ideas and to other disciplines.GA M2P4.a - Recognize and use connections among mathematical ideas.


Obj. 7 - Solve problems involving the concept of odd and even numbers


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GA M2P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M2P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M2P5 - Students will represent mathematics in multiple ways.GA M2P5.a - Create and use representations to organize, record, and communicate mathematical ideas.


Obj. 91 - Use a tally chart to represent data

Obj. 97 - Use a bar graph with a y-axis scale by 2s to represent data

GA M2P5.b - Select, apply, and translate among mathematical representations to solve problems.GA M2P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


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Agency Tag Set NameGeorgia, Math, 2004, Grade 3, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will use decimal fractions and common fractions to represent parts of a whole. They will also understand the four arithmetic operations for whole numbers and use them in basic calculations, and apply them in problem solving situations.

GA M3N1 - Students will further develop their understanding of whole numbers and decimals and ways of representing them.GA M3N1.a - Identify place values from tenths through ten thousands.


Obj. 3 - Determine the value of a digit in a 4- or 5-digit whole numberObj. 4 - Determine which digit is in a specified place in a 4- or 5-digit whole number

GA M3N1.b - Understand the relative sizes of digits in place value notation (10 times, 100 times, 1/10 of a single digit whole number) and ways to represent them including word name, standard form, and expanded form.


Obj. 5 - Represent a 4-digit whole number as thousands, hundreds, tens, and ones

Obj. 6 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Obj. 7 - Represent a 4- or 5-digit whole number in expanded formObj. 8 - Determine the 4- or 5-digit whole number represented in expanded formObj. 9 - Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones

Obj. 10 - Determine the result of changing a digit in a 4- or 5-digit whole number

GA M3N2 - Students will further develop their skills of addition and subtraction and apply them in problem solving.GA M3N2.a - Use the properties of addition and subtraction to compute and verify the results of computation.

GA M3N2.b - Use mental math and estimation strategies to add and subtract.


Obj. 28 - Estimate a sum or difference of whole numbers to 10,000 by rounding



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Obj. 29 - Estimate a sum or difference of two 3- or 4-digit whole numbers using front-end estimationObj. 30 - Estimate a sum or difference of 2- to 4-digit whole numbers using any methodObj. 31 - Estimate a sum of three 2- to 4-digit numbers using any method

Obj. 32 - WP: Estimate a sum or difference of two 3- or 4-digit whole numbers using any method

GA M3N2.c - Solve problems requiring addition and subtraction.


Obj. 13 - Add 3- and 4-digit whole numbers with regroupingObj. 14 - Add three 2- to 3-digit whole numbersObj. 15 - Subtract 3- and 4-digit whole numbers with regroupingObj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping

Topic 2 - Algebraic Thinking Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbersObj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbers

GA M3N2.d - Model addition and subtraction by counting back change using the fewest number of coins.

GA M3N3 - Students will further develop their understanding of multiplication of whole numbers and develop the ability to apply it in problem solving.GA M3N3.a - Describe the relationship between addition and multiplication, i.e., multiplication is defined as repeated addition.GA M3N3.b - Know the multiplication facts with understanding and fluency to 10 x 10.


Obj. 35 - Know basic multiplication facts to 10 x 10

Obj. 39 - WP: Multiply using basic facts to 10 x 10

Topic 2 - Algebraic Thinking Obj. 63 - WP: Determine a multiplication or division sentence for a given situation


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GA M3N3.c - Use arrays and area models to develop understanding of the distributive property and to determine partial products for multiplication of 2- or 3-digit numbers by a 1-digit number.GA M3N3.d - Understand the effect on the product when multiplying by multiples of 10.


Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100

GA M3N3.e - Apply the identity, commutative and associative properties of multiplication and verify the results.GA M3N3.f - Use mental math and estimation strategies to multiply.


Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100

GA M3N3.g - Solve problems requiring multiplication.


Obj. 39 - WP: Multiply using basic facts to 10 x 10

Topic 2 - Algebraic Thinking Obj. 58 - Determine the missing multiplicand in a number sentence involving basic factsObj. 59 - Determine the missing dividend or divisor in a number sentence involving basic factsObj. 63 - WP: Determine a multiplication or division sentence for a given situation

GA M3N4 - Students will understand the meaning of division and develop the ability to apply it in problem solving.GA M3N4.a - Understand the relationship between division and multiplication and between division and subtraction.


Obj. 41 - Complete a multiplication and division fact family

Topic 2 - Algebraic Thinking Obj. 58 - Determine the missing multiplicand in a number sentence involving basic factsObj. 59 - Determine the missing dividend or divisor in a number sentence involving basic factsObj. 60 - Recognize equivalent multiplication or division expressions involving basic facts


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GA M3N4.b - Recognize that division may be two situations: the first is determining how many equal parts of a given size or amount may be taken away from the whole as in repeated subtraction, and the second is determining the size of the parts when the whole is separated into a given number of equal parts as in a sharing model.


Obj. 34 - Use a division sentence to represent objects divided into equal groups

GA M3N4.c - Recognize problem-solving situations in which division may be applied and write corresponding mathematical expressions.


Obj. 34 - Use a division sentence to represent objects divided into equal groups


GA M3N4.d - Explain the meaning of a remainder in division in different circumstances.GA M3N4.e - Divide a 2 and 3-digit number by a 1-digit divisor.


Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10


GA M3N4.f - Solve problems requiring division.


Obj. 40 - WP: Divide using basic facts to 100 ÷ 10

Topic 2 - Algebraic Thinking Obj. 58 - Determine the missing multiplicand in a number sentence involving basic factsObj. 59 - Determine the missing dividend or divisor in a number sentence involving basic factsObj. 63 - WP: Determine a multiplication or division sentence for a given situation

GA M3N4.g - Use mental math strategies to divide.


Obj. 40 - WP: Divide using basic facts to 100 ÷ 10

GA M3N5 - Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations.GA M3N5.a - Identify fractions that are decimal fractions and/or common fractions.


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GA M3N5.b - Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3).GA M3N5.c - Understand the fraction a/b represents a equal sized parts of a whole that is divided into b equal sized parts.


Obj. 44 - Determine a pictorial model of a fraction of a whole

GA M3N5.d - Know and use decimal fractions and common fractions to represent the size of parts created by equal divisions of a whole.


Obj. 44 - Determine a pictorial model of a fraction of a whole

GA M3N5.e - Understand the concept of addition and subtraction of decimal fractions and common fractions with like denominators.GA M3N5.f - Model addition and subtraction of decimal fractions and common fractions with like denominators.GA M3N5.g - Use mental math and estimation strategies to add and subtract decimal fractions and common fractions with like denominators.


Obj. 54 - Determine fraction pairs that total 1

GA M3N5.h - Solve problems involving decimal fractions and common fractions with like denominators. - Students will understand and measure time and length. They will also model and calculate perimeter and area of simple geometric figures.


Obj. 74 - Tell time to the minute

Obj. 76 - Calculate elapsed time within an hour, given two clocks, without regroupingObj. 77 - Calculate elapsed time within an hour, given two clocks, with regroupingObj. 78 - WP: Calculate elapsed time within an hour given two clocks

Obj. 79 - WP: Calculate elapsed time within an hourObj. 80 - WP: Determine the end time given the start time and the elapsed time within an hourObj. 81 - WP: Determine the start time given the end time on a clock and the elapsed time within an hour


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Obj. 82 - WP: Determine the start time given the end time and the elapsed time within an hour

GA M3M1 - Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter-hour.GA M3M2 - Students will measure length choosing appropriate units and tools.GA M3M2.a - Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances.

GA M3M2.b - Measure to the nearest 1/4 inch, 1/2 inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.


Obj. 67 - Measure length to the nearest half inch or quarter inch

GA M3M2.c - Estimate length and represent it using appropriate units.

GA M3M2.d - Compare one unit to another within a single system of measurement.


Obj. 68 - Convert between inches, feet, and yards

Obj. 69 - Convert between centimeters and meters

GA M3M3 - Students will understand and measure the perimeter of geometric figures.GA M3M3.a - Understand the meaning of the linear unit and measurement in perimeter.GA M3M3.b - Understand the concept of perimeter as being the length of the boundary of a geometric figure.


Obj. 87 - WP: Determine the perimeter of a rectangular shape given a grid with a reference unit

GA M3M3.c - Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.


Obj. 86 - Determine a method for finding the perimeter of a shape given the side lengths

Obj. 87 - WP: Determine the perimeter of a rectangular shape given a grid with a reference unitObj. 88 - WP: Determine the perimeter of a shape given a model showing all side lengths

GA M3M4 - Students will understand and measure the area of simple geometric figures (squares and rectangles).


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GA M3M4.a - Understand the meaning of the square unit and measurement in area.GA M3M4.b - Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot, etc.).GA M3M4.c - Determine the area of squares and rectangles by counting, addition, and multiplication with models.


Obj. 90 - WP: Determine the area of a rectangular shape given a picture on a grid

- Students will further develop their understanding of characteristics of previously studied geometric figures.GA M3G1 - Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.GA M3G1.a - Draw and classify previously learned fundamental geometric figures and scalene, isosceles, and equilateral triangles.

GA M3G1.b - Identify and compare the properties of fundamental geometric figures.


Obj. 92 - Identify parallel, perpendicular, and intersecting lines

Obj. 95 - Determine attributes of a triangle or a quadrilateral from a modelObj. 96 - Relate a model of a triangle or a quadrilateral to a list of attributes

GA M3G1.c - Examine and compare angles of fundamental geometric figures.


Obj. 97 - Identify a picture of a 3-dimensional shape

GA M3G1.d - Identify the center, diameter, and radius of a circle. - Students will understand how to express relationships as mathematical expressions.GA M3A1 - Students will use mathematical expressions to represent relationships between quantities and interpret given expressions.GA M3A1.a - Describe and extend numeric and geometric patterns.

Topic 2 - Algebraic Thinking Obj. 64 - Extend a number pattern


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GA M3A1.b - Describe and explain a quantitative relationship represented by a formula (such as the perimeter of a geometric figure).

GA M3A1.c - Use a symbol, such as square and triangle, to represent an unknown and find the value of the unknown in a number sentence.

Topic 2 - Algebraic Thinking Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbers

Obj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbersObj. 58 - Determine the missing multiplicand in a number sentence involving basic factsObj. 59 - Determine the missing dividend or divisor in a number sentence involving basic factsObj. 60 - Recognize equivalent multiplication or division expressions involving basic facts

- Students will gather, organize, and display data and interpret graphs.GA M3D1 - Students will create and interpret simple tables and graphs.

GA M3D1.a - Solve problems by organizing and displaying data in charts, tables, and graphs.GA M3D1.b - Construct and interpret line plot graphs, pictographs, Venn diagrams, and bar graphs using scale increments of 1, 2, 5, and 10.

Topic 4 - Data Analysis, Statistics, and Probability

Obj. 105 - Use a bar graph with a scale interval of 5 or 10 to represent data

Obj. 106 - Answer a question using information from a bar graph with a scale interval of 5 or 10




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Obj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regroupingObj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10


Obj. 78 - WP: Calculate elapsed time within an hour given two clocks

Obj. 79 - WP: Calculate elapsed time within an hourObj. 80 - WP: Determine the end time given the start time and the elapsed time within an hourObj. 81 - WP: Determine the start time given the end time on a clock and the elapsed time within an hour

Obj. 82 - WP: Determine the start time given the end time and the elapsed time within an hourObj. 87 - WP: Determine the perimeter of a rectangular shape given a grid with a reference unitObj. 88 - WP: Determine the perimeter of a shape given a model showing all side lengthsObj. 90 - WP: Determine the area of a rectangular shape given a picture on a grid



GA M3P2.d - Select and use various types of reasoning and methods of proof.


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GA M3P3 - Students will communicate mathematically.GA M3P3.a - Organize and consolidate their mathematical thinking through communication.GA M3P3.b - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.



GA M3P4 - Students will make connections among mathematical ideas and to other disciplines.GA M3P4.a - Recognize and use connections among mathematical ideas.GA M3P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M3P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M3P5 - Students will represent mathematics in multiple ways.GA M3P5.a - Create and use representations to organize, record, and communicate mathematical ideas.


Obj. 105 - Use a bar graph with a scale interval of 5 or 10 to represent data

GA M3P5.b - Select, apply, and translate among mathematical representations to solve problems.GA M3P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


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Agency Tag Set NameGeorgia, Math, 2004, Grade 4, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will further develop their understanding of whole numbers and master the four basic operations with whole numbers by solving problems. They will also understand rounding and when to use it appropriately. Students will further develop their understanding of addition and subtraction of decimal fractions and common fractions with like denominators.

GA M4N1. - Students will further develop their understanding of how whole numbers and decimals are represented in the base-ten numeration system.GA M4N1.a - Identify place value names and places from hundredths through one million.


Obj. 3 - Determine the value of a digit in a 6-digit whole number

Obj. 4 - Determine which digit is in a specified place in a 6-digit whole number

GA M4N1.b - Equate a number's word name, its standard form, and its expanded form.


Obj. 1 - Read a 6-digit whole number

Obj. 2 - Determine the word form of a 6-digit whole numberObj. 5 - Determine the whole number represented in expanded form written in powers of tenObj. 6 - Represent a 6-digit whole number in expanded form using powers of tenObj. 7 - Convert between proper expanded form and improper expanded form up to a 5-digit whole numberObj. 8 - Convert between standard form and improper expanded form up to a 5-digit whole numberObj. 62 - Read a decimal number through the hundredths placeObj. 63 - Determine the word form of a decimal number through the hundredths place

GA M4N2 - Students will understand and apply the concept of rounding numbers.



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GA M4N2.a - Round numbers to the nearest ten, hundred, or thousand.


Obj. 17 - Round a 4- to 6-digit whole number to a specified place

GA M4N2.b - Describe situations in which rounding numbers would be appropriate and determine whether to round to the nearest ten, hundred, or thousand.GA M4N2.c - Determine to which whole number or tenth a given decimal is closest using tools such as a number line, and/or charts.

GA M4N2.d - Round a decimal to the nearest whole number or tenth.


Obj. 80 - Round a decimal number to a specified place through hundredths

GA M4N2.e - Represent the results of computation as a rounded number when appropriate and estimate a sum or difference by rounding numbers.


Obj. 81 - Estimate a decimal number sum or difference by rounding to whole numbers

GA M4N3 - Students will solve problems involving multiplication of 2-3 digit numbers by 1 or 2 digit numbers.


Obj. 20 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000

Obj. 23 - Multiply a 3- or 4-digit whole number by a 1-digit whole number

Obj. 24 - Multiply a 2-digit whole number by a 2-digit whole numberObj. 25 - Multiply a 3-digit whole number by a 2-digit whole numberObj. 26 - Multiply three 1- and 2-digit whole numbersObj. 27 - WP: Multiply a multi-digit whole number by a 1-digit whole numberObj. 28 - WP: Multiply a 2-digit whole number by a 2-digit whole number

Obj. 29 - WP: Multiply a 3-digit whole number by a 2-digit whole number

GA M4N4 - Students will further develop their understanding of division of whole numbers and divide in problem solving situations without calculators.GA M4N4.a - Know the division facts with understanding and fluency.


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GA M4N4.b - Solve problems involving division by 1 or 2-digit numbers (including those that generate a remainder).


Obj. 33 - Divide a multi-digit whole number by 10 or 100 with no remainder

Obj. 34 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 35 - Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 36 - Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 37 - Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 38 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 39 - WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 40 - WP: Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotient


GA M4N4.c - Understand the relationship between dividend, divisor, quotient, and remainder.GA M4N4.d - Understand and explain the effect on the quotient of multiplying or dividing both the divisor and dividend by the same number. (2050 ÷ 50 yields the same answer as 205 ÷ 5).GA M4N5 - Students will further develop their understanding of the meaning of decimals and use them in computations.GA M4N5.a - Understand decimals are a part of the base-ten system.


Obj. 64 - Determine the decimal number from a pictorial model of tenths or hundredthsObj. 65 - Identify a pictorial model of tenths or hundredths of a decimal number


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GA M4N5.b - Understand the relative size of numbers and order two digit decimals.


Obj. 66 - Identify a decimal number to tenths represented by a point on a number lineObj. 67 - Locate a decimal number to tenths on a number lineObj. 72 - Compare decimal numbers through the hundredths place

Obj. 73 - Order decimal numbers through the hundredths place

GA M4N5.c - Add and subtract both one and two digit decimals.


Obj. 74 - Determine decimal number pairs that total 1 or 10Obj. 75 - Add two decimal numbers through hundredthsObj. 76 - Subtract two decimal numbers through hundredthsObj. 77 - WP: Add or subtract money amounts greater than $1Obj. 78 - WP: Solve a money problem involving 2 stepsObj. 79 - WP: Add or subtract decimal numbers of the same place through hundredths

GA M4N5.d - Model multiplication and division of decimals by whole numbers.GA M4N5.e - Multiply and divide both one and two digit decimals by whole numbers.


Obj. 82 - WP: Multiply a money amount by a 1-digit number

Obj. 83 - WP: Divide a money amount by a 1-digit number

GA M4N6 - Students will further develop their understanding of the meaning of decimal fractions and common fractions and use them in computations.GA M4N6.a - Understand representations of equivalent common fractions and/or decimal fractions.


Obj. 50 - Simplify a fraction

Obj. 51 - Determine a set of equivalent fractions

GA M4N6.b - Add and subtract fractions and mixed numbers with like denominators. (Denominators should not exceed twelve.)


Obj. 55 - Add fractions with like denominators no greater than 10

Obj. 59 - Subtract fractions with like denominators no greater than 10

GA M4N6.c - Use mixed numbers and improper fractions interchangeably.


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GA M4N7 - Students will explain and use properties of the four arithmetic operations to solve and check problems.GA M4N7.a - Describe situations in which the four operations may be used and the relationships among them.GA M4N7.b - Compute using the order of operations, including parentheses.

Topic 2 - Algebra Obj. 84 - Evaluate a numeric expression involving two operations

GA M4N7.c - Compute using the commutative, associative, and distributive properties.


Obj. 21 - Apply the distributive property to the multiplication of a 2-digit number by a 1- or 2-digit number

Obj. 22 - Apply the distributive property to multiply a multi-digit number by a 1-digit number

GA M4N7.d - Use mental math and estimation strategies to compute.


Obj. 20 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000Obj. 33 - Divide a multi-digit whole number by 10 or 100 with no remainder

- Students will measure weight in appropriate metric and standard units. They will also measure angles.GA M4M1 - Students will understand the concept of weight and how to measure weight.GA M4M1.a - Use standard and metric units to measure the weight of objects.GA M4M1.b - Know units used to measure weight (gram, kilogram, ounces, pounds, and tons).GA M4M1.c - Compare one unit to another within a single system of measurement.


Obj. 96 - Convert between customary units of weight using whole numbers

Obj. 98 - Convert between metric units of mass using whole numbers

GA M4M2 - Students will understand the concept of angles and how to measure them.GA M4M2.a - Use tools, such as a protractor or angle ruler, and other methods such as paper folding, drawing a diagonal in a square, to measure angles.


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GA M4M2.b - Understand the meaning and measure of a half rotation (180°) and a full rotation (360°).GA M4M2.c - Determine that the sum of the three angles of a triangle is always 180°. - Students will understand and build plane and solid geometric figures. They will also graph points on the coordinate plane.GA M4G1 - Students will define and identify the characteristics of geometric figures through examination and construction.GA M4G1.a - Examine and compare angles in order to classify and identify triangles by their angles.

GA M4G1.b - Describe parallel and perpendicular lines in plane geometric figures.


Obj. 124 - Identify a shape that has parallel or perpendicular sides

GA M4G1.c - Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties.


Obj. 126 - Classify a quadrilateral

GA M4G1.d - Compare and contrast the relationships among quadrilaterals.GA M4G2 - Students will understand fundamental solid figures.

GA M4G2.a - Compare and contrast a cube and a rectangular prism in terms of the number and shape of their faces, edges, and vertices.

GA M4G2.b - Describe parallel and perpendicular lines and planes in connection with the rectangular prism.GA M4G2.c - Build/collect models for solid geometric figures (cubes, prisms, cylinders, pyramids, spheres, and cones) using nets and other representations.GA M4G3 - Students will use the coordinate system.GA M4G3.a - Understand and apply ordered pairs in the first quadrant of the coordinate system.


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GA M4G3.b - Locate a point in the first quadrant in the coordinate plane and name the ordered pair.


Obj. 133 - Identify the location of an ordered pair in the first quadrant using compass directionsObj. 134 - Determine the ordered pair of a point in the first quadrant using compass directions

GA M4G3.c - Graph ordered pairs in the first quadrant. - Students will investigate and represent mathematical relationships between quantities using mathematical expressions in problem-solving situations.

GA M4A1 - Students will represent and interpret mathematical relationships in quantitative expressions.GA M4A1.a - Understand and apply patterns and rules to describe relationships and solve problems.

Topic 2 - Algebra Obj. 86 - Identify a missing term in a multiplication or a division number pattern

Obj. 87 - Extend a growing pictorial or nonnumeric patternObj. 88 - Identify a missing figure in a growing pictorial or nonnumeric patternObj. 89 - Identify a missing figure in a repeating pictorial or nonnumeric patternObj. 90 - Generate a table of paired numbers based on a ruleObj. 91 - Determine a rule that relates two variablesObj. 92 - Extend a number pattern in a table of related pairs

GA M4A1.b - Represent unknowns using symbols, such as square and triangle.GA M4A1.c - Write and evaluate mathematical expressions using symbols and different values. - Students will gather, organize, and display data. They will also compare features of graphs.

GA M4D1 - Students will gather, organize, and display data according to the situation and compare related features.


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GA M4D1.a - Construct and interpret line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs.


Obj. 135 - Read a line graph

Obj. 136 - Use a line graph to represent dataObj. 139 - Read a double-bar graph

Obj. 140 - Use a double-bar graph to represent data

GA M4D1.b - Investigate the features and tendencies of graphs.GA M4D1.c - Compare different graphical representations for a given set of data.GA M4D1.d - Identify missing information and duplications in data.

GA M4D1.e - Determine and justify the range, mode, and median of a set of data. - Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.




Obj. 27 - WP: Multiply a multi-digit whole number by a 1-digit whole numberObj. 28 - WP: Multiply a 2-digit whole number by a 2-digit whole number

Obj. 29 - WP: Multiply a 3-digit whole number by a 2-digit whole number




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Obj. 42 - WP: Solve a 2-step whole number problem using more than 1 operationObj. 77 - WP: Add or subtract money amounts greater than $1Obj. 78 - WP: Solve a money problem involving 2 stepsObj. 79 - WP: Add or subtract decimal numbers of the same place through hundredthsObj. 82 - WP: Multiply a money amount by a 1-digit numberObj. 83 - WP: Divide a money amount by a 1-digit number

GA M4P1.c - Apply and adapt a variety of appropriate strategies to solve problems.


Obj. 42 - WP: Solve a 2-step whole number problem using more than 1 operationObj. 78 - WP: Solve a money problem involving 2 steps

GA M4P1.d - Monitor and reflect on the process of mathematical problem solving.GA M4P2 - Students will reason and evaluate mathematical arguments.


GA M4P2.d - Select and use various types of reasoning and methods of proof.GA M4P3 - Students will communicate mathematically.GA M4P3.a - Organize and consolidate their mathematical thinking through communication.


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GA M4P3.b - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

GA M4P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA M4P3.d - Use the language of mathematics to express mathematical ideas precisely.GA M4P4 - Students will make connections among mathematical ideas and to other disciplines.GA M4P4.a - Recognize and use connections among mathematical ideas.GA M4P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M4P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M4P5 - Students will represent mathematics in multiple ways.GA M4P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA M4P5.b - Select, apply, and translate among mathematical representations to solve problems.GA M4P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


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Agency Tag Set NameGeorgia, Math, 2004, Grade 5, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will further develop their understanding of the concept of whole numbers. They will also understand the meanings of multiplication and division of decimals and use decimals and common fractions in computation, as well as in problem solving situations.GA M5N1 - Students will further develop their understanding of whole numbers.GA M5N1.a - Classify the set of counting numbers into subsets with distinguishing characteristics (odd/even, prime/composite).


Obj. 1 - Determine if a number to 50 is prime or composite

GA M5N1.b - Find multiples and factors.


Obj. 2 - Determine a complete list of whole number factor pairs for a number to 50Obj. 3 - Determine all the factors of a whole number to 50Obj. 7 - Determine the multiple(s) of a number

GA M5N1.c - Analyze and use divisibility rules.


Obj. 10 - Apply divisibility rules for 2, 5, or 10

GA M5N2 - Students will further develop their understanding of decimals as part of the base-ten number system.GA M5N2.a - Understand place value.


Obj. 69 - Determine the value of a digit in a decimal number to thousandths

GA M5N2.b - Analyze the effect on the product when a number is multiplied by 10, 100, 1000, 0.1, 0.01, and .001.GA M5N2.c - Use <, >, or = to compare decimals and justify the comparison.


Obj. 73 - Compare decimal numbers of differing places to thousandths

GA M5N3 - Students will further develop their understanding of the meaning of multiplication and division with decimals and use them.

GA M5N3.a - Model multiplication and division of decimals.GA M5N3.b - Explain the process of multiplication and division, including situations in which the multiplier and divisor are both whole numbers and decimals.



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GA M5N3.c - Multiply and divide with decimals including decimals less than one and greater than one.


Obj. 88 - Multiply a money amount by a 2- or 3-digit whole number

Obj. 89 - WP: Multiply a money amount by a 2-digit whole number

GA M5N3.d - Understand the relationships and rules for multiplication and division of whole numbers also apply to decimals.GA M5N4 - Students will continue to develop their understanding of the meaning of common fractions and compute with them.GA M5N4.a - Understand division of whole numbers can be represented as a fraction (a/b = a ÷ b).


Obj. 30 - Relate a sharing situation to a fraction

GA M5N4.b - Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one.

GA M5N4.c - Find equivalent fractions and simplify fractions.


Obj. 31 - Determine equivalent fractions not in simplest formObj. 32 - Determine the simplest form of a fraction

GA M5N4.d - Model the multiplication and division of common fractions.

GA M5N4.e - Explore finding common denominators using concrete, pictorial, and computational models.GA M5N4.f - Use <, >, or = to compare fractions and justify the comparison.


Obj. 33 - Compare fractions with unlike denominators

GA M5N4.g - Add and subtract common fractions and mixed numbers with unlike denominators.


Obj. 36 - Add fractions with unlike denominators using a model and do not simplify the sumObj. 37 - Add fractions with unlike denominators and do not simplify the sumObj. 38 - Add fractions with unlike denominators that have factors in common and simplify the sumObj. 39 - Add fractions with unlike denominators that have no factors in common


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Obj. 41 - Subtract fractions with unlike denominators using a model and do not simplify the differenceObj. 42 - Subtract fractions with unlike denominators and do not simplify the differenceObj. 43 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceObj. 44 - Subtract fractions with unlike denominators that have no factors in commonObj. 46 - WP: Add or subtract fractions with unlike denominators that have no factors in commonObj. 50 - Add mixed numbers with unlike denominators and simplify the sumObj. 52 - Subtract mixed numbers with unlike denominators and simplify the differenceObj. 54 - WP: Add or subtract mixed numbers with unlike denominators that have no factors in common

GA M5N4.h - Use fractions (proper and improper) and decimals interchangeably.


Obj. 90 - Convert a decimal number through thousandths to a simplified fractionObj. 91 - Convert a fraction with a denominator that is a factor of 10, 100, or 1,000 to decimal notation

GA M5N4.i - Estimate products and quotients.GA M5N5 - Students will understand the meaning of percentage.

GA M5N5.a - Explore and model percents using multiple representations.


Obj. 92 - Determine a model of a percent on a 100 grid

Obj. 93 - Determine the percent represented by a model on a 100 grid

Obj. 95 - Relate an equivalent decimal and percent given a grid

GA M5N5.b - Apply percents to circle graphs.


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- Students will compute the area of geometric plane figures. They will also understand the concept of volume and compute the volume of simple geometric solids and measure capacity. Students will convert from one unit to another within one system of measurement.

GA M5M1 - Students will extend their understanding of area of geometric plane figures.GA M5M1.a - Estimate the area of geometric plane figures.GA M5M1.b - Derive the formula for the area of a parallelogram.GA M5M1.c - Derive the formula for the area of a triangle.GA M5M1.d - Find the areas of triangles and parallelograms using formulae.


Obj. 126 - Use a formula to determine the area of a triangle

Obj. 128 - Use a formula to determine the area of a parallelogram

Obj. 129 - WP: Determine the area of a triangleObj. 130 - WP: Determine the area of a square or rectangle

GA M5M1.e - Estimate the area of a circle through partitioning and tiling.

GA M5M1.f - Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and find the sum of the areas of those shapes.


Obj. 127 - Determine the area of a complex figure divided into basic shapes

GA M5M1.g - Derive the formula for the area of a circle.GA M5M1.h - Find the area of a circle using the formula and pi is approximately 3.14.GA M5M2. - Students will extend their understanding of perimeter to include circumference.GA M5M2.a - Derive the formula for the circumference of a circle.GA M5M2.b - Find the circumference of a circle using the formula and pi is approximately 3.14.


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GA M5M3 - Students will measure capacity with appropriately chosen units and tools.GA M5M3.a - Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to measure capacity.GA M5M3.b - Compare one unit to another within a single system of measurement.


Obj. 119 - WP: Compare customary units of length, weight, or capacity using fractional amounts

Obj. 120 - WP: Compare metric units of length, mass, or capacity using decimal amounts

GA M5M4 - Students will understand and compute the volume of a simple geometric solid.GA M5M4.a - Understand a cubic unit (u³) is represented by a cube in which each edge has the length of 1 unit.GA M5M4.b - Identify the units used in computing volume as cubic centimeters (cm³), cubic meters (m³), cubic inches (in³), cubic feet (ft³), and cubic yards (yd³).GA M5M4.c - Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.GA M5M4.d - Compute the volume of a cube and a rectangular prism using formulae.


Obj. 132 - Determine the volume of a rectangular prism given a diagram

Obj. 133 - WP: Determine the volume of a rectangular prism given a diagramObj. 134 - Determine the volume of a rectangular prismObj. 135 - WP: Determine the volume of a rectangular prism

GA M5M4.e - Estimate the volume of a simple geometric solid.GA M5M4.f - Understand the similarities and differences between volume and capacity. - Students will further develop their understanding of geometric figures.GA M5G1 - Students will understand congruence of geometric figures and the correspondence of their vertices, sides, and angles.


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GA M5G2 - Students will understand the relationship of the circumference of a circle to its diameter is pi (pi is approximately 3.14).

- Students will represent and investigate mathematical expressions algebraically by using variables.GA M5A1 - Students will represent and interpret the relationships between quantities algebraically.GA M5A1.a - Use variables, such as n or x, for unknown quantities in algebraic expressions.

Topic 2 - Algebra Obj. 98 - Use a variable expression with one operation to represent a verbal expressionObj. 100 - WP: Use a variable expression with one operation to represent a situation

GA M5A1.b - Investigate simple algebraic expressions by substituting numbers for the unknown.

Topic 2 - Algebra Obj. 101 - Evaluate a 1-variable expression, involving one operation, using whole number substitution

Obj. 102 - Evaluate a 2-variable expression, involving one operation, using whole number substitution

Obj. 103 - WP: Evaluate a 1-variable expression with one operation using a whole number value

Obj. 104 - WP: Evaluate a 2-variable expression with one operation using whole number values

GA M5A1.c - Determine that a formula will be reliable regardless of the type of number (whole numbers or decimals) substituted for the variable. - Students will gather, organize, and display data and interpret graphs.GA M5D1 - Students will analyze graphs.GA M5D1.a - Analyze data presented in a graph.


Obj. 152 - Answer a question using information from a line graph that does not start at zero or has a broken vertical scaleObj. 153 - WP: Extend a line graph to solve a problemObj. 154 - Read a double- or stacked-bar graph


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Obj. 156 - Answer a question using information from a double- or stacked-bar graph

GA M5D1.b - Compare and contrast multiple graphic representations (circle graphs, line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs) for a single set of data and discuss the advantages/disadvantages of each.

GA M5D1.c - Determine and justify the mean, range, mode, and median of a set of data.


Obj. 161 - Determine the mean of a set of whole number data, whole number resultsObj. 162 - Determine the median of an odd number of data valuesObj. 163 - Determine the mode of a set of whole number dataObj. 164 - Determine the range of a set of whole number data

GA M5D2 - Students will collect, organize, and display data using the most appropriate graph. - Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.




Obj. 129 - WP: Determine the area of a triangle

Obj. 133 - WP: Determine the volume of a rectangular prism given a diagramObj. 135 - WP: Determine the volume of a rectangular prismObj. 137 - Answer a question by analyzing a shape made of cubes

GA M5P1.c - Apply and adapt a variety of appropriate strategies to solve problems.


Obj. 137 - Answer a question by analyzing a shape made of cubes

GA M5P1.d - Monitor and reflect on the process of mathematical problem solving.


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GA M5P2 - Students will reason and evaluate mathematical arguments.



GA M5P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA M5P3.d - Use the language of mathematics to express mathematical ideas precisely.GA M5P4 - Students will make connections among mathematical ideas and to other disciplines.GA M5P4.a - Recognize and use connections among mathematical ideas.GA M5P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M5P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M5P5 - Students will represent mathematics in multiple ways.GA M5P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA M5P5.b - Select, apply, and translate among mathematical representations to solve problems.


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GA M5P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


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Agency Tag Set NameGeorgia, Math, 2004, Grade 6, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will apply these concepts and associated skills in real world situations.GA M6N1 - Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.

GA M6N1.a - Apply factors and multiples.GA M6N1.b - Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic).


Obj. 1 - Determine the prime factorization of a number between 50 and 200

GA M6N1.c - Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.


Obj. 2 - Determine the greatest common factor of three numbers to 100

Obj. 3 - Determine the least common multiple of three numbersObj. 4 - WP: Determine the least common multiple of two or more numbers

GA M6N1.d - Add and subtract fractions and mixed numbers with unlike denominators.


Obj. 13 - Add fractions with unlike denominators and simplify the sum

Obj. 14 - Subtract fractions with unlike denominators and simplify the differenceObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 17 - Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sumObj. 19 - Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the differenceObj. 20 - Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer



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Obj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference

GA M6N1.e - Multiply and divide fractions and mixed numbers.


Obj. 22 - Multiply a fraction by a fractionObj. 23 - Multiply a mixed number by a whole numberObj. 24 - Multiply a mixed number by a fractionObj. 25 - Multiply a mixed number by a mixed numberObj. 29 - Divide a fraction by a fractionObj. 30 - Divide a whole number by a fraction resulting in a fractional quotientObj. 31 - Divide a mixed number by a fractionObj. 32 - Divide a mixed number by a mixed numberObj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fraction

GA M6N1.f - Use fractions, decimals, and percents interchangeably.


Obj. 68 - Convert a mixed number to a decimal number

Obj. 69 - Convert a decimal number to a mixed numberObj. 70 - Convert a fraction to a repeating decimal numberObj. 72 - Convert a decimal number to a percentageObj. 73 - Convert a percentage to a decimal numberObj. 74 - Convert a fraction to a percentageObj. 75 - Convert a percentage to a fraction

GA M6N1.g - Solve problems involving fractions, decimals, and percents.


Obj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference


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Obj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionObj. 35 - WP: Solve a 2-step problem involving fractionsObj. 42 - WP: Add and subtract three decimal numbersObj. 45 - WP: Multiply a money expression by a decimal numberObj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededObj. 67 - WP: Solve a 2-step problem involving decimalsObj. 78 - Determine a percent where a ratio, not in 100ths, is given in wordsObj. 79 - Calculate a percent of a whole number where the answer is a whole numberObj. 80 - WP: Calculate the percent of a whole number where the answer is a whole number

- Students will understand how to determine the volume and surface area of solid figures. They will understand and use the customary and metric systems of measurement to measure quantities efficiently and to represent volume and surface area appropriately.GA M6M1 - Students will convert from one unit to another within one system of measurement (customary or metric) by using proportional relationships.GA M6M2 - Students will use appropriate units of measure for finding length, perimeter, area and volume and will express each quantity using the appropriate unit.GA M6M2.a - Measure length to the nearest half, fourth, eighth and sixteenth of an inch.


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GA M6M2.b - Select and use units of appropriate size and type to measure length, perimeter, area and volume.

GA M6M2.c - Compare and contrast units of measure for perimeter, area, and volume.GA M6M3 - Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids and cones).

GA M6M3.a - Determine the formula for finding the volume of fundamental solid figures.GA M6M3.b - Compute the volumes of fundamental solid figures, using appropriate units of measure.

GA M6M3.c - Estimate the volumes of simple geometric solids.

GA M6M3.d - Solve application problems involving the volume of fundamental solid figures.GA M6M4 - Students will determine the surface area of solid figures (right rectangular prisms and cylinders).

GA M6M4.a - Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets.GA M6M4.b - Compute the surface area of right rectangular prisms and cylinders using formulae.GA M6M4.c - Estimate the surface area of simple geometric solids.GA M6M4.d - Solve application problems involving surface area of right rectangular prisms and cylinders. - Students will further develop their understanding of plane and solid geometric figures, incorporating the use of appropriate technology and using this knowledge to solve authentic problems.GA M6G1 - Students will further develop their understanding of plane figures.


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GA M6G1.a - Determine and use lines of symmetry.


Obj. 135 - Use symmetry to determine a length or an angle measure

GA M6G1.b - Investigate rotational symmetry, including degree of rotation.GA M6G1.c - Use the concepts of ratio, proportion and scale factor to demonstrate the relationships between similar plane figures.GA M6G1.d - Interpret and sketch simple scale drawings.GA M6G1.e - Solve problems involving scale drawings.GA M6G2 - Students will further develop their understanding of solid figures.GA M6G2.a - Compare and contrast right prisms and pyramids.

GA M6G2.b - Compare and contrast cylinders and cones.GA M6G2.c - Interpret and sketch front, back, top, bottom and side views of solid figures.GA M6G2.d - Construct nets for prisms, cylinders, pyramids, and cones. - Students will investigate relationships between two quantities. They will write and solve proportions and simple one-step equations that result from problem situations.GA M6A1 - Students will understand the concept of ratio and use it to represent quantitative relationships.


Obj. 81 - WP: Determine a ratio using whole numbers less than 50

Obj. 82 - Determine if ratios, using whole numbers less than 50, are equivalentObj. 83 - WP: Determine a part given a ratio and the whole where the whole is less than 50Obj. 84 - WP: Determine a part given a ratio and another part where the whole is less than 50Obj. 85 - WP: Determine the whole given a ratio and a part where the whole is less than 50


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GA M6A2 - Students will consider relationships between varying quantities.GA M6A2.a - Analyze and describe patterns arising from mathematical rules, tables, and graphs.

GA M6A2.b - Use manipulatives or draw pictures to solve problems involving proportional relationships.GA M6A2.c - Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.

Topic 2 - Algebra Obj. 102 - Solve a proportion

GA M6A2.d - Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality.GA M6A2.e - Graph proportional relationships in the form y = kx and describe characteristics of the graphs.GA M6A2.f - In a proportional relationship expressed as y = kx, solve for one quantity given values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y = kx.GA M6A2.g - Use proportional reasoning (a/b=c/d and y = kx) to solve problems.

Topic 2 - Algebra Obj. 102 - Solve a proportion

GA M6A3 - Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations.

Topic 2 - Algebra Obj. 98 - Evaluate a 1-variable expression, with two or three operations, using whole number substitution

Obj. 99 - Evaluate a 2-variable expression, with two or three operations, using whole number substitutionObj. 100 - WP: Evaluate a 1- or 2-variable expression or formula using whole numbersObj. 101 - Solve a 1-step equation involving whole numbers


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- Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. They will represent, investigate, and use data to answer those questions. Students will understand experimental and theoretical probability.GA M6D1 - Students will pose questions, collect data, represent and analyze the data, and interpret results.GA M6D1.a - Formulate questions that can be answered by data. Students should collect data by using samples from a larger population (surveys), or by conducting experiments.GA M6D1.b - Using data, construct frequency distributions, frequency tables, and graphs.


Obj. 145 - Use a frequency table to represent 2 related data sets

GA M6D1.c - Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs should include pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots.GA M6D1.d - Use tables and graphs to examine variation that occurs within a group and variation that occurs between groups.GA M6D1.e - Relate the data analysis to the context of the questions posed.GA M6D2 - Students will use experimental and simple theoretical probability and understand the nature of sampling. They will also make predictions from investigations.

GA M6D2.a - Predict the probability of a given event through trials/simulations (experimental probability), and represent the probability as a ratio.


Obj. 151 - Determine an experimental probability given a list of results

Obj. 154 - Make a prediction based on an experimental probability


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GA M6D2.b - Determine, and use a ratio to represent, the theoretical probability of a given event.


Obj. 152 - Determine the probability of a single event

Obj. 155 - Make a prediction based on a theoretical probability

GA M6D2.c - Discover that experimental probability approaches theoretical probability when the number of trials is large. - Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.




Obj. 4 - WP: Determine the least common multiple of two or more numbersObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference

Obj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionObj. 35 - WP: Solve a 2-step problem involving fractionsObj. 45 - WP: Multiply a money expression by a decimal numberObj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededObj. 67 - WP: Solve a 2-step problem involving decimals


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Obj. 80 - WP: Calculate the percent of a whole number where the answer is a whole numberObj. 81 - WP: Determine a ratio using whole numbers less than 50Obj. 83 - WP: Determine a part given a ratio and the whole where the whole is less than 50Obj. 84 - WP: Determine a part given a ratio and another part where the whole is less than 50Obj. 85 - WP: Determine the whole given a ratio and a part where the whole is less than 50





Topic 2 - Algebra Obj. 95 - WP: Use a variable expression with two operations to represent a situation

GA M6P4 - Students will make connections among mathematical ideas and to other disciplines.


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GA M6P4.a - Recognize and use connections among mathematical ideas.GA M6P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M6P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M6P5 - Students will represent mathematics in multiple ways.GA M6P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA M6P5.b - Select, apply, and translate among mathematical representations to solve problems.

Topic 2 - Algebra Obj. 95 - WP: Use a variable expression with two operations to represent a situation

GA M6P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.

GA MRC. - Students will enhance reading in all curriculum areas by:GA M6RC1.a - Reading in all curriculum areasGA M6RC1.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas.GA M6RC1.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourse.GA M6RC1.a.3 - Read technical texts related to various subject areas.

GA M6RC1.b - Discussing booksGA M6RC1.b.1 - Discuss messages and themes from books in all subject areas.GA M6RC1.b.2 - Respond to a variety of texts in multiple modes of discourse.GA M6RC1.b.3 - Relate messages and themes from one subject area to messages and themes in another area.


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GA M6RC1.b.4 - Evaluate the merit of texts in every subject discipline.

GA M6RC1.b.5 - Examine author's purpose in writing.GA M6RC1.b.6 - Recognize the features of disciplinary texts.GA M6RC1.c - Building vocabulary knowledgeGA M6RC1.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.GA M6RC1.c.2 - Use content vocabulary in writing and speaking.GA M6RC1.c.3 - Explore understanding of new words found in subject area texts.GA M6RC1.d - Establishing context

GA M6RC1.d.1 - Explore life experiences related to subject area content.GA M6RC1.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA M6RC1.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2004, Grade 7, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will further develop their understanding of the concept of rational numbers and apply them to real world situations.

GA M7N1 - Students will understand the meaning of positive and negative rational numbers and use them in computation.GA M7N1.a - Find the absolute value of a number and understand it as the distance from zero on a number line.


Obj. 33 - Evaluate the absolute value of an integer

GA M7N1.b - Compare and order rational numbers, including repeating decimals.


Obj. 59 - Compare rational numbers (positive and negative)

Obj. 60 - Order rational numbers (positive and negative)

GA M7N1.c - Add, subtract, multiply, and divide positive and negative rational numbers.


Obj. 30 - WP: Answer a question involving a fraction and a decimal

Obj. 31 - WP: Solve a multi-step problem involving decimal numbersObj. 32 - WP: Solve a multi-step problem involving fractions or mixed numbersObj. 37 - Add integersObj. 39 - Subtract integersObj. 40 - WP: Add and subtract using integersObj. 41 - Multiply integersObj. 42 - Divide integersObj. 43 - WP: Multiply or divide integers

GA M7N1.d - Solve problems using rational numbers.


Obj. 23 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 24 - WP: Determine a whole number given a part and a percentageObj. 25 - WP: Determine the percent of decrease applied to a number

Obj. 26 - WP: Determine the percent of increase applied to a number

Obj. 27 - WP: Determine the result of applying a percent of decrease to a value



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Obj. 28 - WP: Determine the result of applying a percent of increase to a valueObj. 29 - WP: Answer a question involving a fraction and a percentObj. 30 - WP: Answer a question involving a fraction and a decimalObj. 31 - WP: Solve a multi-step problem involving decimal numbersObj. 32 - WP: Solve a multi-step problem involving fractions or mixed numbersObj. 40 - WP: Add and subtract using integersObj. 43 - WP: Multiply or divide integers

- Students will further develop and apply their understanding of plane and solid geometric figures through the use of constructions and transformations. Students will explore the properties of similarity and further develop their understanding of 3-dimensional figures.

GA M7G1 - Students will construct plane figures that meet given conditions.GA M7G1.a - Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

GA M7G1.b - Recognize that many constructions are based on the creation of congruent triangles.GA M7G2 - Students will demonstrate understanding of transformations.


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GA M7G2.a - Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.GA M7G2.b - Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.


Obj. 121 - Determine the coordinates of a translated, a rotated, or a reflected shape on the Cartesian plane

GA M7G3. - Students will use the properties of similarity and apply these concepts to geometric figures.

GA M7G3.a - Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.


Obj. 101 - Identify corresponding parts of congruent shapes

Obj. 102 - Identify congruent shapes given side and angle measures

GA M7G3.b - Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures.


Obj. 103 - Determine a missing dimension given two congruent shapes

Obj. 104 - Determine a missing dimension given two similar shapes

Obj. 105 - WP: Solve a problem involving similar shapes

GA M7G3.c - Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape.

GA M7G4. - Students will further develop their understanding of three-dimensional figures.GA M7G4.a - Describe three-dimensional figures formed by translations and rotations of plane figures through space.GA M7G4.b - Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.


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- Students will demonstrate an understanding of linear relations and fundamental algebraic concepts.GA M7A1 - Students will represent and evaluate quantities using algebraic expressions.GA M7A1.a - Translate verbal phrases to algebraic expressions.

Topic 2 - Algebra Obj. 69 - WP: Use a 2-variable expression to represent a situation

GA M7A1.b - Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.

Topic 2 - Algebra Obj. 61 - Evaluate a rational expression involving variables with two or more terms in the numerator or denominator

Obj. 62 - Evaluate a 1-variable expression, with two or three operations, using integer substitution

Obj. 63 - Evaluate a 2-variable expression, with two or three operations, using integer substitution

Obj. 64 - Evaluate an algebraic expression involving whole number exponentsObj. 65 - WP: Evaluate a variable expressionObj. 66 - WP: Evaluate a variable expression involving exponents

GA M7A1.c - Add and subtract linear expressions.GA M7A2 - Students will understand and apply linear equations in one variable.GA M7A2.a - Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.

Topic 2 - Algebra Obj. 73 - Solve a 1-step linear equation involving integers

Obj. 74 - Solve a 2-step linear equation involving integersObj. 75 - WP: Use a 1-variable 1-step equation to represent a situation

GA M7A2.b - Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

Topic 2 - Algebra Obj. 73 - Solve a 1-step linear equation involving integers

Obj. 74 - Solve a 2-step linear equation involving integers

GA M7A3 - Students will understand relationships between two variables.


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GA M7A3.a - Plot points on a coordinate plane.GA M7A3.b - Represent, describe, and analyze relations from tables, graphs, and formulas.

Topic 2 - Algebra Obj. 68 - Use a variable expression with two operations to represent a table of paired numbers

Obj. 81 - Use a table to represent a linear functionObj. 82 - Use a graph to represent the ordered pairs in a function tableObj. 83 - Determine the graph of a 1-operation linear function

GA M7A3.c - Describe how change in one variable affects the other variable.GA M7A3.d - Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x). - Students will demonstrate understanding of data analysis by posing questions, collecting data, analyzing the data using measures of central tendency and variation, and using the data to answer the questions posed. Students will understand the role of probability in sampling.

GA M7D1 - Students will pose questions, collect data, represent and analyze the data, and interpret results.GA M7D1.a - Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes.GA M7D1.b - Construct frequency distributions.GA M7D1.c - Analyze data using measures of central tendency (mean, median, and mode), including recognition of outliers.


Obj. 132 - Determine the mean of a set of data

Obj. 133 - Determine the mode(s) of a set of dataObj. 134 - Determine the median of a set of dataObj. 135 - WP: Use the mean of a data set to solve a problem


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GA M7D1.d - Analyze data with respect to measures of variation (range, quartiles, interquartile range).

GA M7D1.e - Compare measures of central tendency and variation from samples to those from a census. Observe that sample statistics are more likely to approximate the population parameters as sample size increases.

GA M7D1.f - Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots introduced earlier, and using box-and-whisker plots and scatter plots.


Obj. 125 - Answer a question using information from a circle graph using percentage calculations

Obj. 128 - Answer a question using information from a histogram

GA M7D1.g - Analyze and draw conclusions about data, including describing the relationship between two variables. - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.




Obj. 22 - WP: Determine a percent of a whole number using less than 100%Obj. 23 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 24 - WP: Determine a whole number given a part and a percentageObj. 25 - WP: Determine the percent of decrease applied to a number


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Obj. 26 - WP: Determine the percent of increase applied to a number

Obj. 27 - WP: Determine the result of applying a percent of decrease to a valueObj. 28 - WP: Determine the result of applying a percent of increase to a valueObj. 29 - WP: Answer a question involving a fraction and a percentObj. 30 - WP: Answer a question involving a fraction and a decimalObj. 31 - WP: Solve a multi-step problem involving decimal numbersObj. 32 - WP: Solve a multi-step problem involving fractions or mixed numbers




GA M7P3.c - Analyze and evaluate the mathematical thinking and strategies of others.


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GA M7P3.d - Use the language of mathematics to express mathematical ideas precisely.GA M7P4 - Students will make connections among mathematical ideas and to other disciplines.GA M7P4.a - Recognize and use connections among mathematical ideas.GA M7P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M7P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M7P5 - Students will represent mathematics in multiple ways.GA M7P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA M7P5.b - Select, apply, and translate among mathematical representations to solve problems.GA M7P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


GA M7RC1.b - Discussing books.GA M7RC1.b.1 - Discuss messages and themes from books in all subject areas.


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GA M7RC1.b.2 - Respond to a variety of texts in multiple modes of discourse.GA M7RC1.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA M7RC1.b.4 - Evaluate the merit of texts in every subject discipline.




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Agency Tag Set NameGeorgia, Math, 2004, Grade 8, Performance Standards, State Department of EducationStandard Topic Description Objective Description - Students will understand the numeric and geometric meaning of square root, apply properties of integer exponents and use scientific notation.GA M8N1 - Students will understand different representations of numbers including square roots, exponents, and scientific notation.

GA M8N1.a - Find square roots of perfect squares.


Obj. 12 - Determine the square root of a perfect-square fraction or decimalObj. 13 - Determine both square roots of a perfect square

GA M8N1.b - Recognize the (positive) square root of a number as a length of a side of a square with a given area.GA M8N1.c - Recognize square roots as points and as lengths on a number line.GA M8N1.d - Understand that the square root of 0 is 0 and that every positive number has two square roots that are opposite in sign.GA M8N1.e - Recognize and use the radical symbol to denote the positive square root of a positive number.

GA M8N1.f - Estimate square roots of positive numbers.


Obj. 14 - Determine the two closest integers to a given square root

Obj. 16 - Determine the square root of a whole number to the nearest tenth

GA M8N1.g - Simplify, add, subtract, multiply, and divide expressions containing square roots.

GA M8N1.h - Distinguish between rational and irrational numbers.


Obj. 18 - Identify rational or irrational numbers

GA M8N1.i - Simplify expressions containing integer exponents.


Obj. 1 - Evaluate an integer raised to a whole number powerObj. 2 - Evaluate a zero or negative power of an integerObj. 3 - Evaluate a numerical expression involving integer exponents and/or integer basesObj. 11 - Determine the square of a fraction or a decimal



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GA M8N1.j - Express and use numbers in scientific notation.


Obj. 4 - Convert a number less than 1 to scientific notationObj. 5 - Convert a number less than 1 from scientific notation to standard form

GA M8N1.k - Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation. - Students will use and apply geometric properties of plane figures, including congruence and the Pythagorean theorem.GA M8G1 - Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence.GA M8G1.a - Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.GA M8G1.b - Apply properties of angle pairs formed by parallel lines cut by a transversal.


Obj. 68 - Identify angle relationships formed by parallel lines cut by a transversalObj. 69 - Determine an angle measure formed by parallel lines cut by a transversal

GA M8G1.c - Understand the properties of the ratio of segments of parallel lines cut by one or more transversals.GA M8G1.d - Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.GA M8G2 - Students will understand and use the Pythagorean theorem.

GA M8G2.a - Apply properties of right triangles, including the Pythagorean theorem.


Obj. 71 - Determine the length of the hypotenuse of a right triangle using the Pythagorean theoremObj. 72 - Determine the length of a leg of a right triangle using the Pythagorean theoremObj. 73 - WP: Use the Pythagorean theorem to find a length or a distance

Obj. 74 - Determine a distance on the Cartesian plane using the Pythagorean theorem


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Obj. 75 - Determine if a triangle is a right triangle by using the Pythagorean theorem

GA M8G2.b - Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle.

- Students will use linear algebra to represent, analyze and solve problems. They will use equations, tables, and graphs to investigate linear relations and functions, paying particular attention to slope as a rate of change.

GA M8A1 - Students will use algebra to represent, analyze, and solve problems.GA M8A1.a - Represent a given situation using algebraic expressions or equations in one variable.

Topic 2 - Algebra Obj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations

GA M8A1.b - Simplify and evaluate algebraic expressions.

Topic 2 - Algebra Obj. 31 - Evaluate a 2-variable expression with two or three operations substituting fractions or decimalsObj. 32 - Evaluate an algebraic expression involving negative integer exponentsObj. 33 - Simplify an algebraic expression by combining like terms

Obj. 35 - Multiply two monomial algebraic expressionsObj. 36 - Use the distributive property to simplify an algebraic expression

GA M8A1.c - Solve algebraic equations in one variable, including equations involving absolute values.

Topic 2 - Algebra Obj. 37 - Solve a 1-step equation involving rational numbers

Obj. 38 - Solve a 2-step equation involving rational numbersObj. 41 - WP: Solve a problem involving a 1-variable, 2-step equation

GA M8A1.d - Solve equations involving several variables for one variable in terms of the others.GA M8A1.e - Interpret solutions in problem contexts.


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GA M8A2 - Students will understand and graph inequalities in one variable.GA M8A2.a - Represent a given situation using an inequality in one variable.

Topic 2 - Algebra Obj. 53 - WP: Use a 2-step linear inequality in one variable to represent a situation

GA M8A2.b - Use the properties of inequality to solve inequalities.

Topic 2 - Algebra Obj. 52 - Solve a 2-step linear inequality in one variableObj. 54 - WP: Solve a problem involving a 2-step linear inequality in one variable

GA M8A2.c - Graph the solution of an inequality on a number line.GA M8A2.d - Interpret solutions in problem contexts.GA M8A3 - Students will understand relations and linear functions.

GA M8A3.a - Recognize a relation as a correspondence between varying quantities.GA M8A3.b - Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique.

GA M8A3.c - Distinguish between relations that are functions and those that are not functions.GA M8A3.d - Recognize functions in a variety of representations and a variety of contexts.GA M8A3.e - Use tables to describe sequences recursively and with a formula in closed form.GA M8A3.f - Understand and recognize arithmetic sequences as linear functions with whole number input values.GA M8A3.g - Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function.GA M8A3.h - Identify relations and functions as linear or nonlinear.GA M8A3.i - Translate among verbal, tabular, graphic, and algebraic representations of functions.

Topic 2 - Algebra Obj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situation

Obj. 42 - Determine the graph of a line for a given table of values


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Obj. 43 - Determine the table of values that represents a linear equation with rational coefficients in two variablesObj. 44 - Determine a linear equation in two variables that represents a table of valuesObj. 45 - Determine the graph of a 2-operation linear functionObj. 50 - WP: Determine a linear graph that can represent a situation

GA M8A4 - Students will graph and analyze graphs of linear equations and inequalities.GA M8A4.a - Interpret slope as a rate of change.GA M8A4.b - Determine the meaning of the slope and y-intercept in a given situation.

Topic 2 - Algebra Obj. 48 - WP: Interpret the meaning of the slope of a graphed line

Obj. 49 - WP: Interpret the meaning of the y-intercept of a graphed line

GA M8A4.c - Graph equations of the form y = mx + b.

Topic 2 - Algebra Obj. 45 - Determine the graph of a 2-operation linear function

GA M8A4.d - Graph equations of the form ax + by = c.GA M8A4.e - Graph the solution set of a linear inequality, identifying whether the solution set is an open or a closed half-plane.

Topic 2 - Algebra Obj. 55 - Determine the graph of the solutions to a 2-step linear inequality in one variable

GA M8A4.f - Determine the equation of a line given a graph, numerical information that defines the line or a context involving a linear relationship.

Topic 2 - Algebra Obj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations

Obj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situationObj. 44 - Determine a linear equation in two variables that represents a table of values

GA M8A4.g - Solve problems involving linear relationships.GA M8A5 - Students will understand systems of linear equations and inequalities and use them to solve problems.GA M8A5.a - Given a problem context, write an appropriate system of linear equations or inequalities.


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GA M8A5.b - Solve systems of equations graphically and algebraically, using technology as appropriate.GA M8A5.c - Graph the solution set of a system of linear inequalities in two variables.GA M8A5.d - Interpret solutions in problem contexts. - Students will use and understand set theory and simple counting techniques; determine the theoretical probability of simple events; and make inferences from data, particularly data that can be modeled by linear functions.GA M8D1 - Students will apply basic concepts of set theory.GA M8D1.a - Demonstrate relationships among sets through use of Venn diagrams.


Obj. 87 - Use a Venn diagram to organize summarized data

GA M8D1.b - Determine subsets, complements, intersection, and union of sets.GA M8D1.c - Use set notation to denote elements of a set.GA M8D2 - Students will determine the number of outcomes related to a given event.GA M8D2.a - Use tree diagrams to find the number of outcomes.GA M8D2.b - Apply the addition and multiplication principles of counting.

GA M8D3 - Students will use the basic laws of probability.GA M8D3.a - Find the probability of simple independent events.


Obj. 96 - Determine the probability of three or more independent events

GA M8D3.b - Find the probability of compound independent events.GA M8D4 - Students will organize, interpret, and make inferences from statistical data.GA M8D4.a - Gather data that can be modeled with a linear function.GA M8D4.b - Estimate and determine a line of best fit from a scatter plot.


Obj. 79 - Approximate a trend line for a scatter plot


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- The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.



Topic 2 - Algebra Obj. 41 - WP: Solve a problem involving a 1-variable, 2-step equationObj. 54 - WP: Solve a problem involving a 2-step linear inequality in one variable


Obj. 73 - WP: Use the Pythagorean theorem to find a length or a distance





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GA M8P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA M8P3.d - Use the language of mathematics to express mathematical ideas precisely.GA M8P4 - Students will make connections among mathematical ideas and to other disciplines.GA M8P4.a - Recognize and use connections among mathematical ideas.GA M8P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA M8P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA M8P5 - Students will represent mathematics in multiple ways.GA M8P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA M8P5.b - Select, apply, and translate among mathematical representations to solve problems.GA M8P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


GA M8RC1.b - Discussing books


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GA M8RC1.b.1 - Discuss messages and themes from books in all subject areas.GA M8RC1.b.2 - Respond to a variety of texts in multiple modes of discourse.GA M8RC1.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA M8RC1.b.4 - Evaluate the merit of texts in every subject discipline.




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Agency Tag Set NameGeorgia, Math, 2006, Mathematics I: Algebra/Geometry/Statistics1, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MM1A - Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

GA MM1A1 - Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.GA MM1A1.a - Represent functions using function notation.GA MM1A1.b - Graph the basic functions f(x) = x to the n power, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

Topic 11 - Radical Equations and Functions

Obj. 111 - Determine the graph of a radical function

Topic 13 - Rational Equations and Functions

Obj. 126 - Determine the graph of a rational function

GA MM1A1.c - Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.GA MM1A1.d - Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

Topic 2 - Relations and Functions

Obj. 9 - Determine the domain or range of a function

GA MM1A1.e - Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.GA MM1A1.f - Recognize sequences as functions with domains that are whole numbers.GA MM1A1.g - Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

GA MM1A1.h - Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Algebra 1

Accelerated Math Grades 9 - 12

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Agency Tag Set NameGeorgia, Math, 2006, Mathematics I: Algebra/Geometry/Statistics1, Performance Standards, State Department of EducationStandard Topic Description Objective Description


GA MM1A1.i - Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA MM1A2 - Students will simplify and operate with radical expressions, polynomials, and rational expressions.GA MM1A2.a - Simplify algebraic and numeric expressions involving square root.

Topic 10 - Radical Expressions Obj. 98 - Simplify a monomial numerical expression involving the square root of a whole numberObj. 104 - Simplify a monomial algebraic radical expression

GA MM1A2.b - Perform operations with square roots.

Topic 10 - Radical Expressions Obj. 99 - Multiply monomial numerical expressions involving radicalsObj. 100 - Divide monomial numerical expressions involving radicalsObj. 101 - Add and/or subtract numerical radical expressionsObj. 102 - Multiply a binomial numerical radical expression by a numerical radical expressionObj. 106 - Add or subtract algebraic radical expressionsObj. 107 - Multiply monomial algebraic radical expressionsObj. 108 - Divide monomial algebraic radical expressions

GA MM1A2.c - Add, subtract, multiply, and divide polynomials.

Topic 6 - Polynomial Expressions Obj. 70 - Add polynomial expressions

Obj. 71 - Subtract polynomial expressionsObj. 72 - Multiply a polynomial by a monomialObj. 73 - Multiply two binomials of the form (x +/- a)(x +/- b)Obj. 74 - Multiply two binomials of the form (ax +/- b)(cx +/- d)Obj. 75 - Multiply two binomials of the form (ax +/- by)(cx +/- dy)Obj. 76 - Square a binomialObj. 77 - Multiply two nonlinear binomialsObj. 78 - Multiply a trinomial by a binomial


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Topic 12 - Rational Expressions Obj. 117 - Divide a polynomial expression by a monomialObj. 118 - Divide a polynomial expression by a binomial

GA MM1A2.d - Expand binomials using the Binomial Theorem.GA MM1A2.e - Add, subtract, multiply, and divide rational expressions.

Topic 12 - Rational Expressions Obj. 115 - Multiply rational expressions

Obj. 116 - Divide rational expressions

Obj. 120 - Add or subtract two rational expressions with like denominatorsObj. 121 - Add or subtract two rational expressions with unlike monomial denominatorsObj. 122 - Add or subtract two rational expressions with unlike polynomial denominators

GA MM1A2.f - Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below. (x + y)² = x² + 2xy + y²; (x - y)² = x² - 2xy + y²; (x + y)(x - y) = x² - y²; (x + a)(x + b) = x² + (a + b)x + ab; (x + y)³ = x³ +3x²y + 3xy² + y³; (x - y)³ = x³ -3x²y + 3xy² - y³

Topic 7 - Factor Algebraic Expressions

Obj. 79 - Factor the GCF from a polynomial expression

Obj. 80 - Factor trinomials that result in factors of the form (x +/- a)(x +/- b)

Obj. 81 - Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d)Obj. 82 - Factor trinomials that result in factors of the form (ax +/- by)(cx +/- dy)Obj. 83 - Factor the difference of two squaresObj. 84 - Factor a perfect-square trinomialObj. 85 - Factor a polynomial that has a GCF and two linear binomial factors

GA MM1A2.g - Use area and volume models for polynomial arithmetic.

GA MM1A3 - Students will solve simple equations.


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GA MM1A3.a - Solve quadratic equations in the form ax² + bx + c = 0 where a = 1 by using factorization and finding square roots where applicable.

Topic 8 - Quadratic Equations and Functions

Obj. 91 - Solve a quadratic equation by factoring

GA MM1A3.b - Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.


Obj. 109 - Solve a radical equation that leads to a linear equation

GA MM1A3.c - Use a variety of techniques, including technology, tables and graphs to solve equations resulting from the investigation of x² + bx + c = 0.


Obj. 88 - Solve a quadratic equation by graphing the associated quadratic function

GA MM1A3.d - Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.


Obj. 124 - Solve a rational equation involving terms with monomial denominators

GA MM1G - Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons, and determine distances and points of concurrence.GA MM1G1 - Students will investigate properties of geometric figures in the coordinate plane.GA MM1G1.a - Determine the distance between two points.GA MM1G1.b - Determine the distance between a point and a line.

GA MM1G1.c - Determine the midpoint of a segment.GA MM1G1.d - Understand the distance formula as an application of the Pythagorean theorem.GA MM1G1.e - Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.GA MM1G2 - Students will understand and use the language of mathematical argument and justification.GA MM1G2.a - Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.


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GA MM1G2.b - Understand and use the relationships among a statement and its converse, inverse, and contrapositive.GA MM1G3 - Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.GA MM1G3.a - Determine the sum of interior and exterior angles in a polygon.GA MM1G3.b - Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.GA MM1G3.c - Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).GA MM1G3.d - Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

GA MM1G3.e - Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.GA MM1D - Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.GA MM1D1 - Students will determine the number of outcomes related to a given event.GA MM1D1.a - Apply the addition and multiplication principles of counting.GA MM1D1.b - Calculate and use simple permutations and combinations.GA MM1D2 - Students will use the basic laws of probability.


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GA MM1D2.a - Find the probabilities of mutually exclusive events.

GA MM1D2.b - Find the probabilities of dependent events.GA MM1D2.c - Calculate conditional probabilities.GA MM1D2.d - Use expected value to predict outcomes.GA MM1D3 - Students will relate samples to a population.GA MM1D3.a - Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.GA MM1D3.b - Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.GA MM1D3.c - Understand that a random sample is used to improve the chance of selecting a representative sample.GA MM1D4 - Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).GA MM1P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

GA MM1P1 - Students will solve problems (using appropriate technology).GA MM1P1.a - Build new mathematical knowledge through problem solving.GA MM1P1.b - Solve problems that arise in mathematics and in other contexts.GA MM1P1.c - Apply and adapt a variety of appropriate strategies to solve problems.


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GA MM1P1.d - Monitor and reflect on the process of mathematical problem solving.GA MM1P2 - Students will reason and evaluate mathematical arguments.GA MM1P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.

GA MM1P2.b - Make and investigate mathematical conjectures.

GA MM1P2.c - Develop and evaluate mathematical arguments and proofs.

GA MM1P2.d - Select and use various types of reasoning and methods of proof.GA MM1P3 - Students will communicate mathematically.GA MM1P3.a - Organize and consolidate their mathematical thinking through communication.GA MM1P3.b - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

GA MM1P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA MM1P3.d - Use the language of mathematics to express mathematical ideas precisely.GA MM1P4 - Students will make connections among mathematical ideas and to other disciplines.GA MM1P4.a - Recognize and use connections among mathematical ideas.GA MM1P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MM1P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA MMIP5 - Students will represent mathematics in multiple ways.


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GA MMIP5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA MMIP5.b - Select, apply, and translate among mathematical representations to solve problems.GA MMIP5.c - Use representations to model and interpret physical, social, and mathematical phenomena.GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areasGA MRC.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourseGA MRC.a.3 - Read technical texts related to various subject areas

GA MRC.b - Discussing booksGA MRC.b.1 - Discuss messages and themes from books in all subject areas.GA MRC.b.2 - Respond to a variety of texts in multiple modes of discourse.GA MRC.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b.4 - Evaluate the merit of texts in every subject discipline.GA MRC.b.5 - Examine author's purpose in writing.GA MRC.b.6 - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.


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GA MRC.c.2 - Use content vocabulary in writing and speaking.GA MRC.c.3 - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing contextGA MRC.d.1 - Explore life experiences related to subject area content.GA MRC.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2005, Accelerated Mathematics 1, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MA1N - Students will use the complex number system.GA MA1N1 - Students will represent and operate with complex numbers.

GA MA1N1.a - Write square roots of negative numbers in imaginary form.

GA MA1N1.b - Write complex numbers in the form a + bi.GA MA1N1.c - Add, subtract, multiply, and divide complex numbers.GA MA1N1.d - Simplify expressions involving complex numbers.

GA MA1A - Students will explore functions, solve equations and operate with radical, polynomial and rational expressions.GA MA1A1 - Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.GA MA1A1.a - Represent functions using function notation.GA MA1A1.b - Graph the basic functions f(x) = x to the power n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.


Obj. 111 - Determine the graph of a radical function


Obj. 126 - Determine the graph of a rational function

GA MA1A1.c - Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.GA MA1A1.d - Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

Topic 2 - Relations and Functions

Obj. 9 - Determine the domain or range of a function

GA MA1A1.e - Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.GA MA1A1.f - Recognize sequences as functions with domains that are sets of whole numbers.



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Agency Tag Set NameGeorgia, Math, 2005, Accelerated Mathematics 1, Performance Standards, State Department of EducationStandard Topic Description Objective Description


GA MA1A1.g - Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

GA MA1A1.h - Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

GA MA1A1.i - Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA MA1A2 - Students will simplify and operate with radical expressions, polynomials, and rational expressions.

Topic 10 - Radical Expressions Obj. 105 - Rationalize the denominator of an algebraic radical expression

GA MA1A2.a - Simplify algebraic and numeric expressions involving square root.

Topic 10 - Radical Expressions Obj. 98 - Simplify a monomial numerical expression involving the square root of a whole numberObj. 103 - Rationalize the denominator of a numerical radical expressionObj. 104 - Simplify a monomial algebraic radical expression

GA MA1A2.b - Perform operations with square roots.

Topic 10 - Radical Expressions Obj. 99 - Multiply monomial numerical expressions involving radicalsObj. 100 - Divide monomial numerical expressions involving radicalsObj. 101 - Add and/or subtract numerical radical expressionsObj. 102 - Multiply a binomial numerical radical expression by a numerical radical expressionObj. 106 - Add or subtract algebraic radical expressionsObj. 107 - Multiply monomial algebraic radical expressionsObj. 108 - Divide monomial algebraic radical expressions

GA MA1A2.c - Add, subtract, multiply, and divide polynomials.

Topic 6 - Polynomial Expressions Obj. 70 - Add polynomial expressions


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Obj. 71 - Subtract polynomial expressionsObj. 72 - Multiply a polynomial by a monomialObj. 73 - Multiply two binomials of the form (x +/- a)(x +/- b)Obj. 74 - Multiply two binomials of the form (ax +/- b)(cx +/- d)Obj. 75 - Multiply two binomials of the form (ax +/- by)(cx +/- dy)Obj. 76 - Square a binomialObj. 77 - Multiply two nonlinear binomialsObj. 78 - Multiply a trinomial by a binomial

Topic 12 - Rational Expressions Obj. 117 - Divide a polynomial expression by a monomialObj. 118 - Divide a polynomial expression by a binomial

GA MA1A2.d - Add, subtract, multiply, and divide rational expressions.

Topic 12 - Rational Expressions Obj. 115 - Multiply rational expressions

Obj. 116 - Divide rational expressions

Obj. 120 - Add or subtract two rational expressions with like denominatorsObj. 121 - Add or subtract two rational expressions with unlike monomial denominatorsObj. 122 - Add or subtract two rational expressions with unlike polynomial denominators

GA MA1A2.e - Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below. (x + y)² = x² + 2xy + y²; (x - y)² = x² - 2xy + y²; (x + y)(x - y) = x² - y²; (x + a)(x + b) = x² + (a + b)x + ab; (x + y)³ = x³ + 3x²y + 3xy² + y³; (x - y)³ = x³ - 3x²y + 3xy² - y³

Topic 7 - Factor Algebraic Expressions

Obj. 79 - Factor the GCF from a polynomial expression

Obj. 80 - Factor trinomials that result in factors of the form (x +/- a)(x +/- b)

Obj. 81 - Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d)


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Obj. 82 - Factor trinomials that result in factors of the form (ax +/- by)(cx +/- dy)Obj. 83 - Factor the difference of two squaresObj. 84 - Factor a perfect-square trinomialObj. 85 - Factor a polynomial that has a GCF and two linear binomial factors

GA MA1A2.f - Use area and volume models for polynomial arithmetic.

GA MA1A3 - Students will analyze quadratic functions in the forms f(x) = ax² + bx + c and f(x) = a(x - h)² + k.

GA MA1A3.a - Convert between standard and vertex form.GA MA1A3.b - Graph quadratic functions as transformations of the function f(x) = x².GA MA1A3.c - Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.GA MA1A3.d - Explore arithmetic series and various ways of computing their sums.GA MA1A3.e - Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

GA MA1A4 - Students will solve quadratic equations and inequalities in one variable.GA MA1A4.a - Solve equations graphically using appropriate technology.GA MA1A4.b - Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.


Obj. 89 - Solve a quadratic equation by taking the square root

Obj. 91 - Solve a quadratic equation by factoringObj. 92 - Solve a quadratic equation using the quadratic formula


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GA MA1A4.c - Analyze the nature of roots using technology and using the discriminant.GA MA1A4.d - Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.GA MA1A5 - Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

GA MA1A5.a - Write absolute value functions as piecewise functions.

GA MA1A5.b - Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.GA MA1A5.c - Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Topic 3 - Linear Equations and Inequalities

Obj. 20 - Solve a 1-variable absolute value equation

Obj. 37 - Determine the graph of a 2-variable absolute value equationObj. 43 - Solve a 1-variable absolute value inequalityObj. 44 - Determine the graph of a 1-variable absolute value inequality

GA MA1G - Students will explore, understand and use the formal language of reasoning and justification. Students will apply properties of polygons, circles and spheres, and determine distances and points of concurrence.GA MA1G1 - Students will investigate properties of geometric figures in the coordinate plane.GA MA1G1.a - Determine the distance between two points.GA MA1G1.b - Determine the distance between a point and a line.

GA MA1G1.c - Determine the midpoint of a segment.


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GA MA1G1.d - Understand the distance formula as an application of the Pythagorean theorem.GA MA1G1.e - Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.GA MA1G2 - Students will understand and use the language of mathematical argument and justification.GA MA1G2.a - Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.GA MA1G2.b - Understand and use the relationships among a statement and its converse, inverse, and contrapositive.GA MA1G3 - Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.GA MA1G3.a - Determine the sum of interior and exterior angles in a polygon.GA MA1G3.b - Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.GA MA1G3.c - Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).GA MA1G3.d - Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

GA MA1G3.e - Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.GA MA1G4 - Students will understand the properties of circles.

GA MA1G4.a - Understand and use properties of chords, tangents, and secants as an application of triangle similarity.


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GA MA1G4.b - Understand and use properties of central, inscribed, and related angles.GA MA1G4.c - Use the properties of circles to solve problems involving the length of an arc and the area of a sector.GA MA1G4.d - Justify measurements and relationships in circles using geometric and algebraic properties.

GA MA1G5 - Students will find and compare the measures of spheres.GA MA1G5.a - Use and apply surface area and volume of a sphere.

GA MA1G5.b - Determine the effect on surface area and volume of changing the radius or diameter of a sphere.GA MA1D - Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data. Students will determine algebraic models from data.

GA MA1D1 - Students will determine the number of outcomes related to a given event.GA MA1D1.a - Apply the addition and multiplication principles of counting.

GA MA1D1.b - Calculate and use simple permutations and combinations.GA MA1D2 - Students will use the basic laws of probability.GA MA1D2.a - Find the probabilities of mutually exclusive events.

GA MA1D2.b - Find the probabilities of dependent events.GA MA1D2.c - Calculate conditional probabilities.GA MA1D2.d - Use expected value to predict outcomes.


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GA MA1D3 - Students will relate samples to a population.GA MA1D3.a - Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.GA MA1D3.b - Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.GA MA1D3.c - Understand that a random sample is used to improve the chance of selecting a representative sample.GA MA1D4 - Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).GA MA1D5 - Students will determine an algebraic model to quantify the association between two quantitative variables.GA MA1D5.a - Gather and plot data that can be modeled with linear and quadratic functions.GA MA1D5.b - Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and "eyeballing."

GA MA1D5.c - Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

GA MA1P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

GA MA1P1 - Students will solve problems (using appropriate technology).


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GA MA1P1.a - Build new mathematical knowledge through problem solving.GA MA1P1.b - Solve problems that arise in mathematics and in other contexts.GA MA1P1.c - Apply and adapt a variety of appropriate strategies to solve problems.GA MA1P1.d - Monitor and reflect on the process of mathematical problem solving.GA MA1P2 - Students will reason and evaluate mathematical arguments.GA MA1P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.

GA MA1P2.b - Make and investigate mathematical conjectures.

GA MA1P2.c - Develop and evaluate mathematical arguments and proofs.

GA MA1P2.d - Select and use various types of reasoning and methods of proof.GA MA1P3 - Students will communicate mathematically.GA MA1P3.a - Organize and consolidate their mathematical thinking through communication.GA MA1P3.b - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

GA MA1P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA MA1P3.d - Use the language of mathematics to express mathematical ideas precisely.GA MA1P4 - Students will make connections among mathematical ideas and to other disciplines.GA MA1P4.a - Recognize and use connections among mathematical ideas.


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GA MA1P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MA1P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA MA1P5 - Students will represent mathematics in multiple ways.

GA MA1P5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA MA1P5.b - Select, apply, and translate among mathematical representations to solve problems.GA MA1P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areasGA MRC.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourseGA MRC.a.3 - Read technical texts related to various subject areas

GA MRC.b - Discussing booksGA MRC.b.1 - Discuss messages and themes from books in all subject areas.GA MRC.b.2 - Respond to a variety of texts in multiple modes of discourse.GA MRC.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b.4 - Evaluate the merit of texts in every subject discipline.


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GA MRC.b.5 - Examine author's purpose in writing.GA MRC.b.6 - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.GA MRC.c.2 - Use content vocabulary in writing and speaking.GA MRC.c.3 - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing contextGA MRC.d.1 - Explore life experiences related to subject area content.GA MRC.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2006, Mathematics III: Advanced Algebra/Statistics, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MM3A - Students will investigate exponential, logarithmic and polynomial functions of degree higher than 2. Students will understand matrices and use them to solve problems.GA MM3A1 - Students will analyze graphs of polynomial functions of higher degree.GA MM3A1.a - Graph simple polynomial functions as translations of the function f(x) = ax to the n power.GA MM3A1.b - Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

Topic 6 - Roots, Radicals, and Complex Numbers

Obj. 78 - Graph square roots

Topic 8 - Polynomials Obj. 127 - Graph polynomial functions

GA MM3A1.c - Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.GA MM3A1.d - Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.GA MM3A2 - Students will explore logarithmic functions as inverses of exponential functions.GA MM3A2.a - Define and understand the properties of nth roots.


Obj. 69 - Write square roots as exponential expressions

Obj. 71 - Simplify nth rootsObj. 74 - Add and subtract radical expressions

GA MM3A2.b - Extend properties of exponents to include rational exponents.


Obj. 73 - Simplify expressions with rational exponents

GA MM3A2.c - Define logarithmic functions as inverses of exponential functions.

Topic 9 - Exponents and Logarithms

Obj. 129 - Exponential equations to logarithmic form

Obj. 130 - Logarithmic equations to exponential formObj. 131 - Find logarithms by converting to exponential form

Standards List with Aligned Product SkillsProduct NameAccelerated Math Algebra 2


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Agency Tag Set NameGeorgia, Math, 2006, Mathematics III: Advanced Algebra/Statistics, Performance Standards, State Department of EducationStandard Topic Description Objective Description


GA MM3A2.d - Understand and use properties of logarithms by extending laws of exponents.


Obj. 133 - Properties of logarithms, simplify expressions

Obj. 134 - Properties of logs, find equivalent logsObj. 135 - Solve logarithmic equations

GA MM3A2.e - Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.GA MM3A2.f - Graph functions as transformations of f(x) = a to the x power, f(x) = log of a(x), f(x) = e to the x power, f(x) = ln x.


Obj. 141 - Graph exponential functions

GA MM3A2.g - Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.


Obj. 138 - WP: Interest problems

Obj. 139 - WP: Growth and decay problemsObj. 140 - WP: Earthquake problems

GA MM3A3 - Students will solve a variety of equations and inequalities.

GA MM3A3.a - Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

Topic 8 - Polynomials Obj. 122 - Factor trinomials, ax(x + b)(x - c)

Obj. 124 - Factor sum or difference of 2 cubesObj. 125 - Factor polynomials into binomials and trinomialsObj. 126 - Factor 4-term expressions by grouping

GA MM3A3.b - Solve polynomial, exponential and logarithmic equations analytically, graphically, and using appropriate technology.


Obj. 136 - Solve exponential equations

Obj. 137 - Solve equations involving natural logarithms


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GA MM3A3.c - Solve polynomial, exponential and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

GA MM3A3.d - Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.GA MM3A4 - Students will perform basic operations with matrices.GA MM3A4.a - Add, subtract, multiply and invert matrices, when possible, choosing appropriate methods, including technology.

Topic 5 - Matrices and Determinants

Obj. 59 - Matrices, sums and differences (3 x 3)

Obj. 60 - Matrices, products (3 x 3)

GA MM3A4.b - Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.GA MM3A4.c - Examine the properties of matrices, contrasting them with properties of real numbers.


Obj. 63 - Matrices, inverses

GA MM3A5 - Students will use matrices to formulate and solve problems.


Obj. 64 - Cramer's Rule, solve systems of 2 equations

Obj. 65 - Cramer's Rule, solve systems of 3 equationsObj. 66 - Matrices, solve systems of equationsObj. 67 - WP: Matrices

GA MM3A5.a - Represent a system of linear equations as a matrix equation.GA MM3A5.b - Solve matrix equations using inverse matrices.GA MM3A5.c - Represent and solve realistic problems using systems of linear equations.GA MM3A6 - Students will solve linear programming problems in two variables.

Topic 4 - Systems of Equations and Inequalities

Obj. 57 - Solve linear programming problems

GA MM3A6.a - Solve systems of inequalities in two variables, showing the solutions graphically.


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GA MM3A6.b - Represent and solve realistic problems using linear programming.GA MM3A7 - Students will understand and apply matrix representations of vertex-edge graphs.GA MM3A7.a - Use graphs to represent realistic situations.GA MM3A7.b - Use matrices to represent graphs, and solve problems that can be represented by graphs.GA MM3G - Students will understand and use analytic geometry of conic sections and of planes and spheres in space.GA MM3G1 - Students will investigate the relationships between lines and circles.

Topic 11 - Conics and Second-Degree Equations

Obj. 158 - Graph circles

GA MM3G1.a - Find equations of circles.


Obj. 160 - Circles, write equations given centers and radiiObj. 161 - Circles, write equations using given facts

GA MM3G1.b - Graph a circle given an equation in general form.


Obj. 159 - Circles, general form equations

GA MM3G1.c - Find the equation of a tangent line to a circle at given point.

GA MM3G1.d - Solve a system of equations involving a circle and a line.


Obj. 175 - Solve systems of linear and 2nd-degree equations

GA MM3G1.e - Solve a system of equations involving two circles.GA MM3G2 - Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).


Obj. 174 - Identify equations of conics

GA MM3G2.a - Convert equations of conics by completing the square.

GA MM3G2.b - Graph conic sections, identifying fundamental characteristics.


Obj. 163 - Graph ellipses

Obj. 166 - Graph hyperbolas (standard equation)Obj. 167 - Graph hyperbolas (general equation)Obj. 169 - Hyperbolas, graph inequalities


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Obj. 171 - Graph parabolas (y = x^2)

Obj. 172 - Graph parabolas (x = y^2)

GA MM3G2.c - Write equations of conic sections given appropriate information.


Obj. 165 - Ellipses, write equations using given facts

GA MM3G3 - Students will investigate planes and spheres.GA MM3G3.a - Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.GA MM3G3.b - Apply the distance formula in 3-space.GA MM3G3.c - Recognize and understand equations of planes and spheres.GA MM3D - Students will use a normal distribution to calculate probabilities. They will organize, represent, investigate, interpret, and make inferences using data from both observational studies and experiments.GA MM3D1 - Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.GA MM3D2 - Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

Topic 14 - Statistics Obj. 218 - Normal curves

GA MM3D2.a - Determine intervals about the mean that include a given percent of data.GA MM3D2.b - Determine the probability that a given value falls within a specified interval.

Topic 14 - Statistics Obj. 217 - Calculate z-scores

GA MM3D2.c - Estimate how many items in a population fall within a specified interval.

Topic 14 - Statistics Obj. 216 - Mean and standard deviation

Obj. 217 - Calculate z-scores


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GA MM3D3 - Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.GA MM3P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

GA MM3P1 - Students will solve problems (using appropriate technology).GA MM3P1.a - Build new mathematical knowledge through problem solving.GA MM3P1.b - Solve problems that arise in mathematics and in other contexts.


Obj. 12 - WP: Solve linear equations

Topic 3 - Relations, Functions, and Graphs

Obj. 37 - WP: Function problems

Obj. 40 - WP: Linear equationsTopic 4 - Systems of Equations and Inequalities

Obj. 51 - WP: Solve systems, number problemsObj. 52 - WP: Solve systems, motion and distance problemsObj. 53 - WP: Solve systems, age problemsObj. 54 - WP: Solve systems, coin problemsObj. 55 - WP: Solve systems, mixture and investment problemsObj. 57 - Solve linear programming problems


Obj. 67 - WP: Matrices

Topic 7 - Quadratic Obj. 97 - WP: Graph quadratic functionsObj. 99 - WP: Variation problemsObj. 103 - WP: Other problems using quadratic equations

Topic 8 - Polynomials Obj. 128 - WP: PolynomialsTopic 9 - Exponents and Logarithms




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Obj. 177 - WP: Systems of equations

Topic 12 - Sequences and Series Obj. 184 - WP: Arithmetic sequences

Obj. 190 - WP: Geometric sequencesObj. 195 - WP: Geometric series

Topic 13 - Probability Obj. 196 - Fundamental Counting PrincipleObj. 200 - CombinationsObj. 202 - Probability of single events

Obj. 203 - Probability using Pascal's triangleObj. 204 - Probability of independent eventsObj. 205 - Conditional probabilityObj. 206 - Probability of dependent eventsObj. 207 - Compare odds and probability

Topic 14 - Statistics Obj. 218 - Normal curvesTopic 15 - Trigonometry Obj. 231 - WP: Law of Sines and

Law of CosinesObj. 235 - Find unknown sides of right trianglesObj. 236 - WP: Trigonometry

GA MM3P1.c - Apply and adapt a variety of appropriate strategies to solve problems.GA MM3P1.d - Monitor and reflect on the process of mathematical problem solving.GA MM3P2 - Students will reason and evaluate mathematical arguments.GA MM3P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.



GA MM3P2.d - Select and use various types of reasoning and methods of proof.GA MM3P3 - Students will communicate mathematically.


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GA MM3P3.a - Organize and consolidate their mathematical thinking through communication.GA MM3P3.b - Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

GA MM3P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA MM3P3.d - Use the language of mathematics to express mathematical ideas precisely.GA MM3P4 - Students will make connections among mathematical ideas and to other disciplines.GA MM3P4.a - Recognize and use connections among mathematical ideas.


Obj. 161 - Circles, write equations using given facts

Obj. 165 - Ellipses, write equations using given factsObj. 169 - Hyperbolas, graph inequalitiesObj. 178 - Graph systems of linear and 2nd-degree equationsObj. 179 - Graph systems of 2nd-degree inequalities

Topic 14 - Statistics Obj. 216 - Mean and standard deviation

GA MM3P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MM3P4.c - Recognize and apply mathematics in contexts outside of mathematics.


Obj. 12 - WP: Solve linear equations

Obj. 25 - WP: Absolute value and inequalities



Topic 7 - Quadratic Obj. 103 - WP: Other problems using quadratic equations

Topic 8 - Polynomials Obj. 128 - WP: PolynomialsTopic 9 - Exponents and Logarithms




Obj. 162 - WP: Circles


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Obj. 173 - WP: Production and profit problemsObj. 177 - WP: Systems of equations



Topic 14 - Statistics Obj. 216 - Mean and standard deviationObj. 217 - Calculate z-scoresObj. 218 - Normal curves

Topic 15 - Trigonometry Obj. 231 - WP: Law of Sines and Law of CosinesObj. 235 - Find unknown sides of right trianglesObj. 236 - WP: Trigonometry

GA MM3P5 - Students will represent mathematics in multiple ways.

GA MM3P5.a - Create and use representations to organize, record, and communicate mathematical ideas.


Obj. 19 - Graph inequalities (number line)

Obj. 20 - Graph inequalities, 1-variable (coordinate plane)Obj. 21 - Graph linear inequalities in 2-variablesObj. 22 - Graph absolute value inequalities (number line)Obj. 23 - Graph absolute value ineq (coordinate plane)Obj. 24 - Solve and graph compound inequalities


Obj. 34 - Graph linear equations, ax + by = cObj. 35 - Graph linear equations, y = ax + bObj. 36 - Graph inverses of linear functions


Obj. 48 - Graph systems of equations



Obj. 79 - Graph nth rootsTopic 9 - Exponents and Logarithms

Obj. 141 - Graph exponential functionsObj. 142 - Graph logarithmic functions


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Topic 12 - Sequences and Series Obj. 193 - Write geometric series in sigma notation

Topic 15 - Trigonometry Obj. 227 - Graph sine and cosine functionsObj. 228 - Graph trigonometric functions

GA MM3P5.b - Select, apply, and translate among mathematical representations to solve problems.GA MM3P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.


Obj. 19 - Graph inequalities (number line)

Obj. 20 - Graph inequalities, 1-variable (coordinate plane)Obj. 21 - Graph linear inequalities in 2-variablesObj. 22 - Graph absolute value inequalities (number line)Obj. 23 - Graph absolute value ineq (coordinate plane)Obj. 24 - Solve and graph compound inequalities


Obj. 35 - Graph linear equations, y = ax + bObj. 36 - Graph inverses of linear functions


Obj. 48 - Graph systems of equations



Obj. 79 - Graph nth rootsTopic 9 - Exponents and Logarithms

Obj. 141 - Graph exponential functionsObj. 142 - Graph logarithmic functions

Topic 14 - Statistics Obj. 208 - Line and stem-and-leaf plotsObj. 209 - Box-and-whisker plots

Topic 15 - Trigonometry Obj. 227 - Graph sine and cosine functions

GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas


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GA MRC.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourseGA MRC.a.3 - Read technical texts related to various subject areas

GA MRC.b - Discussing booksGA MRC.b.1 - Discuss messages and themes from books in all subject areas.GA MRC.b.2 - Respond to a variety of texts in multiple modes of discourse.GA MRC.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b.4 - Evaluate the merit of texts in every subject discipline.GA MRC.b.5 - Examine author's purpose in writing.GA MRC.b.6 - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.GA MRC.c.2 - Use content vocabulary in writing and speaking.GA MRC.c.3 - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing contextGA MRC.d.1 - Explore life experiences related to subject area content.GA MRC.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2005, Accelerated Mathematics 2, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MA2A - Students will investigate exponential, logarithmic, and polynomial functions of higher degree; understand matrices and use them to solve problems; and solve linear programming problems in two variables.

GA MA2A1 - Students will explore exponential functions.GA MA2A1.a - Extend properties of exponents to include all integer exponents.GA MA2A1.b - Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

GA MA2A1.c - Graph functions as transformations of f(x) = a to the x power.GA MA2A1.d - Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

GA MA2A1.e - Understand and use basic exponential functions as models of real phenomena.GA MA2A1.f - Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.GA MA2A1.g - Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.GA MA2A2 - Students will explore inverses of functions.GA MA2A2.a - Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.


Obj. 27 - Domain and range, functions

Obj. 30 - Determine if functions are one-to-one



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GA MA2A2.b - Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.


Obj. 33 - Find inverses of functions

GA MA2A2.c - Explore the graphs of functions and their inverses.


Obj. 28 - Domain and range, determine from graphsObj. 34 - Graph linear equations, ax + by = cObj. 35 - Graph linear equations, y = ax + bObj. 36 - Graph inverses of linear functions

Topic 7 - Quadratic Obj. 96 - Graph quadratic functions

Obj. 97 - WP: Graph quadratic functions

GA MA2A2.d - Use composition to verify that functions are inverses of each other.GA MA2A3 - Students will analyze graphs of polynomial functions of higher degree.GA MA2A3.a - Graph simple polynomial functions as translations of the function f(x) = ax to the n power.

Topic 8 - Polynomials Obj. 127 - Graph polynomial functions

GA MA2A3.b - Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.GA MA2A3.c - Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.GA MA2A3.d - Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.GA MA2A4 - Students will explore logarithmic functions as inverses of exponential functions.GA MA2A4.a - Define and understand the properties of nth roots.


Obj. 71 - Simplify nth roots


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GA MA2A4.b - Extend properties of exponents to include rational exponents.


Obj. 70 - Simplify expressions with fractional exponents

Obj. 72 - WP: RootsObj. 73 - Simplify expressions with rational exponents

GA MA2A4.c - Define logarithmic functions as inverses of exponential functions.


Obj. 129 - Exponential equations to logarithmic form

Obj. 130 - Logarithmic equations to exponential form

GA MA2A4.d - Understand and use properties of logarithms by extending laws of exponents.


Obj. 133 - Properties of logarithms, simplify expressions

Obj. 134 - Properties of logs, find equivalent logs

GA MA2A4.e - Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.GA MA2A4.f - Graph functions as transformations of f(x) = a to the x power, f(x) = log base a of x , f(x) = e to the x power, f(x) = ln x.



Obj. 142 - Graph logarithmic functions

GA MA2A4.g - Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.GA MA2A5 - Students will solve a variety of equations and inequalities.

GA MA2A5.a - Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

Topic 7 - Quadratic Obj. 104 - Solve cubic equations

GA MA2A5.b - Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Topic 7 - Quadratic Obj. 104 - Solve cubic equations


Obj. 135 - Solve logarithmic equations


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Obj. 136 - Solve exponential equationsObj. 137 - Solve equations involving natural logarithmsObj. 138 - WP: Interest problemsObj. 139 - WP: Growth and decay problemsObj. 140 - WP: Earthquake problems

GA MA2A5.c - Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Topic 7 - Quadratic Obj. 107 - Solve cubic inequalities with 1-variable

GA MA2A5.d - Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

Topic 7 - Quadratic Obj. 87 - Solve quad eqns, square root rule (real roots)

Obj. 88 - Solve quad eqns, square root rule (complex roots)Obj. 89 - Factor quadratics, real roots

Obj. 90 - Factor quadratics, roots with radicalsObj. 91 - Quadratic formula, 2 real rootsObj. 92 - Quadratic formula, complex rootsObj. 95 - Solve quadratic equations containing rational exprObj. 104 - Solve cubic equations


Obj. 135 - Solve logarithmic equationsObj. 136 - Solve exponential equationsObj. 137 - Solve equations involving natural logarithmsObj. 138 - WP: Interest problemsObj. 139 - WP: Growth and decay problemsObj. 140 - WP: Earthquake problems

GA MA2A6 - Students will perform basic operations with matrices.


Obj. 58 - Matrices, multiply by a constant (2 x 2)

GA MA2A6.a - Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including technology.


Obj. 59 - Matrices, sums and differences (3 x 3)


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Obj. 60 - Matrices, products (3 x 3)

Obj. 63 - Matrices, inversesGA MA2A6.b - Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using technology.


Obj. 63 - Matrices, inverses

GA MA2A6.c - Examine the properties of matrices, contrasting them with properties of real numbers.

GA MA2A7 - Students will use matrices to formulate and solve problems.


Obj. 50 - Solve systems, three equations


Obj. 64 - Cramer's Rule, solve systems of 2 equationsObj. 65 - Cramer's Rule, solve systems of 3 equationsObj. 67 - WP: Matrices

GA MA2A7.a - Represent a system of linear equations as a matrix equation.GA MA2A7.b - Solve matrix equations using inverse matrices.


Obj. 66 - Matrices, solve systems of equations

GA MA2A7.c - Represent and solve realistic problems using systems of linear equations.


Obj. 51 - WP: Solve systems, number problems

Obj. 52 - WP: Solve systems, motion and distance problemsObj. 53 - WP: Solve systems, age problemsObj. 54 - WP: Solve systems, coin problemsObj. 55 - WP: Solve systems, mixture and investment problems

GA MA2A8 - Students will solve linear programming problems in two variables.


Obj. 57 - Solve linear programming problems

GA MA2A8.a - Solve systems of inequalities in two variables, showing the solutions graphically.


Obj. 56 - Solve systems of linear inequalities by graphing

GA MA2A8.b - Represent and solve realistic problems using linear programming.GA MA2A9 - Students will understand and apply matrix representations of vertex-edge graphs.GA MA2A9.a - Use graphs to represent realistic situations.


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GA MA2A9.b - Use matrices to represent graphs, and solve problems that can be represented by graphs.GA MA2G - Students will explore right triangles and right triangular trigonometry. They will understand and apply properties of conic sections, planes, and spheres.GA MA2G1 - Students will identify and use special right triangles.GA MA2G1.a - Determine the lengths of sides of 30°-60°-90° triangles.

GA MA2G1.b - Determine the lengths of sides of 45°-45°-90° triangles.GA MA2G2 - Students will define and apply sine, cosine, and tangent ratios to right triangles.

Topic 15 - Trigonometry Obj. 223 - Find the sine, cosine, or tangent

Obj. 234 - Find a side given side and angle

GA MA2G2.a - Discover the relationship of the trigonometric ratios for similar triangles.GA MA2G2.b - Explain the relationship between the trigonometric ratios of complementary angles.GA MA2G2.c - Solve application problems using the trigonometric ratios.

Topic 15 - Trigonometry Obj. 235 - Find unknown sides of right triangles

GA MA2G3 - Students will investigate the relationships between lines and circles.



GA MA2G3.a - Find equations of circles.


Obj. 159 - Circles, general form equationsObj. 160 - Circles, write equations given centers and radiiObj. 161 - Circles, write equations using given factsObj. 162 - WP: Circles

GA MA2G3.b - Graph a circle given an equation in general form.


Obj. 159 - Circles, general form equations

GA MA2G3.c - Find the equation of a tangent line to a circle at a given point.GA MA2G3.d - Solve a system of equations involving a circle and a line.




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GA MA2G3.e - Solve a system of equations involving two circles.GA MA2G4 - Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).


Obj. 168 - Hyperbolas, find vertices, foci, and asymptotes

Obj. 170 - Parabolas, find vertex from equationObj. 174 - Identify equations of conics

GA MA2G4.a - Convert equations of conics by completing the square.

GA MA2G4.b - Graph conic sections, identifying fundamental characteristics.



Obj. 163 - Graph ellipsesObj. 166 - Graph hyperbolas (standard equation)Obj. 167 - Graph hyperbolas (general equation)Obj. 171 - Graph parabolas (y = x^2)

Obj. 172 - Graph parabolas (x = y^2)

GA MA2G4.c - Write equations of conic sections given appropriate information.


Obj. 164 - Ellipses, general form equations

Obj. 165 - Ellipses, write equations using given facts

GA MA2G5 - Students will investigate planes and spheres.GA MA2G5.a - Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.GA MA2G5.b - Apply the distance formula in 3-space.GA MA2G5.c - Recognize and understand equations of planes and spheres.GA MA2D - Students will make informal inferences about means and standard deviations. Students will use a normal distribution to calculate probabilities. Students will organize, represent, investigate, interpret, and make inferences from both observational studies and experiments.


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GA MA2D1 - Using sample data, students will make informal inferences about population means and standard deviations.GA MA2D1.a - Pose a question and collect sample data from at least two different populations.GA MA2D1.b - Understand and calculate the means and standard deviations of sets of data.

Topic 14 - Statistics Obj. 211 - Means of data sets

Obj. 216 - Mean and standard deviation

GA MA2D1.c - Use means and standard deviations to compare data sets.GA MA2D1.d - Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

GA MA2D2 - Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.GA MA2D3 - Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution).

GA MA2D3.a - Determine intervals about the mean that include a given percent of data.GA MA2D3.b - Determine the probability that a given value falls within a specified interval.GA MA2D3.c - Estimate how many items in a population fall within a specified interval.


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GA MA2D4 - Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.GA MA2P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

GA MA2P1 - Students will solve problems (using appropriate technology).GA MA2P1.a - Build new mathematical knowledge through problem solving.GA MA2P1.b - Solve problems that arise in mathematics and in other contexts.



Obj. 51 - WP: Solve systems, number problemsObj. 52 - WP: Solve systems, motion and distance problemsObj. 53 - WP: Solve systems, age problemsObj. 54 - WP: Solve systems, coin problemsObj. 55 - WP: Solve systems, mixture and investment problemsObj. 56 - Solve systems of linear inequalities by graphingObj. 57 - Solve linear programming problems


Obj. 64 - Cramer's Rule, solve systems of 2 equationsObj. 65 - Cramer's Rule, solve systems of 3 equationsObj. 66 - Matrices, solve systems of equationsObj. 67 - WP: Matrices


Obj. 72 - WP: Roots

Topic 7 - Quadratic Obj. 97 - WP: Graph quadratic functionsObj. 104 - Solve cubic equationsObj. 107 - Solve cubic inequalities with 1-variable


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Obj. 135 - Solve logarithmic equationsObj. 136 - Solve exponential equationsObj. 137 - Solve equations involving natural logarithmsObj. 138 - WP: Interest problemsObj. 139 - WP: Growth and decay problemsObj. 140 - WP: Earthquake problems





GA MA2P1.c - Apply and adapt a variety of appropriate strategies to solve problems.



Obj. 51 - WP: Solve systems, number problemsObj. 52 - WP: Solve systems, motion and distance problemsObj. 53 - WP: Solve systems, age problemsObj. 54 - WP: Solve systems, coin problemsObj. 55 - WP: Solve systems, mixture and investment problems




Obj. 72 - WP: Roots

Topic 7 - Quadratic Obj. 97 - WP: Graph quadratic functionsObj. 104 - Solve cubic equations







GA MA2P1.d - Monitor and reflect on the process of mathematical problem solving.


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GA MA2P2 - Students will reason and evaluate mathematical arguments.GA MA2P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.




GA MA2P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA MA2P3.d - Use the language of mathematics to express mathematical ideas precisely.GA MA2P4 - Students will make connections among mathematical ideas and to other disciplines.GA MA2P4.a - Recognize and use connections among mathematical ideas.GA MA2P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MA2P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA MA2P5 - Students will represent mathematics in multiple ways.

GA MA2P5.a - Create and use representations to organize, record, and communicate mathematical ideas.


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GA MA2P5.b - Select, apply, and translate among mathematical representations to solve problems.GA MA2P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a. - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areasGA MRC.a. - Read both informational and fictional texts in a variety of genres and modes of discourse

GA MRC.a. - Read technical texts related to various subject areasGA MRC.b - Discussing booksGA MRC.b. - Discuss messages and themes from books in all subject areas.GA MRC.b. - Respond to a variety of texts in multiple modes of discourse.

GA MRC.b. - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b. - Evaluate the merit of texts in every subject discipline.GA MRC.b. - Examine author's purpose in writing.GA MRC.b. - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c. - Demonstrate an understanding of contextual vocabulary in various subjects.GA MRC.c. - Use content vocabulary in writing and speaking.GA MRC.c. - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing context


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GA MRC.d. - Explore life experiences related to subject area content.

GA MRC.d. - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d. - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2006, Mathematics I: Algebra/Geometry/Statistics1, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MM1A - Students will explore functions and solve simple equations. Students will simplify and operate with radical, polynomial, and rational expressions.

GA MM1A1 - Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.GA MM1A1.a - Represent functions using function notation.GA MM1A1.b - Graph the basic functions f(x) = x to the n power, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.GA MM1A1.c - Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.GA MM1A1.d - Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.GA MM1A1.e - Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.GA MM1A1.f - Recognize sequences as functions with domains that are whole numbers.GA MM1A1.g - Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

GA MM1A1.h - Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Geometry


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GA MM1A1.i - Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

GA MM1A2 - Students will simplify and operate with radical expressions, polynomials, and rational expressions.GA MM1A2.a - Simplify algebraic and numeric expressions involving square root.GA MM1A2.b - Perform operations with square roots.

Topic 7 - Right Triangles and Trigonometry

Obj. 46 - Solve a problem using multiple non-trigonometric right-triangle relationships

Topic 9 - Area Obj. 73 - Determine the area of a triangle using Heron's formula

GA MM1A2.c - Add, subtract, multiply, and divide polynomials.GA MM1A2.d - Expand binomials using the Binomial Theorem.GA MM1A2.e - Add, subtract, multiply, and divide rational expressions.GA MM1A2.f - Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below. (x + y)² = x² + 2xy + y²; (x - y)² = x² - 2xy + y²; (x + y)(x - y) = x² - y²; (x + a)(x + b) = x² + (a + b)x + ab; (x + y)³ = x³ +3x²y + 3xy² + y³; (x - y)³ = x³ -3x²y + 3xy² - y³

GA MM1A2.g - Use area and volume models for polynomial arithmetic.

GA MM1A3 - Students will solve simple equations.GA MM1A3.a - Solve quadratic equations in the form ax² + bx + c = 0 where a = 1, by using factorization and finding square roots where applicable.GA MM1A3.b - Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.


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GA MM1A3.c - Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x² + bx + c = 0.GA MM1A3.d - Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

GA MM1G - Students will explore, understand, and use the formal language of reasoning and justification. Students will apply properties of polygons, and determine distances and points of concurrence.GA MM1G1 - Students will investigate properties of geometric figures in the coordinate plane.GA MM1G1.a - Determine the distance between two points.

Topic 1 - Basic Concepts of Geometry

Obj. 4 - Determine the distance between two points

GA MM1G1.b - Determine the distance between a point and a line.

GA MM1G1.c - Determine the midpoint of a segment.

Topic 1 - Basic Concepts of Geometry

Obj. 6 - Determine the midpoint of a line segment given the coordinates of the endpoints

GA MM1G1.d - Understand the distance formula as an application of the Pythagorean theorem.GA MM1G1.e - Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.GA MM1G2 - Students will understand and use the language of mathematical argument and justification.GA MM1G2.a - Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.GA MM1G2.b - Understand and use the relationships among a statement and its converse, inverse, and contrapositive.GA MM1G3 - Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.


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GA MM1G3.a - Determine the sum of interior and exterior angles in a polygon.

Topic 5 - Quadrilaterals and Other Polygons

Obj. 26 - Determine the measure of an angle or the sum of the angles in a polygon

GA MM1G3.b - Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

Topic 3 - Relationships Within Triangles

Obj. 20 - Solve a problem involving two triangles by using the hinge theorem and other triangle inequality relationships

GA MM1G3.c - Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

Topic 4 - Congruent Triangles Obj. 23 - Identify a triangle congruence postulate that justifies a congruence statement

Obj. 24 - Identify congruent triangles using triangle congruence postulates or theorems

GA MM1G3.d - Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.


Obj. 27 - Determine a length or an angle measure using general properties of parallelograms

Obj. 28 - Determine a length or an angle measure using properties of squares, rectangles, or rhombiObj. 29 - Determine a length or an angle measure using properties of kitesObj. 30 - Determine a length or an angle measure using properties of trapezoids

GA MM1G3.e - Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.GA MM1D - Students will use counting techniques and determine probability. Students will demonstrate understanding of data analysis by posing questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and make inferences from data.GA MM1D1 - Students will determine the number of outcomes related to a given event.GA MM1D1.a - Apply the addition and multiplication principles of counting.GA MM1D1.b - Calculate and use simple permutations and combinations.


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GA MM1D2 - Students will use the basic laws of probability.GA MM1D2.a - Find the probabilities of mutually exclusive events.

GA MM1D2.b - Find the probabilities of dependent events.GA MM1D2.c - Calculate conditional probabilities.GA MM1D2.d - Use expected value to predict outcomes.GA MM1D3 - Students will relate samples to a population.GA MM1D3.a - Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.GA MM1D3.b - Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.GA MM1D3.c - Understand that a random sample is used to improve the chance of selecting a representative sample.GA MM1D4 - Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).GA MM1P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.



Obj. 21 - WP: Determine a length or an angle measure using triangle relationships


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Obj. 32 - WP: Solve a problem using the properties of angles and/or sides of polygons

Topic 6 - Similarity Obj. 43 - WP: Determine a length using similarity


Obj. 48 - WP: Solve a problem involving a complex figure using the Pythagorean theoremObj. 52 - WP: Determine a length in a right triangle using a sine, cosine, or tangent ratioObj. 53 - WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio

Topic 9 - Area Obj. 72 - WP: Solve a problem involving the area of a quadrilateralObj. 79 - WP: Solve a problem involving the area of a complex shape formed by circles and polygonsObj. 83 - WP: Determine a length or an area involving a sector of a circle

Topic 10 - Surface Area and Volume

Obj. 96 - WP: Solve a problem involving the surface area of a sphere

Obj. 100 - WP: Determine the volume of a sphere or hemisphereObj. 102 - WP: Solve a problem involving the volume of a complex solid figureObj. 106 - WP: Solve a problem involving two solid figures that have the same surface area or volume

GA MM1P1.c - Apply and adapt a variety of appropriate strategies to solve problems.GA MM1P1.d - Monitor and reflect on the process of mathematical problem solving.GA MM1P2 - Students will reason and evaluate mathematical arguments.GA MM1P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.



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GA MM1P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA MM1P3.d - Use the language of mathematics to express mathematical ideas precisely.GA MM1P4 - Students will make connections among mathematical ideas and to other disciplines.GA MM1P4.a - Recognize and use connections among mathematical ideas.GA MM1P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MM1P4.c - Recognize and apply mathematics in contexts outside of mathematics.


Obj. 21 - WP: Determine a length or an angle measure using triangle relationships


Obj. 32 - WP: Solve a problem using the properties of angles and/or sides of polygons

Topic 6 - Similarity Obj. 43 - WP: Determine a length using similarity


Obj. 47 - WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangleObj. 48 - WP: Solve a problem involving a complex figure using the Pythagorean theoremObj. 52 - WP: Determine a length in a right triangle using a sine, cosine, or tangent ratio


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Obj. 53 - WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio

Topic 9 - Area Obj. 72 - WP: Solve a problem involving the area of a quadrilateralObj. 79 - WP: Solve a problem involving the area of a complex shape formed by circles and polygonsObj. 83 - WP: Determine a length or an area involving a sector of a circle

Topic 10 - Surface Area and Volume

Obj. 96 - WP: Solve a problem involving the surface area of a sphere

Obj. 100 - WP: Determine the volume of a sphere or hemisphere

GA MMIP5 - Students will represent mathematics in multiple ways.

GA MMIP5.a - Create and use representations to organize, record, and communicate mathematical ideas.GA MMIP5.b - Select, apply, and translate among mathematical representations to solve problems.GA MMIP5.c - Use representations to model and interpret physical, social, and mathematical phenomena.

Topic 8 - Circles Obj. 67 - Determine an equation of a circle

GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areasGA MRC.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourseGA MRC.a.3 - Read technical texts related to various subject areas

GA MRC.b - Discussing books


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GA MRC.b.1 - Discuss messages and themes from books in all subject areas.GA MRC.b.2 - Respond to a variety of texts in multiple modes of discourse.GA MRC.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b.4 - Evaluate the merit of texts in every subject discipline.GA MRC.b.5 - Examine author's purpose in writing.GA MRC.b.6 - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.GA MRC.c.2 - Use content vocabulary in writing and speaking.GA MRC.c.3 - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing contextGA MRC.d.1 - Explore life experiences related to subject area content.GA MRC.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2005, Accelerated Mathematics 3, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MA3A - Students will explore characteristics of various functions, understand and use concepts of trigonometric functions, investigate and apply sequences and series, and use parametric and polar equations to represent functions and curves.

Topic 1 - Review of Fundamental Concepts of Algebra

Obj. 16 - Domains & range, functions

Obj. 19 - Determine if functions are one-to-one

GA MA3A1 - Students will explore rational functions.GA MA3A1.a - Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.GA MA3A1.b - Find inverses of rational functions, discussing domain and range, symmetry, and function composition.



GA MA3A1.c - Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.


Obj. 10 - Solve inequalities with rational expressions

Obj. 23 - Graph rational functionsObj. 33 - Solve rational equationsObj. 34 - WP: Rational equations

GA MA3A2 - Students will use the circle to define the trigonometric functions.GA MA3A2.a - Define and understand angles measured in degrees and radians, including but not limited to 0°, 30°, 45°, 60°, 90°, their multiples, and equivalences.

Topic 4 - Trigonometric Functions

Obj. 62 - Degrees to radians

Obj. 63 - Radians to degreesGA MA3A2.b - Understand and apply the six trigonometric functions as functions of general angles in standard position.GA MA3A2.c - Find values of trigonometric functions using points on the terminal sides of angles in the standard position.


Obj. 64 - Find exact values of trig functions

Standards List with Aligned Product SkillsProduct NameAccelerated Math Pre-Calculus


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GA MA3A2.d - Understand and apply the six trigonometric functions as functions of arc length on the unit circle.GA MA3A2.e - Find values of trigonometric functions using the unit circle.GA MA3A3 - Students will investigate and use the graphs of the six trigonometric functions.


Obj. 67 - Graph tan & cot functions

GA MA3A3.a - Understand and apply the six basic trigonometric functions as functions of real numbers.

GA MA3A3.b - Determine the characteristics of the graphs of the six basic trigonometric functions.GA MA3A3.c - Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.


Obj. 66 - Graph sin & cos using amp, period, & phase shift

GA MA3A3.d - Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.GA MA3A4 - Students will investigate functions.GA MA3A4.a - Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

GA MA3A4.b - Investigate transformations of functions.



GA MA3A4.c - Investigate characteristics of functions built through sum, difference, product, quotient, and composition.


Obj. 18 - Add, subtract, multiply, & divide functions

Obj. 20 - Find compositions of 2 functions

GA MA3A5 - Students will establish the identities below and use them to simplify trigonometric expressions and verify equivalence statements.


Obj. 69 - Apply sum & diff formula for sin & cos

Obj. 70 - Apply double-angle formulas for sin & cos


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GA MA3A5.1 - tan theta = sin theta/cos thetaGA MA3A5.2 - cot theta = cos theta/sin thetaGA MA3A5.3 - sec theta = 1/cos thetaGA MA3A5.4 - csc theta = 1/sin theta

GA MA3A5.5 - sin² theta + cos² theta = 1GA MA3A5.6 - cot² theta + 1 = csc² thetaGA MA3A5.7 - sin (alpha ± beta) = sin alpha cos beta ± cos alpha sin betaGA MA3A5.8 - cos (alpha ± beta) = cos alpha cos beta ± sin alpha sin betaGA MA3A5.9 - sin (2 theta) = 2 sin theta cos thetaGA MA3A5.10 - cos (2 theta) = cos² theta - sin² thetaGA MA3A6 - Students will solve trigonometric equations both graphically and algebraically.GA MA3A6.a - Solve trigonometric equations over a variety of domains, using technology as appropriate.

Topic 5 - Applications in Trigonometry

Obj. 79 - Solve trig equations

GA MA3A6.b - Use the coordinates of a point on the terminal side of an angle to express x as r cos theta and y as r sin theta.

GA MA3A6.c - Apply the law of sines and the law of cosines.


Obj. 74 - Law of Sines

Obj. 75 - Law of Sines (ambiguous case)Obj. 76 - Law of Cosines

GA MA3A7 - Students will verify and apply 1/2 ab sin C to find the area of a triangle.


Obj. 77 - Find areas of non-right triangles

GA MA3A8 - Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.

GA MA3A8.a - Find values of the above functions using technology as appropriate.


Obj. 78 - Find values of inverse trig functions


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GA MA3A8.b - Determine characteristics of the above functions and their graphs.GA MA3A9 - Students will use sequences and series.GA MA3A9.a - Use and find recursive and explicit formulae for the terms of sequences.

Topic 9 - Sequences and Series Obj. 123 - Find terms of arith seq (1st-term & common diff)

Obj. 124 - Find specified term of arithmetic sequenceObj. 125 - Find terms of arith seq (formula for nth term)Obj. 130 - Find terms of geo seq (1st term & common ratio)Obj. 131 - Find terms of geo seq given first terms

GA MA3A9.b - Recognize and use simple arithmetic and geometric sequences.



GA MA3A9.c - Investigate limits of sequences.GA MA3A9.d - Use mathematical induction to find and prove formulae for sums of finite series.GA MA3A9.e - Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

Topic 9 - Sequences and Series Obj. 127 - Find sums of arithmetic series

Obj. 133 - Find sums of finite geometric seriesObj. 134 - Find sums of infinite geometric seriesObj. 135 - Evaluate geometric series in sigma notation

GA MA3A9.f - Use summation notation to explore series.

Topic 9 - Sequences and Series Obj. 128 - Write arith series in sigma notationObj. 135 - Evaluate geometric series in sigma notation

GA MA3A9.g - Determine geometric series and their limits.

Topic 9 - Sequences and Series Obj. 136 - WP: Geometric series

GA MA3A10 - Students will understand and use vectors.GA MA3A10.a - Represent vectors algebraically and geometrically.


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GA MA3A10.b - Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

Topic 11 - Vectors Obj. 152 - Given 2 points, find a vector & its magnitude

GA MA3A10.c - Add and subtract vectors and compute scalar multiples of vectors.

Topic 11 - Vectors Obj. 151 - Linear combinations of 2 vectors

GA MA3A10.d - Use vectors to solve realistic problems.

Topic 11 - Vectors Obj. 162 - WP: Navigational problems w/ vectors

GA MA3A11 - Students will use complex numbers in trigonometric form.GA MA3A11.a - Represent complex numbers in trigonometric form.

Topic 6 - Polar Coordinates Obj. 86 - Complex #s, a + bi to polar form

GA MA3A11.b - Find products, quotients, powers, and roots of complex numbers in trigonometric form.

Topic 6 - Polar Coordinates Obj. 88 - Multiply & divide complex #s in polar form

Obj. 89 - DeMoivre's Theorem, find rootsObj. 90 - Find powers of complex #s

GA MA3A12 - Students will explore parametric representations of plane curves.GA MA3A12.a - Convert between Cartesian and parametric form.GA MA3A12.b - Graph equations in parametric form showing direction and beginning and ending points where appropriate.GA MA3A13 - Students will explore polar equations.GA MA3A13.a - Express coordinates of points in rectangular and polar form.GA MA3A13.b - Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limacons, and roses.

Topic 6 - Polar Coordinates Obj. 81 - Rectangular to polar coordinates

Obj. 82 - Polar to rectangular coordinates


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GA MA3D - Students will organize, represent, investigate, interpret, and make inferences from data, using the central limit theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.

GA MA3D1 - Using simulation, students will develop the idea of the central limit theorem.GA MA3D2 - Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.GA MA3D3 - Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.GA MA3P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.

GA MA3P1 - Students will solve problems (using appropriate technology).GA MA3P1.a - Build new mathematical knowledge through problem solving.GA MA3P1.b - Solve problems that arise in mathematics and in other contexts.


Obj. 10 - Solve inequalities with rational expressions

Obj. 25 - Solve direct & indirect variation problemsObj. 26 - Solve joint & combined variation problemsObj. 33 - Solve rational equationsObj. 34 - WP: Rational equations


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GA MA3P1.c - Apply and adapt a variety of appropriate strategies to solve problems.


Obj. 25 - Solve direct & indirect variation problems

Obj. 26 - Solve joint & combined variation problemsObj. 34 - WP: Rational equations



GA MA3P1.d - Monitor and reflect on the process of mathematical problem solving.GA MA3P2 - Students will reason and evaluate mathematical arguments.GA MA3P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.




GA MA3P3.c - Analyze and evaluate the mathematical thinking and strategies of others.


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GA MA3P3.d - Use the language of mathematics to express mathematical ideas precisely.GA MA3P4 - Students will make connections among mathematical ideas and to other disciplines.GA MA3P4.a - Recognize and use connections among mathematical ideas.GA MA3P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MA3P4.c - Recognize and apply mathematics in contexts outside of mathematics.GA MA3P5 - Students will represent mathematics in multiple ways.

GA MA3P5.a - Create and use representations to organize, record, and communicate mathematical ideas.


Obj. 22 - Use rigid & nonrigid transformations to graph func

Obj. 23 - Graph rational functionsGA MA3P5.b - Select, apply, and translate among mathematical representations to solve problems.GA MA3P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areasGA MRC.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourseGA MRC.a.3 - Read technical texts related to various subject areas

GA MRC.b - Discussing books


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GA MRC.b.1 - Discuss messages and themes from books in all subject areas.GA MRC.b.2 - Respond to a variety of texts in multiple modes of discourse.GA MRC.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b.4 - Evaluate the merit of texts in every subject discipline.GA MRC.b.5 - Examine author's purpose in writing.GA MRC.b.6 - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.GA MRC.c.2 - Use content vocabulary in writing and speaking.GA MRC.c.3 - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing contextGA MRC.d.1 - Explore life experiences related to subject area content.GA MRC.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Agency Tag Set NameGeorgia, Math, 2006, Mathematics 4, Performance Standards, State Department of EducationStandard Topic Description Objective DescriptionGA MM4A - Students will analyze rational and trigonometric functions. Students will investigate and apply sequences and series and will understand and use vectors.

GA MM4A1 - Students will explore rational functions.GA MM4A1.a - Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.


Obj. 23 - Graph rational functions

Obj. 24 - Graph piecewise-defined functionsObj. 32 - Simplify, multiply, & divide rational expressionsObj. 33 - Solve rational equationsObj. 34 - WP: Rational equations

GA MM4A1.b - Find inverses of rational functions, discussing domain and range, symmetry, and function composition.GA MM4A1.c - Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.GA MM4A2 - Students will use the circle to define the trigonometric functions.GA MM4A2.a - Define and understand angles measured in degrees and radians, including but not limited to 0°, 30°, 45°, 60°, 90°, their multiples, and equivalences.


Obj. 62 - Degrees to radians

Obj. 63 - Radians to degreesGA MM4A2.b - Understand and apply the six trigonometric functions as functions of general angles in standard position.



Obj. 66 - Graph sin & cos using amp, period, & phase shiftObj. 67 - Graph tan & cot functions

Obj. 68 - Graph sec & csc functions


Obj. 73 - WP: Right triangles



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Agency Tag Set NameGeorgia, Math, 2006, Mathematics 4, Performance Standards, State Department of EducationStandard Topic Description Objective Description


Obj. 75 - Law of Sines (ambiguous case)Obj. 76 - Law of CosinesObj. 77 - Find areas of non-right trianglesObj. 79 - Solve trig equations

GA MM4A2.c - Find values of trigonometric functions using points on the terminal sides of angles in the standard position.


Obj. 65 - Find trig values given another trig value



Obj. 78 - Find values of inverse trig functionsObj. 80 - Solve eqns involving inverse trig functions

GA MM4A2.d - Understand and apply the six trigonometric functions as functions of arc length on the unit circle.GA MM4A2.e - Find values of trigonometric functions using the unit circle.





GA MM4A3 - Students will investigate and use the graphs of the six trigonometric functions.GA MM4A3.a - Understand and apply the six basic trigonometric functions as functions of real numbers.



Obj. 65 - Find trig values given another trig valueObj. 69 - Apply sum & diff formula for sin & cosObj. 70 - Apply double-angle formulas for sin & cosObj. 71 - Apply product-sum formulas

Obj. 72 - Verify trig identitiesGA MM4A3.b - Determine the characteristics of the graphs of the six basic trigonometric functions.






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GA MM4A3.c - Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.





GA MM4A3.d - Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.





GA MM4A4 - Students will investigate functions.GA MM4A4.a - Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.


Obj. 16 - Domains & range, functions

Obj. 17 - Evaluate functions for given valuesObj. 18 - Add, subtract, multiply, & divide functions

GA MM4A4.b - Investigate transformations of functions.


Obj. 7 - Solve linear inequalities with 1-variable

Obj. 8 - Solve absolute value inequalitiesObj. 9 - Solve polynomial inequalities

Obj. 11 - Solve quad eqns, square root ruleObj. 16 - Domains & range, functions

Obj. 17 - Evaluate functions for given valuesObj. 18 - Add, subtract, multiply, & divide functionsObj. 20 - Find compositions of 2 functionsObj. 21 - Find inverses of functionsObj. 22 - Use rigid & nonrigid transformations to graph func

Topic 3 - Exponential and Logarithmic Functions

Obj. 54 - Properties of logs, rewrite expressions


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Obj. 58 - Solve log equationsObj. 59 - Solve exponential equations




Obj. 69 - Apply sum & diff formula for sin & cosObj. 71 - Apply product-sum formulas

Obj. 72 - Verify trig identitiesTopic 5 - Applications in Trigonometry


Topic 7 - Conic Sections Obj. 91 - Parabolas, graph given equationsObj. 92 - Parabolas, write eqns from given informationObj. 97 - Ellipses, find centers, vertices, & fociObj. 98 - Ellipses, write eqns from given informationObj. 99 - Ellipses, graph given equationsObj. 100 - Hyperbolas, write eqns from given informationObj. 101 - Hyperbolas, find vertices, asymptotes, & fociObj. 102 - Hyperbola, graph given equations

GA MM4A4.c - Investigate characteristics of functions built through sum, difference, product, quotient, and composition.


Obj. 20 - Find compositions of 2 functions

Obj. 27 - Simplify expressions w/ rational exponentsObj. 28 - Factor expressions w/ rational exponentsObj. 29 - Simplify radical expressions

Obj. 30 - Solve radical equationsObj. 32 - Simplify, multiply, & divide rational expressionsObj. 33 - Solve rational equations


Obj. 54 - Properties of logs, rewrite expressionsObj. 55 - Graph exponential functions

Obj. 56 - Graph log functions


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Obj. 57 - WP: Exponential functions

Obj. 58 - Solve log equationsObj. 59 - Solve exponential equations



Obj. 80 - Solve eqns involving inverse trig functions

GA MM4A5 - Students will establish the identities below and use them to simplify trigonometric expressions and verify equivalence statements.

GA MM4A5.1 - tan theta = sin theta/cos thetaGA MM4A5.2 - cot theta = cos theta/sin thetaGA MM4A5.3 - sec theta = 1/cos thetaGA MM4A5.4 - csc theta = 1/sin theta

GA MM4A5.5 - sin² theta + cos² theta = 1GA MM4A5.6 - 1 + tan² theta = sec² thetaGA MM4A5.7 - 1 + cot² theta = csc² thetaGA MM4A5.8 - sin (alpha ± beta)= sin alpha cos beta ± cos alpha sin betaGA MM4A5.9 - cos (alpha ± beta) = cos alpha cos beta ± sin alpha sin betaGA MM4A5.10 - sin (2 theta) = 2 sin theta cos thetaGA MM4A5.11 - cos (2 theta) = cos² theta - sin² thetaGA MM4A6 - Students will solve trigonometric equations both graphically and algebraically.GA MM4A6.a - Solve trigonometric equations over a variety of domains, using technology as appropriate.




GA MM4A6.b - Use the coordinates of a point on the terminal side of an angle to express x as r cos theta and y as r sin theta.

Topic 6 - Polar Coordinates Obj. 81 - Rectangular to polar coordinates


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Obj. 82 - Polar to rectangular coordinatesObj. 83 - Rectangular equations to polar formObj. 84 - Polar equations to rectangular form

GA MM4A6.c - Apply the law of sines and the law of cosines.


Obj. 74 - Law of Sines

Obj. 75 - Law of Sines (ambiguous case)Obj. 76 - Law of CosinesObj. 77 - Find areas of non-right triangles

GA MM4A7 - Students will verify and apply A = 1/2 ab sin C to find the area of a triangle.


Obj. 77 - Find areas of non-right triangles

GA MM4A8 - Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions.




GA MM4A8.a - Find values of the above functions using technology as appropriate.GA MM4A8.b - Determine characteristics of the above functions and their graphs.GA MM4A9 - Students will use sequences and seriesGA MM4A9.a - Use and find recursive and explicit formulae for the terms of sequences.

Topic 9 - Sequences and Series Obj. 123 - Find terms of arith seq (1st-term & common diff)

Obj. 124 - Find specified term of arithmetic sequenceObj. 125 - Find terms of arith seq (formula for nth term)Obj. 130 - Find terms of geo seq (1st term & common ratio)Obj. 131 - Find terms of geo seq given first terms

GA MM4A9.b - Recognize and use simple arithmetic and geometric sequences.

Topic 9 - Sequences and Series Obj. 132 - WP: Geometric sequences

GA MM4A9.c - Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series.

Topic 9 - Sequences and Series Obj. 127 - Find sums of arithmetic series

Obj. 133 - Find sums of finite geometric seriesObj. 134 - Find sums of infinite geometric series


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Obj. 135 - Evaluate geometric series in sigma notationObj. 136 - WP: Geometric series

GA MM4A9.d - Use summation notation to explore finite series.

Topic 9 - Sequences and Series Obj. 128 - Write arith series in sigma notationObj. 135 - Evaluate geometric series in sigma notation

GA MM4A10 - Students will understand and use vectors.GA MM4A10.a - Represent vectors algebraically and geometrically.

Topic 11 - Vectors Obj. 155 - Angles between 2 vectors

Obj. 156 - Projections of 1 vector onto another

GA MM4A10.b - Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

Topic 11 - Vectors Obj. 152 - Given 2 points, find a vector & its magnitude

Obj. 154 - Dot products of 2 vectors

Obj. 159 - Direction angles of vectors in spaceObj. 162 - WP: Navigational problems w/ vectors

GA MM4A10.c - Add, subtract, and compute scalar multiples of vectors.

Topic 11 - Vectors Obj. 151 - Linear combinations of 2 vectors

Obj. 153 - Find unit vectors in the same direction as vectorsObj. 157 - Cross products of 2 vectors

GA MM4A10.d - Use vectors to solve realistic problems.

Topic 11 - Vectors Obj. 158 - Find the distance between 2 points in spaceObj. 160 - Area of parallelograms from adj side vectorsObj. 161 - Find equations of planes normal to vectorsObj. 162 - WP: Navigational problems w/ vectors

GA MM4D - Students will organize, represent, investigate, interpret, and make inferences from data, using the Central Limit Theorem and the standard normal distribution. Students will apply the Central Limit Theorem to calculate confidence intervals for a population mean using data from large samples. Students will use sample data and confidence intervals to draw conclusions about populations.


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GA MM4D1 - Using simulation, students will develop the idea of the central limit theorem.GA MM4D2 - Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.GA MM4D3 - Students will use confidence intervals and margins of error to make inferences from data about a population. Technology is used to evaluate confidence intervals, but students will be aware of the ideas involved.GA MM4P - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.



Obj. 5 - WP: Linear Equations

Obj. 25 - Solve direct & indirect variation problemsObj. 26 - Solve joint & combined variation problemsObj. 34 - WP: Rational equations



Obj. 60 - WP: Compound interestObj. 61 - WP: Radioactive decay

Topic 7 - Conic Sections Obj. 105 - WP: Conic sectionsTopic 8 - Systems of Linear Equations and Inequalities

Obj. 117 - WP: Systems of linear equationsObj. 121 - Solve linear programming problems



Topic 10 - Probability Obj. 140 - WP: Permutations


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Obj. 143 - WP: CombinationsObj. 144 - Probability of single events

Obj. 145 - Probability of independent eventsObj. 146 - Conditional probabilityObj. 147 - Probability of dependent eventsObj. 148 - Probability of mutually exclusive eventsObj. 149 - Convert odds to probability

Obj. 150 - Find expected valueTopic 11 - Vectors Obj. 158 - Find the distance between

2 points in spaceObj. 162 - WP: Navigational problems w/ vectors

GA MM4P1.c - Apply and adapt a variety of appropriate strategies to solve problems.


Obj. 26 - Solve joint & combined variation problems

Obj. 34 - WP: Rational equationsTopic 3 - Exponential and Logarithmic Functions

Obj. 53 - Find logs by converting to exponential form


Obj. 72 - Verify trig identities

Topic 8 - Systems of Linear Equations and Inequalities


GA MM4P1.d - Monitor and reflect on the process of mathematical problem solving.GA MM4P2 - Students will reason and evaluate mathematical arguments.GA MM4P2.a - Recognize reasoning and proof as fundamental aspects of mathematics.


Topic 9 - Sequences and Series Obj. 122 - Common differences of arithmetic sequences

Obj. 123 - Find terms of arith seq (1st-term & common diff)Obj. 124 - Find specified term of arithmetic sequenceObj. 127 - Find sums of arithmetic seriesObj. 129 - Find ratios of geo seq given 3 termsObj. 130 - Find terms of geo seq (1st term & common ratio)


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Obj. 131 - Find terms of geo seq given first terms

Topic 10 - Probability Obj. 140 - WP: PermutationsObj. 143 - WP: CombinationsObj. 150 - Find expected value



GA MM4P3.c - Analyze and evaluate the mathematical thinking and strategies of others.GA MM4P3.d - Use the language of mathematics to express mathematical ideas precisely.


Obj. 3 - Write eqns parallel/perp to lines through a point


Obj. 117 - WP: Systems of linear equations



Topic 10 - Probability Obj. 140 - WP: PermutationsObj. 144 - Probability of single events

Obj. 146 - Conditional probabilityObj. 147 - Probability of dependent eventsObj. 148 - Probability of mutually exclusive eventsObj. 149 - Convert odds to probability

Topic 11 - Vectors Obj. 152 - Given 2 points, find a vector & its magnitudeObj. 158 - Find the distance between 2 points in spaceObj. 159 - Direction angles of vectors in spaceObj. 162 - WP: Navigational problems w/ vectors


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GA MM4P4 - Students will make connections among mathematical ideas and to other disciplines.GA MM4P4.a - Recognize and use connections among mathematical ideas.




Obj. 52 - Log equations to exponential formObj. 53 - Find logs by converting to exponential form


Obj. 72 - Verify trig identities

Topic 6 - Polar Coordinates Obj. 81 - Rectangular to polar coordinatesObj. 82 - Polar to rectangular coordinatesObj. 83 - Rectangular equations to polar formObj. 84 - Polar equations to rectangular formObj. 86 - Complex #s, a + bi to polar formObj. 87 - Complex #s, polar to a + bi formObj. 88 - Multiply & divide complex #s in polar form


Obj. 113 - Cramer's Rule, solve systems of 2 equationsObj. 114 - Cramer's Rule, solve systems of 3 equationsObj. 116 - Matrices, solve systems of linear equations

Topic 11 - Vectors Obj. 160 - Area of parallelograms from adj side vectors

Topic 12 - Introduction to Calculus

Obj. 171 - Solve problems using definition of continuityObj. 172 - Find derivatives using definition of limit

GA MM4P4.b - Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.GA MM4P4.c - Recognize and apply mathematics in contexts outside of mathematics.


Obj. 5 - WP: Linear Equations

Obj. 15 - WP: Quadratic equationsObj. 25 - Solve direct & indirect variation problemsObj. 26 - Solve joint & combined variation problemsObj. 34 - WP: Rational equations

Topic 2 - Polynomials Obj. 37 - WP: Quadratic functions


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Obj. 60 - WP: Compound interestObj. 61 - WP: Radioactive decay



Topic 7 - Conic Sections Obj. 105 - WP: Conic sectionsTopic 8 - Systems of Linear Equations and Inequalities




Topic 10 - Probability Obj. 137 - Fundamental Counting PrincipleObj. 140 - WP: PermutationsObj. 143 - WP: CombinationsObj. 144 - Probability of single events

Obj. 145 - Probability of independent eventsObj. 146 - Conditional probabilityObj. 147 - Probability of dependent eventsObj. 148 - Probability of mutually exclusive eventsObj. 150 - Find expected value


GA MM4P5 - Students will represent mathematics in multiple ways.

GA MM4P5.a - Create and use representations to organize, record, and communicate mathematical ideas.


Obj. 22 - Use rigid & nonrigid transformations to graph func

Obj. 23 - Graph rational functionsObj. 24 - Graph piecewise-defined functions



Obj. 56 - Graph log functionsTopic 6 - Polar Coordinates Obj. 85 - Graph polar equationsTopic 7 - Conic Sections Obj. 91 - Parabolas, graph given

equationsObj. 93 - Parabolas, graph inequalitiesObj. 96 - Circle, graph given equations


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Obj. 99 - Ellipses, graph given equationsObj. 102 - Hyperbola, graph given equationsObj. 103 - Hyperbolas, graph inequalities

GA MM4P5.b - Select, apply, and translate among mathematical representations to solve problems.


Obj. 2 - Graph lines

Obj. 22 - Use rigid & nonrigid transformations to graph funcObj. 23 - Graph rational functionsObj. 24 - Graph piecewise-defined functions

Topic 2 - Polynomials Obj. 46 - Graph nth-degree polynomials




Topic 6 - Polar Coordinates Obj. 85 - Graph polar equationsTopic 7 - Conic Sections Obj. 91 - Parabolas, graph given

equationsObj. 93 - Parabolas, graph inequalitiesObj. 96 - Circle, graph given equationsObj. 99 - Ellipses, graph given equationsObj. 103 - Hyperbolas, graph inequalities

Topic 12 - Introduction to Calculus

Obj. 163 - Limits, use graphs

GA MM4P5.c - Use representations to model and interpret physical, social, and mathematical phenomena.GA MRC - Students will enhance reading in all curriculum areas by:GA MRC.a - Reading in all curriculum areasGA MRC.a.1 - Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas


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GA MRC.a.2 - Read both informational and fictional texts in a variety of genres and modes of discourseGA MRC.a.3 - Read technical texts related to various subject areas

GA MRC.b - Discussing booksGA MRC.b.1 - Discuss messages and themes from books in all subject areas.GA MRC.b.2 - Respond to a variety of texts in multiple modes of discourse.GA MRC.b.3 - Relate messages and themes from one subject area to messages and themes in another area.GA MRC.b.4 - Evaluate the merit of texts in every subject discipline.GA MRC.b.5 - Examine author's purpose in writing.GA MRC.b.6 - Recognize the features of disciplinary texts.GA MRC.c - Building vocabulary knowledgeGA MRC.c.1 - Demonstrate an understanding of contextual vocabulary in various subjects.GA MRC.c.2 - Use content vocabulary in writing and speaking.GA MRC.c.3 - Explore understanding of new words found in subject area texts.GA MRC.d - Establishing contextGA MRC.d.1 - Explore life experiences related to subject area content.GA MRC.d.2 - Discuss in both writing and speaking how certain words are subject area related.GA MRC.d.3 - Determine strategies for finding content and contextual meaning for unknown words.


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Documents

Georgia Standards Alignment Grades One through Twelve