Utah State Standards Alignments Grades One through Geometrydoc.renlearn.com/KMNet/R004058517GGD313.pdf · UT 1.2.b - Divide sets of objects into two, three, or four parts of equal

Utah State Standards Alignments Grades One through Geometry

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Utah State Standards Alignments

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 ..................................................... 5

Grade 3 ....................................................10

Grade 4 ....................................................18

Grade 5 ....................................................30

Grade 6 ....................................................39

Grade 7 ....................................................46

Pre-Algebra ....................................................53

Algebra 1 ....................................................61

Geometry ....................................................66

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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 NameUtah, Math, 2007, First Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will acquire number sense and perform simple operations with whole numbers.UT 1.1 - Represent and use whole numbers up to 100.UT 1.1.a - Count, read, and write whole numbers.

Skill Area 3 - Numeration Concepts

Skill 2 - NA2 - Ones: Using numerals to indicate quantitySkill 3 - NA3 - Ones: Relate numerals and number wordsSkill 6 - N01 - Tens: Place numerals (10-99) in order of valueSkill 7 - N02 - Tens: Associate numeral with group of objectsSkill 8 - N03 - Tens: Relate numeral and number word

UT 1.1.b - Represent whole numbers using the number line, models, and number sentences.


Skill 2 - NA2 - Ones: Using numerals to indicate quantity

Skill 5 - N00 - Ones: Locate numbers on a number lineSkill 7 - N02 - Tens: Associate numeral with group of objects

UT 1.1.c - Represent whole numbers greater than 10 in groups of tens and ones using objects, pictures, and expanded notation.


Skill 7 - N02 - Tens: Associate numeral with group of objects

UT 1.2 - Identify simple relationships among whole numbers up to 100.

UT 1.2.a - Compare and order sets of objects and numbers using the terms greater than, less than, and equal to when describing the comparisons.

UT 1.2.b - Make reasonable estimates of the quantitative difference between two sets of objects.UT 1.2.c - Identify one more, one less, 10 more, and 10 less than a given number.


Skill 6 - N01 - Tens: Place numerals (10-99) in order of value

Skill 9 - N04 - Tens: Identify one more/one less across decades

UT 1.2.d - Identify numbers missing from a counting sequence.


Skill 1 - NA1 - Ones: Placing numerals in order

Skill Area 6 - Geometry Skill 9 - G01 - Identify numeric patterns

Skill Area 10 - Algebra Skill 1 - A00 - Can skip count by 2, 5, 10 in ascending order

UT 1.2.e - Represent part-whole relationships using the number line.

Standards List with Aligned Product SkillsProduct NameSTAR Math

STAR Math Grade 1

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Agency Tag Set NameUtah, Math, 2007, First Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 1.3 - Model, describe, and illustrate the meanings of addition and subtraction and use these operations to solve problems.UT 1.3.a - Use a variety of models, including objects, length-based models, the number line and the ten frame to describe problem types (i.e., part-whole, combine, separate, compare).UT 1.3.b - Use the properties of addition (i.e., commutativity, associativity, identity element) and the mathematical relationship between addition and subtraction to solve problems.

Skill Area 10 - Algebra Skill 2 - A01 - Simple number sentence

UT 1.3.c - Compute basic addition facts (up to 10 + 10) and the related subtraction facts using strategies (e.g., 6 + 7 = (6 + 4) + 3 = 10 + 3 = 13).

Skill Area 4 - Computation Processes

Skill 1 - C01 - Addition of basic facts to 10

Skill 2 - C02 - Subtraction of basic facts to 10Skill 3 - C03 - Addition of basic facts to 18Skill 4 - C04 - Subtraction of basic facts to 18

Skill Area 9 - Word Problems Skill 1 - W03 - Word problems: Addition of basic factsSkill 2 - W04 - Word problems: Subtraction of basic facts

UT 1.3.d - Find the sum of three one-digit numbers.


Skill 5 - C05 - Addition of three single digit addends

UT 2 - Students will identify and use number patterns and properties to describe and represent mathematical relationships.

UT 2.1 - Recognize, describe, and represent patterns with more than one attribute.UT 2.1.a - Sort and classify objects using more than one attribute.

UT 2.1.b - Identify, create, and label repeating patterns using objects, pictures, and symbolic notation.

UT 2.1.c - Identify, create, and label growing patterns using objects, pictures, and symbolic notation.

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UT 2.1.d - Use patterns to establish skip counting by twos, fives, and tens.


UT 2.2 - Recognize and represent mathematical relationships using symbols and use number sentences with operational symbols to solve problems.UT 2.2.a - Recognize that "=" indicates that the two sides of an equation are expressions of the same number.UT 2.2.b - Recognize that "+" indicates the joining of sets and that "-" indicates the separation of sets.

UT 2.2.c - Write and solve number sentences from problem situations involving addition and subtraction, using symbolic notation for the missing value (e.g., △+ 4 = 7).

UT 2.2.d - Create problem situations from given number sentences involving addition and subtraction.

UT 3 - Students will understand simple geometry and measurement concepts as well as collect, represent, and draw conclusions from data.UT 3.1 - Identify, describe, and create simple geometric figures.UT 3.1.a - Name, create, and sort geometric plane figures (i.e., circle, triangle, rectangle, square, trapezoid, rhombus, parallelogram, hexagon).

Skill Area 6 - Geometry Skill 2 - GA2 - Identify common plane shapes

UT 3.1.b - Identify geometric plane and solid figures (i.e., circle, triangle, rectangle, square, trapezoid, hexagon, rhombus, parallelogram, cube, sphere, cone) in the students' environment.

Skill Area 6 - Geometry Skill 4 - GA4 - Compare common objects to basic shapes

Skill 7 - GA7 - Identify common solid shapes

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UT 3.1.c - Compose and decompose plane and solid figures (e.g., make two triangles from a square) and describe the part-whole relationships, the attributes of the figures, and how they are different and similar.

UT 3.2 - Identify measurable attributes of objects and units of measurement, and use appropriate techniques and tools to determine measurements.UT 3.2.a - Identify the appropriate tools for measuring length, weight, capacity, temperature, and time.UT 3.2.b - Measure the length of an object using nonstandard units and count the units using groups of tens and ones.UT 3.2.c - Identify the value of a penny, nickel, dime, quarter, and dollar, and determine the value of a set of the same coins that total 25¢ or less (e.g., a set of 5 nickels equals 25¢).

Skill Area 7 - Measurement Skill 2 - MA2 - Understand the value of penny, nickel, dime

Skill 3 - MA3 - Determine the value of quarter and dollar

UT 3.2.d - Tell time to the hour and half-hour.

Skill Area 7 - Measurement Skill 5 - MA5 - Tell time to the hour and half hour

UT 3.2.e - Name the months of the year and seasons in order, and use a calendar to determine the day of the week and date.

Skill Area 7 - Measurement Skill 8 - M00 - Order months of the year

UT 3.3 - Collect, organize, and represent simple data.UT 3.3.a - Collect and represent data using tables, tally marks, pictographs, and bar graphs.UT 3.3.b - Describe and interpret data.

Skill Area 8 - Data Analysis and Statistics

Skill 1 - SA1 - Read tally charts

Skill 2 - S00 - Read simple pictographsSkill 3 - S01 - Read tableSkill 4 - S02 - Read bar graphSkill 6 - S04 - Interpret tableSkill 7 - S05 - Interpret bar graphSkill 8 - S06 - Interpret pie graph

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Agency Tag Set NameUtah, Math, 2007, Second Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will acquire number sense with whole numbers and fractions and perform operations with whole numbers.UT 1.1 - Identify and represent the relationships among numbers, quantities, and place value in whole numbers up to 1000.UT 1.1.a - Represent whole numbers in groups of hundreds, tens, and ones using base ten models and write the numeral representing the set in standard and expanded form.



Skill 14 - N09 - Hundreds: Write numerals in expanded form

UT 1.1.b - Identify the place and the value of a given digit in a three-digit numeral.


Skill 13 - N08 - Hundreds: Identify place value of digits

UT 1.1.c - Represent the composition and decomposition of numbers in a variety of ways.UT 1.1.d - Compare and order numbers using the terms, greater than, less than, or equal to, and the symbols, >, <, and =, using various strategies, including the number line.


Skill 1 - NA1 - Ones: Placing numerals in order

Skill 6 - N01 - Tens: Place numerals (10-99) in order of valueSkill 11 - N06 - Hundreds: Place numerals in order of value

UT 1.1.e - Identify and describe even and odd whole numbers.UT 1.2 - Use unit fractions to identify parts of the whole and parts of a set.

UT 1.2.a - Divide geometric shapes into two, three, or four equal parts and identify the parts as halves, thirds, or fourths.

Skill Area 6 - Geometry Skill 8 - G00 - Identify fraction parts of common plane shapes

UT 1.2.b - Divide sets of objects into two, three, or four parts of equal number of objects and identify the parts as halves, thirds, or fourths.

UT 1.2.c - Represent the unit fractions 1/2, 1/3, and 1/4 with objects, pictures, words (e.g., ___out of ___ equal parts), and symbols.


STAR Math Grade 2

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Agency Tag Set NameUtah, Math, 2007, Second Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 1.3 - Estimate, model, illustrate, describe, and solve problems involving two- and three-digit addition and subtraction.UT 1.3.a - Demonstrate quick recall of addition facts (up to 10 + 10) and related subtraction facts.


Skill 1 - C01 - Addition of basic facts to 10

Skill 2 - C02 - Subtraction of basic facts to 10Skill 3 - C03 - Addition of basic facts to 18Skill 4 - C04 - Subtraction of basic facts to 18Skill 5 - C05 - Addition of three single digit addends

Skill Area 9 - Word Problems Skill 1 - W03 - Word problems: Addition of basic factsSkill 2 - W04 - Word problems: Subtraction of basic facts

UT 1.3.b - Model addition and subtraction of two- and three-digit whole numbers (sums and minuends to 1000) in a variety of ways.

UT 1.3.c - Write a story problem that relates to a given addition or subtraction equation, and write a number sentence to solve a story problem that is related to the environment.UT 1.3.d - Demonstrate fluency with two- and three-digit addition and subtraction problems, using efficient, accurate, and generalizable strategies that include standard algorithms and mental arithmetic, and describe why the procedures work.


Skill 6 - C06 - Addition beyond basic facts, no regrouping (2d+1d)

Skill 7 - C07 - Subtraction beyond basic facts, no regrouping (2d-1d)Skill 8 - C08 - Addition beyond basic facts with regrouping (2d+1d, 2d+2d)

Skill 9 - C09 - Subtraction beyond basic facts with regrouping (2d-1d, 2d-2d)Skill 10 - C10 - Addition beyond basic facts with double regrouping (3d+2d, 3d+3d)Skill 11 - C11 - Subtraction beyond basic facts with double regrouping (3d-2d, 3d-3d)

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Skill Area 9 - Word Problems Skill 3 - W06 - Word problems: Addition beyond basic facts, no regrouping (2d+1d)Skill 4 - W08 - Word problems: Addition beyond basic facts with regrouping (2d+1d, 2d+2d)Skill 5 - W09 - Word problems: Subtraction beyond basic facts with regrouping (2d-1d, 2d-2d)

UT 1.3.e - Use the mathematical relationship between addition and subtraction and properties of addition to model and solve problems.

Skill Area 10 - Algebra Skill 2 - A01 - Simple number sentence

UT 1.4 - Model, illustrate, and pictorially record solutions to simple multiplication and division problems.

UT 1.4.a - Represent multiplication with equal groups using concrete objects and skip counting by twos, fives, and tens.UT 1.4.b - Represent division as fair shares using concrete objects or pictures.UT 2 - Students will model, represent, and interpret patterns and number relationships to create and solve problems with addition and subtraction.UT 2.1 - Recognize, describe, create, and extend growing patterns.

UT 2.1.a - Determine the next term in linear patterns (e.g., 2, 4, 6...; the number of hands on one person, two people, three people).



UT 2.1.b - Construct models and skip count by twos, threes, fives, and tens and relate to repeated addition.



UT 2.2 - Model, represent, and interpret number relationships using mathematical symbols.

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UT 2.2.a - Recognize that the not equal to sign indicates a relationship in which the two sides of the inequality are expressions of different numbers.UT 2.2.b - Recognize that symbols such as x, triangle, or diamond in an addition or subtraction equation represent a number that will make the statement true.UT 2.2.c - Use the commutative and associative properties of addition to simplify calculations.UT 3 - Students will understand simple geometry and measurement concepts as well as collect, represent, and draw conclusions from data.UT 3.1 - Describe, classify, and create geometric figures.UT 3.1.a - Describe and classify plane and solid geometric figures (i.e., circle, triangle, rectangle, square, trapezoid, rhombus, parallelogram, pentagon, hexagon, cube, sphere, cone) according to the number of sides and angles or faces, edges, and vertices.

Skill Area 6 - Geometry Skill 6 - GA6 - Recognize elements of basic shapes

UT 3.1.b - Compose and decompose shapes and figures by substituting arrangements of smaller shapes for larger shapes or substituting larger shapes for arrangements of smaller shapes.UT 3.1.c - Compose and decompose shapes and figures and describe the part-whole relationships, similarities, and differences.

UT 3.2 - Identify and use units of measure, iterate (repeat) that unit, and compare the number of iterations to the item being measured.

UT 3.2.a - Identify and use measurement units to measure, to the nearest unit, length (i.e., inch, centimeter), weight in pounds, and capacity in cups.UT 3.2.b - Estimate and measure length by iterating a nonstandard or standard unit of measure.

Skill Area 7 - Measurement Skill 10 - M02 - Customary measures: Estimating linear measures

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Skill 15 - M08 - Estimating linear measure in metric units.

UT 3.2.c - Use different units to measure the length of the same object and recognize that the smaller the unit, the more iterations needed to cover a given length.

UT 3.2.d - Determine the value of a set of up to five coins that total $1.00 or less (e.g., three dimes, one nickel, and one penny equals 36¢).

Skill Area 7 - Measurement Skill 2 - MA2 - Understand the value of penny, nickel, dime

Skill 3 - MA3 - Determine the value of quarter and dollar

UT 3.2.e - Tell time to the quarter-hour and sequence a series of daily events by time (e.g., breakfast at 7:00 a.m., school begins at 9:00 a.m., school ends at 3:00 p.m.).

Skill Area 7 - Measurement Skill 5 - MA5 - Tell time to the hour and half hour

UT 3.3 - Collect, record, organize, display, and interpret numerical data.

UT 3.3.a - Collect and record data systematically, using a strategy for keeping track of what has been counted.UT 3.3.b - Organize and represent the same data in more than one way.

UT 3.3.c - Organize, display, and label information, including keys, using pictographs, tallies, bar graphs, and organized tables.UT 3.3.d - Describe data represented on charts and graphs and answer simple questions related to data representations.



Skill 2 - S00 - Read simple pictographsSkill 4 - S02 - Read bar graph

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Agency Tag Set NameUtah, Math, 2007, Third Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will understand the base-ten numeration system, place value concepts, simple fractions and perform operations with whole numbers.UT 1.1 - Represent whole numbers up to 10,000, comprehend place value concepts, and identify relationships among whole numbers using base-ten models and symbolic notation.UT 1.1.a - Read, write, and represent whole numbers using standard and expanded form.


Skill 3 - NA3 - Ones: Relate numerals and number words

Skill 8 - N03 - Tens: Relate numeral and number wordSkill 12 - N07 - Hundreds: Relate numeral and number wordSkill 14 - N09 - Hundreds: Write numerals in expanded formSkill 16 - N12 - Thousands: Relate numeral and number wordSkill 18 - N14 - Thousands: Write numerals in expanded form

UT 1.1.b - Demonstrate multiple ways to represent numbers using models and symbolic representations (e.g., fifty is the same as two groups of 25, the number of pennies in five dimes, or 75 - 25).



UT 1.1.c - Identify the place and the value of a given digit in a four-digit numeral and round numbers to the nearest ten, hundred, and thousand.



Skill 17 - N13 - Thousands: Identify place value of digits

UT 1.1.d - Order and compare whole numbers on a number line and use the symbols <, >, not equal to sign, and = when comparing whole numbers.UT 1.1.e - Identify factors and multiples of whole numbers.UT 1.2 - Use fractions to describe and compare parts of the whole.


STAR Math Grade 3

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Agency Tag Set NameUtah, Math, 2007, Third Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 1.2.a - Identify the denominator of a fraction as the number of equal parts of the unit whole and the numerator of a fraction as the number of equal parts being considered.UT 1.2.b - Define regions and sets of objects as a whole and divide the whole into equal parts using a variety of objects, models, and illustrations.

UT 1.2.c - Name and write a fraction to represent a portion of a unit whole for halves, thirds, fourths, sixths, and eighths.


UT 1.2.d - Place fractions on the number line and compare and order fractions using models, pictures, the number line, and symbols.

UT 1.2.e - Find equivalent fractions using concrete and pictorial representations.UT 1.3 - Model problems involving addition, subtraction, multiplication, and division.UT 1.3.a - Demonstrate the meaning of multiplication and division of whole numbers through the use of a variety of representations (e.g., equal-sized groups, arrays, area models, and equal jumps on a number line for multiplication, partitioning and sharing for division).

UT 1.3.b - Use a variety of strategies and tools, such as repeated addition or subtraction, equal jumps on the number line, and counters arranged in arrays to model multiplication and division problems.

UT 1.3.c - Demonstrate, using objects, that multiplication and division by the same number are inverse operations (e.g., 3 x __ = 12 is the same as 12 ÷ 3 = __ and __ = 4).UT 1.3.d - Demonstrate the effect of place value when multiplying whole numbers by 10.

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UT 1.3.e - Write a story problem that relates to a given addition, subtraction, or multiplication equation, and write a number sentence to solve a problem related to the students' environment.

UT 1.4 - Compute and solve problems involving addition and subtraction of 3- and 4- digit numbers and basic facts of multiplication and division.UT 1.4.a - Use a variety of methods to facilitate computation (e.g., estimation, mental math strategies, paper and pencil).




Skill 9 - C09 - Subtraction beyond basic facts with regrouping (2d-1d, 2d-2d)Skill 10 - C10 - Addition beyond basic facts with double regrouping (3d+2d, 3d+3d)Skill 11 - C11 - Subtraction beyond basic facts with double regrouping (3d-2d, 3d-3d)Skill 12 - C12 - Multiplication basic factsSkill 13 - C13 - Division basic facts

Skill 18 - C18 - Addition of whole numbers: any difficulty

Skill Area 5 - Estimation Skill 1 - E06 - Estimation problems: Addition beyond basic facts, no regrouping (2d+1d)Skill 2 - E07 - Estimation problems: Subtraction beyond basic facts, no regrouping (2d-1d)Skill 5 - E18 - Estimation problems: Addition of whole numbers, any difficultySkill 6 - E19 - Estimation problems: Subtraction of whole numbers, any difficultySkill 7 - E20 - Estimation problems: Multiplication of whole numbers, any difficulty

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Skill Area 9 - Word Problems Skill 3 - W06 - Word problems: Addition beyond basic facts, no regrouping (2d+1d)Skill 4 - W08 - Word problems: Addition beyond basic facts with regrouping (2d+1d, 2d+2d)Skill 5 - W09 - Word problems: Subtraction beyond basic facts with regrouping (2d-1d, 2d-2d)Skill 6 - W12 - Word problems: Multiplication of basic factsSkill 7 - W13 - Word problems: Division of basic factsSkill 12 - W18 - Word problems: Addition of whole numbers, any difficultySkill 13 - W19 - Word problems: Subtraction of whole numbers, any difficulty

UT 1.4.b - Find the sum or difference of numbers, including monetary amounts, using models and strategies such as expanded form, compensation, partial sums, and the standard algorithm.




Skill 9 - C09 - Subtraction beyond basic facts with regrouping (2d-1d, 2d-2d)Skill 10 - C10 - Addition beyond basic facts with double regrouping (3d+2d, 3d+3d)Skill 11 - C11 - Subtraction beyond basic facts with double regrouping (3d-2d, 3d-3d)Skill 18 - C18 - Addition of whole numbers: any difficulty

Skill Area 9 - Word Problems Skill 3 - W06 - Word problems: Addition beyond basic facts, no regrouping (2d+1d)Skill 4 - W08 - Word problems: Addition beyond basic facts with regrouping (2d+1d, 2d+2d)Skill 5 - W09 - Word problems: Subtraction beyond basic facts with regrouping (2d-1d, 2d-2d)

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Skill 12 - W18 - Word problems: Addition of whole numbers, any difficulty

UT 1.4.c - Compute basic multiplication facts (0-10) and related division facts using a variety of strategies based on properties of addition and multiplication (i.e., commutative, associative, identity, zero, and the distributive properties).

UT 2 - Students will use patterns, symbols, operations, and properties of addition and multiplication to represent and describe simple number relationships.

UT 2.1 - Create, represent, and analyze growing patterns.UT 2.1.a - Create and extend growing patterns using objects, numbers, and tables.



UT 2.1.b - Describe how patterns are extended using manipulatives, pictures, and numerical representations.UT 2.2 - Recognize, represent, and simplify simple number relationships using symbols, operations, and properties.UT 2.2.a - Represent numerical relationships as expressions, equations, and inequalities.UT 2.2.b - Solve equations involving equivalent expressions (e.g., 6 + 4 = __ ; + 7).UT 2.2.c - Use the >, <, and = symbols to compare two expressions involving addition and subtraction (e.g., 4 + 6 __ 3 + 2; 3 + 5 __ 16 - 9).

UT 2.2.d - Recognize and use the commutative, associative, distributive, and identity properties of addition and multiplication, and the zero property of multiplication.


Skill 10 - N05 - Tens: Understand the concept of zero

UT 3 - Students will describe and analyze attributes of two-dimensional shapes.

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UT 3.1 - Describe and compare attributes of two-dimensional shapes.

Skill Area 9 - Word Problems Skill 13 - W19 - Word problems: Subtraction of whole numbers, any difficulty

UT 3.1.a - Identify, describe, and classify polygons (e.g., pentagons, hexagons, octagons).

Skill Area 6 - Geometry Skill 2 - GA2 - Identify common plane shapes

UT 3.1.b - Identify attributes for classifying triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).UT 3.1.c - Identify attributes for classifying quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).UT 3.1.d - Identify right angles in geometric figures, or in appropriate objects, and determine whether other angles are greater or less than a right angle.UT 3.2 - Demonstrate the meaning of congruence through applying transformations.UT 3.2.a - Demonstrate the effect of reflection, translation, or rotation using objects.

Skill Area 6 - Geometry Skill 3 - GA3 - Identify common plane shapes when rotated

UT 3.2.b - Determine whether two polygons are congruent by reflecting, translating, or rotating one polygon to physically fit on top of the other.

Skill Area 6 - Geometry Skill 3 - GA3 - Identify common plane shapes when rotated

UT 4 - Students will select and use appropriate units and measurement tools to solve problems.

UT 4.1 - Select and use appropriate tools and units to estimate and measure length, weight, capacity, time, and perimeter of two-dimensional figures.

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UT 4.1.a - Describe the part-whole relationships (e.g., 3 feet in a yard, a foot is 1/3 of a yard) between metric units of length (i.e., centimeter, meter), and among customary units of length (i.e., inch, foot, yard), capacity (i.e., cup, quart), and weight (i.e., pound, ounce).

UT 4.1.b - Measure the length of objects to the nearest centimeter, meter, half- and quarter-inch, foot, and yard.UT 4.1.c - Measure capacity using cups and quarts, and measure weight using pounds and ounces.UT 4.1.d - Identify the number of minutes in an hour, the number of hours in a day, the number of days in a year, and the number of weeks in a year.UT 4.1.e - Describe perimeter as a measurable attribute of two-dimensional figures, and estimate and measure perimeter with metric and customary units.

Skill Area 6 - Geometry Skill 11 - G03 - Perimeter: square

Skill 12 - G04 - Perimeter: rectangle

Skill 13 - G05 - Perimeter: triangleUT 4.2 - Solve problems involving measurements.UT 4.2.a - Determine simple equivalence's of measurements (e.g., 30 inches = 2 feet and 6 inches; 6 cups = 1½ quarts; 90 min. = 1 hr. 30 min.).

Skill Area 7 - Measurement Skill 9 - M01 - Customary measures: Inches, feet, yards

Skill 11 - M04 - Customary measures: Pints, quarts, gallonsSkill 12 - M05 - Metric prefixes

UT 4.2.b - Compare given objects according to measurable attributes (i.e., length, weight, capacity).

Skill Area 7 - Measurement Skill 1 - MA1 - Use simple vocabulary of measurement

UT 4.2.c - Solve problems involving perimeter.

Skill Area 6 - Geometry Skill 11 - G03 - Perimeter: square

Skill 12 - G04 - Perimeter: rectangle

Skill 13 - G05 - Perimeter: triangleUT 4.2.d - Determine elapsed time in hours (e.g., 7:00 a.m. to 2:00 p.m.).

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UT 5 - Students will collect and organize data to make predictions and identify basic concepts of probability.UT 5.1 - Collect, organize, and display data to make predictions.UT 5.1.a - Collect, read, represent, and interpret data using tables, graphs, and charts, including keys (e.g., pictographs, bar graphs, frequency tables, line plots).



Skill 2 - S00 - Read simple pictographsSkill 3 - S01 - Read tableSkill 4 - S02 - Read bar graphSkill 6 - S04 - Interpret tableSkill 7 - S05 - Interpret bar graph

UT 5.1.b - Make predictions based on a data display.UT 5.2 - Identify basic concepts of probability.UT 5.2.a - Describe the results of events using the terms "certain," "likely," "unlikely," and "impossible."

UT 5.2.b - Conduct simple probability experiments, record possible outcomes systematically, and display results in an organized way (e.g., chart, graph).UT 5.2.c - Use results of simple probability experiments to describe the likelihood of a specific outcome in the future.

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Agency Tag Set NameUtah, Math, 2007, Fourth Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will acquire number sense and perform operations with whole numbers, simple fractions, and decimals.UT 1.1 - Demonstrate multiple ways to represent whole numbers and decimals, from hundredths to one million, and fractions.UT 1.1.a - Read and write numbers in standard and expanded form.


Skill 14 - N09 - Hundreds: Write numerals in expanded formSkill 18 - N14 - Thousands: Write numerals in expanded formSkill 22 - N19 - Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form

UT 1.1.b - Demonstrate multiple ways to represent whole numbers and decimals by using models and symbolic representations (e.g., 36 is the same as the square of six, three dozen, or 9 x 4).UT 1.1.c - Identify the place and the value of a given digit in a six-digit numeral, including decimals to hundredths, and round to the nearest tenth.



Skill 17 - N13 - Thousands: Identify place value of digitsSkill 21 - N18 - Ten thousands, hundred thousands, millions, billions: Identify place value of digits

Skill 26 - N24 - Fractions and decimals: Read word names for decimals to thousandthsSkill 27 - N25 - Fractions and decimals: Identify place value of digits in decimalsSkill 31 - N29 - Fractions and decimals: Round decimals to tenths, hundredths

UT 1.1.d - Divide regions, lengths, and sets of objects into equal parts using a variety of models and illustrations.UT 1.1.e - Name and write a fraction to represent a portion of a unit whole, length, or set for halves, thirds, fourths, fifths, sixths, eighths, and tenths.



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Agency Tag Set NameUtah, Math, 2007, Fourth Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 1.1.f - Identify and represent square numbers using models and symbols.UT 1.2 - Analyze relationships among whole numbers, commonly used fractions, and decimals to hundredths.UT 1.2.a - Compare the relative size of numbers (e.g., 475 is comparable to 500; 475 is small compared to 10,000 but large compared to 98).

UT 1.2.b - Order whole numbers up to six digits, simple fractions, and decimals using a variety of methods (e.g., number line, fraction pieces) and use the symbols <, >, and = to record the relationships.


Skill 11 - N06 - Hundreds: Place numerals in order of value

Skill 15 - N11 - Thousands: Place numerals in order of valueSkill 19 - N16 - Ten thousands, hundred thousands, millions, billions: Place numerals in order of value

UT 1.2.c - Identify a number that is between two given numbers (e.g., 3.2 is between 3 and 4; find a number between 0.1 and 0.2).UT 1.2.d - Identify equivalences between fractions and decimals by connecting models to symbols.UT 1.2.e - Generate equivalent fractions and simplify fractions using models, pictures, and symbols.


Skill 23 - N21 - Fractions and decimals: Convert fraction to equivalent fraction

UT 1.3 - Model and illustrate meanings of multiplication and division of whole numbers and the addition and subtraction of fractions.

UT 1.3.a - Model multiplication (e.g., equal-sized groups, rectangular arrays, area models, equal intervals on the number line), place value, and properties of operations to represent multiplication of a one- or two-digit factor by a two-digit factor and connect the representation to an algorithm.

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UT 1.3.b - Use rectangular arrays to interpret factoring (e.g., find all rectangular arrays of 36 tiles and relate the dimensions of the arrays to factors of 36).UT 1.3.c - Demonstrate the mathematical relationship between multiplication and division (e.g., 3 x __ = 12 is the same as 12 ÷ 3 = __ and __ = 4) and use that relationship to explain that division by zero is not possible.UT 1.3.d - Represent division of a three-digit dividend by a one-digit divisor, including whole number remainders, using a variety of methods (e.g., rectangular arrays, manipulatives, pictures), and connect the representation to an algorithm.

UT 1.3.e - Use models to add and subtract simple fractions where one single-digit denominator is 1, 2, or 3 times the other (e.g., 2/4 + 1/4; 3/4 - 1/8).UT 1.4 - Solve problems involving multiplication and division of whole numbers and addition and subtraction of simple fractions and decimals.

UT 1.4.a - Use estimation, mental math, paper and pencil, and calculators to perform mathematical calculations and identify when to use each one appropriately.


Skill 12 - C12 - Multiplication basic facts

Skill 13 - C13 - Division basic facts

Skill 14 - C14 - Multiplication beyond basic facts, no regrouping (2dx1d)

Skill 15 - C15 - Division beyond basic facts, no remainders (2d/1d)Skill 16 - C16 - Multiplication with regrouping (2dx1d, 2dx2d)Skill 17 - C17 - Division with remainders (2d/1d, 3d/1d)Skill 21 - C22 - Addition of fractions: like single digit denominators

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Skill 22 - C23 - Subtraction of fractions: like single digit denominatorsSkill 31 - C33 - Addition of decimals, place change (e.g. 2 + .45)

Skill 32 - C35 - Subtraction of decimals, place change (e.g. 5-.4)

Skill Area 5 - Estimation Skill 1 - E06 - Estimation problems: Addition beyond basic facts, no regrouping (2d+1d)Skill 2 - E07 - Estimation problems: Subtraction beyond basic facts, no regrouping (2d-1d)Skill 3 - E14 - Estimation problems: Multiplication beyond basic facts, no regrouping (2dx1d)Skill 4 - E15 - Estimation problems: Division beyond basic facts, no remainders (2d/1d)Skill 5 - E18 - Estimation problems: Addition of whole numbers, any difficultySkill 6 - E19 - Estimation problems: Subtraction of whole numbers, any difficultySkill 13 - E32 - Estimation problems: Addition of decimals, no place change (e.g. 2.34+10.32)Skill 14 - E33 - Estimation problems: Addition of decimals, place change (e.g. 2+.45)Skill 15 - E34 - Estimation problems: Subtraction of decimals, no place change (e.g. .53 - .42)Skill 16 - E35 – Estimation problems: Subtraction of decimals, place change (e.g. 5 - .4)

Skill Area 9 - Word Problems Skill 6 - W12 - Word problems: Multiplication of basic factsSkill 7 - W13 - Word problems: Division of basic factsSkill 8 - W14 - Word problems: Multiplication beyond basic facts, no regrouping (2dx1d)Skill 9 - W15 - Word problems: Division beyond basic facts, no remainders (2d/1d)Skill 10 - W16 - Word problems: Multiplication with regrouping (2dx1d, 2dx2d)

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Skill 11 - W17 - Word problems: Division with remainders (2d/1d, 3d/1d)Skill 14 - W20 - Word problems: Multiplication of whole numbers, any difficultySkill 16 - W22 - Word problems: Addition of fractions, like single digit denominatorsSkill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominatorsSkill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)

UT 1.4.b - Select appropriate methods to solve a single operation problem and estimate computational results or calculate them directly, depending on the context and numbers involved in a problem.



Skill 15 - C15 - Division beyond basic facts, no remainders (2d/1d)Skill 16 - C16 - Multiplication with regrouping (2dx1d, 2dx2d)Skill 17 - C17 - Division with remainders (2d/1d, 3d/1d)Skill 21 - C22 - Addition of fractions: like single digit denominators



Skill Area 5 - Estimation Skill 1 - E06 - Estimation problems: Addition beyond basic facts, no regrouping (2d+1d)Skill 2 - E07 - Estimation problems: Subtraction beyond basic facts, no regrouping (2d-1d)Skill 3 - E14 - Estimation problems: Multiplication beyond basic facts, no regrouping (2dx1d)

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Skill 4 - E15 - Estimation problems: Division beyond basic facts, no remainders (2d/1d)Skill 5 - E18 - Estimation problems: Addition of whole numbers, any difficultySkill 6 - E19 - Estimation problems: Subtraction of whole numbers, any difficultySkill 13 - E32 - Estimation problems: Addition of decimals, no place change (e.g. 2.34+10.32)Skill 14 - E33 - Estimation problems: Addition of decimals, place change (e.g. 2+.45)Skill 15 - E34 - Estimation problems: Subtraction of decimals, no place change (e.g. .53 - .42)Skill 16 - E35 – Estimation problems: Subtraction of decimals, place change (e.g. 5 - .4)

Skill Area 9 - Word Problems Skill 8 - W14 - Word problems: Multiplication beyond basic facts, no regrouping (2dx1d)Skill 9 - W15 - Word problems: Division beyond basic facts, no remainders (2d/1d)Skill 10 - W16 - Word problems: Multiplication with regrouping (2dx1d, 2dx2d)Skill 11 - W17 - Word problems: Division with remainders (2d/1d, 3d/1d)Skill 14 - W20 - Word problems: Multiplication of whole numbers, any difficultySkill 16 - W22 - Word problems: Addition of fractions, like single digit denominatorsSkill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominatorsSkill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)

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UT 1.4.c - Write a story problem that relates to a given multiplication or division equation, and select and write a number sentence to solve a problem related to the environment.

UT 1.4.d - Solve problems involving simple fractions and interpret the meaning of the solution (e.g., A pie has been divided into six pieces and one piece is already gone. How much of the whole pie is there when Mary comes in? If Mary takes two pieces, how much of the whole pie has she taken? How much of the pie is left?)

Skill Area 9 - Word Problems Skill 16 - W22 - Word problems: Addition of fractions, like single digit denominators

Skill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominators

UT 1.5 - Compute problems involving multiplication and division of whole numbers and addition and subtraction of simple fractions and decimals.

UT 1.5.a - Demonstrate quick recall of basic multiplication and division facts.


Skill 12 - C12 - Multiplication basic facts

Skill 13 - C13 - Division basic facts

Skill Area 9 - Word Problems Skill 6 - W12 - Word problems: Multiplication of basic factsSkill 7 - W13 - Word problems: Division of basic facts

UT 1.5.b - Multiply up to a three- digit factor by a two-digit factor with fluency, using efficient procedures.



Skill 16 - C16 - Multiplication with regrouping (2dx1d, 2dx2d)

Skill Area 9 - Word Problems Skill 8 - W14 - Word problems: Multiplication beyond basic facts, no regrouping (2dx1d)Skill 10 - W16 - Word problems: Multiplication with regrouping (2dx1d, 2dx2d)Skill 14 - W20 - Word problems: Multiplication of whole numbers, any difficulty

UT 1.5.c - Divide up to a three-digit dividend by a one-digit divisor with fluency, using efficient procedures.


Skill 15 - C15 - Division beyond basic facts, no remainders (2d/1d)

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Skill 17 - C17 - Division with remainders (2d/1d, 3d/1d)

Skill Area 9 - Word Problems Skill 9 - W15 - Word problems: Division beyond basic facts, no remainders (2d/1d)Skill 11 - W17 - Word problems: Division with remainders (2d/1d, 3d/1d)

UT 1.5.d - Add and subtract decimals and simple fractions where one single-digit denominator is 1, 2, or 3 times the other (e.g., 2/4 + 1/4 = 3/4; 1/3 - 1/6 = 1/6).


Skill 21 - C22 - Addition of fractions: like single digit denominators



Skill Area 9 - Word Problems Skill 16 - W22 - Word problems: Addition of fractions, like single digit denominatorsSkill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominatorsSkill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)

UT 2 - Students will use patterns and relations to represent mathematical problems and number relationships.

UT 2.1 - Identify, analyze, and determine rules for describing numerical patterns involving operations and nonnumerical growing patterns.UT 2.1.a - Analyze growing patterns using objects, pictures, numbers, and tables to determine a rule for the pattern.UT 2.1.b - Recognize, represent, and extend simple patterns involving multiples and other number patterns (e.g., square numbers) using objects, pictures, numbers, and tables.


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UT 2.1.c - Identify simple relationships in real-life contexts and use mathematical operations to describe the pattern (e.g., the number of legs on a given number of chairs may be determined by counting by fours or by multiplying the number of chairs by 4).UT 2.2 - Use algebraic expressions, symbols, and properties of the operations to represent, simplify, and solve mathematical equations and inequalities.

UT 2.2.a - Use the order of operations to evaluate, simplify, and compare mathematical expressions involving the four operations, parentheses, and the symbols <, >, and = (e.g., 2x (4 - 1) + 3; of the two quantities 7 - (3 - 2) or (7 - 3) - 2, which is greater?).UT 2.2.b - Express single-operation problem situations as equations and solve the equation.

Skill Area 10 - Algebra Skill 3 - A02 - Translate word problem to equation

UT 2.2.c - Recognize that a symbol represents the same number throughout an equation or expression (e.g., triangle symbol + triangle symbol = 8; thus, triangle symbol = 4).UT 2.2.d - Describe and use the commutative, associative, distributive, and identity properties of addition and multiplication, and the zero property of multiplication.UT 3 - Students will understand attributes and properties of plane geometric objects and spatial relationships.UT 3.1 - Identify and describe attributes of two-dimensional geometric shapes.UT 3.1.a - Name and describe lines that are parallel, perpendicular, and intersecting.

Skill Area 6 - Geometry Skill 21 - G14 - Identify parallel lines

Skill 22 - G15 - Identify intersecting linesSkill 23 - G16 - Identify perpendicular lines

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UT 3.1.b - Identify and describe right, acute, obtuse, and straight angles.

Skill Area 6 - Geometry Skill 28 - G21 - Classify angles (obtuse, etc.)

UT 3.1.c - Identify and describe the radius and diameter of a circle.

Skill Area 6 - Geometry Skill 10 - G02 - Circle terms

UT 3.1.d - Identify and describe figures that have line symmetry and rotational symmetry.

Skill Area 6 - Geometry Skill 5 - GA5 - Understand basic symmetry

UT 3.2 - Specify locations using grids and maps.UT 3.2.a - Locate coordinates in the first quadrant of a coordinate grid.

UT 3.2.b - Give the coordinates in the first quadrant of a coordinate grid.

UT 3.2.c - Locate regions on a map of Utah.UT 3.2.d - Give the regions of a position on a map of Utah.UT 3.3 - Visualize and identify geometric shapes after applying transformations.UT 3.3.a - Identify a translation, rotation, or a reflection of a geometric shape.UT 3.3.b - Recognize that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, 3/4, and full turns.UT 4 - Students will describe relationships among units of measure, use appropriate measurement tools, and use formulas to find area measurements.

UT 4.1 - Describe relationships among units of measure for length, capacity, and weight, and determine measurements of angles using appropriate tools.UT 4.1.a - Describe the relative size among metric units of length (i.e., millimeter, centimeter, meter), between metric units of capacity (i.e., milliliter, liter), and between metric units of weight (i.e., gram, kilogram).

Skill Area 7 - Measurement Skill 12 - M05 - Metric prefixes

UT 4.1.b - Describe the relative size among customary units of capacity (i.e., cup, pint, quart, gallon).

Skill Area 7 - Measurement Skill 11 - M04 - Customary measures: Pints, quarts, gallons

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UT 4.1.c - Estimate and measure capacity using milliliters, liters, cups, pints, quarts, and gallons, and measure weight using grams and kilograms.UT 4.1.d - Recognize that angles are measured in degrees and develop benchmark angles (e.g., 45°, 60°, 120°) using 90° angles to estimate angle measurement.

Skill Area 7 - Measurement Skill 14 - M07 - Measures of angles

UT 4.1.e - Measure angles using a protractor or angle ruler.UT 4.2 - Recognize and describe area as a measurable attribute of two-dimensional shapes and calculate area measurements.

Skill Area 6 - Geometry Skill 14 - G06 - Area: square

Skill 15 - G07 - Area: rectangleSkill 16 - G08 - Area: right triangle

UT 4.2.a - Quantify area by finding the total number of same-sized units of area needed to fill the region without gaps or overlaps.UT 4.2.b - Recognize that a square that is 1 unit on a side is the standard unit for measuring area.

UT 4.2.c - Develop the area formula for a rectangle and connect it with the area model for multiplication.

UT 4.2.d - Develop and use the area formula for a right triangle by comparing with the formula for a rectangle (e.g., two of the same right triangles makes a rectangle).UT 4.2.e - Develop, use, and justify the relationships among area formulas of triangles and parallelograms by decomposing and comparing with areas of right triangles and rectangles.UT 4.2.f - Determine possible perimeters, in whole units, for a rectangle with a fixed area, and determine possible areas when given a rectangle with a fixed perimeter.

UT 5 - Students will interpret and organize collected data to make predictions, answer questions, and describe basic concepts of probability.

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UT 5.1 - Collect, organize, and display data to answer questions.UT 5.1.a - Identify a question that can be answered by collecting data.

UT 5.1.b - Collect, read, and interpret data from tables, graphs, charts, surveys, and observations.


Skill 6 - S04 - Interpret table

Skill 7 - S05 - Interpret bar graphUT 5.1.c - Represent data using frequency tables, bar graphs, line plots, and stem and leaf plots.UT 5.1.d - Identify and distinguish between clusters and outliers of a data set.UT 5.2 - Describe and predict simple random outcomes.UT 5.2.a - Describe the results of experiments involving random outcomes as simple ratios (e.g., 4 out of 9, 4/9).


Skill 11 - S11 - Probability: Simple

UT 5.2.b - Conduct simple probability experiments, with and without replacement, record possible outcomes systematically, and display results in an organized way.

UT 5.2.c - Use the results of simple probability experiments, with and without replacement, to describe the likelihood of a specific outcome in the future.

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Agency Tag Set NameUtah, Math, 2007, Fifth Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.UT 1.1 - Represent whole numbers and decimals from thousandths to one billion, fractions, percents, and integers.UT 1.1.a - Read and write numbers in standard and expanded form.


Skill 18 - N14 - Thousands: Write numerals in expanded formSkill 22 - N19 - Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form

UT 1.1.b - Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and symbolic representations (e.g., 108 = 2 x 50 + 8; 108 = 10² + 8; 90% = 90 out of 100 squares on a hundred chart).


Skill 18 - N14 - Thousands: Write numerals in expanded form

Skill 22 - N19 - Ten thousands, hundred thousands, millions, billions: Write numerals in expanded form

UT 1.1.c - Identify, read, and locate fractions, mixed numbers, decimals, and integers on the number line.


Skill 28 - N26 - Fractions and decimals: Identify position of decimals on number line

Skill 29 - N27 - Fractions and decimals: Identify position of fractions on number line

UT 1.1.d - Represent repeated factors using exponents.UT 1.1.e - Describe situations where integers could be used in the students' environment.UT 1.2 - Explain relationships and equivalencies among integers, fractions, decimals, and percents.UT 1.2.a - Compare fractions by finding a common denominator.UT 1.2.b - Order integers, fractions (including mixed numbers), and decimals using a variety of methods, including the number line.


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Agency Tag Set NameUtah, Math, 2007, Fifth Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 1.2.c - Rewrite mixed numbers and improper fractions from one form to the other and represent each using regions, sets of objects, or line segments.


Skill 30 - N28 - Fractions and decimals: Convert improper fraction to mixed number

UT 1.2.d - Represent commonly used fractions as decimals and percents in a variety of ways (e.g., models, fraction strips, pictures, calculators, algorithms).


Skill 24 - N22 - Fractions and decimals: Convert fraction to decimal

UT 1.2.e - Model and calculate equivalent forms of a fraction (including simplest form).



UT 1.2.f - Rename whole numbers as fractions with different denominators (e.g., 5 = 5/1, 3 = 6/2, 1 = 7/7).

UT 1.3 - Use number theory concepts to develop and use divisibility tests; classify whole numbers to 50 as prime, composite, or neither; and find common multiples and factors.

UT 1.3.a - Identify patterns with skip counting and multiples to develop and use divisibility tests for determining whether a whole number is divisible by 2, 3, 5, 6, 9, and 10.

UT 1.3.b - Use strategies for classifying whole numbers to 50 as prime, composite, or neither.UT 1.3.c - Rewrite a composite number between 2 and 50 as a product of only prime numbers.


Skill 40 - N38 - Advanced concepts: Knows meaning of primes and composites

UT 1.3.d - Find common multiples and factors and apply to adding and subtracting fractions.


Skill 23 - C24 - Addition of fractions: unlike single digit denominators

Skill 24 - C25 - Subtraction of fractions: unlike single digit denominators

Skill Area 9 - Word Problems Skill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominators

UT 1.4 - Model and illustrate meanings of multiplication and division.

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UT 1.4.a - Represent division-with-remainder using whole numbers, decimals, or fractions.UT 1.4.b - Describe the effect of place value when multiplying and dividing whole numbers and decimals by 10, 100, and 1,000.UT 1.4.c - Model multiplication of fractions and decimals (e.g., tenths multiplied by tenths, a whole number multiplied by tenths, or a whole number with tenths multiplied by tenths) in a variety of ways (e.g., manipulatives, number line and area models, patterns).UT 1.5 - Solve problems involving one or two operations.

Skill Area 9 - Word Problems Skill 8 - W14 - Word problems: Multiplication beyond basic facts, no regrouping (2dx1d)Skill 9 - W15 - Word problems: Division beyond basic facts, no remainders (2d/1d)Skill 10 - W16 - Word problems: Multiplication with regrouping (2dx1d, 2dx2d)Skill 11 - W17 - Word problems: Division with remainders (2d/1d, 3d/1d)Skill 14 - W20 - Word problems: Multiplication of whole numbers, any difficultySkill 16 - W22 - Word problems: Addition of fractions, like single digit denominatorsSkill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominatorsSkill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 22 - W2S - Word problems: Two-stepSkill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)Skill 25 - W36 - Word problems: Multiplication of decimals

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UT 1.5.a - Determine when it is appropriate to use estimation, mental math strategies, paper and pencil, and algorithms.UT 1.5.b - Make reasonable estimations of fraction and decimal sums, differences, and products, including knowing whether results obtained using a calculator are reasonable.

Skill Area 5 - Estimation Skill 9 - E24 - Estimation problems: Addition of fractions, unlike single digit denominators

Skill 10 - E25 - Estimation problems: Subtraction of fractions, unlike single digit denominatorsSkill 13 - E32 - Estimation problems: Addition of decimals, no place change (e.g. 2.34+10.32)Skill 14 - E33 - Estimation problems: Addition of decimals, place change (e.g. 2+.45)Skill 15 - E34 - Estimation problems: Subtraction of decimals, no place change (e.g. .53 - .42)Skill 16 - E35 – Estimation problems: Subtraction of decimals, place change (e.g. 5 - .4)

UT 1.5.c - Write number sentences that can be used to solve a two-step problem.UT 1.5.d - Interpret division-with-remainder problems as they apply to the environment (e.g., If there are 53 people, how many vans are needed if each van holds 8 people?).

UT 1.6 - Demonstrate proficiency with multiplication and division of whole numbers and compute problems involving addition, subtraction, and multiplication of decimals and fractions.


Skill 33 - C36 - Multiplication of decimals

Skill Area 9 - Word Problems Skill 25 - W36 - Word problems: Multiplication of decimals

UT 1.6.a - Multiply multi-digit whole numbers by a two-digit whole number with fluency, using efficient procedures.



Skill 16 - C16 - Multiplication with regrouping (2dx1d, 2dx2d)

Skill Area 9 - Word Problems Skill 8 - W14 - Word problems: Multiplication beyond basic facts, no regrouping (2dx1d)

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Skill 10 - W16 - Word problems: Multiplication with regrouping (2dx1d, 2dx2d)Skill 14 - W20 - Word problems: Multiplication of whole numbers, any difficulty

UT 1.6.b - Divide multi-digit dividends by a one-digit divisor with fluency, using efficient procedures.



Skill 17 - C17 - Division with remainders (2d/1d, 3d/1d)

Skill Area 9 - Word Problems Skill 9 - W15 - Word problems: Division beyond basic facts, no remainders (2d/1d)Skill 11 - W17 - Word problems: Division with remainders (2d/1d, 3d/1d)

UT 1.6.c - Add and subtract decimals with fluency, using efficient procedures.


Skill 31 - C33 - Addition of decimals, place change (e.g. 2 + .45)


Skill Area 9 - Word Problems Skill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)

UT 1.6.d - Add and subtract fractions with fluency.



Skill 22 - C23 - Subtraction of fractions: like single digit denominatorsSkill 23 - C24 - Addition of fractions: unlike single digit denominators

Skill 24 - C25 - Subtraction of fractions: unlike single digit denominators

Skill Area 9 - Word Problems Skill 16 - W22 - Word problems: Addition of fractions, like single digit denominatorsSkill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominatorsSkill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominators

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UT 1.6.e - Multiply fractions. Skill Area 4 - Computation Processes

Skill 25 - C26 - Multiplication of fractions: single digit denominators

UT 2 - Students will use patterns and relations to represent and analyze mathematical problems and number relationships using algebraic symbols.UT 2.1 - Identify, analyze and determine a rule for predicting and extending numerical patterns involving operations whole numbers, decimals, and fractions.UT 2.1.a - Analyze and make predictions about numeric patterns, including decimals and fractions.

UT 2.1.b - Determine a rule for the pattern using organized lists, tables, objects, and variables.UT 2.2 - Use algebraic expressions, inequalities, or equations to represent and solve simple real-world problems.UT 2.2.a - Use properties and the order of operations involving addition, subtraction, multiplication, division, and the use of parentheses to compute with whole numbers, decimals, and fractions.

UT 2.2.b - Use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities with whole number solutions (e.g., 6x = 54; x + 3 = 7).


UT 3 - Students will use spatial reasoning to recognize, describe, and analyze geometric shapes and principles.UT 3.1 - Describe relationships between two- and three-dimensional shapes and analyze attributes and properties of geometric shapes.

UT 3.1.a - Draw, label, and describe line segments, rays, lines, parallel lines, and perpendicular lines.

Skill Area 6 - Geometry Skill 19 - G12 - Identify rays

Skill 20 - G13 - Identify line segments

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Skill 21 - G14 - Identify parallel lines

Skill 23 - G16 - Identify perpendicular lines

UT 3.1.b - Draw, label, and define an angle as two rays sharing a common endpoint (vertex).UT 3.1.c - Classify triangles and quadrilaterals and analyze the relationships among the shapes in each classification (e.g., a square is a rectangle).UT 3.1.d - Relate pyramids and right prisms to the two-dimensional shapes (nets) from which they were created.UT 3.1.e - Identify properties and attributes of solids (i.e., right prisms, pyramids, cylinders, cones) and describe them by the number of edges, faces, and vertices as well as the types of faces.

UT 3.2 - Specify locations in a coordinate plane.UT 3.2.a - Locate points defined by ordered pairs of integers.UT 3.2.b - Write an ordered pair for a point in a coordinate plane with integer coordinates.UT 3.2.c - Specify possible paths between locations on a coordinate plane and compare distances of the various paths.UT 4 - Students will determine area of polygons and surface area and volume of three-dimensional shapes.

UT 4.1 - Determine the area of polygons and apply to real-world problems.

Skill Area 6 - Geometry Skill 14 - G06 - Area: square

Skill 15 - G07 - Area: rectangleSkill 16 - G08 - Area: right triangle

UT 4.1.a - Determine the area of a trapezoid by the composition and decomposition of rectangles, triangles, and parallelograms.UT 4.1.b - Determine the area of irregular and regular polygons by the composition and decomposition of rectangles, triangles, and parallelograms.

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UT 4.1.c - Compare areas of polygons using different units of measure within the same measurement system (e.g., square feet, square yards).UT 4.2 - Recognize, describe, and determine surface area and volume of three-dimensional shapes.UT 4.2.a - Quantify volume by finding the total number of same-sized units of volume needed to fill the space without gaps or overlaps.

UT 4.2.b - Recognize that a cube having a 1 unit edge is the standard unit for measuring volume expressed as a cubic unit.UT 4.2.c - Derive and use the formula to determine the volume of a right prism with a triangular or rectangular base.

Skill Area 6 - Geometry Skill 18 - G10 - Volume: rectangular prism

UT 4.2.d - Relate the formulas for the areas of triangles, rectangles, or parallelograms to the surface area of a right prism.UT 4.2.e - Derive and use the formula to determine the surface area of a right prism and express surface area in square units.UT 5 - Students will construct, analyze, and construct reasonable conclusions from data and apply basic concepts of probability.UT 5.1 - Formulate and answer questions using statistical methods to compare data, and propose and justify inferences based on data.

UT 5.1.a - Construct, analyze, and display data using an appropriate format (e.g., line plots, bar graphs, line graphs).UT 5.1.b - Recognize the differences in representing categorical and numerical data.UT 5.1.c - Identify minimum and maximum values for a set of data.UT 5.1.d - Identify and calculate the mean, median, mode, and range.


Skill 9 - S07 - Statistics: Mean

Skill 10 - S08 - Statistics: Median

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UT 5.2 - Apply basic concepts of probability.UT 5.2.a - Describe the results of experiments involving random outcomes using a variety of notations (e.g., 4 out of 9, 4/9).



UT 5.2.b - Recognize that probability is always a value between 0 and 1 (inclusively).UT 5.2.c - Express the likelihood of an outcome in a simple experiment as a value between 0 and 1 (inclusively).



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Agency Tag Set NameUtah, Math, 2007, Sixth Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will expand number sense to include operations with rational numbers.UT 1.1 - Represent rational numbers in a variety of ways.UT 1.1.a - Recognize a rational number as a ratio of two integers, a to b, where b is not equal to zero.

UT 1.1.b - Change whole numbers with exponents to standard form (e.g., 2 to the 4th power = 16) and recognize that any non-zero whole number to the zero power equals 1 (e.g., 9 to the 0 power = 1).


Skill 36 - N34 - Advanced concepts: Recognize meaning of exponents (2-10)

UT 1.1.c - Write a whole number in expanded form using exponents (e.g., 876,539 = 8 x 10 to the 5th power + 7 x 10 to the 4th power + 6 x 10³ + 5 x 10² + 3 x 10¹ + 9 x 10 to the 0 power).UT 1.1.d - Express numbers in scientific notation using positive powers of ten.


Skill 39 - N37 - Advanced concepts: Can use scientific notation

UT 1.2 - Explain relationships and equivalencies among rational numbers.UT 1.2.a - Place rational numbers on the number line.


Skill 28 - N26 - Fractions and decimals: Identify position of decimals on number lineSkill 29 - N27 - Fractions and decimals: Identify position of fractions on number line

UT 1.2.b - Compare and order rational numbers, including positive and negative mixed fractions and decimals, using a variety of methods and symbols, including the number line and finding common denominators.UT 1.2.c - Find equivalent forms for common fractions, decimals, percents, and ratios, including repeating or terminating decimals.




Skill 25 - N23 - Fractions and decimals: Convert decimal to fraction


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Agency Tag Set NameUtah, Math, 2007, Sixth Grade, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


Skill 32 - N30 - Fractions and decimals: Relate decimals to percents

UT 1.2.d - Relate percents less than 1% or greater than 100% to equivalent fractions, decimals, whole numbers, and mixed numbers.

UT 1.2.e - Recognize that the sum of an integer and its additive inverse is zero.UT 1.3 - Use number theory concepts to find prime factorizations, least common multiples, and greatest common factors.

UT 1.3.a - Determine whether whole numbers to 100 are prime, composite, or neither.UT 1.3.b - Find the prime factorization of composite numbers to 100.


Skill 40 - N38 - Advanced concepts: Knows meaning of primes and composites

UT 1.3.c - Find the greatest common factor and least common multiple for two numbers using a variety of methods (e.g., list of multiples, prime factorization).


Skill 41 - N39 - Advanced concepts: Can determine greatest common factor

Skill 42 - N40 - Advanced concepts: Can determine least common multiple

UT 1.4 - Model and illustrate meanings of operations and describe how they relate.UT 1.4.a - Relate fractions to multiplication and division and use this relationship to explain procedures for multiplying and dividing fractions.


Skill 25 - C26 - Multiplication of fractions: single digit denominators

Skill 26 - C27 - Division of fractions: single digit denominators

UT 1.4.b - Recognize that ratios derive from pairs of rows in the multiplication table and connect with equivalent fractions.UT 1.4.c - Give mixed number and decimal solutions to division problems with whole numbers.UT 1.5 - Solve problems involving multiple steps.

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UT 1.5.a - Select appropriate methods to solve a multi-step problem involving multiplication and division of fractions and decimals.UT 1.5.b - Use estimation to determine whether results obtained using a calculator are reasonable.UT 1.5.c - Use estimation or calculation to compute results, depending on the context and numbers involved in the problem.UT 1.5.d - Solve problems involving ratios and proportions.


Skill 38 - C41 - Proportions

Skill 39 - C42 - RatiosSkill Area 9 - Word Problems Skill 30 - W41 - Word problems:

ProportionsSkill 31 - W42 - Word problems: Ratios

UT 1.6 - Demonstrate proficiency with the four operations, with positive rational numbers, and with addition and subtraction of integers.

UT 1.6.a - Multiply and divide a multi-digit number by a two-digit number, including decimals.



Skill 16 - C16 - Multiplication with regrouping (2dx1d, 2dx2d)Skill 17 - C17 - Division with remainders (2d/1d, 3d/1d)Skill 33 - C36 - Multiplication of decimalsSkill 34 - C37 - Division of decimals

Skill Area 9 - Word Problems Skill 14 - W20 - Word problems: Multiplication of whole numbers, any difficultySkill 25 - W36 - Word problems: Multiplication of decimalsSkill 26 - W37 - Word problems: Division decimals

UT 1.6.b - Add, subtract, multiply, and divide fractions and mixed numbers.



Skill 22 - C23 - Subtraction of fractions: like single digit denominatorsSkill 23 - C24 - Addition of fractions: unlike single digit denominators

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Skill 24 - C25 - Subtraction of fractions: unlike single digit denominatorsSkill 25 - C26 - Multiplication of fractions: single digit denominatorsSkill 26 - C27 - Division of fractions: single digit denominatorsSkill 27 - C28 - Addition of mixed numbersSkill 28 - C29 - Subtraction of mixed numbersSkill 29 - C30 - Multiplication of mixed numbersSkill 30 - C31 - Division of mixed numbers

Skill Area 9 - Word Problems Skill 16 - W22 - Word problems: Addition of fractions, like single digit denominatorsSkill 17 - W23 - Word problems: Subtraction of fractions, like single digit denominatorsSkill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 20 - W28 - Word problems: Addition of mixed numbersSkill 21 - W29 - Word problems: Subtraction of mixed numbers

UT 1.6.c - Add and subtract integers.

UT 2 - Students will use patterns, relations, and algebraic expressions to represent and analyze mathematical problems and number relationships.UT 2.1 - Analyze algebraic expressions, tables, and graphs to determine patterns, relations, and rules.UT 2.1.a - Describe simple relationships by creating and analyzing tables, equations, and expressions.


UT 2.1.b - Draw a graph and write an equation from a table of values.UT 2.1.c - Draw a graph and create a table of values from an equation.

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UT 2.2 - Write, interpret, and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations.UT 2.2.a - Solve single variable linear equations using a variety of strategies.

Skill Area 10 - Algebra Skill 4 - A03 - Linear equations: 1 unknown

UT 2.2.b - Recognize that expressions in different forms can be equivalent and rewrite an expression to represent a quantity in a different way.UT 2.2.c - Evaluate and simplify expressions and formulas, substituting given values for the variables (e.g., 2x + 4; x = 2; therefore, 2 (2) + 4 = 8).UT 3 - Students will use spatial and logical reasoning to recognize, describe, and analyze geometric shapes and principles.UT 3.1 - Identify and analyze attributes and properties of geometric shapes to solve problems.

UT 3.1.a - Identify the midpoint of a line segment and the center and circumference of a circle.UT 3.1.b - Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.UT 3.1.c - Develop and use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle in a triangle or quadrilateral.

Skill Area 6 - Geometry Skill 29 - G22 - Using parts of a triangle

UT 3.2 - Visualize and identify geometric shapes after applying transformations on a coordinate plane.UT 3.2.a - Rotate a polygon about the origin by a multiple of 90° and identify the location of the new vertices.

UT 3.2.b - Translate a polygon either horizontally or vertically on a coordinate grid and identify the location of the new vertices.

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UT 3.2.c - Reflect a polygon across either the x- or y-axis and identify the location of the new vertices.

UT 4 - Students will understand and apply measurement tools and techniques and find the circumference and area of a circle.UT 4.1 - Describe and find the circumference and area of a circle.UT 4.1.a - Explore the relationship between the radius and diameter of a circle to the circle's circumference to develop the formula for circumference.UT 4.1.b - Find the circumference of a circle using a formula.UT 4.1.c - Describe pi as the ratio of the circumference to the diameter of a circle.UT 4.1.d - Decompose a circle into a number of wedges and rearrange the wedges into a shape that approximates a parallelogram to develop the formula for the area of a circle.UT 4.1.e - Find the area of a circle using a formula.

Skill Area 6 - Geometry Skill 17 - G09 - Area: circle

UT 4.2 - Identify and describe measurable attributes of objects and units of measurement, and solve problems involving measurement.

UT 4.2.a - Recognize that measurements are approximations and describe how the size of the unit used in measuring affects the precision.UT 4.2.b - Convert units of measurement within the metric system and convert units of measurement within the customary system.



UT 4.2.c - Compare a meter to a yard, a liter to a quart, and a kilometer to a mile.

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UT 4.2.d - Determine when it is appropriate to estimate or use precise measurement when solving problems.UT 4.2.e - Derive and use the formula to determine the surface area and volume of a cylinder.UT 5 - Students will analyze, draw conclusions, and make predictions based upon data and apply basic concepts of probability.UT 5.1 - Design investigations to reach conclusions using statistical methods to make inferences based on data.UT 5.1.a - Design investigations to answer questions.UT 5.1.b - Extend data display and comparisons to include scatter plots and circle graphs.UT 5.1.c - Compare two similar sets of data on the same graph and compare two graphs representing the same set of data.UT 5.1.d - Recognize that changing the scale influences the appearance of a display of data.UT 5.1.e - Propose and justify inferences and predictions based on data.UT 5.2 - Apply basic concepts of probability and justify outcomes.UT 5.2.a - Write the results of a probability experiment as a fraction between zero and one, or an equivalent percent.



UT 5.2.b - Compare experimental results with theoretical results (e.g., experimental: 7 out of 10 tails; whereas, theoretical 5 out of 10 tails).

UT 5.2.c - Compare individual, small group, and large group results of a probability experiment in order to more accurately estimate the actual probabilities.

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Agency Tag Set NameUtah, Math, 2007, Math 7, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will expand number sense to understand, perform operations, and solve problems with rational numbers.UT 1.1 - Represent rational numbers in a variety of ways.UT 1.1.a - Demonstrate multiple ways to represent whole numbers, decimals, fractions, percents, and integers using models and real-life examples.UT 1.1.b - Simplify numerical expressions with whole number exponents using order of operations, and recognize that any positive number to the 0 power is 1.

UT 1.1.c - Represent numbers greater than one using scientific notation.


Skill 39 - N37 - Advanced concepts: Can use scientific notation

UT 1.1.d - Select the most appropriate form of a rational number for a given context.UT 1.2 - Compare and order rational numbers, including positive and negative fractions, positive and negative mixed numbers, and positive and negative decimals.UT 1.2.a - Identify, read, and locate rational numbers on a number line.



UT 1.2.b - Compare pairs of rational numbers in different forms.UT 1.2.c - Order rational numbers with and without a number line.UT 1.3 - Explain relationships and equivalences among rational numbers.UT 1.3.a - Find equivalent forms for common fractions, decimals, percents, and ratios, including repeating or terminating decimals.




Skill 25 - N23 - Fractions and decimals: Convert decimal to fraction


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Agency Tag Set NameUtah, Math, 2007, Math 7, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


Skill 32 - N30 - Fractions and decimals: Relate decimals to percents

UT 1.3.b - Predict the effect of operating with fractions, decimals, percents, and integers as an increase or a decrease of the original value.

UT 1.3.c - Recognize and use the identity properties of addition and multiplication, the multiplicative property of zero, the commutative and associative properties of addition and multiplication, and the distributive property of multiplication over addition.UT 1.3.d - Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.


Skill 33 - N31 - Advanced concepts: Determine square roots of perfect squares

Skill Area 10 - Algebra Skill 2 - A01 - Simple number sentenceSkill 4 - A03 - Linear equations: 1 unknown

UT 1.4 - Model meanings of ratios and operations with rational numbers.

UT 1.4.a - Demonstrate that the fraction a/b represents a divided by b.

UT 1.4.b - Recognize percents as ratios based on 100 and decimals as ratios based on powers of 10.UT 1.4.c - Extend the multiplication of whole numbers to multiplication of fractions using area models, measurement models, and the number line.UT 1.4.d - Compare the division of whole numbers to the division of fractions using area or set models, the number line, and missing factors.

UT 1.5 - Solve problems involving rational numbers.UT 1.5.a - Compute fluently using all four operations with integers and positive fractions and decimals.


Skill 43 - N41 - Advanced concepts: Recognizes use of negative numbers

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Skill 24 - C25 - Subtraction of fractions: unlike single digit denominatorsSkill 25 - C26 - Multiplication of fractions: single digit denominatorsSkill 26 - C27 - Division of fractions: single digit denominatorsSkill 27 - C28 - Addition of mixed numbersSkill 28 - C29 - Subtraction of mixed numbersSkill 29 - C30 - Multiplication of mixed numbersSkill 30 - C31 - Division of mixed numbersSkill 31 - C33 - Addition of decimals, place change (e.g. 2 + .45)

Skill 32 - C35 - Subtraction of decimals, place change (e.g. 5-.4)Skill 33 - C36 - Multiplication of decimalsSkill 34 - C37 - Division of decimals

Skill Area 9 - Word Problems Skill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 20 - W28 - Word problems: Addition of mixed numbersSkill 21 - W29 - Word problems: Subtraction of mixed numbersSkill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)Skill 25 - W36 - Word problems: Multiplication of decimalsSkill 26 - W37 - Word problems: Division decimals

UT 1.5.b - Solve problems using factors, multiples, prime factorization, relatively prime numbers, and common divisibility rules.

Skill Area 9 - Word Problems Skill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominators

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Skill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 20 - W28 - Word problems: Addition of mixed numbersSkill 21 - W29 - Word problems: Subtraction of mixed numbers

UT 1.5.c - Solve application problems involving rational numbers.

Skill Area 9 - Word Problems Skill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 20 - W28 - Word problems: Addition of mixed numbersSkill 21 - W29 - Word problems: Subtraction of mixed numbersSkill 23 - W33 - Word problems: Addition of decimals, place change (e.g. 2+.45)Skill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)Skill 25 - W36 - Word problems: Multiplication of decimalsSkill 26 - W37 - Word problems: Division decimals

UT 1.5.d - Determine if an answer is reasonable using estimation.UT 2 - Students will use proportional reasoning to solve problems.

UT 2.1 - Solve problems involving ratios, rates, proportions and percentages.UT 2.1.a - Solve ratio and rate problems using informal methods involving multiplication and division.


Skill 39 - C42 - Ratios

Skill Area 9 - Word Problems Skill 30 - W41 - Word problems: ProportionsSkill 31 - W42 - Word problems: Ratios

UT 2.1.b - Solve percent problems using ratio and proportion, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.


Skill 35 - C38 - Percent A (10 is what % of 40)

Skill 36 - C39 - Percent B (20% of 50 is what)Skill 37 - C40 - Percent C (30 is 50% of what)

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Skill Area 9 - Word Problems Skill 27 - W38 - Word problems: Percent A (10 is what % of 40)Skill 28 - W39 - Word problems: Percent B (20% of 50 is what)Skill 29 - W40 - Word problems: Percent C (30 is 50% of what)

UT 2.1.c - Solve problems involving proportions, rates, and measures.


Skill 38 - C41 - Proportions

Skill Area 9 - Word Problems Skill 30 - W41 - Word problems: Proportions

UT 2.2 - Apply the properties of proportionality to different units of measurement.UT 2.2.a - Convert from one unit of measurement to an equivalent unit of measurement in the same system using a given conversion factor.



UT 2.2.b - Understand that in a proportional relationship, all dimensions change by the same scale factor.UT 2.2.c - Create and interpret scale drawings and approximate distance on maps using proportions.

UT 3 - Students will develop fluency with the language and operations of algebra to analyze and represent relationships.UT 3.1 - Evaluate, simplify, and solve algebraic expressions and equations.

UT 3.1.a - Write a variable expression to identify pattern relationships, and use those expressions to make predictions.UT 3.1.b - Translate verbal expressions into algebraic expressions.UT 3.1.c - Simplify and evaluate algebraic expressions.UT 3.1.d - Show that performing the same operation on both sides of an equation will produce an equivalent equation.

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UT 3.1.e - Solve single-variable linear equations and inequalities of the form ax + b = c, ax + b < c, or ax + b > c.


Skill 8 - A07 - Linear inequalities: 1 unknown

UT 3.2 - Represent relationships using graphs, tables, and other models.UT 3.2.a - Identify integer coordinates when given the graph of a point on a rectangular coordinate system.

UT 3.2.b - Graph ordered pairs of integers on a rectangular coordinate system.UT 3.2.c - Model real-world problems using graphs, tables, equations, manipulatives, and pictures.

UT 4 - Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.UT 4.1 - Draw, label, and describe attributes of geometric figures to determine geometric relationships.UT 4.1.a - Draw, label, and describe relationships among line segments, rays, lines, parallel lines, and perpendicular lines, including midpoint of a line segment.

Skill Area 6 - Geometry Skill 19 - G12 - Identify rays

Skill 20 - G13 - Identify line segments

UT 4.1.b - Draw, label, and describe relationships among vertical, adjacent, complementary, and supplementary angles.

Skill Area 6 - Geometry Skill 27 - G20 - Vertical and supplementary angles

UT 4.1.c - Draw, label, and describe attributes of angles, triangles, and quadrilaterals.UT 4.2 - Determine measurements in metric and customary units using appropriate tools and formulas.

UT 4.2.a - Estimate metric and customary measures using everyday objects and comparisons.

Skill Area 7 - Measurement Skill 10 - M02 - Customary measures: Estimating linear measures

Skill 15 - M08 - Estimating linear measure in metric units.

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UT 4.2.b - Measure length, area, volume, and angles to appropriate levels of precision.UT 4.2.c - Calculate the measurement of everyday objects using formulas for perimeters and areas of triangles and quadrilaterals, and circumferences and areas of circles.

Skill Area 6 - Geometry Skill 17 - G09 - Area: circle

UT 4.2.d - Calculate the measurement of everyday objects using formulas for surface area and volume of right triangular and rectangular prisms and cylinders.


UT 5 - Students will understand concepts from probability and statistics and apply statistical methods to solve problems.UT 5.1 - Use basic concepts of probability to determine the likelihood of an event and compare the results of various experiments.UT 5.1.a - Write the results of a probability experiment as a fraction, ratio, or decimal, between zero and one, or as a percent between zero and one hundred, inclusive.



UT 5.1.b - Compare experimental results with theoretical probability.UT 5.1.c - Compare individual, small group, and large group results of a probability experiment.UT 5.2 - Display and compare data to make predictions and formulate conclusions.UT 5.2.a - Display data using tables, scatter plots, and circle graphs.

UT 5.2.b - Compare two similar sets of data on the same graph.UT 5.2.c - Compare two different kinds of graphs representing the same set of data.UT 5.2.d - Propose and justify inferences and predictions based on data.

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Agency Tag Set NameUtah, Math, 2007, Pre-Algebra, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will expand number sense to understand, perform operations, and solve problems with rational numbers.UT 1.1 - Compute fluently with understanding and make reasonable estimates with rational numbers.

Skill Area 5 - Estimation Skill 9 - E24 - Estimation problems: Addition of fractions, unlike single digit denominators

Skill 10 - E25 - Estimation problems: Subtraction of fractions, unlike single digit denominatorsSkill 11 - E28 - Estimation problems: Addition of mixed numbers

Skill 12 - E29 - Estimation problems: Subtraction of mixed numbers

UT 1.1.a - Compute fluently using all four operations with integers, and explain why the corresponding algorithms work.


Skill 43 - N41 - Advanced concepts: Recognizes use of negative numbers

UT 1.1.b - Compute fluently using all four operations with rational numbers, including negative fractions and decimals, and explain why the corresponding algorithms work.



Skill 24 - C25 - Subtraction of fractions: unlike single digit denominatorsSkill 25 - C26 - Multiplication of fractions: single digit denominatorsSkill 26 - C27 - Division of fractions: single digit denominatorsSkill 27 - C28 - Addition of mixed numbersSkill 28 - C29 - Subtraction of mixed numbersSkill 29 - C30 - Multiplication of mixed numbersSkill 30 - C31 - Division of mixed numbersSkill 32 - C35 - Subtraction of decimals, place change (e.g. 5-.4)Skill 33 - C36 - Multiplication of decimalsSkill 34 - C37 - Division of decimals

Skill Area 9 - Word Problems Skill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominators


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Agency Tag Set NameUtah, Math, 2007, Pre-Algebra, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


Skill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 20 - W28 - Word problems: Addition of mixed numbersSkill 21 - W29 - Word problems: Subtraction of mixed numbersSkill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)Skill 25 - W36 - Word problems: Multiplication of decimalsSkill 26 - W37 - Word problems: Division decimals

UT 1.1.c - Check the reasonableness of results using estimation.

UT 1.2 - Analyze relationships among rational numbers, including negative rational numbers, and operations involving these numbers.

UT 1.2.a - Order rational numbers in various forms, including scientific notation (positive and negative exponents), and place numbers on a number line.


Skill 28 - N26 - Fractions and decimals: Identify position of decimals on number line

Skill 29 - N27 - Fractions and decimals: Identify position of fractions on number line

UT 1.2.b - Predict the effect of operating with fractions, decimals, percents, and integers as an increase or a decrease of the original value.

UT 1.2.c - Recognize and use the identity properties of addition and multiplication, the multiplicative property of zero, the commutative and associative properties of addition and multiplication, and the distributive property of multiplication over addition.UT 1.2.d - Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.


Skill 33 - N31 - Advanced concepts: Determine square roots of perfect squares



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UT 1.3 - Solve problems involving rational numbers using addition, subtraction, multiplication, and division.UT 1.3.a - Recognize the absolute value of a rational number as its distance from zero.UT 1.3.b - Simplify numerical expressions, including those with whole number exponents and absolute values, using the order of operations.UT 1.3.c - Solve problems involving rational numbers, percents, and proportions.



Skill 24 - C25 - Subtraction of fractions: unlike single digit denominatorsSkill 25 - C26 - Multiplication of fractions: single digit denominatorsSkill 26 - C27 - Division of fractions: single digit denominatorsSkill 27 - C28 - Addition of mixed numbersSkill 28 - C29 - Subtraction of mixed numbersSkill 29 - C30 - Multiplication of mixed numbersSkill 30 - C31 - Division of mixed numbersSkill 32 - C35 - Subtraction of decimals, place change (e.g. 5-.4)Skill 33 - C36 - Multiplication of decimalsSkill 34 - C37 - Division of decimals

Skill 35 - C38 - Percent A (10 is what % of 40)Skill 36 - C39 - Percent B (20% of 50 is what)Skill 37 - C40 - Percent C (30 is 50% of what)Skill 38 - C41 - Proportions

Skill Area 9 - Word Problems Skill 18 - W24 - Word problems: Addition of fractions, unlike single digit denominatorsSkill 19 - W25 - Word problems: Subtraction of fractions, unlike single digit denominatorsSkill 20 - W28 - Word problems: Addition of mixed numbers


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Skill 21 - W29 - Word problems: Subtraction of mixed numbersSkill 24 - W35 - Word problems: Subtraction of decimals, place change (e.g. 5-.4)Skill 25 - W36 - Word problems: Multiplication of decimalsSkill 26 - W37 - Word problems: Division decimalsSkill 27 - W38 - Word problems: Percent A (10 is what % of 40)Skill 28 - W39 - Word problems: Percent B (20% of 50 is what)Skill 29 - W40 - Word problems: Percent C (30 is 50% of what)Skill 30 - W41 - Word problems: Proportions

UT 2 - Students will use proportion and similarity to solve problems.UT 2.1 - Model and illustrate meanings of ratios, percents, and decimals.UT 2.1.a - Compare ratios to determine if they are equivalent.UT 2.1.b - Compare ratios using the unit rate.UT 2.1.c - Represent percents as ratios based on 100 and decimals as ratios based on powers of ten.UT 2.1.d - Graph proportional relationships and identify the unit rate as the slope of the related line.

UT 2.2 - Solve a wide variety of problems using ratios and proportional reasoning.UT 2.2.a - Set up and solve problems involving proportional reasoning using variables.

Skill Area 9 - Word Problems Skill 30 - W41 - Word problems: Proportions

UT 2.2.b - Solve percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease.


Skill 35 - C38 - Percent A (10 is what % of 40)

Skill 36 - C39 - Percent B (20% of 50 is what)Skill 37 - C40 - Percent C (30 is 50% of what)

Skill Area 9 - Word Problems Skill 27 - W38 - Word problems: Percent A (10 is what % of 40)Skill 28 - W39 - Word problems: Percent B (20% of 50 is what)


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Skill 29 - W40 - Word problems: Percent C (30 is 50% of what)

UT 2.2.c - Solve ratio and rate problems using informal methods.



Skill Area 9 - Word Problems Skill 31 - W42 - Word problems: Ratios

UT 2.3 - Recognize similar polygons and use properties of similar triangles to solve problems and define the slope of a line.UT 2.3.a - Define similar polygons as polygons with corresponding angles congruent and corresponding sides that are proportional.

UT 2.3.b - Identify pairs of similar triangles using two pairs of congruent angles, or two pairs of proportional sides with congruent included angles.

UT 2.3.c - Find missing lengths of similar triangles, including inaccessible lengths, using proportions.UT 2.3.d - Define the slope of a line as the ratio of the vertical change to the horizontal change between two points, and show that the slope is constant using similarity of right triangles.UT 3 - Students will develop fluency with the language and operations of algebra to analyze and represent relationships.UT 3.1 - Generalize and express patterns using algebraic expressions.

UT 3.1.a - Compare representations of a relation using tables, graphs, algebraic symbols, and mathematical rules.

Skill Area 10 - Algebra Skill 7 - A06 - Graph of linear equation (integers add, subtract)


UT 3.1.b - Describe simple patterns using a mathematical rule or algebraic expression.UT 3.1.c - Create and extend simple numerical and visual patterns.

UT 3.2 - Evaluate, simplify, and solve algebraic expressions, equations, and inequalities.


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UT 3.2.a - Evaluate algebraic expressions, including those with whole number exponents, when given values for the variable(s).UT 3.2.b - Simplify algebraic expressions using the order of operations, algebraic properties, and exponent rules.UT 3.2.c - Solve single-variable linear equations and inequalities, including those that must be simplified on one side or those with variables on both sides of an equation.



UT 3.3 - Represent relationships using graphs, tables, and other models.UT 3.3.a - Identify approximate rational coordinates when given the graph of a point on a rectangular coordinate system.UT 3.3.b - Graph ordered pairs of rational numbers on a rectangular coordinate system.UT 3.3.c - Graph linear equations using ordered pairs or tables.UT 3.3.d - Recognize that all first order equations produce linear graphs.UT 3.3.e - Model real-world problems using graphs, tables, equations, manipulatives, and pictures, and identify extraneous information.

UT 4 - Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.UT 4.1 - Apply the properties of proportionality of different units of measure.UT 4.1.a - Convert units of measure within the same system.

Skill Area 7 - Measurement Skill 9 - M01 - Customary measures: Inches, feet, yardsSkill 11 - M04 - Customary measures: Pints, quarts, gallonsSkill 12 - M05 - Metric prefixes

UT 4.1.b - Create and interpret scale drawings and approximate distance on maps using scale factors.


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UT 4.1.c - Solve problems using scale factors.UT 4.2 - Derive formulas for surface areas and volume of three-dimensional figures.UT 4.2.a - Derive formulas for and calculate surface area and volume of right prisms and cylinders using appropriate units.


UT 4.2.b - Explain that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related and the cube of the scale factor describes how corresponding volumes are related.

UT 4.2.c - Find lengths, areas, and volumes of similar figures, using the scale factor.UT 4.2.d - Select appropriate two- and three-dimensional figures to model real-world objects, and solve a variety of problems involving surface areas and volumes of cylinders and prisms.


UT 5 - Students will understand concepts from probability and statistics and apply statistical methods to solve problems.UT 5.1 - Calculate probabilities of events and compare theoretical and experimental probability.UT 5.1.a - Solve counting problems using the Fundamental Counting Principle.UT 5.1.b - Calculate the probability of an event or sequence of events with and without replacement using models.


Skill 12 - S12 - Probability: Joint

UT 5.1.c - Recognize that the sum of the probability of an event and the probability of its complement is equal to one.UT 5.1.d - Make approximate predictions using theoretical probability and proportions.


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UT 5.1.e - Collect and interpret data to show that as the number of trials increases, experimental probability approaches the theoretical probability.UT 5.2 - Formulate questions and answer the questions by organizing and analyzing data.UT 5.2.a - Formulate questions that can be answered through data collection and analysis.UT 5.2.b - Determine the 25th and 75th percentiles (first and third quartiles) to obtain information about the spread of data.UT 5.2.c - Graphically summarize data of a single variable using histograms and box-and-whisker plots.UT 5.2.d - Compute the mean and median of a numerical characteristic and relate these values to the histogram of the data.


Skill 9 - S07 - Statistics: Mean

Skill 10 - S08 - Statistics: MedianUT 5.2.e - Use graphical representations and numerical summaries to answer questions and interpret data.


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Agency Tag Set NameUtah, Math, 2007, Algebra 1, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will expand number sense to understand, perform operations, and solve problems with real numbers.UT 1.1 - Represent real numbers as points on the number line and distinguish rational numbers from irrational numbers.UT 1.1.a - Define a rational number as a point on the number line that can be expressed as the ratio of two integers, and points that cannot be so expressed as irrational.

UT 1.1.b - Classify numbers as rational or irrational, knowing that rational numbers can be expressed as terminating or repeating decimals and irrational numbers can be expressed as non-terminating, non-repeating decimals.

UT 1.1.c - Classify pi and square roots of non-perfect square numbers as irrational.UT 1.1.d - Place rational and irrational numbers on a number line between two integers.



UT 1.2 - Compute fluently and make reasonable estimates with rational and irrational numbers.UT 1.2.a - Simplify, add, subtract, multiply, and divide expressions with square roots.UT 1.2.b - Evaluate and simplify numerical expressions containing rational numbers and square roots using the order of operations.UT 1.2.c - Compute solutions to problems, represent answers in exact form, and determine the reasonableness of answers.UT 1.2.d - Calculate the measures of the sides of a right triangle using the Pythagorean Theorem.

Skill Area 6 - Geometry Skill 30 - G23 - Pythagorean theorem

UT 2 - Students will extend concepts of proportion to represent and analyze linear relations.



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Agency Tag Set NameUtah, Math, 2007, Algebra 1, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 2.1 - Represent and analyze the slope of a line.UT 2.1.a - Identify the slope of a line when given points, a graph, or an equation.

Skill Area 10 - Algebra Skill 20 - A19 - Determine slope

UT 2.1.b - Identify horizontal and vertical lines given the equations or slopes.UT 2.1.c - Determine the effect of changes in slope or y-intercept in y = mx + b.UT 2.1.d - Determine and explain the meaning of slopes and intercepts using real-world examples.

UT 2.2 - Model and interpret problems having a constant rate of change using linear functions.UT 2.2.a - Write algebraic expressions or equations to generalize visual patterns, numerical patterns, relations, data sets, or scatter plots.UT 2.2.b - Represent linear equations in slope-intercept form, y = mx + b, and standard form, Ax+ By =C.

UT 2.2.c - Distinguish between linear and non-linear functions by examining a table, equation, or graph.UT 2.2.d - Interpret the slope of a linear function as a rate of change in real-world situations.UT 2.3 - Represent and analyze linear relationships using algebraic equations, expressions, and graphs.

UT 2.3.a - Write the equation of a line when given two points or the slope and a point on the line.UT 2.3.b - Approximate the equation of a line given the graph of a line.

UT 2.3.c - Identify the x- and y-intercepts from an equation or graph of a line or a table of values.

Skill Area 10 - Algebra Skill 21 - A20 - Determine intercept

UT 2.3.d - Graph linear relations and inequalities by plotting points, by finding x- and y-intercepts, or by using the slope and any point on the line.

Skill Area 10 - Algebra Skill 7 - A06 - Graph of linear equation (integers add, subtract)


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Skill 9 - A08 - Linear inequalities: 2 unknownSkill 10 - A09 - Graph linear inequalities

UT 3 - Students will develop fluency with the language and operations of algebra to analyze and represent relationships.UT 3.1 - Simplify polynomials and the quotient of monomials.UT 3.1.a - Simplify and evaluate monomial expressions and formulas.

UT 3.1.b - Add and subtract polynomials.

Skill Area 10 - Algebra Skill 13 - A12 - Polynomials: Addition and subtraction

UT 3.1.c - Multiply monomials by a polynomial.UT 3.1.d - Multiply binomials. Skill Area 10 - Algebra Skill 14 - A13 - Polynomials:

Multiplication and divisionUT 3.1.e - Simplify the quotient of monomials using positive exponents.

UT 3.2 - Solve and interpret linear equations and inequalities in various situations including real-world problems.UT 3.2.a - Solve single-variable linear equations and inequalities algebraically and graphically.



UT 3.2.b - Solve real-world problems involving constant rates of change.



Skill Area 9 - Word Problems Skill 31 - W42 - Word problems: Ratios

UT 3.2.c - Solve equations for a specified variable.UT 3.2.d - Solve proportions that include algebraic first-degree expressions.UT 3.3 - Solve and interpret pairs of linear equations and inequalities.UT 3.3.a - Solve systems of two linear equations graphically and algebraically with and without technology.

Skill Area 10 - Algebra Skill 15 - A14 - Solve system of 2 equations (2 unknowns)

UT 3.3.b - Determine the number of possible solutions for a system of two linear equations.


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UT 3.3.c - Graph a system of linear inequalities and identify the solution.

UT 3.4 - Factor polynomials with common monomial factors and factor simple quadratic expressions.

UT 3.4.a - Find the greatest common monomial factor of a polynomial.

Skill Area 10 - Algebra Skill 19 - A18 - Factor common term from binomial expression

UT 3.4.b - Factor trinomials with integer coefficients of the form x² + bx + c.UT 3.4.c - Factor the difference of two squares and perfect square trinomials.UT 3.5 - Solve quadratic equations using factoring or by taking square roots.UT 3.5.a - Solve quadratic equations that can be simplified to the form x² = a where a is greater than or equal to 0 by taking square roots.

Skill Area 10 - Algebra Skill 16 - A15 - Quadratic equations: Solve using square root rule

UT 3.5.b - Solve quadratic equations using factoring.

Skill Area 10 - Algebra Skill 17 - A16 - Quadratic equations: Solve by factoring

UT 3.5.c - Write a quadratic equation when given the solutions.UT 4 - Students will understand concepts from statistics and apply statistical methods to solve problems.

UT 4.1 - Summarize, display, and analyze bivariate data.UT 4.1.a - Collect, record, organize, and display a set of data with at least two variables.UT 4.1.b - Determine whether the relationship between two variables is approximately linear or non-linear by examination of a scatter plot.

UT 4.1.c - Characterize the relationship between two linear related variables as having positive, negative, or approximately zero correlation.UT 4.2 - Estimate, interpret, and use lines fit to bivariate data.UT 4.2.a - Estimate the equation of a line of best fit to make and test conjectures.


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UT 4.2.b - Interpret the slope and y-intercept of a line through data.UT 4.2.c - Predict y-values for given x-values when appropriate using a line fitted to bivariate numerical data.


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Agency Tag Set NameUtah, Math, 2007, Geometry, Core Curriculum, State Department of EducationStandard Skill Area Description Skill DescriptionUT 1 - Students will use algebraic, spatial, and logical reasoning to solve geometry problems.UT 1.1 - Use inductive and deductive reasoning to develop mathematical arguments.UT 1.1.a - Write conditional statements, converses, and inverses, and determine the truth value of these statements.UT 1.1.b - Formulate conjectures using inductive reasoning.UT 1.1.c - Prove a statement false by using a counterexample.UT 1.2 - Analyze characteristics and properties of angles.

Skill Area 6 - Geometry Skill 24 - G17 - Use properties of parallel lines

UT 1.2.a - Use accepted geometric notation for lines, segments, rays, angles, similarity, and congruence.

UT 1.2.b - Identify and determine relationships in adjacent, complementary, supplementary, or vertical angles and linear pairs.

Skill Area 6 - Geometry Skill 25 - G18 - Use properties of intersecting lines

Skill 27 - G20 - Vertical and supplementary angles

UT 1.2.c - Classify angle pairs formed by two lines and a transversal.UT 1.2.d - Prove relationships in angle pairs.UT 1.2.e - Prove lines parallel or perpendicular using slope or angle relationships.UT 1.3 - Analyze characteristics and properties of triangles.UT 1.3.a - Prove congruency and similarity of triangles using postulates and theorems.UT 1.3.b - Prove the Pythagorean Theorem in multiple ways, find missing sides of right triangles using the Pythagorean Theorem, and determine whether a triangle is a right triangle using the converse of the Pythagorean Theorem.


UT 1.3.c - Prove and apply theorems involving isosceles triangles.

UT 1.3.d - Apply triangle inequality theorems.



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Agency Tag Set NameUtah, Math, 2007, Geometry, Core Curriculum, State Department of EducationStandard Skill Area Description Skill Description


UT 1.3.e - Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle, and justify the concurrency theorems.

UT 1.4 - Analyze characteristics and properties of polygons and circles.

UT 1.4.a - Use examples and counterexamples to classify subsets of quadrilaterals.UT 1.4.b - Prove properties of quadrilaterals using triangle congruence relationships, postulates, and theorems.UT 1.4.c - Derive, justify, and use formulas for the number of diagonals, lines of symmetry, angle measures, perimeter, and area of regular polygons.UT 1.4.d - Define radius, diameter, chord, secant, arc, sector, central angle, inscribed angle, and tangent of a circle, and solve problems using their properties.UT 1.4.e - Show the relationship between intercepted arcs and inscribed or central angles, and find their measures.UT 1.5 - Perform basic geometric constructions, describing and justifying the procedures used.UT 1.5.a - Investigate geometric relationships using constructions.UT 1.5.b - Copy and bisect angles and segments.UT 1.5.c - Construct perpendicular and parallel lines.UT 1.5.d - Justify procedures used to construct geometric figures.UT 1.5.e - Discover and investigate conjectures about geometric properties using constructions.UT 1.6 - Analyze characteristics and properties of three-dimensional figures.UT 1.6.a - Identify and classify prisms, pyramids, cylinders and cones based on the shape of their base(s).


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UT 1.6.b - Identify three-dimensional objects from different perspectives using nets, cross-sections, and two-dimensional views.

UT 1.6.c - Describe the symmetries of three-dimensional figures.

UT 1.6.d - Describe relationships between the faces, edges, and vertices of polyhedra.UT 2 - Students will use the language and operations of algebra to explore geometric relationships with coordinate geometry.UT 2.1 - Describe the properties and attributes of lines and line segments using coordinate geometry.

UT 2.1.a - Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes.

UT 2.1.b - Find the distance between two given points and find the coordinates of the midpoint.UT 2.1.c - Write an equation of a line perpendicular or a line parallel to a line through a given point.UT 2.2 - Describe spatial relationships using coordinate geometry.UT 2.2.a - Graph a circle given the equation in the form(x - h)² + (y - k)² = r², and write the equation when given the graph.UT 2.2.b - Determine whether points in a set are collinear.UT 3 - Students will extend concepts of proportion and similarity to trigonometric ratios.UT 3.1 - Use triangle relationships to solve problems.UT 3.1.a - Solve problems using the properties of special right triangles, e.g., 30°, 60°, 90° or 45°, 45°, 90°.

UT 3.1.b - Identify the trigonometric relationships of sine, cosine, and tangent with the appropriate ratio of sides of a right triangle.


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UT 3.1.c - Express trigonometric relationships using exact values and approximations.UT 3.2 - Use the trigonometric ratios of sine, cosine, and tangent to represent and solve for missing parts of triangles.UT 3.2.a - Find the angle measure in degrees when given the trigonometric ratio.UT 3.2.b - Find the trigonometric ratio given the angle measure in degrees, using a calculator.UT 3.2.c - Find unknown measures of right triangles using sine, cosine, and tangent functions and inverse trigonometric functions.UT 4 - Students will use algebraic, spatial, and logical reasoning to solve measurement problems.UT 4.1 - Find measurements of plane and solid figures.UT 4.1.a - Find linear and angle measures in real-world situations using appropriate tools or technology.

UT 4.1.b - Develop surface area and volume formulas for polyhedra, cones, and cylinders.UT 4.1.c - Determine perimeter, area, surface area, lateral area, and volume for prisms, cylinders, pyramids, cones, and spheres when given the formulas.


UT 4.1.d - Calculate or estimate the area of an irregular region.UT 4.1.e - Find the length of an arc and the area of a sector when given the angle measure and radius.

UT 4.2 - Solve real-world problems using visualization and spatial reasoning.UT 4.2.a - Solve problems using the Pythagorean Theorem and its converse.


UT 4.2.b - Solve problems using the distance formula.UT 4.2.c - Solve problems involving trigonometric ratios.UT 4.2.d - Solve problems involving geometric probability.


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Documents

Utah State Standards Alignments Grades One through Geometrydoc.renlearn.com/KMNet/R004058517GGD313.pdf · UT 1.2.b - Divide sets of objects into two, three, or four parts of equal