HHH Curriculum Guide Math Grade 4

Math Curriculum Guide

4th Grade

2011 – 2012 School Year

Dear Colleague, Please use this curriculum guide to assist in your unit, lesson and assessment plans as you progress through the school year. As additional guidance, included below is further clarrification regarding the “Content Key” symbols used throughout this document:

Content Key Description

√ Grade Level Content Content that is part of the current grade level set of standards. Students should be assessed fully on their ability to demonstrate an understanding of these concepts.

Previous Content

Content that was part of a previous grade level set of standards. Students should be assessed fully on their ability to demonstrate an understanding of these concepts. You may be able to condense material here based upon your students maintained knowledge of this information.

Exposure Content for Future Study

Content that is part of a future grade level set of standards. Students should be assessed, at an exposure level, on their ability to demonstrate an understanding of these concepts. It is not expected that all students develop a mastery level of understanding of these concepts at this time.

Additionally, in preparation for the upcoming implementation and transistion into the Common Core State Standards (CCSS), it is imperitative that we begin fostering the mathematical mindsets and practices of our students that are embodied within these new standards. Also within these standards, there will be a stronger emphasis placed on specific areas of study. In following the guidance of the New York State Education Department, as a district, we have decided to plan for an intensive focus of study to occur within the topics of the meaning and understanding of fractions and decimals. Time will be made available to develop these units of study (topics 10, 11 and 12) together with district colleagues.

4th Grade HHH Math Curriculum Guide

Topic 1: Numeration Weeks of Sept. 6 & Sept. 12, 5 Days

Essential Understandings Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

Thousands Be mindful of the increments on the number line. This can be confusing for students. 1-1

&

1-2 Millions

This lesson is a preview to 5.N.1. To address all lesson objectives, be sure to add expanded form to the Interactive Learning Lesson.

1-3 Comparing and Ordering Whole Numbers

1-4 Rounding Whole Numbers

A portion of this lesson previews 5.N.24. When teaching rounding, slowly build to rounding to Millions. Be aware, that some supplementation may be necessary.

1-5 Using Money to Understand Decimals

1-6 Counting Money and Making Change

The focus of this lesson is counting up to make change. The focus of this lesson does not include the subtraction algorithm. Students should be encouraged to use money manipulatives to assist them when making change. Supplementation may be necessary. Consider utilizing the center activities for this lesson. Allow opportunities for students to demonstrate an understanding of this concept before moving on.

• A number in the thousands can be represented with place-value blocks or a number line. A number can be written in standard form using digits only, expanded form by writing the sum of the value of the digits, or word form using periods from a place-value chart.

• Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value.

• Place value can be used to compare and order numbers.

• Rounding whole numbers is a process for finding the multiple of 10, 100, and so on closest to a given number.

• Relationships among dollars, dimes, and pennies are a good model for decimal numeration.

• When counting money, it is often easiest to start with the bills or coins that have the greatest value. Counting up is usually an efficient way to make change.

• Some problems can be solved by generating a list of outcomes and organizing that list in a systematic way so all outcomes are accounted for. 1-7

Problem Solving: Make and Organized List

Need more opportunities to practice combinations and organized lists.

Consider assessing topics 1 and 2 together.

√ Grade Level Content Previous Content Exposure Content for Future Study


Topic 2: Adding and Subtracting Whole Numbers Weeks of Sept. 12, Sept. 19 & Sept. 26, 8 Days


Content Key


2-1 Using Mental Math to Add and Subtract Since the addition properties were discussed in Third Grade, students

should have a foundation for this topic.

2-2 Estimating Sums and Differences of Whole Numbers

No Changes

2-3 Problem Solving Missing or Extra Information

Use Center Activities and Intervention Kit for extra practice.

Adding Whole Numbers Mixed Problem Solving

No Change 2-4

&

2-5 Subtracting Whole Numbers No Changes

2-6 Subtracting Across Zeros More practice problems needed with subtracting with zero’s (larger

numbers with zero’s)

• Representing numbers and numerical expressions in equivalent forms can make some calculations easy to do mentally. There is more than one way to do a mental calculation.

• There is more than one way to estimate a sum or difference. Each estimation technique gives a way to replace numbers with other numbers that are close and easy to compute with mentally.

• Some problems have data missing needed to find the answer, and some problems have extra data not needed to solve the problem.

• The standard addition and subtraction algorithms for multi-digit numbers break the calculation into simpler calculations using place value starting with the ones, then the tens, and so on.

• Information can often be shown using a picture or diagram and by writing and completing a number sentence or equation.

2-7 Problem Solving Draw a Picture and Write an Equation

No Changes




Topic 3: Multiplication Meanings and Facts Weeks of Sept. 26 & Oct. 3, 6 Days


Content Key


3-1

Meaning of Multiplication Mixed Problem Solving

Connecting cubes not provided with 4th grade kit Look at pacing. Possibility of combining lessons within this topic.

3-2 Patterns for Facts No Changes

3-3 Multiplication Problems No Changes

3-4 3 and 4 as Factors No Changes

6,7 and 8 as Factors No Change 3-5

&

3-6 10,11 and 12 as Factors No Change

• Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication. Repeated addition and arrays are two ways to think about multiplication.

• There are patterns in the products for multiplication facts with factors of 2 and 5.

• Two numbers can be multiplied in any order. The product of any number and 0 is zero. The product of any number and 1 is that number.

• Basic multiplication facts with 3,4,6,7,8,10,11 or 12 as a factor can be found by breaking apart the unknown fact into known facts. The answers to the known facts are added to get the final product. Patterns can be used to find products involving factors of 10, 11, and 12

• Information can often be shown using a picture or diagram and by writing and completing a number sentence or equation. 3-7

Problem Solving Draw a Picture and Write an Equation

No Change




Topic 4: Division Meanings and Facts Weeks of Oct. 3, 10 & Oct.17, 7 Days


Content Key


4-1 Meanings of Division No Change

4-2 Relating Multiplication and Division

Can possibly be combined with 4-3 and 4-4

4-3 Special Quotients No Change

4-4 Using Multiplication Facts to Find Division Facts

No Change

• Some real-world problems can be solved using division. Sharing and repeated subtraction are two ways to think about division.

• Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.

• Any number (except 0) divided by itself is equal to 1. Any number divided by 1 is that number. Zero divided by any number (except 0) is zero. Zero cannot be a divisor.

• Information in a problem can often be shown using a picture or diagram and by writing and completing a number sentence or equation. 4-5

Problem Solving Draw a Picture and Write an Equation

No Change




Topic 5: Multiplying by 1-Digit Numbers Weeks of Oct. 17 & Oct. 24, Oct. 31, 9 Days

Essential Understandings Lesson Number and Title Content Key


5-1 Multiplying by Multiples of 10 and 100 No Change

5-2 Using Mental Math to Multiply Emphasize the definition of a Compatible Number as numbers

that are easy to work with mentally.

5-3 Using Rounding to Estimate Answers may vary. Create guidelines with your students when

using rounding to estimate.

5-4 Problem Solving Reasonableness Answers may vary. Create guidelines with your students when

using rounding to estimate.

5-5 Using and Expanded Algorithm Represent partial products both vertically and horizontally to

make connections to previous “break-apart” lessons.

5-6 Multiplying 2-Digit by 1-Digit Numbers No Change


• Basic facts and place-value patterns can be used to find products when a factor is 10 or 100.

• There is more than one way to do a mental calculation.

• Rounding and substituting compatible numbers are two ways to estimate products.

• Answers to problems should always be checked for reasonableness. This can be done with estimation when appropriate and checking the answer against the question and conditions in the problem.

• There is an expanded algorithm for multiplying where numbers are broken apart using place value and the parts are used to find partial products. The partial products are then added together to find the product.

• The standard algorithm for multiplying three-digit by one-digit numbers is just an extension to the hundreds place of the algorithm for multiplying two-digit by one-digit numbers.

• Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence.

5-8 Problem Solving Draw a Picture and Write an Equation

No Change



Topic 6: Patterns and Expressions Weeks of Oct. 31 & Nov. 7, 5 Days


Content Key


6-1 Variables and Expressions Carefully monitor practice questions for this topic. Students can use

inverse operations when asked to divide with two-digit divisors.

6-2 Addition and Subtraction Expressions

No Change

6-3 Multiplication and Division Expressions Supplementation may be necessary. Expose children to

“Input/Output” examples.

• Some mathematical phrases can be represented using a variable in an algebraic expression. The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation.

• Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

• Some problems can be solved by using objects to act out the actions in the problem. Some problems can be solved by reasoning about the conditions in the problem.

6-4 Problem Solving Use Objects and Reasoning

No Change



Topic 7: Multiplying by 2-Digit Numbers Weeks of Nov. 14 & Nov. 21, 8 Days


Content Key


7-1 Using Mental Math to Multiply 2-Digit Numbers

No Change

7-2 Estimating Products Answers may vary. Use reasonableness when rounding.

7-3 Arrays and an Expanded Algorithm Extra time may be necessary. A variety of methods are introduced in

one lesson.

7-4 Multiplying 2-Digit Numbers by Multiples of Ten

No Change


7-6 Special Cases No Change

• Basic facts and place-value patterns can be used to mentally multiply a 2-digit number by a multiple of 10, 100, or 1,000.

• Rounding and substituting compatible numbers are two ways to estimate products.

• The expanded algorithm for multiplying by 2-digit numbers is just an extension of the expanded algorithm for multiplying with 1-digit numbers.

• The standard algorithm for multiplying 2-digit by 2-digit numbers is just an extension of the algorithm for multiplying multi-digit numbers by one-digit numbers.

• The standard algorithm for multiplying 2-digit by 2-digit numbers is just an extension of the algorithm for multiplying multi-digit numbers by one-digit numbers.

• The standard multiplication algorithm is a shortcut for the expanded algorithm. Regrouping is used rather than showing all partial products.

• Sometimes the answer to one problem/question is needed to find the answer to another problem/question.

7-7 Problem Solving Two-Question Problems

No Change



Topic 8: Dividing by 1-Digit Divisors Weeks of Nov. 28 & Dec. 5, 10 Days


Content Key


8-1 Using Mental Math to Divide No Change

8-2 Estimating Quotients Compatible numbers are numbers that are easier to work with.

8-3 Dividing with Remainders No Change

8-4 Connecting Models and Symbols No Change

8-5 Dividing 2-Digit by 1-Digit Numbers No Change

8-6 Dividing 3-Digit by 1-Digit Numbers No Change

8-7 Deciding Where to Start Dividing No Change

8-8 Factors No Change

8-9 Primate and Composite Numbers No Change

• Basic facts and place-value patterns can be used to divide multiples of 10 and 100 by 1-digit numbers

• Substituting compatible numbers is an efficient technique for estimating quotients.

• The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder.

• The sharing interpretation of division can be used to model the standard division algorithm.

• The standard division algorithm breaks the calculation into simpler calculations using basic facts, place value, the relationship between multiplication and division, and estimation.

• The relationship between multiplication, division, and estimation can help determine the place value of the largest digit in a quotient.

• Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers.

• Some counting numbers have exactly two factor; others have more than two.

• Some problems can be solved by first find and solving a sub-problem(s) and then using that answer(s) to solve the original problem. 8-10

Problem Solving Multiple-Step Problems

No Change

√ Grade Level Content Previous Content



Topic 9: Lines, Angles and Shapes Weeks of Dec. 12 & Dec. 19, 8 Days


Content Key


9-1 Points, Lines, and Planes

9-2 Line Segments, Rays, and Angles

9-3 Measuring Angles

9-4 Polygons

9-5 Triangles

9-6 Quadrilaterals

• Point, line and plane are the core attributes of space objects, and real-world situations can be used to think about these attributes.

• Line segments and rays are sets of points that describe parts of lines, shapes, and solids. Angles are formed by two intersecting lines or by rays with a common endpoint and are classified by size.

• Then unit for measuring the size of the opening of an angle is 1 degree.

• Two-dimensional or plan shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles.



• Commonalities in attributes of objects or situations can be found and used to make generalizations about relationships.

9-7 Problem Solving Make and Test Generalizations




Topic 14: Area and Perimeter Week of Dec. 19, 2 Days


Content Key


14-1 Understanding Area • The amount of space inside a shape is its area,

and area can be estimated or found using square units.

• The distance around a figure is its perimeter. Formulas exist for finding the perimeter of some polygons.

14-6 Perimeter



Topic 15: Solids Weeks of Jan. 2 & Jan. 9, 5 Days


Content Key


15-1 Solids

15-2 Views of Solids: Nets

15-3 Views of solids: Perspective Students should be exposed to these understandings only

• Three-dimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces, edges, and vertices. Many everyday objects closely approximate standard geometric solids.

• Some solids can be shown as a plane shape made up of other shapes. The plane shape can be folded to construct the solid.

• Views of solids from different perspectives can sometimes be used to completely describe the solid.

• Some problems can be solved by identifying elements that repeat in a predictable way.

15-5 Problem Solving Look for a Pattern



Topic 19: Transformations, Congruence and Symmetry Weeks of Jan.9 & Jan. 16, 6 Days


Content Key


19-1 Translations

19-1, 19-2, & 19-3 were combined in 2011

19-2 Reflections

19-1, 19-2, & 19-3 were combined in 2011

19-3 Rotations

19-1, 19-2, & 19-3 were combined in 2011

19-4 Congruent Figures

19-4 & 19-5 were combined in 2011

• Shapes in the plane can be translated to another position in the plane. The translated image is the same size and shape as the original figure.

• Shapes in the plane can be reflected across a line. The reflected image is the same size and shape as the original figure.

• Shapes in the plane can be rotated around a point. The rotated image is the same size and shape as the original figure.

• Congruent figures remain congruent through translations, reflections, and rotations.

• Some shapes can be reflected across one or more lines passing through the shape so the shape folds onto itself exactly. 19-5 Line Symmetry




Topic 10: Understanding Fractions Weeks of Jan. 16 & Jan. 23, 7 Days


Content Key


10-1 Regions and Sets 10-1 & 10-2 were combined in 2011

10-2 Fractions and Division

10-3 Estimating Fractional Amounts 10-3, 10-7, & 10-8 were combined in 2011

10-4 Equivalent Fractions 10-4 & 10-9 were combined in 2011

Comparing Fractions 10-3, 10-7, & 10-8 were combined in 2011 10-7

&

10-8 Ordering Fractions 10-3, 10-7, & 10-8 were combined in 2011

• A fraction describes the division of a whole (region, set, segment) into equal parts. A fraction is relative to the size of the whole.

• A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole to be divided.

• The relationship between multiplication, division, and estimation can help determine the place value of the largest digit in a quotient.

• The same fractional amount can be represented by an infinite set of different by equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number.

• If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction. If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction.

• Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to the other numbers.

• Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand.

10-9 Problem Solving Writing to Explain 10-4 & 10-9 were combined in 2011



Topic 11: Adding and Subtracting Fractions Week of Jan. 30, 1 Day


Content Key


• To add or subtract fractions with like denominators, add or subtract the numerators and write the sum or difference over the common denominator

11-1

Adding and Subtracting Fractions with Like Denominators



Topic 12: Understanding Decimals Weeks of Jan. 30 & Feb. 6, 6 Days


Content Key


12-1 Decimal Place Value

12-2 Comparing and Ordering Decimals

Read and write decimals – compare only to hundredths

12-3 Fractions and Decimals

12-4Fractions and Decimals on the Number Line

12-5Mixed Numbers and Decimals on the Number Line

• Decimal numeration is just an extension of whole number numeration.

• Place value can be used to compare and order numbers.

• A decimal is another name for a fraction. • Each fraction, mixed number, and decimal can be

associated with a unique point on the number line.

• Information in a problem can often be shown using a diagram and used to solve the problem.

12-6 Problem Solving Draw a Picture



Topic 13: Operations with Decimals Weeks of Feb. 6 & Feb. 13, 5 Days


Content Key


13-1Rounding Decimals Mixed Problem Solving

13-3Modeling Addition and Subtraction of Decimals


• Rounding decimals is a process for finding the multiple of 0.1, 0.01, etc., closest to a given number.

• Models and algorithms for adding or subtracting multi-digit decimals are just an extension of models and algorithms for adding or subtracting multi-digit whole numbers. 13-4 Adding and

Subtracting Decimals 13-3 & 13-4 were combined in 2011



Topic 16: Measurement, Time and Temperature

Weeks of Feb. 27 & Mar. 5, 9 Days



16-1 Using Customary Units of Length

16-2 Customary Units of Capacity

Review of 3rd grade measurement

16-3 Units of Weight

16-4 Changing Customary Units Equivalents without memorizing (know inches & feet)

16-5 Using Metric Units of Length

16-6 Metric Units of Capacity

16-7 Units of Mass

16-9 Units of Time

16-9 & 16-10 were combined in 2011. Don’t cross AM and PM.

• Length can be estimated and measured in different systems (customary, metric) and using different units in each system that are related to each other.

• Capacity is a measure of the amount of liquid a container can hold. Capacity can be measured in different systems (customary, metric) and using different units in each system that are related to each other.

• The weight of an object is a measure of how heavy an object is.

• Relationships between customary measurements units can be expressed as a ratio (e.g., 12 inches to 1ft or 12 in. = 1ft).Relationships exist that enable you to convert between customary units of the same attribute by multiplying or dividing.

• Length can be estimated and measured in different systems (customary, metric) and using different units in each system that are related to each other.

• Capacity is a measure of the amount of liquid a container can hold. Capacity can be measured in different systems (customary, metric) and using different units in each system that are related to each other.

• Mass is a measure of the quantity of matter in an object. Weight and mass are different measures.

• Time can be expressed using different units that are related to each other.

• The duration of an event can be measured if one knows that start and end times for the event. 16-10 Elapsed Time

16-9 & 16-10 were combined in 2011. Don’t cross AM and PM.




Topic 17: Data and Graphs Week of Mar. 5 & Mar. 12, 4 Days


Content Key


17-1 Data from Surveys

17-2 Interpreting Graphs

17-5 Line Graphs Coach resources may be helpful

• Some questions can be answered using a survey. An appropriately selected sample can be used to make predictions about a population.

• Each type of graph is most appropriate for certain kinds of data. Line graphs made from ordered pairs can be used to show a relationship between two sets of data.

• Some problems can be solved by making, reading, and analyzing a graph.

17-10 Problem Solving Making a Graph



Topic 18: Adding and Subtracting Fractions Week of Mar. 12, 1 Day


Content Key


• A solution to an inequality is a value that makes the inequality true. 18-4 Understanding

Inequalities



Topic 20: Probability Weeks of Mar. 12 & Mar. 19, 7 Days


Content Key


20-1 Finding a Combination 20-1 and 20-2 were combined in 2011

20-2 Outcomes and Tree Diagrams 20-1 and 20-2 were combined in 2011

20-3 Writing Probability as a Fraction

• Counting techniques exist for finding the number of possible combinations.

• The outcomes of an event can be represented pictorially using a tree diagram and counted to find the number of possible outcomes.

• The chance or likelihood of an event occurring, called its probability, can be expressed as a number between 0 and 1 inclusive.

• Some problems can be solved by reasoning about the conditions in the problem.

20-4 Problem Solving Use Reasoning




Post NYS Assessment Topics: 14, 15 & 19 Weeks of May 14 & May 21, 8 Days


Content Key


14-2 Area of Squares and Rectangles Information to be discussed after the assessment

14-3 Area of Irregular Shapes Information to be discussed after the assessment

14-4 Area of Parallelograms Information to be discussed after the assessment

14-5 Area of Triangles

Information to be discussed after the assessment

14-7 Same Perimeter, Different Area


14-8 Same Area, Different Perimeter Information to be discussed after the assessment

14-9

Problem Solving Solve a Simpler Problem and Make a Table


15-4 Volume


19-6 Rotational Symmetry


• The amount of space inside a shape is its area, and area can be estimated or found using square units. Formulas exist for finding the area of some polygons.

• The area of some irregular shapes can be found by breaking apart the original shape into other shapes for which the areas can be found. Area can be estimated in square units.

• The formula for the area of a parallelogram is derived from the formula for the area of a rectangle.

• The formula for the area of a triangle is derived from the formula for the area of a parallelogram.

• There are relationships between the perimeter and area of a polygon.

• There are relationships between the perimeter and area of a polygon.

• Some problems can be solved by breaking apart or changing the problem into simpler ones. Recording information in a table can help one understand and solve some problems.

• Volume is the amount of space inside a solid figure. Volume can be measured by counting the number of cubic units needed to fill a three-dimensional object.

• Some shapes can be rotated around a point in less than one complete turn and turn onto itself exactly

• Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem.

19-7 Problem Solving Draw a Picture Information to be discussed after the assessment




Post NYS Assessment Topics: 10, 11 & 13 Weeks of May 21 & May 28, 6 Days


Content Key


10-5

Fractions in Simplest Form


10-6

Improper Fractions and Mixed Numbers Mixed Problem Solving


11-2Adding Fractions with Unlike Denominators

Information to be discussed after assessment

11-3Subtracting Fractions with Unlike Denominators

Information to be discussed after assessment

11-4Problem Solving Draw a Picture and Write an Equation


13-2Estimating Sums and Difference of Decimals


13-5Multiplying a Whole Number by a Decimal


13-6 Dividing a Decimal by a Whole Number Information to be discussed after the assessment

• A fraction can be expressed in its simplest form by dividing the numerator and denominator by common factors until there are no common factors other than 1.

• Fractional amounts greater than 1 can be represented using a whole number and a fraction. Whole number amounts can be represented as fractions. When the numerator and denominator are equal, the fraction equals 1.

• Line segments and rays are sets of pints that describe parts of lines, shapes, and solids. Angles are formed by two intersecting lines or by rays with a common endpoint and are classified by size.

• To subtract with unlike denominators, change to an equivalent calculation with like denominators.

• Information can often be shown using a diagram by writing and completing a number sentence or equation.

• Techniques for estimating calculations with whole numbers can also be used to estimate calculations with decimals.

• Multiplying a whole number by a decimal is similar to multiplying two whole numbers. Estimation and place value can determine the location of the decimal point in the product.

• Dividing a decimal by a whole number is similar to dividing two whole numbers. Estimation and place value can determine the location of the decimal point in the quotient.

• Some problems can be solved by making a reasoned first try for what the answer might be, and then by using additional reasoning to arrive at the correct answer.

13-7 Problem Solving Try, Check, and Revise Information to be discussed after the assessment



Post NYS Assessment Topics: 16 & 17 Weeks of June 4 & June 11, 8 Days



16-8 Changing Metric Units


16-11 Temperature Information to be discussed after the assessment

16-12 Problem Solving Work Backwards Information to be discussed after the assessment

17-3 Line Plots Information to be discussed after the assessment

17-4 Ordered Pairs Information to be discussed after the assessment

17-6 Mean


17-7 Median, Mode, and Range


17-8 Stem-and-Leaf Plot


• Relationships between metric units can be expressed as a ratio (e.g., 10mm to 1 cm or 1 mm = 1 cm). Relationships exist that enable you to convert between metric units of the same attribute by multiplying or dividing.

• Temperature can be expressed using degrees Fahrenheit or Celsius. Temperature change can be found using addition or subtraction.

• Some problems with the initial data point unknown can be solved by starting the end result and by reversing the steps and processes work backward to find the initial data point.

• Each type of graph is most appropriate for certain kinds of data. A line plot organizes data on a number line and is useful for showing visually how data are distributed.

• The Cartesian Coordinate System is a scheme that uses perpendicular number lines intersecting at zero on each axis to name the location of points in the plane.

• There is more than one way to describe the center or typical number in a numerical data set. The mean is the average of a set of numerical data.

• There is more than one way to describe the center or typical number in a numerical data set; median and mode are two ways. Range is one way to describe how data are distributed.

• Each type of graph is most appropriate for certain kinds of data. Stem-and-leaf plots can be used to show how data are distributed.

• Each type of graph is most appropriate for certain kinds of data. A circle graph is most appropriate for certain kinds of data. A circle graph shows how portions of a set of data compare with the whole. 17-9 Reading Circle

Graphs Information to be discussed after the assessment



Post NYS Assessment Topic 18 Weeks of June 11 & June 18, 4 Days


Content Key


18-1 Equal or Not Equal


18-2Solving Addition and Subtraction Equations


18-3Solving Multiplication and Division Equations


• Two algebraic expressions are equal if the value of each expression is the same when each variable is replaced with its assigned number and the resulting calculations are completed.

• A solution to an equation is a value of the unknown (or unknowns) that makes the equation true. Equations of the form x + a = b or x - a = b can be solved using properties of equality and inverse operations.

• Equations of the form ax = b or ______ = b (a ≠ 0) can be solved using properties of equality and inverse operations.

• Some problems with the initial data point unknown can be solved by starting with the end result and, by reversing the steps and processes, work backward to find the initial data point.

18-5 Problem Solving Work Backward Information to be discussed after the assessment


Documents

HHH Curriculum Guide Math Grade 4