montana standards alignment 2009 ... - doc.renlearn.com

Montana Standards Alignment 2009 Essential Learning Expectations, produced by the State Department of Education

Kindergarten through Grades: 9-12

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

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

www.renlearn.com

Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending

registration in the United States and other countries.

http://www.renlearn.com/

© 2012 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.

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Montana 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 and the product skills aligned to

those standards. This alignment report shows the breadth of standards coverage for the purpose

and focus of this product.

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

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

First Grade ........................................................................................................ 4

Second Grade ....................................................................................................... 8

Third Grade ........................................................................................................ 14

Fourth Grade ....................................................................................................... 23

Fifth Grade ........................................................................................................ 28

Sixth Grade ........................................................................................................ 35

Seventh Grade ...................................................................................................... 43

Eighth Grade ....................................................................................................... 49

Grades: 9-12 ....................................................................................................... 57

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Note to Educator:

Thank you for your interest in Renaissance Learning technology. At Renaissance

Learning, we recognize the impact that standards and assessment reform have on schools.

We share the concerns of educators and administrators that students perform well and

that teachers have the resources they need to support their efforts to address standards and

assessments.

Renaissance Learning provides alignment reports to customers to show how the skills

within each product align to the skills within academic standards. The alignment report

presents all of the academic math standards for a specific state/agency with the aligned

Renaissance Learning product skills indented below each standard.

Academic standards encompass the entire set of learning and expectations that teachers

are responsible for. Renaissance Learning recognizes that teachers are the key to using

products to address the entire set of standards. Renaissance Learning products are ideally

suited to support teachers and academic standards. The Renaissance Learning alignment

report supports teachers in this role by clearly identifying specific product skills that are

aligned to the multiple skills within the standards.

P.O. Box 8036

Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204

Fax: (715) 424-4242

www.renlearn.com

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On the alignment report you will see the word “Core” next to some of the skills. Core

skills are the most critical mathematics skills for a student to learn at a grade level. They

are key building blocks in a student’s mathematics education. Students need to have

proficiency with core skills to be successful in math at their grade levels and to progress

in the grades that follow. Core skills are indicated on Renaissance Learning’s research-

based and empirically validated Core Progress math learning progression. Core Progress

Math identifies the continuum of concepts and skills needed for success in math. The

continuum begins with early numeracy and progresses to the level of mathematics

required for college and careers. All of the skills in the Core Progress Math contribute to

STAR Math Enterprise Assessment. Alignments for STAR Math Enterprise include

alignments to the Common Core State Standards (CCSS) Mathematics Standards.

In the alignment report, you will notice that most skills have a grade-level indicator at the

end of the text. In addition to these grade-level skills, the report includes skills that are

not grade specific and do not have a grade-level indicator. These skills are designated

Overall Product Skills. They are skills that all students gain through use of the product.

We hope this report answers your questions regarding the alignment of Renaissance

Learning technology and materials to standards. The complete alignment strategy

document is available. The Math document is number R39616. If you have any questions

about the alignment report, please feel free to call us at (800) 338-4204.

Sincerely,

Renaissance Learning

STAR Math Enterprise

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Compare objects using the vocabulary of measurement [Grade 1] Core Skill

Geometry and Measurement Order objects according to size [Early Numeracy]

MT 1.5.A - Order and compare objects by length or weight using both direct and indirect methods.

MT 1.5 - Select and apply appropriate standard units and tools to measure length, time, and temperature within relevant scientific and cultural situations, including those of Montana American Indians.

MT 1.4 - Identify and model common fractions such as, tenths, fourths, thirds, and halves; and decimals such as money and place value to 0.001; and recognize and compare equivalent representations.

Numbers and Operations Compose an equivalent number out of two numbers by using pictures [Early Numeracy]

Decompose a number into two numbers by using pictures [Early Numeracy]

MT 1.3.A - Use objects to show joining and separating problems.

MT 1.3 - Develop multiplication and division concepts, apply number and operation models and strategies, and reason and justify using properties of operations.

Know basic subtraction facts to 20 minus 10 [Grade 1] Core Skill

Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

Numbers and Operations Use turn-around facts to find the sum of two numbers [Early Numeracy]

WP: Use basic addition or subtraction facts to solve problems [Grade 1]

Core Skill

MT 1.2 - Estimate sums, differences, products, and quotients when solving problems. Add, subtract, multiply (three-digit by two-digit factors), and divide (two-digit dividends by one-digit divisors) to solve problems. Demonstrate fluency with basic facts.

Identify the object in a given ordinal position up to "tenth" [Early Numeracy]

Numbers and Operations Recognize ordinal numbers 1st - 10th [Early Numeracy]

Answer a question involving an ordinal number up to "tenth" [Grade 1]

MT 1.1.B - Compare and order sets of objects or numerals by both cardinal and ordinal meanings (i.e., first, second, third, last).

Numbers and Operations Count up to 10 objects [Early Numeracy]

Determine equivalent forms of a number, up to 10 [Grade 1] Core Skill

MT 1.1.A - Represent quantities with numbers up to 10; verbally, with manipulatives, and in writing.

MT 1.1 - Demonstrate relationships among whole numbers; identify place value up to 100,000 and compare numbers (e.g., greater than, less than, and equal to).

MT 1 - A student, applying reasoning and problem solving, will use number sense and operations to represent numbers in multiple ways, understand relationships among numbers and number systems, make reasonable estimates, and compute fluently within a variety of relevant cultural contexts, including those of Montana American Indians.

Kindergarten

MontanaEssential Learning Expectations

Kindergarten


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MT 4 - A student, applying reasoning and problem solving, will use algebraic concepts and procedures to understand processes involving number, operation, and variables and will use procedures and function concepts to model the quantitative and functional relationships that describe change within a variety of relevant cultural contexts, including those of Montana American Indians.

MT 3.5 - Define and determine area and perimeter of common polygons using concrete tools such as grid paper, objects, or technology and justify the strategy used.

MT 3.4 - Estimate and measure linear attributes of objects in metric units such as centimeters and meters and customary units such as inch, foot, and yard.

MT 3.3 - Use spatial reasoning to identify slides and flips of congruent figures within artistic and cultural contexts, including those of Montana American Indians.

MT 3.2.B - Use three-dimensional shapes to identify spheres, cubes and cylinders in their environment.

MT 3.2.A - Using concrete models, visually identify and describe spheres, cubes, and cylinders.

MT 3.2 - Describe attributes of three-dimensional shapes such as cubes and other rectangular prisms, pyramids, cylinders, cones, and spheres.

MT 3.1.B - Use two-dimensional shapes to represent objects in their environment.

Geometry and Measurement Identify a circle, a triangle, a square, or a rectangle [Grade 1] Core Skill

MT 3.1.A - Visually identify and describe squares, triangles, circles, and rectangles.

MT 3.1 - Describe, compare, and analyze attributes of two-dimensional shapes.

MT 3 - A student, applying reasoning and problem solving, will understand geometric properties, spatial relationships, and transformation of shapes, and will use spatial reasoning and geometric models to analyze mathematical situations within a variety of relevant and cultural contexts, including those of Montana American Indians.

MT 2.3 - Describe events from multicultural contexts, including those of Montana American Indians, as likely or unlikely and discuss the degree of likelihood using words such as certain, equally likely, and impossible.

MT 2.2.A - Describe one or more attributes in a set of data to solve problems.

MT 2.2 - Solve problems and make decisions using data descriptors such as minimum, maximum, median, and mode within scientific and cultural contexts, including those of Montana American Indians.

Geometry and Measurement Sort objects according to one attribute [Early Numeracy]

MT 2.1.A - Sort data by one or more attributes using manipulatives (e.g., Large, small; color; Does it roll? Does it stack?).

MT 2.1 - Collect, represent, and organize data in tables, dot plots, bar graphs, pictographs, and stem-and-leaf plots using technology when appropriate.

MT 2 - A student, applying reasoning and problem solving, will use data representation and analysis, simulations, probability, statistics, and statistical methods to evaluate information and make informed decisions within a variety of relevant cultural contexts, including those of Montana American Indians.

Compare and order objects by attributes of height or length [Grade 1]

Core Skill


Kindergarten


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MT 4.5 - Model problem situations with manipulatives or technology and use multiple representations such as words, pictures, tables, or graphs to draw conclusions using cultural contexts, including those of Montana American Indians.

Numbers and Operations Determine the value of a collection of like coins [Grade 1]

Determine the value of a collection of mixed coins [Grade 1]

MT 4.4.A - Demonstrate equivalence with multiple representations (e.g., manipulatives, scales, coins).

MT 4.4 - Develop an understanding of equivalence by expressing numbers, measures, and numerical expressions involving operations in a variety of ways.

MT 4.3 - Use number patterns to investigate properties of numbers such as even or odd and properties of operations such as commutative, associative, distributive, and the multiplicative and additive identities.

MT 4.2 - Use letters, boxes, or symbols to represent numbers in simple expressions or equations to demonstrate a basic understanding of variables.

Extend a repeating picture pattern [Grade 1]

Algebra Complete a picture pattern [Early Numeracy]

Extend a pictorial growth pattern [Grade 1]

MT 4.1.A - Identify, duplicate, and extend simple repeating and growing (e.g., AB, ABB, ABBB...) patterns using models.

MT 4.1 - Describe, extend, and make generalizations about geometric or numeric patterns.


Kindergarten


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MT 1.3.A - Use concrete models, including objects and number lines to represent addition and subtraction situations.


Algebra WP: Determine a basic addition- or subtraction-fact number sentence for a given situation [Grade 1]

Core Skill

Numbers and Operations Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

MT 1.2.B - Use a variety of strategies to determine basic addition and subtraction facts.

Add two 2-digit numbers without regrouping [Grade 1] Core Skill

Numbers and Operations Add a 2-digit and a 1-digit number without regrouping [Grade 1] Core Skill

Subtract a 1-digit number from a 2-digit number without regrouping [Grade 1]

Core Skill


Core Skill

MT 1.2.A - Demonstrate a strategy for solving one and two-digit addition and subtraction problems using concrete models.


Locate a number to 20 on a number line [Grade 1] Core Skill

Numbers and Operations Identify a number to 20 represented by a point on a number line [Grade 1]

Core Skill

MT 1.1.C - Represent numbers on the number line.

Determine the 2-digit number represented as tens and ones [Grade 1]

Core Skill

Numbers and Operations Represent a 2-digit number as tens and ones [Grade 1] Core Skill

Determine the value of a digit in a 2-digit number [Grade 1] Core Skill

MT 1.1.B - Model two-digit numbers in terms of tens and ones.

Order whole numbers to 100 in ascending order [Grade 1] Core Skill

Numbers and Operations Compare whole numbers to 100 using words [Grade 1] Core Skill

MT 1.1.A - Compare and order numbers to 100.



First Grade


First Grade


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Data Analysis, Statistics, and Probability

Use a pictograph to represent data (1 symbol = more than 1 object) [Grade 2]

Core Skill

MT 2.1.A - Use objects to display data in bar graphs or pictographs.



MT 1.5.B - Describe time using appropriate terminology when talking about daily life, science, and culture; including that of Montana American Indians.

Geometry and Measurement Tell time to the hour [Grade 1] Core Skill

MT 1.5.A - Identify hours on an analog clock.


MT 1.4.A - Model and identify part/whole relationships within context.


Add a 2-digit and a 1-digit number without regrouping [Grade 1] Core Skill

Add two 2-digit numbers without regrouping [Grade 1] Core Skill

WP: Use basic addition or subtraction facts to solve problems [Grade 1]

Core Skill

Numbers and Operations Determine equivalent forms of a number, up to 10 [Grade 1] Core Skill

Determine the missing portion in a partially screened (hidden) collection of up to 10 objects [Grade 1]

Core Skill

WP: Add or subtract a 1- and 2-digit number without regrouping [Grade 1]

Core Skill

WP: Add or subtract two 2-digit numbers without regrouping [Grade 1]

Core Skill


Core Skill


Core Skill

MT 1.3.C - Create addition and subtraction problems in context.

Overall Product Skills Use strategies to derive solutions for problems

MT 1.3.B - Use counting strategies and numeric reasoning to solve problems involving addition and subtraction.


First Grade


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Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectively [Grade 1]

Core Skill

Numbers and Operations Count by 2s to 50 starting from a multiple of 2 [Grade 1] Core Skill

MT 4.1.A - Identify and extend simple repeating (e.g., 4, a, 4, a, 4...) and growing (e.g., 3, 5, 7, 9...) number patterns.




Geometry and Measurement Compare objects using the vocabulary of measurement [Grade 1] Core Skill

MT 3.4.A - Estimate and measure the length of objects using non-standard units laid end-to-end (e.g., lay paper clips end-to-end and count how many using groups of tens and ones).



MT 3.2.B - Use three-dimensional shapes to identify rectangular prisms, pyramids and cones in their environment.

MT 3.2.A - Use models to visually identify and describe rectangular prisms, pyramids and cones.


Geometry and Measurement Compose a new shape out of two other shapes [Early Numeracy]

Decompose a shape into two new shapes [Early Numeracy]

MT 3.1.A - Compose and decompose figures using two-dimensional shapes and identify the attributes (e.g., build a hexagon using six equilateral triangles).




Numbers and Operations Compare sets of objects using words [Grade 1]

MT 2.2.A - Solve problems by counting and making comparisons of objects.


First Grade


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Algebra Extend a repeating picture pattern [Grade 1]

MT 4.5.A - Use models to describe how a pattern is changing (e.g., triangle, square, triangle; triangle, square, square, triangle; triangle, square, square, square, triangle).




MT 4.4.B - Exchange coins to show equivalence using pennies, nickles, and dimes.

Numbers and Operations Determine equivalent forms of a number, up to 10 [Grade 1] Core Skill

MT 4.4.A - Recognize and generate equivalent representations of a number with multiple addends and subtrahends.


Numbers and Operations Identify odd and even numbers less than 100 [Grade 1] Core Skill

MT 4.3.B - Use number patterns to justify a number as even and odd numbers.

Numbers and Operations Add zero to any number less than 100 [Grade 1]

MT 4.3.A - Use models to represent and justify zero as the identity for addition.


Determine a missing subtrahend in a basic subtraction-fact number sentence [Grade 1]

Core Skill

Algebra Determine a missing addend in a basic addition-fact number sentence [Grade 1]

Core Skill

WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence [Grade 1]

Core Skill

MT 4.2.A - Recognize and find unknowns represented by symbols (e.g., boxes, spaces, blanks, circles).


Complete a skip pattern starting from a multiple of 2, 5, or 10 [Grade 2]

Core Skill


First Grade


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MT 1.2.A - Use concrete models to estimate a quantity.




Determine cent amounts that total a dollar [Grade 2] Core Skill

MT 1.1.C - Identify, combine and compare values of money in coins to $1 and dollars to $100, including $1, $5, $10, and $20.

Compare whole numbers to 1,000 using the symbols <, >, and = [Grade 2]

Core Skill

Order whole numbers to 1,000 in ascending order [Grade 2] Core Skill

Order whole numbers to 1,000 in descending order [Grade 2] Core Skill

Compare whole numbers to 1,000 using words [Grade 2]

Numbers and Operations Read a whole number to 1,000 [Grade 2] Core Skill

MT 1.1.B - Read, write, compare and order multi-digit whole numbers to 1000.

Determine the result of changing a digit in a 3-digit whole number [Grade 2]

Model a number using hundreds, tens, and ones to 1,000 [Grade 2]

Numbers and Operations Determine the value of a digit in a 3-digit number [Grade 2]

Determine which digit is in a specified place in a 3-digit whole number [Grade 2]

Recognize a number from a model of hundreds, tens, and ones to 1,000 [Grade 2]

Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones [Grade 2]

Core Skill

Determine the 3-digit number represented as hundreds, tens, and ones [Grade 2]

Core Skill

Represent a 3-digit number as hundreds, tens, and ones [Grade 2] Core Skill

MT 1.1.A - Identify relationships between the digits and their place value to 1000, including expanded form.



Second Grade


Second Grade


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Geometry and Measurement Select the appropriate measurement tool for length, weight, temperature, time, or capacity [Grade 1]


MT 1.4.A - Model halves and quarters using money and time.


MT 1.3.B - Use models, properties and place value strategies to illustrate up to three digit addition and subtraction problems, including invented strategies that come from contextual clues.

MT 1.3.A - Describe and use mental math strategies for addition and subtraction.


Add two 2-digit numbers with regrouping, given a model [Grade 2]

Add two 2-digit numbers with regrouping [Grade 2] Core Skill

Add three 2-digit numbers with one regrouping, sum less than 100 [Grade 2]

Add two 3-digit numbers without regrouping [Grade 2]

Numbers and Operations Add two 2-digit numbers without regrouping [Grade 1] Core Skill


Core Skill

Determine a number pair that totals 100 [Grade 2] Core Skill

Add 2- and 3-digit numbers with no more than one regrouping [Grade 2]

Core Skill

Subtract a 1- or 2-digit number from a 3-digit number with one regrouping [Grade 2]

Core Skill

Subtract a 3-digit number from a 3-digit number with one regrouping [Grade 2]

Core Skill

Apply the inverse relationship between addition and subtraction with 2- and 3-digit numbers [Grade 2]

Add two 3-digit numbers with one regrouping [Grade 2] Core Skill



Core Skill

MT 1.2.C - Apply a successful strategy to add and subtract multi-digit whole numbers through three-digits with fluency.

Numbers and Operations Know basic addition facts to 10 plus 10 [Grade 1] Core Skill

Know basic subtraction facts to 20 minus 10 [Grade 1] Core Skill

MT 1.2.B - Recall basic addition facts through sums of 20 and related subtraction facts.


Second Grade


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Geometry and Measurement Determine the common attributes in a set of geometric shapes [Grade 1]

Core Skill


Determine the common attributes in a set of geometric shapes [Grade 1]

Core Skill

Geometry and Measurement Compare and order objects by attributes of height or length [Grade 1]

Core Skill




Determine if a situation is certain or impossible [Grade 3]

Determine which event is least likely or most likely to occur [Grade 3]


MT 2.2.A - Use the minimum, maximum, and range of a data set to solve problems pertaining to daily life, science, and culture; including that of Montana American Indians.



Read a multi-category tally chart [Grade 2]

Use a tally chart to represent data [Grade 2]

MT 2.1.A - Collect data and organize it in a table or chart.



Core Skill

Use a bar graph with a y-axis scale by 2s to represent data [Grade 2] Core Skill

Read a bar graph with a y-axis scale by 2s [Grade 2]



Tell time to the quarter hour [Grade 2] Core Skill

Geometry and Measurement Tell time to the half hour [Grade 1] Core Skill

MT 1.5.A - Identify time to the nearest half and quarter hour on an analog clock.


Second Grade


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Algebra Determine the rule for an addition or subtraction number pattern [Grade 2]

Core Skill

MT 4.1.A - Create and extend numeric and geometric patterns and relationships involving addition and subtraction.

Algebra Determine an addition or subtraction number pattern given a rule [Grade 2]

Determine the rule for an addition or subtraction number pattern [Grade 2]

Core Skill

Complete a skip pattern of 2, 5, or 10 starting from any number [Grade 2]

Core Skill

Count on by 100s from any number [Grade 2] Core Skill

Extend a number pattern involving addition [Grade 2] Core Skill

Determine a repeating pattern corresponding to the same pattern expressed using different elements [Grade 2]

Extend a number pattern [Grade 3]

Extend a number pattern involving subtraction [Grade 2] Core Skill

Extend a pattern given a table of related number pairs [Grade 2]



Core Skill


Core Skill



Geometry and Measurement Relate area to the number of square units [Grade 2]


MT 3.4.C - Select appropriate measurement tool and compare lengths to solve problems.

Measure length in centimeters [Grade 2] Core Skill

Geometry and Measurement Measure length in inches [Grade 2] Core Skill

MT 3.4.B - Estimate and measure length of objects using centimeters and inches.

MT 3.4.A - Describe the inverse relationship between the size of a unit and the number of units needed to measure a given object.




Second Grade


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MT 4.4.A - Use models to justify the transitive property of equality (e.g., since 1+ 6 = 7 and 7 = 2+ 5 then 1+ 6 = 2 + 5).



Core Skill


Complete a skip pattern of 2, 5, or 10 starting from any number [Grade 2]

Core Skill


Core Skill

MT 4.3.B - Describe numeric patterns using skip counting by 2's, 5's, and 10's.

MT 4.3.A - Use models to represent the commutative and associative properties of addition.


WP: Determine a missing addend or subtrahend in a basic addition- or subtraction-fact number sentence [Grade 1]

Core Skill

Determine a missing subtrahend in a basic subtraction-fact number sentence [Grade 1]

Core Skill

Determine a missing addend in a number sentence involving 2-digit numbers [Grade 2]

Algebra Determine a missing addend in a basic addition-fact number sentence [Grade 1]

Core Skill

Determine a missing subtrahend in a number sentence involving 2-digit numbers [Grade 2]

MT 4.2.B - Solve equations in which the unknown number appears in a variety of positions. (e.g., 2 + 3 = ___ + 1).

Algebra WP: Determine a basic addition- or subtraction-fact number sentence for a given situation [Grade 1]

Core Skill

MT 4.2.A - Use contextual information to create single-digit number and picture sentences using basic addition and subtraction facts.


Algebra Extend a repeating picture pattern [Grade 1]

Extend a pictorial growth pattern [Grade 1]

MT 4.1.B - Describe and compare repeating and growing patterns.

Extend a number pattern involving addition [Grade 2] Core Skill

Extend a number pattern involving subtraction [Grade 2] Core Skill


Second Grade


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Algebra Extend a pictorial growth pattern [Grade 1]

MT 4.5.A - Describe and organize growth patterns to draw conclusions about quantitative change using daily life, scientific or cultural context, including those of Montana American Indians.



Second Grade


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Know basic division facts for 11 and 12 [Grade 3]

WP: Multiply using basic facts to 10 x 10 [Grade 3] Core Skill

WP: Divide using basic facts to 100 ÷ 10 [Grade 3] Core Skill

Numbers and Operations Know basic multiplication facts to 10 x 10 [Grade 3] Core Skill

Know basic multiplication facts for 11 and 12 [Grade 3]

Know basic division facts to 100 ÷ 10 [Grade 3] Core Skill

Complete a multiplication and division fact family [Grade 3]

Multiply a 1-digit whole number by a multiple of 10 to 100 [Grade 3]

Multiply a 2-digit whole number by a 1-digit number [Grade 3]


Determine the 4- or 5-digit whole number represented in expanded form [Grade 3]

Core Skill

Compare 4- or 5-digit whole numbers using the symbols <, >, and = [Grade 3]

Order 4- or 5-digit whole numbers in ascending or descending order [Grade 3]

Determine the word form of a 4- or 5-digit whole number [Grade 3] Core Skill

Numbers and Operations Read a 4- or 5-digit whole number [Grade 3] Core Skill

Represent a 4-digit whole number as thousands, hundreds, tens, and ones [Grade 3]

Core Skill

Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones [Grade 3]

Core Skill

Represent a 4- or 5-digit whole number in expanded form [Grade 3] Core Skill

MT 1.1.A - Represent, read, compare and order whole numbers to 10,000.

Determine which digit is in a specified place in a 4- or 5-digit whole number [Grade 3]

Numbers and Operations Determine the value of a digit in a 4- or 5-digit whole number [Grade 3]

Determine the result of changing a digit in a 4- or 5-digit whole number [Grade 3]



Third Grade


Third Grade


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Estimate a sum or difference of two 3- or 4-digit whole numbers using front-end estimation [Grade 3]

Estimate a sum or difference of whole numbers to 10,000 by rounding [Grade 3]

Estimate a sum or difference of 2- to 4-digit whole numbers using any method [Grade 3]

Core Skill

WP: Estimate a sum or difference of two 3- or 4-digit whole numbers using any method [Grade 3]

Core Skill

Estimate a sum of three 2- to 4-digit numbers using any method [Grade 3]

WP: Add or subtract 3- and 4-digit whole numbers with regrouping [Grade 3]

Core Skill


Core Skill

Numbers and Operations Add 2- and 3-digit numbers with no more than one regrouping [Grade 2]

Core Skill

Add two 3-digit numbers with one regrouping [Grade 2] Core Skill

Subtract a 3-digit number from a 3-digit number with one regrouping [Grade 2]

Core Skill

Subtract 3- and 4-digit whole numbers with regrouping [Grade 3] Core Skill

Add three 2- to 3-digit whole numbers [Grade 3]

Add 3- and 4-digit whole numbers with regrouping [Grade 3] Core Skill

MT 1.2.B - Compute and solve addition and subtraction problems procedurally and contextually and check reasonableness of answer.


Core Skill


Numbers and Operations Estimate a sum or difference of whole numbers to 10,000 by rounding [Grade 3]


Core Skill


MT 1.2.A - Select and apply appropriate methods for estimating sums and differences.

Estimate a product of whole numbers using any method [Grade 4] Core Skill

Multiply a 3-digit whole number by a 2-digit whole number [Grade 4]

WP: Estimate a product of two whole numbers using any method [Grade 4]

Core Skill

Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient [Grade 4]


Third Grade


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Identify a pictorial model of tenths or hundredths of a decimal number [Grade 4]

Core Skill

Identify a decimal number to tenths represented by a point on a number line [Grade 4]

Core Skill

Numbers and Operations Read a decimal number through the hundredths place [Grade 4] Core Skill

Determine the decimal number from a pictorial model of tenths or hundredths [Grade 4]

Core Skill


MT 1.3.E - Use strategies and properties of operations to explain single-digit multiplication and division problems.

MT 1.3.D - Create contextual multiplication and partitive and measurement division problems.

Numbers and Operations Divide objects into equal groups using pictures [Grade 2]

WP: Divide objects into equal groups by sharing [Grade 2] Core Skill

Use a division sentence to represent objects divided into equal groups [Grade 3]

Core Skill

MT 1.3.C - Use manipulatives to solve contextual multiplication and division problems.

Determine the remainder when dividing objects into equal groups [Grade 2]

Numbers and Operations Recognize the number of equal groups using pictures [Grade 2]

Divide objects into equal groups using pictures [Grade 2]

Determine the number of equal groups of objects excluding the remainder [Grade 2]


Core Skill

WP: Divide objects into equal groups by sharing [Grade 2] Core Skill

MT 1.3.B - Use objects and number lines to show the partitive and measurement methods of division.

Represent repeated addition as multiplication [Grade 2]

Numbers and Operations Use a multiplication sentence to represent the sum of equal groups [Grade 2]

Relate a multiplication sentence to an array model [Grade 2]

Use a multiplication sentence to represent an area or an array model [Grade 3]

Core Skill

MT 1.3.A - Describe and use multiple representations for multiplication.


Numbers and Operations WP: Determine the amount of change from whole dollar amounts [Grade 3]

Core Skill

MT 1.2.C - Use an appropriate method to make change up to $1.


Third Grade


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Convert hours to minutes or minutes to seconds [Grade 3]

WP: Add or subtract compound units of length in inches and feet with conversion [Grade 3]

Calculate elapsed time within an hour, given two clocks, with regrouping [Grade 3]

Calculate elapsed time within an hour, given two clocks, without regrouping [Grade 3]

Add or subtract compound units of length in inches and feet with no conversion [Grade 3]

Convert between centimeters and meters [Grade 3]

Add or subtract compound units of length in inches and feet with conversion [Grade 3]

WP: Add or subtract compound units of length in inches and feet with no conversion [Grade 3]

WP: Calculate elapsed time within an hour [Grade 3]

WP: Calculate elapsed time within an hour given two clocks [Grade 3]

Convert between inches, feet, and yards [Grade 3]

Geometry and Measurement Measure length to the nearest half inch or quarter inch [Grade 3]


Numbers and Operations Identify equivalent fractions using models [Grade 3] Core Skill

MT 1.4.C - Use models to represent equivalent fractions.

Numbers and Operations Compare fractions using models [Grade 3] Core Skill

Order fractions using models [Grade 3] Core Skill

MT 1.4.B - Compare and order common fractions (i.e., tenths, fourths, thirds and halves) using models and strategies.

Determine a pictorial model of a fraction of a set of objects [Grade 3]

Core Skill

Numbers and Operations Determine a pictorial model of a fraction of a whole [Grade 3] Core Skill

Locate a fraction on a number line [Grade 3] Core Skill

Identify a fraction represented by a point on a number line [Grade 3] Core Skill

MT 1.4.A - Represent fractions using an area model, and/or parts of a set model and locate points on a number line model.

Locate a decimal number to tenths on a number line [Grade 4] Core Skill

Determine the fraction equivalent to a decimal number model [Grade 4]

Core Skill

Determine the decimal number equivalent to a fraction model [Grade 4]

Core Skill


Third Grade


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MT 2.2.A - Use mode and the median in an odd numbered data set to solve problems and make decisions pertaining to daily life, science, and culture; including that of Montana American Indians.


Answer a question using information from a line plot [Grade 3]

Use a line plot to represent data [Grade 3]

Answer a question using information from a frequency table [Grade 3]

Use a frequency table to represent data [Grade 3]


Read a line plot [Grade 3]

MT 2.1.A - Organize and represent data into frequency tables and dot plots (line plots).

Answer a question using information from a pictograph (1 symbol = more than 1 object) [Grade 2]

Core Skill


Read a pictograph (1 symbol = more than 1 object) [Grade 2]


Core Skill

Answer a question using information from a bar graph with a scale interval of 5 or 10 [Grade 3]

Use a bar graph with a scale interval of 5 or 10 to represent data [Grade 3]



Geometry and Measurement Tell time to 5-minute intervals [Grade 2] Core Skill

MT 1.5.A - Identify time to the nearest five minutes on an analog clock.

WP: Determine the start time given the end time and the elapsed time within an hour [Grade 3]

WP: Determine the start time given the end time on a clock and the elapsed time within an hour [Grade 3]

WP: Determine the end time given the start time and the elapsed time within an hour [Grade 3]

Determine a date using a calendar [Grade 3]

WP: Determine temperature change given a picture of thermometers [Grade 3]

Read a thermometer in degrees Fahrenheit or Celsius [Grade 3]


Third Grade


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Determine lines of symmetry [Grade 4] Core Skill

Geometry and Measurement Identify symmetry in a 2-dimensional shape [Grade 2]

MT 3.3.C - Identify lines of reflectional symmetry in two-dimensional figures.

Geometry and Measurement Determine the result of a flip, a turn, or a slide [Grade 4] Core Skill

MT 3.3.B - Explore the effects of a flip and slide on various shapes.

Geometry and Measurement Identify congruent shapes [Grade 3]

MT 3.3.A - Determine if two-dimensional figures are congruent using manipulatives or visual methods.


MT 3.2.B - Identify two-dimensional shapes within three-dimensional solids."

MT 3.2.A - Describe attributes of three-dimensional solids (e.g., number of faces, shapes of faces).


WP: Determine the perimeter of a shape given a model showing all side lengths [Grade 3]

Geometry and Measurement WP: Determine the perimeter of a rectangular shape given a grid with a reference unit [Grade 3]

MT 3.1.B - Build, draw, and analyze two-dimensional shapes to solve problems.

Geometry and Measurement Determine attributes of a triangle or a quadrilateral from a model [Grade 3]

Relate a polygon to attributes or characteristics [Grade 4]

Relate a model of a triangle or a quadrilateral to a list of attributes [Grade 3]

MT 3.1.A - Describe, compare, and analyze attributes of two-dimensional shapes, including sides and angles.




Determine if a situation is certain or impossible [Grade 3]

Determine which event is least likely or most likely to occur [Grade 3]

MT 2.3.A - Perform simple probability experiments to describe events from multicultural contexts, including those of Montana American Indians, as certain, equally likely, or impossible to occur.



Third Grade


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MT 4.1.C - Compare and contrast similarities and differences between growing patterns.

Algebra Identify a missing term in a multiplication or a division number pattern [Grade 4]

Core Skill

MT 4.1.A - Create and analyze simple numeric and geometric patterns and relationships involving multiplication and division.

Identify a missing figure in a repeating pictorial or nonnumeric pattern [Grade 4]

Core Skill

Extend a growing pictorial or nonnumeric pattern [Grade 4]

Algebra Extend a number pattern [Grade 3]

Identify a missing figure in a growing pictorial or nonnumeric pattern [Grade 4]

Core Skill



WP: Determine the perimeter of a shape given a model showing all side lengths [Grade 3]

Geometry and Measurement WP: Determine the perimeter of a rectangular shape given a grid with a reference unit [Grade 3]

MT 3.5.A - Define and determine perimeter of common polygons using concrete tools (e.g., grid paper, objects, or technology) and justify the strategy used.

Determine the area of a shape composed of rectangles given a picture on a grid [Grade 3]

Geometry and Measurement Relate area to the number of square units [Grade 2]

WP: Determine the area of a rectangular shape given a picture on a grid [Grade 3]

Determine the area of a polygon on a grid [Grade 4] Core Skill


Geometry and Measurement Measure length to the nearest half inch or quarter inch [Grade 3]

Measure length to the nearest eighth of an inch [Grade 4]

MT 3.4.A - Estimate and measure linear attributes of objects using fractional parts in customary units.

Measure length in centimeters [Grade 2] Core Skill

Geometry and Measurement Measure length in inches [Grade 2] Core Skill



Third Grade


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Determine a set of equivalent fractions [Grade 4]

Determine the decimal number equivalent to a fraction with a denominator of 10 or 100 [Grade 4]

Identify equivalent fractions using models [Grade 3] Core Skill

Numbers and Operations Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones [Grade 2]

Core Skill

Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones [Grade 3]

Core Skill

Algebra Determine equivalent addition expressions involving 2-digit numbers [Grade 2]


Core Skill

Determine a fraction equivalent to a decimal, using a denominator of 10 or 100 [Grade 4]

Determine the decimal number equivalent to a fraction model [Grade 4]

Core Skill


MT 4.3.B - Use models to represent and justify the commutative and associative properties of multiplication.

MT 4.3.A - Make a logical argument for one as the identity for multiplication.


Algebra Recognize equivalent multiplication or division expressions involving basic facts [Grade 3]

MT 4.2.A - Use equivalence to determine a missing value in an open sentence.

Determine the missing addend in a number sentence involving 3-digit numbers [Grade 3]

WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers [Grade 2]

Determine a missing subtrahend in a number sentence involving 2-digit numbers [Grade 2]

Determine the missing subtrahend in a number sentence involving 3-digit numbers [Grade 3]

Algebra Determine a missing addend in a number sentence involving 2-digit numbers [Grade 2]

Determine the missing dividend or divisor in a number sentence involving basic facts [Grade 3]

Determine the missing multiplicand in a number sentence involving basic facts [Grade 3]



Third Grade


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MT 4.5.A - Model a problem or situation with multiple representations using words, pictures, or tables, using daily life, scientific and cultural contexts, including those of Montana American Indians.


MT 4.4.A - Express equivalency of measures including time, length, and money.

Recognize equivalent multiplication or division expressions involving basic facts [Grade 3]


Third Grade


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Numbers and Operations Know basic multiplication facts to 10 x 10 [Grade 3] Core Skill

Know basic division facts to 100 ÷ 10 [Grade 3] Core Skill

MT 1.2.B - Recall basic multiplication facts to products up to 100 and related division facts.

Estimate a product of whole numbers by rounding [Grade 4]

WP: Estimate the sum or difference of two whole numbers, all values less than 1,000,000 [Grade 4]


Core Skill


WP: Estimate a quotient using any method [Grade 5] Core Skill

Estimate a quotient using any method [Grade 5] Core Skill


Core Skill


Numbers and Operations Estimate a sum or difference of whole numbers to 10,000 by rounding [Grade 3]



Core Skill

MT 1.2.A - Estimate sums, differences, products, and quotients when solving contextual problems.


Determine the 4- or 5-digit whole number represented in expanded form [Grade 3]

Core Skill

Numbers and Operations Represent a 4- or 5-digit whole number in expanded form [Grade 3] Core Skill

Order 4- or 5-digit whole numbers in ascending or descending order [Grade 3]

MT 1.1.A - Represent, read, compare and order numbers to 100,000.



Fourth Grade


Fourth Grade


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Numbers and Operations Determine the decimal number equivalent to a fraction model [Grade 4]

Core Skill

MT 1.4.D - Make connections using models, fraction notation, and decimal notation to represent equivalence.

Numbers and Operations Read a decimal number through the hundredths place [Grade 4] Core Skill

MT 1.4.C - Read and write decimal notation to 0.001 and explain the connection to the place value system.

Identify a pictorial model of tenths or hundredths of a decimal number [Grade 4]

Core Skill

Locate a decimal number to tenths on a number line [Grade 4] Core Skill

Numbers and Operations Determine the decimal number from a pictorial model of tenths or hundredths [Grade 4]

Core Skill

MT 1.4.B - Model decimals using various concrete materials and pictorial representations.

MT 1.4.A - Use models to identify equivalent symbolic representations of improper fractions and mixed numbers.


MT 1.3.C - Use invented strategies, concrete materials, number lines, and contextual clues to divide 2-digit dividends by 1-digit divisors.

MT 1.3.B - Use models, properties and place value strategies to illustrate and justify multiplication for three-digit factors by 2-digit factors with fluency and check reasonableness of the answer.

Multiply a 2-digit whole number by a 1-digit number [Grade 3]

Numbers and Operations WP: Multiply using basic facts to 10 x 10 [Grade 3] Core Skill

Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000 [Grade 4]

Core Skill

MT 1.3.A - Use mental math strategies to solve multiplication problems.


MT 1.2.D - Use invented strategies, concrete materials, number lines, and contextual clues to divide 2-digit dividends by 1-digit divisors.

WP: Multiply a 2-digit whole number by a 2-digit whole number [Grade 4]

Core Skill

Multiply a 2-digit whole number by a 2-digit whole number [Grade 4]

Core Skill

Numbers and Operations Multiply a 2-digit whole number by a 1-digit number [Grade 3]

WP: Multiply a 3-digit whole number by a 2-digit whole number [Grade 4]

MT 1.2.C - Apply a successful strategy for multiplying whole numbers up to 3-digit factors by 2-digit factors with fluency and check reasonableness of the answer.


Fourth Grade


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Read a line plot [Grade 3]

Answer a question using information from a line plot [Grade 3]

Answer a question using information from a table [Grade 4]


Answer a question using information from a pictograph (1 symbol = more than 1 object) [Grade 2]

Core Skill

MT 2.2.A - Analyze frequency tables, bar graphs, pictographs, dot plots (line plots), and stem-and-leaf plots to solve problems and make decisions pertaining to daily life, science, and culture; including that of Montana American Indians.



Use a bar graph with a y-axis scale by 2s to represent data [Grade 2] Core Skill

MT 2.1.A - Collect, organize and represent data using a bar graph and stem-and-leaf plot.



Geometry and Measurement Read a thermometer in degrees Fahrenheit or Celsius [Grade 3]

MT 1.5.B - Use the appropriate tools to collect time, temperature, and length data for daily life and science/cultural contexts; including that of Montana American Indians.

WP: Calculate elapsed time exceeding an hour with regrouping hours [Grade 4]

Core Skill

Geometry and Measurement Calculate elapsed time exceeding an hour with regrouping [Grade 4] Core Skill

MT 1.5.A - Determine the amount of elapsed time.


Convert a decimal number through thousandths to a simplified fraction [Grade 5]


Core Skill

Convert a fraction with a denominator that is a factor of 10, 100, or 1,000 to decimal notation [Grade 5]


Fourth Grade


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Numbers and Operations Use a multiplication sentence to represent an area or an array model [Grade 3]

Core Skill

MT 4.2.A - Create simple expressions or equations using letters, boxes, or symbols to represent numbers.


Determine a rule that relates two variables [Grade 4] Core Skill

Algebra Determine the rule for an addition or subtraction number pattern [Grade 2]

Core Skill

Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

MT 4.1.A - Generalize a numeric and geometric pattern by writing a rule using words and/or symbols.


MT 4 - A student, applying reasoning and problem solving, will use algebraic concepts and procedures to understand processes involving number, operation, and variables and will use procedures and function concepts to model the quantitative and functional relationships that describe change within a variety of relevant cultural contexts, including those of Montana American Indians..

MT 3.5.C - Develop and justify the formula for the area of a rectangle.

MT 3.5.B - Select appropriate units, strategies and tools for solving problems that involve estimating or measuring area of common polygons.

MT 3.5.A - Make a logical argument for a square as the standard unit of measurement for area.


MT 3.4.B - Use meters, feet, and yards to estimate and to measure length of an object.

MT 3.4.A - Label and select appropriate unit of measurement and measurement tools to determine the length of objects.


MT 3.3.B - Design and analyze simple tilings and tessellations within artistic and cultural contexts, including those of Montana American Indians."

MT 3.3.A - Identify and create slides and flips of congruent figures within artistic and cultural contexts, including those of Montana American Indians.



MT 3.1.A - Model and identify area as an attribute of a two-dimensional shape using concrete tools (e.g., manipulatives and grid paper).



Fourth Grade


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Core Skill

Numbers and Operations Use a multiplication sentence to represent an area or an array model [Grade 3]

Core Skill

Algebra WP: Determine a multiplication or division sentence for a given situation [Grade 3]

Core Skill

MT 4.5.A - Model numeric problems and contextual situations including those of Montana American Indians using multiple representations to draw conclusions.


MT 4.4.A - Express equivalence of numerical expressions in a variety of ways.


Numbers and Operations Apply the distributive property to multiply a multi-digit number by a 1-digit number [Grade 4]

Core Skill

MT 4.3.B - Use the distributive property to multiply.

MT 4.3.A - Use models to represent the distributive property.



Core Skill

Algebra WP: Determine a multiplication or division sentence for a given situation [Grade 3]

Core Skill


Fourth Grade


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Numbers and Operations Determine all the factors of a whole number to 50 [Grade 5]

Determine the common factors for two whole numbers to 50 [Grade 5]

Determine the greatest common factor of two whole numbers to 50 [Grade 5]

MT 1.3.A - Determine and explain common factors and common multiples.

MT 1.3 - Use number theory concepts such as prime factorization, greatest common factor, and least common multiple in problem situations.

MT 1.2.B - Explain whether or not a solution is reasonable based on the context.



Core Skill

Numbers and Operations WP: Estimate the sum or difference of two whole numbers, all values less than 1,000,000 [Grade 4]

Estimate a product of whole numbers by rounding [Grade 4]

WP: Estimate a quotient using any method [Grade 5] Core Skill

Estimate a quotient using any method [Grade 5] Core Skill

Estimate a quotient using compatible numbers [Grade 5]

MT 1.2.A - Use multiple strategies to estimate operations on whole numbers.

MT 1.2 - Select and apply appropriate estimation strategies to judge the reasonableness of solutions to problems including those computed on a calculator. Demonstrate correct use of order of operations.

Numbers and Operations Compare decimal numbers of differing places to thousandths [Grade 5]

Core Skill

Order decimal numbers of differing places to thousandths in ascending or descending order [Grade 5]

Core Skill

MT 1.1.B - Compare and order decimals using area and linear models.

Order fractions using models [Grade 3] Core Skill

Numbers and Operations Compare fractions using models [Grade 3] Core Skill

Compare fractions with unlike denominators [Grade 5] Core Skill

Order fractions with unlike denominators in ascending or descending order [Grade 5]

Core Skill

MT 1.1.A - Compare and order fractions using area, set, and linear models.

MT 1.1 - Recognize, model, and compare different forms of integers and rational numbers including percents, fractions, decimals, and numbers using exponents and scientific notation.


Fifth Grade


Fifth Grade


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Numbers and Operations Add fractions with like denominators no greater than 10 [Grade 4] Core Skill

WP: Add fractions with like denominators no greater than 10 and simplify the sum [Grade 4]

Subtract fractions with like denominators no greater than 10 [Grade 4]

Core Skill

MT 1.4.D - Add and subtract fractions fluently with like and unlike denominators including contextual situations.

MT 1.4.C - Use models, place value or properties to represent addition and subtraction of fractions and decimals.

Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimal [Grade 5]

Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed number [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotient [Grade 5]

Divide a multi-digit whole number by a 1-digit number, with no remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 1-digit number, with a remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed number [Grade 5]

Core Skill

Numbers and Operations Divide a multi-digit whole number by multiples of 100 or 1,000 [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotient [Grade 5]

Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotient [Grade 5]

Core Skill

MT 1.4.B - Divide multi-digit whole numbers, by 1 digit and 2 digit divisors fluently including invented strategies or standard algorithms.

Numbers and Operations Apply the distributive property to multiply a multi-digit number by a 1-digit number [Grade 4]

Core Skill

MT 1.4.A - Use models, place value, properties, and the relationship of division to multiplication to represent multi-digit division.

MT 1.4 - Compute fluently and solve multi-step problems using integers, fractions, decimals, and numbers in exponential form.

Determine the multiple(s) of a number [Grade 5]

Determine the least common multiple of two whole numbers [Grade 5]

Determine common multiples for two whole numbers [Grade 5]


Fifth Grade


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Add decimal numbers and whole numbers [Grade 5] Core Skill

Subtract two decimal numbers of differing places to thousandths [Grade 5]

Core Skill

WP: Determine the amount of change from whole dollar amounts [Grade 3]

Core Skill

Add two decimal numbers of differing places to thousandths [Grade 5]

Core Skill

WP: Add or subtract a decimal number through thousandths and a whole number [Grade 5]

Core Skill

Numbers and Operations Determine money amounts that total $10 [Grade 3] Core Skill

Subtract a decimal number from a whole number or a whole number from a decimal number [Grade 5]

WP: Add or subtract decimal numbers through thousandths [Grade 5]

Core Skill

MT 1.4.E - Add and subtract decimals fluently to the thousandths including contextual situations.

Subtract fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

WP: Add or subtract fractions with like denominators and simplify the sum or difference [Grade 5]

Core Skill

WP: Add or subtract fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

Subtract fractions with unlike denominators that have factors in common and simplify the difference [Grade 5]

Core Skill

WP: Subtract fractions with like denominators no greater than 10 and simplify the difference [Grade 4]

Add fractions with unlike denominators that have factors in common and simplify the sum [Grade 5]

Core Skill

Add fractions with unlike denominators that have no factors in common [Grade 5]

Core Skill

WP: Add or subtract fractions with unlike denominators and simplify the sum or difference [Grade 6]

Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum [Grade 6]

WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference [Grade 6]

Subtract mixed numbers with unlike denominators and simplify the difference [Grade 5]

WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference [Grade 5]

Core Skill

Add fractions with unlike denominators and simplify the sum [Grade 6]


Fifth Grade


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Answer a question using information from a line graph [Grade 4] Core Skill


Read a line graph [Grade 4] Core Skill

Answer a question using information from a double-bar graph [Grade 4]

Core Skill

Read a double-bar graph [Grade 4] Core Skill

MT 2.2.A - Analyze double bar graphs and line graphs to solve problems within daily life, scientific, and cultural contexts including those of Montana American Indians.

MT 2.2 - Interpret, analyze, and evaluate data using mean, median, range, and quartiles to identify trends and make decisions and predictions about data within scientific and cultural contexts, including those of Montana American Indians.


Use a line graph to represent data [Grade 4] Core Skill

MT 2.1.B - Organize and represent data using a line graph and ordered pairs in the first quadrant on a coordinate grid with the appropriate scale.


Use a double-bar graph to represent data [Grade 4] Core Skill

MT 2.1.A - Collect, organize, and represent data using a double bar graph.

MT 2.1 - Collect data from a variety of contexts (e.g., science, history, and culture, including Montana American Indians). Organize and represent data in box plots, scatter plots, histograms, and circle graphs using technology when appropriate.


Algebra Solve a proportion [Grade 6]

MT 1.6 - Understand and apply proportional relationships to model real world situations and to solve problems involving rates, ratios, proportions, percents, and direct variation.

Convert between customary units of weight using whole numbers [Grade 4]

Geometry and Measurement Convert between customary units of capacity using whole numbers [Grade 4]

Convert between metric units of capacity using whole numbers [Grade 4]

Convert between customary units of weight using fractional amounts [Grade 5]

MT 1.5.A - Estimate, measure and label length, capacity, and mass in relevant scientific and cultural situations, including those of Montana American Indians.

MT 1.5 - Use metric and standard units of measurement in relevant scientific and cultural situations, including those of Montana American Indians, compare and convert within systems, and use appropriate technology.


Fifth Grade


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MT 3.4.D - Make a logical argument for volume being the number of unit cubes required to fill a solid without gaps or overlaps.

Geometry and Measurement Determine the surface area of a rectangular prism [Grade 5] Core Skill

WP: Find the surface area of a rectangular prism [Grade 5] Core Skill

MT 3.4.C - Use models to find the surface area of rectangular prisms and label with appropriate units.

Classify an angle given its measure [Grade 4] Core Skill

Geometry and Measurement Classify an angle given a picture [Grade 4] Core Skill

MT 3.4.B - Estimate, measure, identify, and draw angles using the appropriate tools.

MT 3.4.A - Describe angle as a measure of rotation.

MT 3.4 - Measure and compute angles, perimeter, area, surface area, and volume including the use of formulas and choosing appropriate units.

MT 3.3 - Define, identify, and execute transformations including translations, rotations, reflections, and dilations with appropriate technology.

Geometry and Measurement Identify a figure that has reflectional or rotational symmetry [Grade 5]

MT 3.2.A - Model and determine if a two-dimensional figure has rotational symmetry.

MT 3.2 - Use spatial reasoning to determine congruence, similarity, and symmetry of objects in mathematics, art, science, and culture, including Montana American Indians.

MT 3.1.C - Unfold a rectangular prism to a net and compose a net into a rectangular prism.

MT 3.1.B - Describe polyhedrons by the number of edges, faces, and/or vertices as well as the types of faces.

MT 3.1.A - Describe, compare, and classify two-dimensional shapes, including regular and irregular polygons.

MT 3.1 - Define, classify and compare properties of solids and plane figures, including lines and angles.


Determine an experimental probability given a list of results [Grade 6]


Determine the probability of a single event given the total number of possible outcomes [Grade 5]

Determine the probability of a single event [Grade 6]

MT 2.3.A - Determine the experimental and theoretical probability of a simple situation. (e. g., probability of rolling a three on one roll of a six-sided die).

MT 2.3 - Create sample spaces and simulations from events found in different cultures, including those of Montana American Indians, determine experimental and theoretical probabilities, and use probability to make predictions.


Fifth Grade


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Algebra Solve a 1-step equation involving whole numbers [Grade 6] Core Skill

MT 4.3.A - Model, estimate, and solve one-step equations and verify the solution.

MT 4.3 - Use number properties and inverse operations to solve multi-step equations and inequalities involving a single variable.

MT 4.2 - Identify linear and non-linear functional relationships and contrast their properties using tables, graphs, or equations with appropriate technology.

WP: Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

Algebra Determine the variable expression with one operation for a table of paired numbers [Grade 5]

Core Skill

WP: Use a 2-variable equation to represent a situation involving a direct proportion [Grade 6]

Core Skill

WP: Use a 1-variable 1-step equation to represent a situation [Grade 7]

Core Skill

MT 4.1.A - Use patterns, models, and relationships to write simple equations and expressions.

MT 4.1 - Create and use tables, graphs or diagrams, symbolic expressions, and verbal descriptions to represent, analyze, and generalize a variety of patterns involving numbers and operations.


MT 3.5.D - Determine and justify the formula for the perimeter of a rectangle.

MT 3.5.C - Use models to determine and justify a formula for the volume of a rectangular prism.

WP: Determine the area of a square or rectangle [Grade 5] Core Skill

Determine the area of a complex shape [Grade 6] Core Skill

Geometry and Measurement Use a formula to determine the area of a triangle [Grade 5] Core Skill

MT 3.5.B - Determine and justify the areas of complex shapes made from rectangles, parallelograms, and triangles.

Geometry and Measurement Use a formula to determine the area of a triangle [Grade 5] Core Skill

WP: Determine the area of a square or rectangle [Grade 5] Core Skill

WP: Determine the area of a triangle [Grade 5] Core Skill

MT 3.5.A - Develop and justify a formula for the area of a parallelogram and triangle.

MT 3.5 - Develop informal arguments to verify geometric relationships and solve problems such as an informal justification of the Pythagorean Theorem in a variety of contexts.

WP: Determine the volume of a rectangular prism [Grade 5] Core Skill

Geometry and Measurement Determine the volume of a rectangular prism given a diagram [Grade 5]

Core Skill

MT 3.4.E - Select appropriate units, strategies and tools for solving problems that involve estimating or measuring volume of rectangular prisms.


Fifth Grade


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MT 4.5 - Identify and compute rate of change/slope and intercepts from equations, graphs, and tables; model and solve contextual problems involving linear proportions or direct variation using cultural contexts, including those of Montana American Indians.

MT 4.4 - Recognize, simplify, and generate equivalent forms of algebraic expressions, justifying each step with properties of operations.


Fifth Grade


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Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified place [Grade 5]

Core Skill

Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified place [Grade 5]

Core Skill

Numbers and Operations Estimate a fraction sum using benchmark numbers 0, 1/2, and 1 [Grade 5]

Estimate a fraction difference using benchmark numbers 0, 1/2, and 1 [Grade 5]

MT 1.2.A - Use estimation strategies to judge the reasonableness of operations on fractions and decimals.


Convert a decimal number to a mixed number [Grade 6]

Convert a mixed number to a decimal number [Grade 6]

Convert a fraction to a repeating decimal number [Grade 6]

Convert a percentage to a fraction [Grade 6]

Convert a fraction to a percentage [Grade 6]

Convert a fraction with a denominator that is a factor of 10, 100, or 1,000 to decimal notation [Grade 5]

Numbers and Operations Convert a decimal number through thousandths to a simplified fraction [Grade 5]

MT 1.1.B - Convert between fractions and decimals in order to solve problems.

Relate an equivalent decimal and percent given a grid [Grade 5]

Relate an equivalent fraction and percent given a grid [Grade 5]

Numbers and Operations Determine a model of a percent on a 100 grid [Grade 5]

Determine the percent represented by a model on a 100 grid [Grade 5]

WP: Determine the percent a whole number is of another whole number, with a result less than 100% [Grade 7]

Core Skill

Determine a percent where a ratio, not in 100ths, is given in words [Grade 6]

Core Skill

Determine the approximate percent of a region shaded [Grade 6]

MT 1.1.A - Use a model to represent percent.



Sixth Grade


Sixth Grade


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Multiply a mixed number by a mixed number [Grade 6] Core Skill

Determine the reciprocal of a whole number, a proper fraction, or an improper fraction [Grade 6]

Multiply a mixed number by a fraction [Grade 6] Core Skill

Numbers and Operations Multiply a fraction by a fraction [Grade 6] Core Skill

Multiply a mixed number by a whole number [Grade 6] Core Skill

Divide a fraction by a whole number resulting in a fractional quotient [Grade 6]

Core Skill

Divide a fraction by a fraction [Grade 6] Core Skill

MT 1.4.B - Multiply and divide fractions fluently.

MT 1.4.A - Justify strategies for multiplying and dividing fractions, mixed numbers and decimals.


Determine the least common multiple of two whole numbers [Grade 5]

Determine common multiples for two whole numbers [Grade 5]

Numbers and Operations Determine the greatest common factor of two whole numbers to 50 [Grade 5]

Determine the greatest common factor of three numbers to 100 [Grade 6]

WP: Determine the least common multiple of two or more numbers [Grade 6]

Determine the least common multiple of three numbers [Grade 6]

MT 1.3.A - Solve problems using least common multiple and greatest common factor and check the reasonableness of the solution.


Evaluate a numerical expression involving three operations, with parentheses, using order of operations [Grade 5]

Evaluate a numerical expression of four or more operations, with parentheses, using order of operations [Grade 6]

Core Skill

Numbers and Operations Evaluate a numerical expression involving three operations, with no parentheses, using order of operations [Grade 5]

MT 1.2.B - Use correct order of operations with whole number with no more than one level of parentheses.

WP: Estimate the product of two decimals [Grade 6] Core Skill

WP: Estimate the quotient of two decimals [Grade 6] Core Skill

WP: Estimate the sum or difference of two decimal numbers through thousandths using any method [Grade 5]

Core Skill


Sixth Grade


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Geometry and Measurement WP: Add or subtract customary measures of capacity requiring unit conversion [Grade 6]

WP: Add or subtract metric measures of capacity requiring unit conversion [Grade 6]

WP: Add or subtract customary measures of weight requiring unit conversion [Grade 6]

MT 1.5.A - Compare and convert units of measure within the same system of measurement, including length, capacity, mass and time; and label appropriately.


WP: Solve a 2-step problem involving decimals [Grade 6] Core Skill

WP: Multiply two decimal numbers to thousandths [Grade 6] Core Skill

WP: Divide a decimal number through thousandths by a 1- or 2-digit whole number [Grade 6]

Core Skill

Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole number [Grade 6]

Core Skill

WP: Multiply a decimal number through thousandths by a whole number [Grade 6]

Core Skill

WP: Multiply or divide two mixed numbers or a mixed number and a fraction [Grade 6]

Core Skill

WP: Solve a 2-step problem involving fractions [Grade 6] Core Skill

Multiply a decimal number through thousandths by a whole number [Grade 6]

Core Skill

WP: Solve a multi-step problem involving fractions or mixed numbers [Grade 7]

Core Skill

Numbers and Operations Divide a whole number by a 1-digit whole number resulting in a decimal quotient through thousandths [Grade 6]

Core Skill

WP: Multiply or divide a fraction by a fraction [Grade 6] Core Skill

WP: Solve a multi-step problem involving decimal numbers [Grade 7]

Core Skill

WP: Divide a whole number by a decimal number through thousandths, rounded quotient if needed [Grade 6]

Core Skill

WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if needed [Grade 6]

Core Skill

WP: Divide a whole number by a 1- or 2-digit whole number resulting in a decimal quotient [Grade 6]

Core Skill

MT 1.4.C - Solve contextual problems using multiplication and division of fractions and decimals.

Divide a whole number by a fraction resulting in a fractional quotient [Grade 6]

Core Skill

Divide a mixed number by a mixed number [Grade 6]


Sixth Grade


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WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine the whole given a ratio and a part where the whole is less than 50 [Grade 6]

Core Skill

WP: Use a unit rate, with a whole number or whole cent value, to solve a problem [Grade 6]

Core Skill

WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

Numbers and Operations WP: Determine a part given a ratio and the whole where the whole is less than 50 [Grade 6]

Core Skill

MT 1.6.C - Use multiplicative reasoning to solve ratio and rate problems and explain the answer (e.g., Terry can run 4 laps in 12 minutes, and Susan can run 2 laps in 5 minutes, who is the faster runner?).

MT 1.6.B - Write equivalent ratios using multiplication or division strategies.

WP: Determine a unit rate [Grade 7] Core Skill

Numbers and Operations WP: Determine a unit rate with a whole number value [Grade 6] Core Skill

MT 1.6.A - Identify ratios (part-part, part-whole, rates as ratios) and unit rates in various contexts.


MT 1.5.B - Use scientific and cultural situations, including those of Montana American Indians, to solve measurement problems.

WP: Multiply or divide metric measures of capacity requiring unit conversion [Grade 6]

WP: Multiply or divide customary measures of weight requiring unit conversion [Grade 6]

WP: Add or subtract metric measures of mass requiring unit conversion [Grade 6]

WP: Multiply or divide customary measures of capacity requiring unit conversion [Grade 6]

Convert between Fahrenheit and Celsius temperature given a formula [Grade 6]

Determine a time in different time zones [Grade 6]

WP: Multiply or divide metric measures of mass requiring unit conversion [Grade 6]


Sixth Grade


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MT 3.1.A - Describe and compare a variety of pyramids and prisms (e.g., pentagonal, hexagonal).




Determine the probability for independent events [Grade 7]

MT 2.3.B - Determine the theoretical probability of two independent events by using a tree diagram, list, or table (e.g., flip a coin and roll a die).

Determine the probability of a single event [Grade 6]


Determine an experimental probability given a list of results [Grade 6]

MT 2.3.A - Determine the experimental probability of two independent events using a simple experiment (e.g., probability of outcomes when rolling a six-sided die twice).


Determine the mode of a set of whole number data [Grade 5]

Determine the median of an odd number of data values [Grade 5] Core Skill

Determine the mean of a set of whole number data [Grade 6]


Determine the mean of a set of whole number data, whole number results [Grade 5]

Determine the median of a set of whole number data [Grade 6]

MT 2.2.A - Interpret and analyze one set of data using measures of center (median, mean, mode) and variability (maximum, minimum, range).


MT 2.1.A - Use the appropriate representation of data collected from a variety of contexts (e.g., science, history, and culture, including those of Montana American Indians).



WP: Use a unit rate to solve a problem [Grade 7] Core Skill

Algebra WP: Solve a proportion [Grade 7] Core Skill


Sixth Grade


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Core Skill

Algebra Determine a rule that relates two variables [Grade 4] Core Skill

MT 4.1.A - Describe patterns and relationships using words, tables, graphs, diagrams, and mathematical sentences.



Determine the circumference of a circle using 3.14 for pi [Grade 6]

Geometry and Measurement Determine the circumference of a circle using 22/7 for pi [Grade 6]

WP: Determine the circumference of a circle [Grade 6]

MT 3.5.B - Use models to determine and justify a formula for the circumference of a circle (e.g., the ratio of circumference to diameter equals pi).

MT 3.5.A - Use models to determine and justify a formula for the volume of a rectangular prism.


Geometry and Measurement Determine the missing side length of a rectangle given a side length and the area [Grade 4]

Core Skill

WP: Determine a missing dimension given the area and another dimension [Grade 5]

Core Skill

MT 3.4.B - Solve for the unknown piece of information regarding areas of rectangles, parallelograms and triangles or volume of rectangular prisms.

Geometry and Measurement Determine the volume of a rectangular or a triangular prism [Grade 7]

Core Skill

MT 3.4.A - Use area and volume formulas to solve problems with decimal and fractional dimensions.


Geometry and Measurement Identify a figure that has reflectional or rotational symmetry [Grade 5]


Geometry and Measurement Identify congruent shapes shown on a grid or within pattern block arrangements, with different orientations [Grade 6]


MT 3.1.C - Draw orthogonal views of a three-dimensional block structure.

MT 3.1.B - Decompose a prism and pyramid into a net and compose a net into a prism or pyramid.


Sixth Grade


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Algebra WP: Use a 1-variable 1-step equation to represent a situation [Grade 7]

Core Skill

MT 4.3.A - Write and evaluate mathematical expressions and equations for a given situation.


Algebra WP: Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Core Skill

Use a first quadrant graph to represent the values from a table generated in context [Grade 5]

Core Skill

Use a 2-variable equation to construct an input-output table [Grade 6]

Core Skill

MT 4.2.A - Use tables and graphs to describe a functional relationship between two quantities.


WP: Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Core Skill


Core Skill


Core Skill

Algebra Generate a table of paired numbers based on a rule [Grade 4] Core Skill

Determine a rule that relates two variables [Grade 4] Core Skill

Use a first quadrant graph to represent the values from a table generated in context [Grade 5]

Core Skill


Core Skill

Use a 2-variable equation to represent a relationship expressed in a table [Grade 6]

Core Skill

WP: Use a 2-variable equation to represent a situation involving a direct proportion [Grade 6]

Core Skill

WP: Use a 2-variable linear equation to represent a situation [Grade 6]

Core Skill

MT 4.1.B - Demonstrate fluency between two various representations (tables, graphs, verbal descriptions, symbolic expressions) of a linear pattern.


Core Skill


Core Skill

WP: Generate a table of paired numbers based on a variable expression with one operation [Grade 5]

Core Skill


Core Skill


Sixth Grade


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MT 4.4.A - Apply the commutative, associative, distributive properties and order of operations to show that two numeric expressions are equivalent.



MT 4.3.B - Solve and justify one-step equations using number sense and properties of operations.


Sixth Grade


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Numbers and Operations Determine the prime factorization of a number between 50 and 200 [Grade 6]

MT 1.3.B - Write the prime factorization of a number with and without exponents.

MT 1.3.A - Determine if numbers are prime or composite and explain the strategy used.


MT 1.2.B - Use a calculator to solve multi-step problems and check reasonableness with appropriate estimation strategies.

Numbers and Operations WP: Estimate a given percent of a number [Grade 8] Core Skill

MT 1.2.A - Use estimation strategies and judge the reasonableness of percent problems.


Approximate the location of a square root on a number line [Grade 8]

Core Skill

Numbers and Operations Evaluate the positive square root of a perfect square [Grade 7]

Determine the two closest integers to a given square root [Grade 8] Core Skill

MT 1.1.E - Estimate and explain the square root of any whole number.

Numbers and Operations Identify or locate an integer on a number line [Grade 6]

Subtract integers using a number line [Grade 7]

Add integers using a number line [Grade 7]

MT 1.1.D - Compare, order, and graph integers on a number line.

Numbers and Operations Add integers using a model [Grade 7]

MT 1.1.C - Use models to represent integers.

MT 1.1.B - Deduce values of fraction/decimal/percent equivalencies using common fractions/decimals/percents (e.g., since 1/4=25% then 3/4=75%).

Convert a percentage to a fraction [Grade 6]

Numbers and Operations Convert a fraction to a percentage [Grade 6]

Compare numbers in decimal and fractional forms [Grade 6] Core Skill

MT 1.1.A - Recall decimal and percent equivalents for common fractions.



Seventh Grade


Seventh Grade


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WP: Determine the percent a whole number is of another whole number, with a result less than 100% [Grade 7]

Core Skill

WP: Determine a percent of a whole number using less than 100% [Grade 7]

Core Skill

WP: Determine the whole given a ratio and a part where the whole is less than 50 [Grade 6]

Core Skill

Numbers and Operations WP: Determine a part given a ratio and the whole where the whole is less than 50 [Grade 6]

Core Skill

WP: Use a unit rate, with a whole number or whole cent value, to solve a problem [Grade 6]

Core Skill

WP: Determine a unit rate with a whole number value [Grade 6] Core Skill

MT 1.6.A - Use proportions to solve contextual problems including scale drawings, rates, ratios, and percent problems.


MT 1.5.C - Use appropriate tools and technology to estimate and measure, with appropriate units, in scientific and cultural situations, including those of Montana American Indians.

MT 1.5.B - Use rates to justify conversions between units within the same system (e.g., miles per hour to feet per second).

MT 1.5.A - Solve problems involving derived measures.


Numbers and Operations Evaluate an integer raised to a whole number power [Grade 8] Core Skill

MT 1.4.C - Evaluate expressions with integers and whole number exponents with and without calculator.

WP: Multiply or divide integers [Grade 7] Core Skill

Numbers and Operations WP: Add and subtract using integers [Grade 7] Core Skill

MT 1.4.B - Solve and create problems using integers and check the reasonableness of the answer.

Subtract integers using a number line [Grade 7]

Add integers [Grade 7] Core Skill

Numbers and Operations Add integers using a number line [Grade 7]

Subtract integers [Grade 7] Core Skill

Divide integers [Grade 7] Core Skill

Multiply integers [Grade 7] Core Skill

MT 1.4.A - Use and justify the strategies and procedures for computing with integers.


Determine the prime factorization of a number using exponents [Grade 7]


Seventh Grade


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Use a histogram to represent data [Grade 7] Core Skill


Use a circle graph to represent percentage data [Grade 7] Core Skill

MT 2.1.A - Organize and represent data using histograms and circle graphs.



WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine a whole number given a part and a percentage [Grade 7]

Core Skill

WP: Answer a question involving a fraction and a percent [Grade 7] Core Skill

WP: Determine the percent of increase applied to a number [Grade 7]

Core Skill

WP: Determine the percent of decrease applied to a number [Grade 7]

Core Skill

WP: Determine the result of applying a percent of increase to a value [Grade 7]

Core Skill

WP: Determine the result of applying a percent of decrease to a value [Grade 7]

Core Skill

WP: Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill

WP: Determine the percent one number is of another number [Grade 8]

Core Skill

WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill


WP: Determine a given percent of a number [Grade 8] Core Skill

WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50 [Grade 7]

Core Skill

WP: Use a unit rate to solve a problem [Grade 7] Core Skill



Seventh Grade


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Geometry and Measurement Identify congruent shapes shown on a grid or within pattern block arrangements, with different orientations [Grade 6]

MT 3.2.A - Use transformations to determine similarity and/or congruence of two-dimensional and three-dimensional objects in mathematics, art, science, and culture, including Montana American Indians.


MT 3.1.A - Decompose a cylinder into its two-dimensional shapes and compose its two-dimensional shapes into a cylinder.



MT 2.3.A - Create simple simulations and collect data to predict the theoretical probability of the event. B. Use the theoretical probability of an event to make a prediction for a large number of trials and justify your reasoning (e.g., probability of rolling a sum of two when rolling a pair of dice is 1/6; how many times would you expect a sum of two if you rolled the pair of dice 360 times).


MT 2.2.B - Justify an appropriate selection of data representation.


Answer a question using information from a circle graph using percentage calculations [Grade 7]

Core Skill

Answer a question using information from a histogram [Grade 7] Core Skill

MT 2.2.A - Analyze histograms and circle graphs to solve problems within daily life, scientific, and cultural contexts including those of Montana American Indians.


MT 2.1.C - Given a set of data from science, history, and culture, including those of Montana American Indians compare representative displays, and justify an appropriate selection of data representation.


Use a scatter plot to organize data [Grade 8]

MT 2.1.B - Organize and represent data using a scatter plot with the appropriate scale.

Use a circle graph to organize data [Grade 8]


Seventh Grade


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MT 3.5.C - Make a logical argument for how a scale factor affects the area and volume of similar two- and three-dimensional objects.

MT 3.5.B - Develop and justify a formula for the area of a trapezoid (e.g., decompose a trapezoid into common polygons or use a composition of two trapezoids to create another common polygon).

MT 3.5.A - Develop and justify the area formula of a circle (e.g., decompose a circle into a number of wedges and rearrange them into a shape that approximates a parallelogram).


Geometry and Measurement Determine a missing dimension given two similar shapes [Grade 7] Core Skill

WP: Solve a problem involving similar shapes [Grade 7] Core Skill

MT 3.4.C - Determine the lengths, areas, and volume using proportional reasoning and scale factors of similar two- and three-dimensional objects.

WP: Determine the volume of a cylinder [Grade 7]

Determine the surface area of a cylinder [Grade 7]

Geometry and Measurement Determine the volume of a cylinder [Grade 7]

MT 3.4.B - Determine the surface area and volume of cylinders and label with appropriate units.

Determine the area of a circle using 3.14 for pi [Grade 7]

Determine the area of a circle in terms of pi [Grade 7]

Geometry and Measurement Determine the area of a trapezoid [Grade 7]

WP: Determine the area of a circle using 3.14 for pi [Grade 7]

Determine the area of a circle using 22/7 for pi [Grade 7]

MT 3.4.A - Determine the area of circles and trapezoids and label with appropriate units.


Determine the coordinates of a translated, a rotated, or a reflected shape on the Cartesian plane [Grade 7]

Geometry and Measurement Determine the result of a reflection, a rotation, or a translation on the Cartesian plane [Grade 6]

MT 3.3.A - Define, identify and execute a translation, a rotation, and a reflection with and without technology.


Seventh Grade


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Numbers and Operations WP: Determine a unit rate with a whole number value [Grade 6] Core Skill


MT 4.5.A - Identify the unit rate of change and justify how it relates to the slope of a line.


MT 4.4.A - Use properties of equality and rational numbers to rewrite an algebraic expression in multiple ways and show that the expressions are equivalent.


Determine some solutions to a 1-variable linear inequality [Grade 7]

Algebra Determine the graph of an inequality on a number line [Grade 7]

Determine the graph of the solution set of a 1-step linear inequality [Grade 7]

MT 4.3.B - Use properties of whole numbers and inverse operations to solve one-step inequalities in one variable and graph the solution on a number line.


Solve a 1-step equation involving rational numbers [Grade 8] Core Skill

Solve a 1-step linear equation involving integers [Grade 7] Core Skill

MT 4.3.A - Use properties of whole numbers and inverse operations to solve one-step equations and check the reasonableness of the answer.


MT 4.2.B - Distinguish between linear and non-linear functional relationships graphed with and without technology.

MT 4.2.A - Use graphs, tables, and equations to distinguish proportional relationships from other relationships, including inverse proportionality between two quantities.


Algebra WP: Use a 2-variable equation to represent a situation involving a direct proportion [Grade 6]

Core Skill

MT 4.1.A - Represent proportional relationships using multiple representations (tables, graphs, verbal descriptions, symbolic expressions) of data and make connections among the representations.


Seventh Grade


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WP: Determine the least common multiple of two or more numbers [Grade 6]

Numbers and Operations Determine the greatest common factor of three numbers to 100 [Grade 6]

MT 1.3.A - Apply number theory concepts such as prime factorization, greatest common factor, and least common multiple to solve problems.


Numbers and Operations Evaluate a numerical expression, with parentheses and exponents, using order of operations [Grade 7]

MT 1.2.A - Use a calculator to evaluate numeric expressions involving order of operations and check reasonableness with appropriate estimation strategies.


Approximate the location of a square root on a number line [Grade 8]

Core Skill

Numbers and Operations Determine the two closest integers to a given square root [Grade 8] Core Skill

MT 1.1.C - Estimate and explain the square root of any whole number from 1-225.

Locate a positive or negative rational number on a number line [Grade 7]

Numbers and Operations Identify a positive or negative rational number represented by a point on a number line [Grade 7]

Compare rational numbers (positive and negative) [Grade 7]

Order rational numbers (positive and negative) [Grade 7]

MT 1.1.B - Compare, order, and graph rational numbers on a number line.

Convert a whole number greater than 10 from scientific notation to standard form [Grade 7]

Numbers and Operations Convert a whole number greater than 10 to scientific notation [Grade 7]

Convert a number less than 1 to scientific notation [Grade 8] Core Skill

Convert a number less than 1 from scientific notation to standard form [Grade 8]

Core Skill

MT 1.1.A - Read, write, and compare numbers using integer exponents and scientific notation.



Eighth Grade


Eighth Grade


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WP: Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill

WP: Determine a given percent of a number [Grade 8] Core Skill

Determine a number given a part and a decimal percentage or a percentage more than 100% [Grade 8]

Core Skill


Numbers and Operations Determine the percent one number is of another number [Grade 8] Core Skill

MT 1.6.A - Use proportions to solve contextual problems including similarity and congruence.


MT 1.5.A - Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians.


Evaluate a numerical expression involving integer exponents and/or integer bases [Grade 8]

Core Skill

Evaluate a numerical expression involving nested parentheses [Grade 8]

Numbers and Operations Evaluate a numerical expression, with parentheses and exponents, using order of operations [Grade 7]

Evaluate an integer raised to a whole number power [Grade 8] Core Skill

Algebra Evaluate an algebraic expression involving whole number exponents [Grade 7]

Determine an equivalent form of a variable expression involving exponents [Grade 8]

Evaluate an algebraic expression involving negative integer exponents [Grade 8]

WP: Evaluate a variable expression involving exponents [Grade 7]

MT 1.4.B - Evaluate numeric expressions including nested parentheses, exponents, and other grouping symbols.

WP: Solve a multi-step problem involving fractions or mixed numbers [Grade 7]

Core Skill

Numbers and Operations WP: Solve a multi-step problem involving decimal numbers [Grade 7]

Core Skill

MT 1.4.A - Solve multi-step problems containing rational numbers and numbers in exponential form.


Algebra Factor the difference of two squares [Algebra 1]

Determine the prime factorization of a number using exponents [Grade 7]


Eighth Grade


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MT 2.2.D - Compare and analyze the strengths and limitations of using each descriptive statistical measure and evaluate how changes in data affect those statistics.

MT 2.2.C - Estimate the line of best fit on a scatter plot to make decisions and predictions about data within daily life, scientific, and cultural contexts, including those of Montana American Indians.

MT 2.2.B - Compare and analyze the data represented in two or more parallel box plots.

MT 2.2.A - Describe and interpret a box plot using the 5 # summary, the interquartile range, and percentiles.


MT 2.1.B - Create and justify the appropriate visual representation for given data sets from science, history, and culture, including those of Montana American Indians with and without technology.


Determine the quartiles of a data set [Grade 8]

MT 2.1.A - Collect, organize, and represent univariate data in box plots.



Convert a rate from one unit to another with a change in both units [Grade 7]

Core Skill

Geometry and Measurement Convert a rate from one unit to another with a change in one unit [Grade 7]

Core Skill

Numbers and Operations WP: Use a unit rate to solve a problem [Grade 7] Core Skill

WP: Solve a distance-rate-time problem that involves unit conversions [Grade 8]

MT 1.6.C - Use rates to justify conversions between units of measure (e.g., convert miles/hour to feet/second).

Algebra WP: Use direct variation to solve a problem [Grade 7]

MT 1.6.B - Rewrite a proportion as a direct variation equation to model a real world situation.

Determine a measure of length, weight or mass, or capacity or volume using proportional relationships [Grade 8]

Core Skill

Geometry and Measurement WP: Solve a problem involving similar shapes [Grade 7] Core Skill


Eighth Grade


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Geometry and Measurement Identify vertical, adjacent, complementary, or supplementary angles [Grade 7]

MT 3.4.A - Use attributes of angles created by intersecting lines and parallel lines cut by transversals to solve problems involving missing sides or angles.


MT 3.3.A - Define, identify and execute a dilation with and without technology.


Identify congruent shapes given side and angle measures [Grade 7]

Geometry and Measurement Identify corresponding parts of congruent shapes [Grade 7]

MT 3.2.B - Justify congruency of figures using sides and angle relationships.

Geometry and Measurement Determine the scale factor relating two similar polygons [Geometry]

MT 3.2.A - Justify similarity of figures using proportional reasoning and angle relationships.


Determine an angle measure formed by parallel lines cut by a transversal [Grade 8]

Geometry and Measurement Identify angle relationships formed by parallel lines cut by a transversal [Grade 8]

Identify angle relationships formed by multiple lines and transversals [Geometry]

Determine the measure of an angle formed by parallel lines and one or more transversals [Geometry]

Core Skill

MT 3.1.B - Describe and define the angles created by intersecting rays, intersecting lines, and parallel lines cut by transversals.

MT 3.1.A - Name and describe the basic objects of plane geometry.



MT 2.3.C - Identify misleading presentations of data found in the media and predict the effects of conclusions drawn.

MT 2.3.B - Describe and apply the addition rule for probabilities of events that are mutually exclusive and for events that are not mutually exclusive.

MT 2.3.A - Create and test conjectures made from the results of experiments and simulations using experimental and theoretical probabilities from scientific and cultural events, including those of Montana American Indians.


Eighth Grade


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Determine the table of values that represents a linear equation with rational coefficients in two variables [Grade 8]

Core Skill


Core Skill

Algebra Use a 2-variable equation to construct an input-output table [Grade 6]

Core Skill

Determine a linear equation in two variables that represents a table of values [Grade 8]

Core Skill

MT 4.1.A - Create and use multiple representations (tables, graphs, verbal descriptions, symbolic expressions) of data to generalize the patterns and make connections among all representations.



MT 3.5.C - Make a logical argument for the Pythagorean Theorem (e.g., decompose a square in two different ways).

MT 3.5.B - Develop and justify the theorem for the sum of the interior angles of a triangle equaling 180º.

Geometry and Measurement Determine the area of a regular polygon [Geometry]

MT 3.5.A - Develop and justify a formula (informal or formal) for area of regular polygons (e.g., decompose a regular polygon into congruent isosceles triangles).


Determine the length of a leg of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

Geometry and Measurement Determine the length of the hypotenuse of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

WP: Use the Pythagorean theorem to find a length or a distance [Grade 8]

Core Skill

MT 3.4.B - Use Pythagorean Theorem to find a missing side of right triangles to calculate perimeter, area, surface area and volume, and label with appropriate units.

Determine an angle measure formed by parallel lines cut by a transversal [Grade 8]

Identify angle relationships formed by parallel lines cut by a transversal [Grade 8]

Determine the measure of a missing angle using angle relationships [Grade 7]

Determine the measure of an angle formed by parallel lines and one or more transversals [Geometry]

Core Skill


Eighth Grade


- 54 of 63 -12/4/2012


WP: Solve a problem involving a 2-step linear inequality in one variable [Grade 8]

Core Skill

Algebra Solve a 2-step linear inequality in one variable [Grade 8] Core Skill

Determine the graph of the solutions to a 2-step linear inequality in one variable [Grade 8]

Core Skill

Solve a 1-variable linear inequality with the variable on both sides [Algebra 1]

Core Skill

MT 4.3.B - Use properties of numbers and inverse operations to solve multi-step linear inequalities in one variable, graph the solution on a number line and check the reasonableness of the solution.


Solve a 1-variable linear equation that requires simplification and has the variable on one side [Algebra 1]

Solve a 1-variable linear equation with the variable on both sides [Algebra 1]

Core Skill


Algebra Solve a 1-step linear equation involving integers [Grade 7] Core Skill

MT 4.3.A - Solve multi-step linear equations incorporating multiple grouping symbols and check the reasonableness of the solution.


MT 4.2.D - Compare and contrast the properties of functional and non-functional relations using technology when appropriate.

MT 4.2.C - Compare and contrast the properties of linear and non-linear relationships using technology when appropriate.

Algebra Determine if a relation is a function [Algebra 1]

MT 4.2.B - Determine from a set of ordered pairs, a table, graph, or a rule whether a relation is a function.

Determine the slope of a line given two points on the line [Algebra 1]

Core Skill

Algebra Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill

Determine the slope of a line given an equation of the line [Algebra 1]

Core Skill

Determine the x- or y-intercept of a line given an equation [Algebra 1]

Core Skill

MT 4.2.A - Identify the properties (slope, intercepts, continuity, and discreteness) of linear relationships using multiple representations.



Eighth Grade


- 55 of 63 -12/4/2012


Core Skill

MT 4.5.C - Model and solve contextual problems involving linear proportions or direct variation using cultural contexts, including those of Montana American Indians.

Solve a system of linear equations in two variables using any method [Algebra 1]

Core Skill

Solve a system of linear equations in two variables by substitution [Algebra 1]

Algebra Solve a system of linear equations in two variables by graphing [Algebra 1]

Solve a system of linear equations in two variables by elimination [Algebra 1]

Determine the number of solutions to a system of linear equations [Algebra 1]

MT 4.5.B - Identify the solution to a system of linear equations by determining whether the lines are parallel, intersecting, or the same line.

Determine the slope of a line given two points on the line [Algebra 1]

Core Skill

Determine the x- or y-intercept of a line given its graph [Grade 8] Core Skill

Algebra Determine the slope of a line given its graph or a graph of a line with a given slope [Grade 8]

Core Skill

Determine the slope of a line given an equation of the line [Algebra 1]

Core Skill

Determine the x- or y-intercept of a line given an equation [Algebra 1]

Core Skill

MT 4.5.A - Determine the slope, x-intercept, and y-intercept of a line given its graph, equation, or two points on the line.


Use the distributive property to simplify an algebraic expression [Grade 8]

Determine an equivalent form of a variable expression involving exponents [Grade 8]

Algebra Simplify an algebraic expression by combining like terms [Grade 8] Core Skill

Apply the product of powers property to a monomial numerical expression [Algebra 1]

Factor the GCF from a polynomial expression [Algebra 1] Core Skill

Multiply two binomials of the form (x +/- a)(x +/- b) [Algebra 1]

MT 4.4.A - Generate equivalent forms of algebraic expressions including those involving like terms and justify each step with properties of operations.


Eighth Grade


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Geometry and Measurement Determine a length using parallel lines and proportional parts [Geometry]

Core Skill


Eighth Grade


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MT 1.5 - Identify givens and unknowns in familiar and unfamiliar situations (e.g., finance, culture, including Montana American Indians, and nature) and describe relationships between variables.

MT 1.4.B - Apply real-number properties to solve problems.

MT 1.4.A - Define and classify real numbers by the subset to which they belong.

MT 1.4 - Analyze and apply the properties of numbers and number systems.

Evaluate a numerical expression involving one or more exponents and multiple forms of rational numbers [Algebra 1]

Core Skill

Simplify a monomial numerical expression involving the square root of a whole number [Algebra 1]

Core Skill

Rationalize the denominator of a numerical radical expression [Algebra 1]

Simplify a monomial algebraic radical expression [Algebra 1] Core Skill

MT 1.3.B - Simplify real number expressions containing rational exponents, radicals or irrational numbers.

Compare rational numbers and/or irrational numbers in various forms [Grade 8]

Identify rational or irrational numbers [Grade 8]

Numbers and Operations Evaluate a zero or negative power of an integer [Grade 8]

MT 1.3.A - Express a real number in a variety of equivalent forms using rational exponents, radicals, or irrational numbers.

MT 1.3 - Given a representation of a number or expression, find equivalent representations using multiple notations (e.g., x to the 1/2 power vs. sq rt x and visual representation of multiplying binomials).

MT 1.2.C - Round solutions and choose the appropriate precision to report the answer based on the context of the problem.

MT 1.2.B - Use estimated values of irrational numbers to check for reasonableness of solution to problems.

MT 1.2.A - Identify and explain situations where an estimate is adequate and appropriate.

MT 1.2 - Identify situations where estimation is appropriate and determine the degree of accuracy needed for a given problem situation (and the appropriate precision in which to report answers).

MT 1.1.B - Describe the effects of operations with very large or very small numbers.

MT 1.1.A - Evaluate expressions containing very large and very small numbers using multiple notations.

MT 1.1 - Use multiple notations to perform and interpret the effects of operations on very large and very small numbers with and without technology.


Grades: 9-12


Grades: 9-12


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Analyze the effect that changing elements in a data set has on the mean, the median, or the range [Grade 8]

MT 2.1.D - Explain how linear transformations of univariate data affect shape, center, and spread (e.g. adding or multiplying a constant to each data set, adding an outlier).


Determine the median of the data in a frequency table or a bar graph [Grade 8]

Determine the mean of the data in a frequency table or a bar graph [Grade 8]

MT 2.1.C - Calculate and interpret measures of spread to make comparisons among sets of data.


Use a scatter plot to organize data [Grade 8]

Determine if a scatter plot shows a positive relationship, a negative relationship, or no relationship between the variables [Grade 8]

Approximate a trend line for a scatter plot [Grade 8]

Answer a question using information from a scatter plot [Grade 8]

MT 2.1.B - Describe and interpret the tendency of bivariate data in a scatter plot.


Use a circle graph to organize data [Grade 8]

MT 2.1.A - For univariate data, be able to display the distribution, describe its shape, and select and calculate summary statistics.

MT 2.1 - Select, create, and compare graphical or numerical representations of data sets using technology when appropriate. Reason about distributions using measures of central tendency and spread (e.g., percentiles, quartiles, inter-quartile range, and standard deviation).


Algebra Determine the independent or dependent variable in a given situation [Algebra 1]

MT 1.5.B - Identify independent and dependent variables when a dependency exists.

WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations [Grade 8]

Core Skill


Core Skill

Algebra WP: Use a 2-variable linear equation to represent a situation [Grade 6]

Core Skill

WP: Solve a problem involving a 1-variable, 2-step equation [Grade 8]

Core Skill

WP: Use a 2-variable equation with rational coefficients to represent a situation [Grade 8]

Core Skill

MT 1.5.A - Given a situation, including those of Montana American Indians, determine the unknowns, write and solve the equation or system of equations, and interpret the results.


Grades: 9-12


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Determine the probability of three or more dependent events [Grade 8]


Determine the probability of three or more independent events [Grade 8]

Determine the probability of an event consisting of mutually exclusive events [Grade 8]

MT 2.4.C - Determine the probabilities of complementary events and calculate the probability of the outcome of events.

Determine the number of combinations possible in a given situation [Grade 8]


Determine the number of permutations possible in a given situation [Grade 8]

MT 2.4.B - Use the Fundamental Counting Principle to determine the size of a finite sample space and the probabilities of the events in those spaces.


Determine the probability for independent events [Grade 7]

MT 2.4.A - Distinguish between independent and dependent compound events and apply the multiplication rule for probability to determine the probability for the events.

MT 2.4 - Use technology as needed to determine the possible number of outcomes for an event or compound event using the fundamental counting principle, permutations, combinations, and other systematic counting methods.

MT 2.3.C - Solve problems using the concepts of conditional probability and independent events in multicultural situations, including those of Montana American Indians.

MT 2.3.B - Make, evaluate, and justify decisions based on probabilities.

MT 2.3.A - Compute and interpret the expected value of random events.

MT 2.3 - Make, evaluate, and justify decisions based on probabilities in multicultural situations, including those of Montana American Indians (e.g., finding expected value and using rules of probability).

MT 2.2.C - Interpret and justify how sample statistics reflect the values of population parameters.

MT 2.2.B - Design and conduct a survey based on an appropriate sample then interpret and determine the validity of the results.

Determine if a question is likely to produce a biased survey result [Grade 8]


Determine if a sample is likely to be representative of the larger population [Grade 8]

MT 2.2.A - Analyze, interpret and evaluate the validity of a survey and identify possible sources of bias.

MT 2.2 - Evaluate the validity of reports based on collected and/or published data by considering the source of the data, the design of the study, and the way data are displayed, analyzed, and interpreted.


Compare the medians, the modes, or the ranges of the data in a double stem-and-leaf plot [Grade 8]

MT 2.1.E - Construct and interpret a back-to-back stem-and-leaf plot.


Grades: 9-12


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MT 3.3.A - Perform transformations of shapes in a plane with and without the coordinate system.

MT 3.3 - Identify, analyze, and use transformational, coordinate, and synthetic geometric approaches to solve problems.

MT 3.2.D - Use geometric models and spatial reasoning to solve problems in the context of art, science, and culture, including those of Montana American Indians.

MT 3.2.C - Construct geometric representations with and without technology.

MT 3.2.B - Visualize and draw three-dimensional objects from different perspectives and identify cross sections.

MT 3.2.A - Build and create isometric drawings, foundational drawings, and orthographic drawings of geometric solids and their views.

MT 3.2 - Use spatial reasoning and geometric models to solve problems with and without technology in the contexts of art, science, and culture, including Montana American Indians.

MT 3.1.B - Apply deductive and inductive reasoning to solve geometric problems.

MT 3.1.A - Formulate and evaluate conjectures based on geometric properties.

MT 3.1 - Formulate and evaluate conjectures about geometric objects and their properties, with and without technology, applying inductive reasoning when appropriate.


MT 2.5.C - Calculate the correlation coefficient of a set of data with technology, and interpret the coefficient as a measure of the strength and direction of the relationship between the variables.


Answer a question using information from a scatter plot [Grade 8]

MT 2.5.B - Make and justify the validity of predictions (interpolate, extrapolate) based on mathematical models (e.g., linear).


Approximate a trend line for a scatter plot [Grade 8]

MT 2.5.A - Given a set of bivariate data, develop an equation that models the relationship between the variables and determine its validity (e.g., linear with and without technology).

MT 2.5 - Model two-variable data using curve fitting with and without technology. Write an equation for a given model and decide when or if predictions based on this equation are valid.


Determine the number of permutations possible in a given situation [Grade 8]

Determine the number of combinations possible in a given situation [Grade 8]

MT 2.4.D - Use permutations and combinations to count outcomes and determine probabilities of events.

Make a prediction involving the probability of compound events [Grade 8]


Grades: 9-12


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Identify a triangle similarity postulate that justifies a similarity statement [Geometry]

Core Skill

Geometry and Measurement Identify a triangle congruence postulate that justifies a congruence statement [Geometry]

Core Skill

MT 3.5.C - Make and evaluate logical arguments justifying congruency and similarity of figures (e.g., triangles and quadrilaterals).

MT 3.5.B - Make and evaluate logical arguments justifying properties of figures on the coordinate plane (e.g., triangles and quadrilaterals).

MT 3.5.A - Use deductive reasoning, indirect proof and counterexamples to justify geometric conjectures and properties.

MT 3.5 - Establish the validity of geometric conjectures using deductive reasoning, indirect proof, and counterexamples, and critique arguments made by others.

MT 3.4.C - Use the law of sines and cosines to find indirect measurements in on-right triangles.

Determine the surface area of a rectangular prism [Grade 5] Core Skill

WP: Find the surface area of a rectangular prism [Grade 5] Core Skill

Geometry and Measurement Determine the volume of a rectangular prism [Grade 5]

WP: Determine the volume of a rectangular prism [Grade 5] Core Skill

Determine the volume of a rectangular or a triangular prism [Grade 7]

Core Skill

Determine the volume of a sphere or hemisphere [Geometry] Core Skill

Determine the surface area of a sphere [Geometry] Core Skill

WP: Determine the surface area of a geometric solid [Grade 7] Core Skill

MT 3.4.B - Use appropriate strategies to find the measures of length, perimeter, area, surface area and volume of composite figures and solids (e.g., pyramids, cones).

Determine the length of a leg of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

WP: Use the Pythagorean theorem to find a length or a distance [Grade 8]

Core Skill

Geometry and Measurement Determine the length of the hypotenuse of a right triangle using the Pythagorean theorem [Grade 8]

Core Skill

MT 3.4.A - Find sides and angles of right triangles using the Pythagorean Theorem, proportionality and trigonometric ratios.

MT 3.4 - Determine measures of two- and three-dimensional objects and their elements using trigonometric ratios, proportionality, the Pythagorean Theorem, and angle relationships.

MT 3.3.C - Use specific geometric approaches to solve problems (e.g., computer applications, physical models).

MT 3.3.B - Model and describe simple transformations and their compositions (e.g., composition of two reflections over parallel lines produces a translation).


Grades: 9-12


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Solve a 1-step equation involving whole numbers [Grade 6] Core Skill

MT 4.3.A - Solve and graph equations and inequalities within the real number system, justify each step and interpret the solution(s) (e.g. linear, absolute value and quadratic).

MT 4.3 - Solve a variety of equations, inequalities and systems of equations and inequalities, justify the solution process, and interpret the solution in context.


Core Skill

WP: Use a 2-variable linear equation to represent a situation [Grade 6]

Core Skill


Core Skill

WP: Use a 2-variable equation with rational coefficients to represent a situation [Grade 8]

Core Skill

WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations [Grade 8]

Core Skill

MT 4.2.A - Determine an equation or inequality that best models a contextual problem (e.g. linear, quadratic, or exponential).

MT 4.2 - Determine the appropriate symbolic representation of a given contextual situation (e.g., variables and parameters in equations, inequalities, functions, and matrices).

MT 4.1.C - Classify a pattern, table, or graph as arithmetic or geometric and write the rule in recursive and explicit form.

Determine a linear equation in two variables that represents a table of values [Grade 8]

Core Skill

Determine the table of values that represents a linear equation with rational coefficients in two variables [Grade 8]

Core Skill

Algebra Determine the graph of a 1-operation linear function [Grade 7] Core Skill

Determine the graph of a 2-operation linear function [Grade 8] Core Skill

Determine the graph of a given quadratic function [Algebra 1] Core Skill

Determine an equation that represents a graphed line [Algebra 1] Core Skill

MT 4.1.B - Represent functions in a variety of ways and justify the choice for solving a given problem.

Algebra Determine the slope-intercept form or the standard form of a linear equation [Algebra 1]

Core Skill

MT 4.1.A - Generate equivalent forms of linear equations such as slope-intercept, point-slope, and standard form and justify the choice for solving a given problem.

MT 4.1 - Represent functions in a variety of ways including tables, graphs or diagrams, verbal descriptions, and symbolic expressions in recursive and explicit form. Justify the choice of an appropriate form for solving a given problem.



Grades: 9-12


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MT 4.5.B - Decide if a solution is reasonable in the context of the original situation.

MT 4.5.A - Justify the selection of a function as the best choice to model a problem situation including those involving Montana American Indians, analyze the results, and make future predictions (e.g., linear, quadratic and exponential).

MT 4.5 - Given data or a problem situation, select and use an appropriate function model to analyze results or make a prediction with and without technology using cultural contexts, including those of Montana American Indians.

MT 4.4.B - Represent and use functions in equivalent forms to identify and perform transformations.

MT 4.4.A - Describe how changing one or more parameters in one of the general forms of a function effects the graph and behavior of the function (e.g., linear, quadratic, and exponential).

MT 4.4 - Analyze the effects of transformations on families of functions and recognize their characteristics. Represent and use functions in equivalent forms to identify and perform transformations.

Solve a system of linear equations in two variables using any method [Algebra 1]

Core Skill

MT 4.3.B - Solve systems of equations or inequalities using graphing, substitution, elimination, and matrices, justify and interpret the solution(s) (e.g., linear).

Solve a quadratic equation using the quadratic formula [Algebra 1] Core Skill



Solve a 2-step linear inequality in one variable [Grade 8] Core Skill

Determine some solutions to a 1-variable linear inequality [Grade 7]

Solve a proportion involving decimals [Grade 7] Core Skill



Determine the graph of the solutions to a 2-step linear inequality in one variable [Grade 8]

Core Skill

Solve a 1-variable absolute value inequality [Algebra 1] Core Skill

Solve a quadratic equation by taking the square root [Algebra 1]

Solve a quadratic equation by factoring [Algebra 1] Core Skill

Solve a 1-variable linear equation with the variable on both sides [Algebra 1]

Core Skill

Solve a 1-variable linear inequality with the variable on both sides [Algebra 1]

Core Skill

Determine the graph of a 2-variable linear inequality [Algebra 1]


Grades: 9-12

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