utah standards alignment kindergarten through grade...

Utah Standards Alignment Kindergarten through Grade Twelve

Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other countries. P.O. Box 8036 • Wisconsin Rapids, WI 54495-8036 Phone: (800) 338-4204 • Fax: (715) 424-4242 www.renlearn.com

© 2011 by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the express written consent of Renaissance Learning, Inc.

Any standards referenced in this document are the property of their respective copyright holders.

ii

Utah Standards Alignment

Standards list with Aligned Product Skills

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

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

Kindergarten ................................................................1

Grade 1 ................................................................4

Grade 2 ................................................................9

Grade 3 ..............................................................15

Grade 4 ..............................................................22

Grade 5 ..............................................................32

Grade 6 ..............................................................42

Grade 7 ..............................................................51

Pre-Algebra .............................................................63

Algebra 1 .............................................................76

Geometry ..............................................................82

iii

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

P.O. Box 8036 Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204 Fax: (715) 424-4242

www.renlearn.com

Agency Tag Set NameUtah, Math, 2007, Kindergarten, Core Curriculum, State Department of EducationStandard Domain Description Skill DescriptionUT 1 - Students will understand simple number concepts and relationships.UT 1.1 - Identify and use whole numbers up to 30.UT 1.1.a - Represent whole numbers using concrete, pictorial, and symbolic representations.

Domain 1 - Number and Operations (NO)

Skill 1 - Count objects to 20

UT 1.1.b - Order a set of up to ten objects and use ordinal numbers from first to tenth to identify the position of the object in the chosen order.


Skill 5 - Answer a question involving an ordinal number up to "tenth"

UT 1.1.c - Use one-to-one correspondence when counting a set of objects and develop a strategy for keeping track of counted and uncounted objects.



UT 1.2 - Identify and use simple relationships among whole numbers up to 30.UT 1.2.a - Estimate quantities in a set of objects using multiples of 10 as benchmark numbers.UT 1.2.b - Compose and decompose quantities to establish a relationship between the parts and the whole.

UT 1.2.c - Recognize 5 or 10 as a part of the part-whole relationship of numbers.UT 1.2.d - Compare sets of objects and determine whether they have the same, fewer, or more objects.

UT 1.3 - Model, describe, and illustrate meanings of addition and subtraction for whole numbers less than ten.UT 1.3.a - Demonstrate the joining and separating of sets of objects to solve problems.UT 1.3.b - Describe the joining or separating of sets with informal language when using models.UT 1.3.c - Record pictorially the results from joining or separating of sets.UT 2 - Students will sort and classify objects as well as recognize and create simple patterns.

Standards List with Aligned Product SkillsProduct NameSTAR Math Enterprise

STAR Math Enterprise Kindergarten

050411Page 1 of 86

Agency Tag Set NameUtah, Math, 2007, Kindergarten, Core Curriculum, State Department of EducationStandard Domain Description Skill Description


UT 2.1 - Identify, sort, and classify objects according to common attributes.UT 2.1.a - Sort objects into groups by attribute and identify which attribute was used.

Domain 3 - Geometry and Measurement (GM)

Skill 413 - Identify a shape with given attributes

UT 2.1.b - Describe multiple ways to sort and classify a group of objects.

UT 2.2 - Identify, duplicate, describe, and extend simple repeating and growing patterns.UT 2.2.a - Identify and describe simple repeating patterns with numbers and shapes.UT 2.2.b - Duplicate and extend simple repeating patterns with numbers and shapes.UT 2.2.c - Describe simple growing patterns with shapes.UT 2.2.d - Identify simple patterns in the environment.UT 3 - Students will understand basic geometry and measurement concepts as well as collect and organize data.UT 3.1 - Identify and create simple geometric shapes and describe simple spatial relationships.UT 3.1.a - Identify, name, describe, and draw circles, triangles, rectangles, and squares in various sizes and orientations.


Skill 414 - Identify a circle, a triangle, a square, or a rectangle

Skill 479 - Compare common objects to basic shapes

UT 3.1.b - Combine shapes to create two-dimensional objects (e.g., using a triangle and square to create a picture of a house).UT 3.1.c - Use words to describe position and distance.


Skill 415 - Use basic terms to describe position

UT 3.1.d - Investigate two- and three-dimensional shapes including hexagons, trapezoids, spheres, cubes, and cones.UT 3.2 - Identify and use measurable attributes of objects and units of measurement.UT 3.2.a - Identify clocks and calendars as tools that measure time.


050411Page 2 of 86

Agency Tag Set NameUtah, Math, 2007, Kindergarten, Core Curriculum, State Department of EducationStandard Domain Description Skill Description


UT 3.2.b - Identify a day, week, and month on a calendar and name the days of the week in order.

UT 3.2.c - Identify pennies, nickels, dimes, and quarters as units of money.


Skill 407 - Identify a coin or the value of a coin

UT 3.2.d - Compare two objects by measurable attributes (i.e., length, weight) and order several objects by measurable attributes (i.e., length, weight).


Skill 412 - Compare objects using the vocabulary of measurement

UT 3.3 - Collect and organize simple data.UT 3.3.a - Pose questions and gather data about self and surroundings.

UT 3.3.b - Organize data obtained from sorting and classifying objects.

Domain 4 - Data Analysis, Statistics, and Probability (SP)

Skill 541 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)


050411Page 3 of 86

Agency Tag Set NameUtah, Math, 2007, First Grade, Core Curriculum, State Department of EducationStandard Domain 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 22 - Relate a whole number to the word form of the number to 100

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


Skill 6 - Identify a number to 20 represented by a point on a number lineSkill 7 - Locate a number to 20 on a number line

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


Skill 13 - Count objects grouped in tens and ones

Skill 20 - Represent a 2-digit number as tens and onesSkill 21 - Determine the 2-digit number represented as tens and ones

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.


Skill 23 - Compare whole numbers to 100 using words

Skill 24 - Order whole numbers to 100 in ascending order

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 8 - Determine one more than or one less than a given number

Skill 9 - Determine one more than or one less than a given number across decadesSkill 10 - Determine ten more than or ten less than a given number

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


Skill 2 - Complete a sequence of numbers to 10Skill 3 - Count on by ones from a number less than 100Skill 4 - Count back by ones from a number less than 20


STAR Math Enterprise Grade 1

050411Page 4 of 86

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


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

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 57 - Add or subtract zero to or from any number less than 100

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 47 - Determine equivalent forms of a number, up to 10

Skill 49 - Know basic addition facts to 10 plus 10Skill 50 - Know basic subtraction facts to 20 minus 10

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


Skill 68 - Add three 1-digit numbers

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.

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


Skill 11 - Count by 2s to 50 starting from a multiple of 2


050411Page 5 of 86



Skill 12 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively

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., "Triangle" + 4 = 7).


Skill 62 - WP: Determine a basic addition-fact number sentence for a given situation

Skill 63 - WP: Determine a basic subtraction-fact number sentence for a given situation

Domain 2 - Algebra (AL) Skill 335 - Determine a missing addend in a basic addition-fact number sentenceSkill 336 - WP: Determine a missing addend in a basic addition-fact number sentenceSkill 337 - Determine a missing subtrahend in a basic subtraction-fact number sentenceSkill 338 - WP: Determine a missing subtrahend in a basic subtraction-fact number sentence

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.


050411Page 6 of 86



UT 3.1.a - Name, create, and sort geometric plane figures (i.e., circle, triangle, rectangle, square, trapezoid, rhombus, parallelogram, hexagon).


Skill 480 - Identify figures that are the same size and shape

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 417 - Identify a common solid shape

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 407 - Identify a coin or the value of a coin

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


Skill 446 - 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.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.


Skill 541 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)Skill 542 - Use a pictograph to represent data (1 symbol = more than 1 object)


050411Page 7 of 86



UT 3.3.b - Describe and interpret data.


Skill 520 - Read a tally chart

Skill 521 - Read a 2-category tally chart


050411Page 8 of 86

Agency Tag Set NameUtah, Math, 2007, Second Grade, Core Curriculum, State Department of EducationStandard Domain 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 20 - Represent a 2-digit number as tens and ones

Skill 26 - Represent a 3-digit number as hundreds, tens, and ones

Skill 27 - Determine the 3-digit number represented as hundreds, tens, and onesSkill 28 - Recognize equivalent forms of a 3-digit number using hundreds, tens, and onesSkill 29 - Represent a 3-digit whole number in expanded form

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


Skill 25 - Identify the place of a digit in a 3-digit number

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 23 - Compare whole numbers to 100 using words

Skill 24 - Order whole numbers to 100 in ascending orderSkill 31 - Compare whole numbers to 1,000 using the symbols <, >, and =

Skill 32 - Order whole numbers to 1,000 in ascending or descending order

UT 1.1.e - Identify and describe even and odd whole numbers.


Skill 18 - Identify odd and even numbers less than 100

UT 1.2 - Use unit fractions to identify parts of the whole and parts of a set.



050411Page 9 of 86

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


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

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 49 - Know basic addition facts to 10 plus 10

Skill 50 - Know basic subtraction facts to 20 minus 10

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 53 - Add a 2-digit number and a 1-digit number without regrouping

Skill 55 - Add two 2-digit numbers without regroupingSkill 56 - Subtract a 1-digit number from a 2-digit number without regroupingSkill 57 - Add or subtract zero to or from any number less than 100Skill 58 - Subtract a 2-digit number from a 2-digit number without regrouping


050411Page 10 of 86



Skill 69 - Determine a number pair that totals 100Skill 70 - Add a 2-digit number and a 1- or 2-digit number with regrouping

Skill 72 - Add 2- and 3-digit numbers with no more than one regrouping

Skill 73 - Add two 3-digit numbers with one regroupingSkill 74 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingSkill 75 - WP: Subtract a 1- or 2-digit number from a 2-digit number with one regroupingSkill 76 - Subtract a 1- or 2-digit number from a 3-digit number with one regrouping

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


Skill 71 - WP: Add a 2-digit number and a 1- or 2-digit number with regrouping

Skill 77 - Subtract a 3-digit number from a 3-digit number with one regrouping

Domain 2 - Algebra (AL) Skill 337 - Determine a missing subtrahend in a basic subtraction-fact 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.


Skill 14 - Complete a skip pattern starting from a multiple of 2, 5, or 10

Skill 15 - Complete a skip pattern of 2 or 5 starting from any numberSkill 16 - Complete a skip pattern of 10 starting from any numberSkill 86 - Use a multiplication sentence to represent an area or an array model

UT 1.4.b - Represent division as fair shares using concrete objects or pictures.


050411Page 11 of 86



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).


Skill 11 - Count by 2s to 50 starting from a multiple of 2

Skill 12 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectivelySkill 13 - Count objects grouped in tens and onesSkill 14 - Complete a skip pattern starting from a multiple of 2, 5, or 10

Skill 15 - Complete a skip pattern of 2 or 5 starting from any numberSkill 16 - Complete a skip pattern of 10 starting from any numberSkill 17 - Count on by 100s from any number

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


Skill 15 - Complete a skip pattern of 2 or 5 starting from any number

UT 2.2 - Model, represent, and interpret number relationships using mathematical symbols.UT 2.2.a - Recognize that "not equal to" 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.


050411Page 12 of 86



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 417 - Identify a common solid shape

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.


Skill 430 - Measure length in inches

Skill 431 - Measure length in centimeters

UT 3.2.b - Estimate and measure length by iterating a nonstandard or standard unit of measure.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.


Skill 430 - Measure length in inches


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¢).


050411Page 13 of 86



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 446 - Tell time to the hour and half hour

Skill 447 - Tell time to the quarter 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.


Skill 541 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)

Skill 542 - Use a pictograph to represent data (1 symbol = more than 1 object)Skill 543 - Use a bar graph with a y-axis scale by 2s to represent data

UT 3.3.d - Describe data represented on charts and graphs and answer simple questions related to data representations.


Skill 520 - Read a tally chart

Skill 521 - Read a 2-category tally chartSkill 522 - Answer a question using information from a 2-category tally chartSkill 523 - Read a simple pictograph

Skill 524 - Answer a question using information from a pictograph (1 symbol = more than 1 object)Skill 527 - Read a bar graphSkill 528 - Answer a question using information from a bar graphSkill 529 - Answer a question using information from a bar graph with a y-axis scale by 2s


050411Page 14 of 86

Agency Tag Set NameUtah, Math, 2007, Third Grade, Core Curriculum, State Department of EducationStandard Domain 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 35 - Represent a 4-digit whole number as thousands, hundreds, tens, and onesSkill 36 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Skill 37 - Represent a 4-digit whole number 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).


Skill 69 - Determine a number pair that totals 100


Skill 408 - Determine cent amounts that total a dollar

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 25 - Identify the place of a digit in a 3-digit number

UT 1.1.d - Order and compare whole numbers on a number line and use the symbols <, >, "not equal to," and = when comparing whole numbers.


Skill 31 - Compare whole numbers to 1,000 using the symbols <, >, and =

UT 1.1.e - Identify factors and multiples of whole numbers.UT 1.2 - Use fractions to describe and compare parts of the whole.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.



050411Page 15 of 86

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


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.


Skill 124 - Identify a fraction represented by a point on a number line

Skill 125 - Locate a fraction on a number lineSkill 126 - Compare fractions using modelsSkill 127 - Order fractions using models

UT 1.2.e - Find equivalent fractions using concrete and pictorial representations.


Skill 128 - Identify equivalent fractions using models

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).


Skill 86 - Use a multiplication sentence to represent an area or an array model

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 "Square" = 12 is the same as 12 ÷ 3 = "Square" and "Square" = 4).UT 1.3.d - Demonstrate the effect of place value when multiplying whole numbers by 10.


050411Page 16 of 86



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 66 - Estimate a sum or difference of 2- to 4-digit whole numbers using any method

Skill 73 - Add two 3-digit numbers with one regroupingSkill 74 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingSkill 76 - Subtract a 1- or 2-digit number from a 3-digit number with one regroupingSkill 78 - Add 3- and 4-digit whole numbers with regroupingSkill 80 - Subtract a 2- or 3-digit number from a 3-digit number with two regroupingsSkill 87 - Know basic multiplication facts to 10 x 10Skill 104 - Know basic division facts to 100 ÷ 10

Domain 2 - Algebra (AL) Skill 315 - WP: Determine the operation needed for a given situation

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 73 - Add two 3-digit numbers with one regrouping

Skill 74 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingSkill 76 - Subtract a 1- or 2-digit number from a 3-digit number with one regroupingSkill 78 - Add 3- and 4-digit whole numbers with regroupingSkill 81 - Subtract 3- and 4-digit whole numbers with regrouping


050411Page 17 of 86



Skill 186 - WP: Determine the amount of change from whole dollar amounts

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).


Skill 87 - Know basic multiplication facts to 10 x 10

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.

Domain 2 - Algebra (AL) Skill 304 - Extend a number pattern involving addition

Skill 305 - Extend a number pattern involving subtractionSkill 306 - Identify a missing figure in a growing pictorial or nonnumeric pattern


Skill 428 - Identify a missing figure in a geometric pattern

UT 2.1.b - Describe how patterns are extended using manipulatives, pictures, and numerical representations.

Domain 2 - Algebra (AL) Skill 303 - Determine the rule for an addition or subtraction number pattern

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 = "Triangle" + 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).


050411Page 18 of 86



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 57 - Add or subtract zero to or from any number less than 100

Skill 93 - Apply the distributive property to multiply a multi-digit number by a 1-digit number

UT 3 - Students will describe and analyze attributes of two-dimensional shapes.UT 3.1 - Describe and compare attributes of two-dimensional shapes.

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


Skill 422 - Classify an obtuse angle or an acute angle given a picture

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 482 - Determine the result of a flip, a turn, or a slide

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.

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


050411Page 19 of 86



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

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).


Skill 435 - Convert between inches, feet, and yards

Skill 436 - Convert between customary units of capacitySkill 437 - Convert within metric units of mass, length, and capacity

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.UT 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 436 - Convert between customary units of capacity

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


Skill 452 - Determine the perimeter of a triangleSkill 455 - WP: Determine the perimeter of a rectangle


050411Page 20 of 86



UT 4.2.d - Determine elapsed time in hours (e.g., 7:00 a.m. to 2:00 p.m.).

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 524 - Answer a question using information from a pictograph (1 symbol = more than 1 object)

Skill 525 - Read a tableSkill 526 - Answer a question using information from a tableSkill 528 - Answer a question using information from a bar graphSkill 530 - Read a line plotSkill 531 - Answer a question using information from a line plotSkill 532 - Read a circle graphSkill 533 - Answer a question using information from a circle graph

Skill 534 - Read a line graphSkill 535 - Answer a question using information from a line graphSkill 544 - Use a line plot to represent dataSkill 545 - Use a line graph to represent data

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.


050411Page 21 of 86

Agency Tag Set NameUtah, Math, 2007, Fourth Grade, Core Curriculum, State Department of EducationStandard Domain 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 35 - Represent a 4-digit whole number as thousands, hundreds, tens, and onesSkill 36 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Skill 37 - Represent a 4-digit whole number in expanded formSkill 41 - Determine the 4- or 5-digit whole number represented in expanded formSkill 42 - Represent a 5-digit whole number 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).


Skill 28 - Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones

Skill 69 - Determine a number pair that totals 100Skill 168 - Determine the decimal number from a pictorial model of tenths or hundredthsSkill 169 - Identify a pictorial model of tenths or hundredths of a decimal number

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 40 - Determine the value of a digit in a 6-digit number

Skill 177 - Identify the place of a digit in a decimal number through hundredths

UT 1.1.d - Divide regions, lengths, and sets of objects into equal parts using a variety of models and illustrations.


Skill 103 - WP: Divide objects into equal groups by sharing



050411Page 22 of 86

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


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.


Skill 122 - Determine a pictorial model of a fraction of a whole

Skill 123 - Determine a pictorial model of a fraction of a set of objects


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 31 - Compare whole numbers to 1,000 using the symbols <, >, and =

Skill 32 - Order whole numbers to 1,000 in ascending or descending orderSkill 126 - Compare fractions using modelsSkill 127 - Order fractions using modelsSkill 131 - Compare fractions with unlike denominatorsSkill 132 - Order fractions with unlike denominators in ascending or descending orderSkill 173 - Compare decimal numbers through the hundredths placeSkill 174 - Order decimal numbers through the hundredths place

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).


050411Page 23 of 86



UT 1.2.d - Identify equivalences between fractions and decimals by connecting models to symbols.


Skill 165 - Determine the decimal number equivalent to a fraction model

UT 1.2.e - Generate equivalent fractions and simplify fractions using models, pictures, and symbols.



Skill 163 - Determine the fraction equivalent to a decimal number model

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.


Skill 86 - Use a multiplication sentence to represent an area or an array model

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).


Skill 133 - Add fractions with like 1-digit denominators

Skill 135 - Subtract fractions with like 1-digit denominators


050411Page 24 of 86



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 91 - Estimate the product of a 2-digit number and a 1-digit number

Skill 92 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000Skill 94 - Multiply a 3- or 4-digit whole number by a 1-digit whole number

Skill 96 - WP: Multiply a 2-digit whole number by a 1- or 2-digit whole numberSkill 98 - WP: Multiply a multi-digit whole number by a 1-digit whole numberSkill 107 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Skill 108 - WP: Solve a 2-step whole number problem using more than one operationSkill 109 - WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient

Skill 110 - Estimate the quotient of a 2-digit whole number divided by a 1-digit whole number with no remainder in the quotientSkill 116 - WP: Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotient

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.


050411Page 25 of 86



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 134 - WP: Add fractions with like denominators no greater than 10 and simplify the sum

Skill 136 - WP: Subtract fractions with like denominators no greater than 10Skill 137 - WP: Subtract fractions with like denominators no greater than 10 and simplify the difference

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 87 - Know basic multiplication facts to 10 x 10

Skill 104 - Know basic division facts to 100 ÷ 10

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


Skill 89 - Multiply a 2-digit whole number by a 1-digit whole number with no regrouping

Skill 95 - Multiply a 2-digit whole number by a 1- or 2-digit whole number with regroupingSkill 97 - Multiply a 2-digit whole number by a 2-digit whole number

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


Skill 106 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientSkill 115 - Divide a 2- or 3-digit whole number by a 1-digit whole number with a remainder in the quotient

Domain 2 - Algebra (AL) Skill 317 - Use a division sentence to represent objects divided into equal groups


050411Page 26 of 86



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 133 - Add fractions with like 1-digit denominators

Skill 135 - Subtract fractions with like 1-digit denominators

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.

Domain 2 - Algebra (AL) Skill 303 - Determine the rule for an addition or subtraction number pattern

Skill 309 - Determine a rule that relates two variables

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.

Domain 2 - Algebra (AL) Skill 304 - Extend a number pattern involving addition

Skill 305 - Extend a number pattern involving subtraction

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?).


050411Page 27 of 86



UT 2.2.b - Express single-operation problem situations as equations and solve the equation.

Domain 2 - Algebra (AL) Skill 339 - Determine a missing addend in a number sentence involving 2-digit numbersSkill 341 - Solve a 1-step equation involving whole numbers

UT 2.2.c - Recognize that a symbol represents the same number throughout an equation or expression (e.g., "Triangle" + "Triangle" = 8; thus, "Triangle" = 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 419 - Identify parallel lines

Skill 420 - Identify intersecting line segmentsSkill 426 - Identify perpendicular lines

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


Skill 421 - Classify a right angle or a straight angle given a picture

Skill 422 - Classify an obtuse angle or an acute angle given a picture

Skill 423 - Classify an angle given its measure

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


Skill 498 - Relate the radius to the diameter in a circle

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


Skill 481 - Determine lines of symmetry

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

Domain 2 - Algebra (AL) Skill 318 - Determine the ordered pair of a point in the first quadrant

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


050411Page 28 of 86



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.


Skill 482 - Determine the result of a flip, a turn, or a slide

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).

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

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.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.


050411Page 29 of 86



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.


Skill 460 - Determine the area of a square

Skill 461 - Determine the area of a rectangle given the length and width

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).


Skill 465 - Determine the area of a right triangle

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.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 534 - Read a line graph

Skill 535 - Answer a question using information from a line graphSkill 536 - Read a double-bar graph

Skill 537 - Answer a question using information from a double-bar graph


050411Page 30 of 86



UT 5.1.c - Represent data using frequency tables, bar graphs, line plots, and stem and leaf plots.


Skill 545 - Use a line graph to represent data

Skill 546 - Use a double-bar graph to represent data

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).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.


050411Page 31 of 86

Agency Tag Set NameUtah, Math, 2007, Fifth Grade, Core Curriculum, State Department of EducationStandard Domain 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 29 - Represent a 3-digit whole number in expanded formSkill 30 - Relate a 3-digit whole number to its word formSkill 35 - Represent a 4-digit whole number as thousands, hundreds, tens, and onesSkill 36 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Skill 37 - Represent a 4-digit whole number in expanded formSkill 38 - Relate a 4- or 5-digit whole number to its word formSkill 41 - Determine the 4- or 5-digit whole number represented in expanded formSkill 42 - Represent a 5-digit whole number in expanded formSkill 45 - Relate a 7- to 10-digit whole number to the word form of the number

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 161 - Convert a mixed number to an improper fraction

Skill 162 - Convert an improper fraction to a mixed numberSkill 163 - Determine the fraction equivalent to a decimal number modelSkill 164 - Convert a fraction or mixed number in hundredths or thousandths to a decimal numberSkill 165 - Determine the decimal number equivalent to a fraction model



050411Page 32 of 86

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


Skill 166 - Convert a decimal number in hundredths or thousandths to a fractionSkill 187 - Determine money amounts that total $10Skill 242 - Convert a decimal number to a percentageSkill 243 - Convert a percentage to its decimal equivalent

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



Skill 125 - Locate a fraction on a number lineSkill 129 - Locate a mixed number on a number lineSkill 170 - Identify a decimal number to tenths represented by a point on a number lineSkill 171 - Locate a decimal number to tenths on a 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.


Skill 130 - Identify a fraction equivalent to a given fractionSkill 131 - Compare fractions with unlike denominators

UT 1.2.b - Order integers, fractions (including mixed numbers), and decimals using a variety of methods, including the number line.


Skill 127 - Order fractions using models

Skill 129 - Locate a mixed number on a number lineSkill 132 - Order fractions with unlike denominators in ascending or descending orderSkill 174 - Order decimal numbers through the hundredths place

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 129 - Locate a mixed number on a number line


050411Page 33 of 86



Skill 161 - Convert a mixed number to an improper fractionSkill 162 - Convert an improper fraction to a 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 164 - Convert a fraction or mixed number in hundredths or thousandths to a decimal number

Skill 165 - Determine the decimal number equivalent to a fraction model

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


Skill 145 - Add fractions with unlike denominators that have factors in common and simplify the sum

Skill 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the difference


050411Page 34 of 86



Skill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominators

UT 1.4 - Model and illustrate meanings of multiplication and division.UT 1.4.a - Represent division-with-remainder using whole numbers, decimals, or fractions.


Skill 118 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotientSkill 119 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed number

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.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 150 - Estimate the sum of mixed numbers

Skill 158 - Estimate the sum of fractions with unlike 1-digit denominatorsSkill 159 - Estimate the difference between fractions with unlike 1-digit denominatorsSkill 160 - Estimate the difference between mixed numbers with unlike denominators


050411Page 35 of 86



Skill 176 - Round a decimal number to a specified place through hundredthsSkill 190 - Estimate the sum of a whole number and a decimal number

Skill 191 - Estimate the sum of two decimal numbersSkill 194 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 199 - Estimate the difference of two decimal numbersSkill 200 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 203 - Estimate the difference of a whole number and a decimal number

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?).


Skill 121 - WP: Divide a whole number and interpret the remainder

UT 1.6 - Demonstrate proficiency with multiplication and division of whole numbers and compute problems involving addition, subtraction, and multiplication of decimals and fractions.UT 1.6.a - Multiply multi-digit whole numbers by a two-digit whole number with fluency, using efficient procedures.


Skill 97 - Multiply a 2-digit whole number by a 2-digit whole number

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


Skill 106 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientSkill 115 - Divide a 2- or 3-digit whole number by a 1-digit whole number with a remainder in the quotient

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


Skill 192 - Add two decimal numbers of differing places to thousandths

Skill 195 - Add decimal numbers and whole numbers


050411Page 36 of 86



Skill 196 - Subtract two decimal numbers of differing places to thousandthsSkill 201 - Subtract a decimal number from a whole number

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


Skill 133 - Add fractions with like 1-digit denominatorsSkill 135 - Subtract fractions with like 1-digit denominatorsSkill 145 - Add fractions with unlike denominators that have factors in common and simplify the sum

Skill 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominators

UT 1.6.e - Multiply fractions. Domain 1 - Number and Operations (NO)

Skill 207 - Multiply a fraction by a fractionSkill 209 - Multiply a mixed number by a fraction

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.

Domain 2 - Algebra (AL) Skill 310 - Determine the variable expression with one operation for a table of paired numbers


050411Page 37 of 86



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 424 - Identify line segments

Skill 426 - Identify perpendicular lines

Skill 427 - Identify raysUT 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.


050411Page 38 of 86



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.

Domain 2 - Algebra (AL) Skill 319 - Determine the ordered pair of a point in any quadrant

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.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.


Skill 469 - Determine the area of a complex shape

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 487 - Determine the volume of a rectangular prism

Skill 488 - WP: Determine the volume of a rectangular prism


050411Page 39 of 86



Skill 491 - Determine the volume of a rectangular or a triangular 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.


Skill 489 - Determine the surface area of a rectangular prism

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).


Skill 534 - Read a line graph

Skill 535 - Answer a question using information from a line graphSkill 536 - Read a double-bar graph

Skill 537 - Answer a question using information from a double-bar graph

Skill 544 - Use a line plot to represent dataSkill 545 - Use a line graph to represent dataSkill 546 - Use a double-bar graph to represent data

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 550 - Determine the mean of a set of whole number data

Skill 551 - Determine the median of an odd number of data valuesSkill 552 - Determine the median of an even number of data values

UT 5.2 - Apply basic concepts of probability.


050411Page 40 of 86



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).


050411Page 41 of 86

Agency Tag Set NameUtah, Math, 2007, Sixth Grade, Core Curriculum, State Department of EducationStandard Domain 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 268 - Evaluate or represent an expression of a whole number raised to a whole number power

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 46 - Convert a whole number greater than 10 to scientific notation

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


Skill 129 - Locate a mixed number on a number lineSkill 171 - Locate a decimal number to tenths on a 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.


Skill 131 - Compare fractions with unlike denominators

Skill 132 - Order fractions with unlike denominators in ascending or descending orderSkill 167 - Compare numbers in decimal and fractional formsSkill 178 - Compare decimal numbers of differing places to thousandthsSkill 179 - Order decimal numbers of differing places to thousandths in ascending or descending orderSkill 183 - Order numbers in decimal and fractional forms



050411Page 42 of 86

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


UT 1.2.c - Find equivalent forms for common fractions, decimals, percents, and ratios, including repeating or terminating decimals.


Skill 130 - Identify a fraction equivalent to a given fraction

Skill 161 - Convert a mixed number to an improper fractionSkill 162 - Convert an improper fraction to a mixed numberSkill 164 - Convert a fraction or mixed number in hundredths or thousandths to a decimal numberSkill 166 - Convert a decimal number in hundredths or thousandths to a fractionSkill 242 - Convert a decimal number to a percentageSkill 243 - Convert a percentage to its decimal equivalent

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


Skill 244 - Convert a decimal number in thousandths to a percentage

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 142 - Identify the prime factors of a 2-digit number

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 143 - Determine the greatest common factor of two whole numbers

Skill 144 - Determine the least common multiple of two whole numbers

UT 1.4 - Model and illustrate meanings of operations and describe how they relate.


050411Page 43 of 86



UT 1.4.a - Relate fractions to multiplication and division and use this relationship to explain procedures for multiplying and dividing fractions.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.


Skill 119 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed numberSkill 204 - Divide a whole number by a 1-digit whole number resulting in a decimal quotient through thousandths

Skill 205 - Divide a whole number by a 2-digit whole number resulting in a decimal quotient through thousandths

Skill 206 - WP: Divide a whole number by a 1- or 2-digit whole number resulting in a decimal quotient

UT 1.5 - Solve problems involving multiple steps.UT 1.5.a - Select appropriate methods to solve a multi-step problem involving multiplication and division of fractions and decimals.


Skill 216 - WP: Solve a 2-step problem involving fractions

Skill 217 - WP: Solve a multi-step problem involving fractions or mixed numbersSkill 240 - WP: Solve a 2-step problem involving decimalsSkill 241 - WP: Solve a multi-step problem involving decimal numbers

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 245 - WP: Use a unit rate, with a whole number or whole cent value, to solve a problemSkill 246 - WP: Determine a unit rate with a whole number valueSkill 247 - Determine if ratios are equivalent


050411Page 44 of 86



Skill 248 - WP: Determine if ratios are equivalentSkill 249 - WP: Determine a part given a ratio and the whole where the whole is less than 50Skill 250 - WP: Determine the whole given a ratio and a part where the whole is less than 50Skill 251 - Solve a proportion involving whole numbersSkill 252 - WP: Solve a proportion

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 95 - Multiply a 2-digit whole number by a 1- or 2-digit whole number with regroupingSkill 118 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotientSkill 119 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed numberSkill 205 - Divide a whole number by a 2-digit whole number resulting in a decimal quotient through thousandths

Skill 221 - Multiply a decimal number through thousandths by a whole numberSkill 226 - Multiply decimal numbers less than one in hundredths or thousandthsSkill 229 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal places

Skill 231 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole numberSkill 233 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths


050411Page 45 of 86



Skill 234 - Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed

Skill 235 - Divide decimal numbersUT 1.6.b - Add, subtract, multiply, and divide fractions and mixed numbers.



Skill 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominatorsSkill 207 - Multiply a fraction by a fractionSkill 208 - Multiply a mixed number by a whole numberSkill 209 - Multiply a mixed number by a fractionSkill 211 - Divide a fraction by a fractionSkill 212 - Divide a whole number by a fraction resulting in a fractional quotientSkill 214 - Divide a fraction by a whole number resulting in a fractional quotientSkill 218 - Multiply mixed numbersSkill 219 - Divide mixed numbers

UT 1.6.c - Add and subtract integers. Domain 1 - Number and Operations (NO)

Skill 276 - Add integers

Skill 277 - Subtract integersUT 2 - Students will use patterns, relations, and algebraic expressions to represent and analyze mathematical problems and number relationships.


050411Page 46 of 86



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.


Skill 311 - WP: Determine the variable expression with one operation for a table of paired numbersSkill 312 - WP: Generate a table of paired numbers based on a variable expression with one operation

Skill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportionSkill 352 - WP: Use a 2-variable linear equation to represent a situationSkill 353 - Use a 2-variable equation to construct an input-output table

Skill 354 - Use a 2-variable equation to represent a relationship expressed in a table

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

Domain 2 - Algebra (AL) Skill 320 - Use a table to represent the values from a first-quadrant graph

Skill 354 - Use a 2-variable equation to represent a relationship expressed in a table

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

Domain 2 - Algebra (AL) Skill 321 - Determine the graph of a 1-operation linear functionSkill 322 - Determine the graph of a 2-operation linear functionSkill 353 - Use a 2-variable equation to construct an input-output table

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.

Domain 2 - Algebra (AL) Skill 341 - Solve a 1-step equation involving whole numbers

Skill 344 - Solve a proportion involving decimals


050411Page 47 of 86



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).

Domain 2 - Algebra (AL) Skill 331 - Evaluate a 2-variable expression, with two or three operations, using whole number substitution

Skill 332 - WP: Evaluate a 1- or 2-variable expression or formula using whole numbers

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 501 - Determine a missing angle measure in 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.UT 3.2.c - Reflect a polygon across either the x- or y-axis and identify the location of the new vertices.


050411Page 48 of 86



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 473 - Determine the area of a 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.UT 4.2.d - Determine when it is appropriate to estimate or use precise measurement when solving problems.


050411Page 49 of 86



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.


Skill 547 - Use a circle graph to represent percentage data

Skill 549 - Use a scatter plot to organize data

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.


Skill 555 - Determine the probability of a single event

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.


050411Page 50 of 86

Agency Tag Set NameUtah, Math, 2007, Math 7, Core Curriculum, State Department of EducationStandard Domain 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.


Skill 267 - Evaluate a numerical expression of four or more operations, with parentheses, using order of operations

Skill 268 - Evaluate or represent an expression of a whole number raised to a whole number power

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


Skill 46 - Convert a whole number greater than 10 to 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.



Skill 182 - Estimate a decimal number from its position on a number line

UT 1.2.b - Compare pairs of rational numbers in different forms.


Skill 167 - Compare numbers in decimal and fractional forms

UT 1.2.c - Order rational numbers with and without a number line.


Skill 132 - Order fractions with unlike denominators in ascending or descending orderSkill 179 - Order decimal numbers of differing places to thousandths in ascending or descending orderSkill 183 - Order numbers in decimal and fractional forms

UT 1.3 - Explain relationships and equivalences among rational numbers.



050411Page 51 of 86

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


UT 1.3.a - Find equivalent forms for common fractions, decimals, percents, and ratios, including repeating or terminating decimals.


Skill 130 - Identify a fraction equivalent to a given fraction

Skill 161 - Convert a mixed number to an improper fractionSkill 162 - Convert an improper fraction to a mixed numberSkill 164 - Convert a fraction or mixed number in hundredths or thousandths to a decimal numberSkill 166 - Convert a decimal number in hundredths or thousandths to a fractionSkill 242 - Convert a decimal number to a percentageSkill 243 - Convert a percentage to its decimal equivalent

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 282 - Evaluate the positive square root of a perfect square

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.


050411Page 52 of 86



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 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominatorsSkill 188 - Determine the sum of a whole number and a decimal number to hundredthsSkill 192 - Add two decimal numbers of differing places to thousandths

Skill 195 - Add decimal numbers and whole numbersSkill 196 - Subtract two decimal numbers of differing places to thousandthsSkill 201 - Subtract a decimal number from a whole numberSkill 207 - Multiply a fraction by a fractionSkill 208 - Multiply a mixed number by a whole numberSkill 209 - Multiply a mixed number by a fractionSkill 211 - Divide a fraction by a fraction


050411Page 53 of 86



Skill 212 - Divide a whole number by a fraction resulting in a fractional quotientSkill 214 - Divide a fraction by a whole number resulting in a fractional quotientSkill 218 - Multiply mixed numbersSkill 219 - Divide mixed numbersSkill 220 - Multiply a decimal number through thousandths by 10, 100, or 1,000Skill 221 - Multiply a decimal number through thousandths by a whole numberSkill 226 - Multiply decimal numbers less than one in hundredths or thousandthsSkill 227 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Skill 228 - Divide a decimal number by 10, 100, or 1,000Skill 229 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal places



Skill 235 - Divide decimal numbersSkill 237 - Divide a decimal number by a decimal number through thousandths, rounded quotient if neededSkill 276 - Add integersSkill 277 - Subtract integersSkill 279 - Multiply integersSkill 280 - Divide integers


050411Page 54 of 86



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


Skill 142 - Identify the prime factors of a 2-digit number

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


Skill 147 - WP: Add fractions with unlike 1-digit denominators

Skill 151 - WP: Add mixed numbers with unlike denominatorsSkill 154 - WP: Subtract fractions with unlike 1-digit denominatorsSkill 157 - WP: Subtract mixed numbers with unlike denominatorsSkill 189 - WP: Determine the sum of a decimal number and a whole numberSkill 197 - WP: Add or subtract decimal numbers through thousandthsSkill 198 - WP: Add or subtract a decimal number through thousandths and a whole numberSkill 202 - WP: Subtract a decimal number from a whole number

Skill 213 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionSkill 215 - WP: Multiply or divide a fraction by a fractionSkill 216 - WP: Solve a 2-step problem involving fractionsSkill 217 - WP: Solve a multi-step problem involving fractions or mixed numbersSkill 222 - WP: Multiply a decimal number through thousandths by a whole numberSkill 225 - WP: Multiply two decimal numbersSkill 230 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberSkill 232 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededSkill 238 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if needed


050411Page 55 of 86



Skill 240 - WP: Solve a 2-step problem involving decimalsSkill 241 - WP: Solve a multi-step problem involving decimal numbers

UT 1.5.d - Determine if an answer is reasonable using estimation.


Skill 150 - Estimate the sum of mixed numbersSkill 158 - Estimate the sum of fractions with unlike 1-digit denominatorsSkill 159 - Estimate the difference between fractions with unlike 1-digit denominatorsSkill 160 - Estimate the difference between mixed numbers with unlike denominatorsSkill 190 - Estimate the sum of a whole number and a decimal number

Skill 191 - Estimate the sum of two decimal numbersSkill 193 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any methodSkill 194 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 199 - Estimate the difference of two decimal numbersSkill 200 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 203 - Estimate the difference of a whole number and a decimal numberSkill 223 - WP: Estimate the product of two decimalsSkill 239 - WP: Estimate the quotient of two decimals

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 245 - WP: Use a unit rate, with a whole number or whole cent value, to solve a problemSkill 246 - WP: Determine a unit rate with a whole number value


050411Page 56 of 86



Skill 248 - WP: Determine if ratios are equivalentSkill 259 - WP: Determine a unit rate

Skill 260 - WP: Use a unit rate to solve a problem

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


Skill 288 - WP: Determine the percent of decrease applied to a number

Skill 289 - WP: Determine the percent of increase applied to a numberSkill 290 - WP: Determine the result of applying a percent of decrease to a valueSkill 291 - WP: Determine the result of applying a percent of increase to a valueSkill 294 - WP: Determine a given percent of a numberSkill 295 - WP: Determine the percent one number is of another numberSkill 296 - WP: Determine a number given a part and a decimal percentage or a percentage more than 100%Skill 297 - WP: Estimate a given percent of a numberSkill 298 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%Skill 299 - WP: Determine a percent of a whole number using percents less than 100Skill 300 - WP: Determine a whole number given a part and a percent

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


Skill 252 - WP: Solve a proportion

Skill 261 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50Skill 262 - WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50


050411Page 57 of 86



Skill 263 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50Skill 264 - WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50Skill 265 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Skill 266 - WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50


Skill 440 - WP: Solve a measurement problem involving a proportional relationshipSkill 499 - Determine a missing dimension given two similar shapes

Skill 500 - WP: Solve a problem involving similar shapes

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.


050411Page 58 of 86



UT 3.1.a - Write a variable expression to identify pattern relationships, and use those expressions to make predictions.


Skill 311 - WP: Determine the variable expression with one operation for a table of paired numbersSkill 312 - WP: Generate a table of paired numbers based on a variable expression with one operation

UT 3.1.b - Translate verbal expressions into algebraic expressions.

Domain 2 - Algebra (AL) Skill 355 - Use a 1-variable, 1-step equation to represent a verbal statement

UT 3.1.c - Simplify and evaluate algebraic expressions.

Domain 2 - Algebra (AL) Skill 331 - Evaluate a 2-variable expression, with two or three operations, using whole number substitutionSkill 332 - WP: Evaluate a 1- or 2-variable expression or formula using whole numbersSkill 333 - Evaluate a 2-variable expression, with two or three operations, using integer substitution

Skill 375 - Simplify an algebraic expression by combining like terms

UT 3.1.d - Show that performing the same operation on both sides of an equation will produce an equivalent equation.UT 3.1.e - Solve single-variable linear equations and inequalities of the form ax + b = c, ax + b < c, or ax + b > c.

Domain 2 - Algebra (AL) Skill 343 - Solve a 2-step linear equation involving integers

Skill 346 - Solve a 2-step equation involving rational numbersSkill 394 - Solve a 2-step linear inequality in one variable

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.


050411Page 59 of 86



UT 3.2.c - Model real-world problems using graphs, tables, equations, manipulatives, and pictures.

Domain 2 - Algebra (AL) Skill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportion

Skill 352 - WP: Use a 2-variable linear equation to represent a situationSkill 356 - WP: Use a 1-variable 1-step equation to represent a situation

Skill 359 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operationsSkill 360 - WP: Use a 2-variable equation with rational coefficients to represent a situation

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 424 - Identify line segments

Skill 425 - Identify perpendicular or parallel lines when given a transversal

UT 4.1.b - Draw, label, and describe relationships among vertical, adjacent, complementary, and supplementary angles.UT 4.1.c - Draw, label, and describe attributes of angles, triangles, and quadrilaterals.


Skill 423 - Classify an angle given its measure

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.

UT 4.2.b - Measure length, area, volume, and angles to appropriate levels of precision.


Skill 438 - Identify an angle given its measure


050411Page 60 of 86



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 453 - Determine the perimeter of a rectangle given a picture showing length and width

Skill 454 - Determine the perimeter of a squareSkill 455 - WP: Determine the perimeter of a rectangleSkill 464 - WP: Determine the area of a square or rectangleSkill 465 - Determine the area of a right triangleSkill 466 - Use a formula to determine the area of a triangleSkill 467 - WP: Determine the area of a triangleSkill 471 - Determine the area of a quadrilateralSkill 473 - Determine the area of a 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.


Skill 487 - Determine the volume of a rectangular prism

Skill 488 - WP: Determine the volume of a rectangular prismSkill 489 - Determine the surface area of a rectangular prismSkill 490 - WP: Find the surface area of a rectangular prismSkill 491 - Determine the volume of a rectangular or a triangular prism

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.


050411Page 61 of 86



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.


Skill 547 - Use a circle graph to represent percentage data


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.


050411Page 62 of 86

Agency Tag Set NameUtah, Math, 2007, Pre-Algebra, Core Curriculum, State Department of EducationStandard Domain 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.

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


Skill 276 - Add integers

Skill 277 - Subtract integersSkill 279 - Multiply integersSkill 280 - Divide integers

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 146 - Add fractions with unlike 1-digit denominatorsSkill 148 - Add fractions with unlike denominators that have no factors in commonSkill 149 - Add mixed numbers with unlike denominatorsSkill 152 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceSkill 153 - Subtract fractions with unlike 1-digit denominatorsSkill 155 - Subtract fractions with unlike denominators that have no factors in commonSkill 156 - Subtract mixed numbers with unlike denominatorsSkill 188 - Determine the sum of a whole number and a decimal number to hundredthsSkill 192 - Add two decimal numbers of differing places to thousandths

Skill 195 - Add decimal numbers and whole numbersSkill 196 - Subtract two decimal numbers of differing places to thousandthsSkill 201 - Subtract a decimal number from a whole number


STAR Math Enterprise Grades 7 - 8

050411Page 63 of 86

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


Skill 207 - Multiply a fraction by a fractionSkill 208 - Multiply a mixed number by a whole numberSkill 209 - Multiply a mixed number by a fractionSkill 211 - Divide a fraction by a fractionSkill 212 - Divide a whole number by a fraction resulting in a fractional quotientSkill 214 - Divide a fraction by a whole number resulting in a fractional quotientSkill 218 - Multiply mixed numbersSkill 219 - Divide mixed numbersSkill 220 - Multiply a decimal number through thousandths by 10, 100, or 1,000Skill 221 - Multiply a decimal number through thousandths by a whole numberSkill 224 - Multiply two decimal numbersSkill 226 - Multiply decimal numbers less than one in hundredths or thousandthsSkill 227 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Skill 228 - Divide a decimal number by 10, 100, or 1,000Skill 229 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal places




050411Page 64 of 86



Skill 235 - Divide decimal numbersSkill 237 - Divide a decimal number by a decimal number through thousandths, rounded quotient if needed

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


Skill 150 - Estimate the sum of mixed numbers

Skill 158 - Estimate the sum of fractions with unlike 1-digit denominatorsSkill 159 - Estimate the difference between fractions with unlike 1-digit denominatorsSkill 160 - Estimate the difference between mixed numbers with unlike denominatorsSkill 190 - Estimate the sum of a whole number and a decimal number

Skill 191 - Estimate the sum of two decimal numbersSkill 193 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any methodSkill 194 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 199 - Estimate the difference of two decimal numbersSkill 200 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeSkill 203 - Estimate the difference of a whole number and a decimal numberSkill 223 - WP: Estimate the product of two decimalsSkill 239 - WP: Estimate the quotient of two decimals

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


050411Page 65 of 86



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 132 - Order fractions with unlike denominators in ascending or descending orderSkill 179 - Order decimal numbers of differing places to thousandths in ascending or descending orderSkill 183 - Order numbers in decimal and fractional forms

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 282 - Evaluate the positive square root of a perfect square

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.


Skill 267 - Evaluate a numerical expression of four or more operations, with parentheses, using order of operations

UT 1.3.c - Solve problems involving rational numbers, percents, and proportions.


Skill 147 - WP: Add fractions with unlike 1-digit denominators

Skill 151 - WP: Add mixed numbers with unlike denominatorsSkill 154 - WP: Subtract fractions with unlike 1-digit denominators


050411Page 66 of 86



Skill 157 - WP: Subtract mixed numbers with unlike denominatorsSkill 189 - WP: Determine the sum of a decimal number and a whole numberSkill 197 - WP: Add or subtract decimal numbers through thousandthsSkill 198 - WP: Add or subtract a decimal number through thousandths and a whole numberSkill 202 - WP: Subtract a decimal number from a whole number

Skill 213 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionSkill 215 - WP: Multiply or divide a fraction by a fractionSkill 216 - WP: Solve a 2-step problem involving fractionsSkill 217 - WP: Solve a multi-step problem involving fractions or mixed numbersSkill 222 - WP: Multiply a decimal number through thousandths by a whole numberSkill 225 - WP: Multiply two decimal numbersSkill 230 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberSkill 232 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededSkill 236 - WP: Divide a whole number by a decimal numberSkill 238 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededSkill 240 - WP: Solve a 2-step problem involving decimalsSkill 241 - WP: Solve a multi-step problem involving decimal numbersSkill 245 - WP: Use a unit rate, with a whole number or whole cent value, to solve a problemSkill 246 - WP: Determine a unit rate with a whole number value


050411Page 67 of 86



Skill 249 - WP: Determine a part given a ratio and the whole where the whole is less than 50Skill 250 - WP: Determine the whole given a ratio and a part where the whole is less than 50Skill 252 - WP: Solve a proportionSkill 259 - WP: Determine a unit rate

Skill 260 - WP: Use a unit rate to solve a problemSkill 261 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50Skill 262 - WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50

Skill 263 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50Skill 264 - WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50Skill 265 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Skill 266 - WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50

Skill 288 - WP: Determine the percent of decrease applied to a numberSkill 289 - WP: Determine the percent of increase applied to a numberSkill 290 - WP: Determine the result of applying a percent of decrease to a valueSkill 291 - WP: Determine the result of applying a percent of increase to a valueSkill 294 - WP: Determine a given percent of a numberSkill 295 - WP: Determine the percent one number is of another number


050411Page 68 of 86



Skill 296 - WP: Determine a number given a part and a decimal percentage or a percentage more than 100%Skill 298 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%Skill 299 - WP: Determine a percent of a whole number using percents less than 100Skill 300 - WP: Determine a whole number given a part and a percent

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.


Skill 247 - Determine if ratios are equivalentSkill 248 - WP: Determine if ratios 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.

Domain 2 - Algebra (AL) Skill 344 - Solve a proportion involving decimals

Skill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportion

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


Skill 253 - Determine the percent a whole number is of another whole number

Skill 255 - Determine a given percent of a numberSkill 288 - WP: Determine the percent of decrease applied to a numberSkill 289 - WP: Determine the percent of increase applied to a number


050411Page 69 of 86



Skill 290 - WP: Determine the result of applying a percent of decrease to a valueSkill 291 - WP: Determine the result of applying a percent of increase to a valueSkill 293 - Determine a percent of a number given a percent that is not a whole percentSkill 294 - WP: Determine a given percent of a numberSkill 295 - WP: Determine the percent one number is of another numberSkill 296 - WP: Determine a number given a part and a decimal percentage or a percentage more than 100%Skill 298 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%Skill 299 - WP: Determine a percent of a whole number using percents less than 100Skill 300 - WP: Determine a whole number given a part and a percentSkill 301 - Determine the percent one number is of another numberSkill 302 - Determine a number given a part and a decimal percentage or a percentage more than 100%

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


Skill 245 - WP: Use a unit rate, with a whole number or whole cent value, to solve a problemSkill 246 - WP: Determine a unit rate with a whole number valueSkill 259 - WP: Determine a unit rate

Skill 260 - WP: Use a unit rate to solve a problem

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.


050411Page 70 of 86



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.UT 3.1.b - Describe simple patterns using a mathematical rule or algebraic expression.

Domain 2 - Algebra (AL) Skill 311 - WP: Determine the variable expression with one operation for a table of paired numbers

UT 3.1.c - Create and extend simple numerical and visual patterns.

Domain 2 - Algebra (AL) Skill 312 - WP: Generate a table of paired numbers based on a variable expression with one operation

Skill 314 - Find a specified term in an arithmetic sequence

UT 3.2 - Evaluate, simplify, and solve algebraic expressions, equations, and inequalities.UT 3.2.a - Evaluate algebraic expressions, including those with whole number exponents, when given values for the variable(s).

Domain 2 - Algebra (AL) Skill 331 - Evaluate a 2-variable expression, with two or three operations, using whole number substitutionSkill 332 - WP: Evaluate a 1- or 2-variable expression or formula using whole numbersSkill 333 - Evaluate a 2-variable expression, with two or three operations, using integer substitution


050411Page 71 of 86



UT 3.2.b - Simplify algebraic expressions using the order of operations, algebraic properties, and exponent rules.

Domain 2 - Algebra (AL) Skill 375 - Simplify an algebraic expression by combining like terms

Skill 379 - Apply the product of powers property to a monomial algebraic expressionSkill 382 - Apply the quotient of powers property to monomial algebraic expressions

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.


Skill 342 - Solve a 1-step linear equation involving integersSkill 343 - Solve a 2-step linear equation involving integersSkill 345 - Solve a 1-step equation involving rational numbersSkill 346 - Solve a 2-step equation involving rational numbersSkill 347 - WP: Solve a problem involving a 1-variable, 2-step equationSkill 348 - Solve a 1-variable linear equation with the variable on both sidesSkill 393 - Determine the solution set of a 1-variable linear inequalitySkill 394 - Solve a 2-step linear inequality in one variableSkill 395 - WP: Solve a problem involving a 2-step linear inequality in one variableSkill 397 - Solve a 1-variable linear inequality with the variable on both sides

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.


050411Page 72 of 86



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.

Domain 2 - Algebra (AL) Skill 351 - WP: Use a 2-variable equation to represent a situation involving a direct proportion

Skill 352 - WP: Use a 2-variable linear equation to represent a situationSkill 356 - WP: Use a 1-variable 1-step equation to represent a situation

Skill 359 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operationsSkill 360 - WP: Use a 2-variable equation with rational coefficients to represent a situation

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 435 - Convert between inches, feet, and yardsSkill 436 - Convert between customary units of capacitySkill 437 - Convert within metric units of mass, length, and capacity

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

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.




050411Page 73 of 86



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.


Skill 492 - WP: Solve a problem involving the volume of a geometric solid

Skill 493 - WP: Determine the surface area of a geometric solid

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.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.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.


050411Page 74 of 86



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 550 - Determine the mean of a set of whole number data

Skill 551 - Determine the median of an odd number of data valuesSkill 552 - Determine the median of an even number of data valuesSkill 553 - Determine the median of a set of data given a frequency table

UT 5.2.e - Use graphical representations and numerical summaries to answer questions and interpret data.


Skill 538 - Answer a question using information from a histogram

Skill 539 - Answer a question using information from a scatter plot

Skill 540 - Answer a question using information from a circle graph using percentage calculations


050411Page 75 of 86

Agency Tag Set NameUtah, Math, 2007, Algebra 1, Core Curriculum, State Department of EducationStandard Domain 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.


Skill 287 - Approximate the location of a square root on a number line

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.


Skill 273 - Simplify a monomial numerical expression involving the square root of a whole number

UT 1.2.b - Evaluate and simplify numerical expressions containing rational numbers and square roots using the order of operations.


Skill 272 - Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbers

UT 1.2.c - Compute solutions to problems, represent answers in exact form, and determine the reasonableness of answers.


Skill 241 - WP: Solve a multi-step problem involving decimal numbers

Skill 288 - WP: Determine the percent of decrease applied to a numberSkill 289 - WP: Determine the percent of increase applied to a numberSkill 292 - WP: Answer a question involving a fraction and a percent



050411Page 76 of 86

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


Skill 298 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%Skill 299 - WP: Determine a percent of a whole number using percents less than 100Skill 300 - WP: Determine a whole number given a part and a percent

UT 1.2.d - Calculate the measures of the sides of a right triangle using the Pythagorean Theorem.


Skill 502 - Use the Pythagorean theorem to determine a length

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

Domain 2 - Algebra (AL) Skill 370 - Determine the slope of a line given two points on the line or the graph of the lineSkill 372 - Determine the slope of a line given an equation of the line

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.

Domain 2 - Algebra (AL) Skill 367 - WP: Interpret the meaning of the slope of a graphed line

Skill 368 - WP: Interpret the meaning of the y-intercept of a graphed line

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.

Domain 2 - Algebra (AL) Skill 311 - WP: Determine the variable expression with one operation for a table of paired numbers

Skill 358 - Determine a linear equation in two variables that represents a table of values

UT 2.2.b - Represent linear equations in slope-intercept form, y = mx + b, and standard form, Ax+ By =C.

Domain 2 - Algebra (AL) Skill 361 - Determine the slope-intercept form or the standard form of a linear equation


050411Page 77 of 86



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.

Domain 2 - Algebra (AL) Skill 367 - WP: Interpret the meaning of the slope of a graphed line

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.

Domain 2 - Algebra (AL) Skill 362 - Determine an equation of a line given the slope and y-intercept of the lineSkill 364 - Determine an equation for a line given the slope of the line and a point on the line that is not the y-interceptSkill 365 - Determine an equation of a line given two points on the line

UT 2.3.b - Approximate the equation of a line given the graph of a line.

Domain 2 - Algebra (AL) Skill 363 - Determine an equation for a line given a graph

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

Domain 2 - Algebra (AL) Skill 366 - Determine the x- or y-intercept of a line given its graph

Skill 369 - Determine the x- or y-intercept of a line given an equation

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.

Domain 2 - Algebra (AL) Skill 324 - Determine the graph of a line using given information

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.

Domain 2 - Algebra (AL) Skill 376 - Multiply two monomial algebraic expressions

Skill 379 - Apply the product of powers property to a monomial algebraic expressionSkill 380 - Apply the power of a power property to a monomial algebraic expressionSkill 381 - Apply the power of a product property to a monomial algebraic expression


050411Page 78 of 86



Skill 382 - Apply the quotient of powers property to monomial algebraic expressionsSkill 383 - Apply the power of a quotient property to monomial algebraic expressions

UT 3.1.b - Add and subtract polynomials.

Domain 2 - Algebra (AL) Skill 384 - Add or subtract polynomial expressions

UT 3.1.c - Multiply monomials by a polynomial.UT 3.1.d - Multiply binomials. Domain 2 - Algebra (AL) Skill 377 - Multiply two binomials

Skill 385 - Multiply two binomials of the form (ax +/- b)(cx +/- d)

UT 3.1.e - Simplify the quotient of monomials using positive exponents.

Domain 2 - Algebra (AL) Skill 382 - Apply the quotient of powers property to monomial algebraic expressions

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.


Skill 342 - Solve a 1-step linear equation involving integersSkill 343 - Solve a 2-step linear equation involving integersSkill 345 - Solve a 1-step equation involving rational numbersSkill 346 - Solve a 2-step equation involving rational numbersSkill 348 - Solve a 1-variable linear equation with the variable on both sidesSkill 393 - Determine the solution set of a 1-variable linear inequalitySkill 394 - Solve a 2-step linear inequality in one variableSkill 396 - Determine the graph of the solutions to a 2-step linear inequality in one variableSkill 397 - Solve a 1-variable linear inequality with the variable on both sides

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

UT 3.2.c - Solve equations for a specified variable.

Domain 2 - Algebra (AL) Skill 349 - Rewrite an equation to solve for a specified variable

UT 3.2.d - Solve proportions that include algebraic first-degree expressions.

Domain 2 - Algebra (AL) Skill 344 - Solve a proportion involving decimals


050411Page 79 of 86



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.

Domain 2 - Algebra (AL) Skill 373 - Solve a system of linear equations in two variables using any method

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

Domain 2 - Algebra (AL) Skill 386 - Factor the GCF from a polynomial 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.

Domain 2 - Algebra (AL) Skill 402 - Solve a quadratic equation using the square root rule

UT 3.5.b - Solve quadratic equations using 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.


050411Page 80 of 86



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.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.


050411Page 81 of 86

Agency Tag Set NameUtah, Math, 2007, Geometry, Core Curriculum, State Department of EducationStandard Domain 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.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.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.


Skill 483 - Identify a triangle congruence postulate that justifies a congruence statementSkill 485 - Identify a triangle similarity postulate that justifies a similarity statement

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.


Skill 502 - Use the Pythagorean theorem to determine a length

Skill 503 - WP: Use the Pythagorean theorem to find a length or a distance



050411Page 82 of 86

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


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

UT 1.3.d - Apply triangle inequality theorems.


Skill 507 - Solve a problem using inequalities in a triangle

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.


Skill 477 - WP: Determine a length or an area involving a sector of a circle

Skill 478 - Determine the measure of an arc or an angle given the area of a sector of a circleSkill 516 - Solve a problem involving the length of an arcSkill 517 - Determine the length of a line segment, the measure of an angle, or the measure of an arc using a tangent to a circleSkill 518 - Determine a length using a line segment tangent to a circle and the radius that intersects the tangent

UT 1.4.e - Show the relationship between intercepted arcs and inscribed or central angles, and find their measures.


Skill 515 - Determine the measure of an arc or a central angle using the relationship between the arc and the central angleSkill 519 - Determine the measure of an arc or an angle using the relationship between an inscribed angle and its intercepted arc


050411Page 83 of 86



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).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.


Skill 505 - Determine the midpoint of a line segment given the coordinates of the endpoints

UT 2.1.c - Write an equation of a line perpendicular or a line parallel to a line through a given point.


050411Page 84 of 86



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°.


Skill 514 - Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

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

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.


050411Page 85 of 86



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



Skill 493 - WP: Determine the surface area of a geometric solidSkill 496 - Determine the surface area of a sphereSkill 497 - Determine the volume of a sphere or hemisphere

UT 4.1.d - Calculate or estimate the area of an irregular region.


Skill 469 - Determine the area of a complex shape

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.


Skill 503 - WP: Use the Pythagorean theorem to find a length or a distance

UT 4.2.b - Solve problems using the distance formula.


Skill 504 - Solve a problem involving the distance formula

UT 4.2.c - Solve problems involving trigonometric ratios.UT 4.2.d - Solve problems involving geometric probability.


050411Page 86 of 86

utah standards alignment kindergarten through grade...

Documents