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# Expressions and Equations

• Work with radicals and integer exponents.
• Understand the connections between proportional relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.

## Domain Description

Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.

## Standards in this Domain

• MAT-08.EE.01 - Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.
• MAT-08.EE.02 - Use square root and cube root symbols to represent solutions to equations of the form = p and  = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
• MAT-08.EE.03 - Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.
• MAT-08.EE.04 - Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
• MAT-08.EE.05 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
• MAT-08.EE.06 - Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
• MAT-08.EE.07 - Solve linear equations in one variable.
• MAT-08.EE.08 - Analyze and solve pairs of simultaneous linear equations.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-08.EE.01

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Work with radicals and integer exponents MAT-08.EE.01 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,32 x 3-5 = 3-3 = 1/33 = 1/27.

## Student Learning Targets:

### Knowledge Targets

• I can apply all five properties of integer exponents to generate equivalent numerical expressions.

### Reasoning Targets

• I can apply more than one property of exponents to simplify multi-step expressions.

### Skills Domain (Performance) Targets

• I can solve word problems involving properties of exponents.

## Resources

### Vocabulary

• Power
• Exponent
• Base

#### MAT-08.EE.02

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Work with radicals and integer exponents MAT-08.EE.02 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

## Student Learning Targets:

### Knowledge Targets

• I can use square root symbols to represent solutions to equations in the form x² = p where p is a positive rational number.
• I can use cube root symbols to represent solutions to equations in the form x³ = p where p is a positive rational number.
• I can recognize that squaring a number and taking the square root of a number are inverse operations.
• I can recognize that cubing a number and taking the cube root of a number are inverse operations.

### Reasoning Targets

• I can evaluate the square root of a perfect square.
• I can evaluate the cube root of a perfect cube.
• I can explain why the square root of a non-perfect square is irrational.

## Resources

### Vocabulary

• square root
• cube root
• perfect square
• perfect cube

#### MAT-08.EE.03

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Work with radicals and integer exponents MAT-08.EE.03 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10⁸ and the population of the world as 7 × 10⁹, and determine that the world population is more than 20 times larger.

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## Proficiency Scale

 Score Description Sample Activity 4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. - 2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). 2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). - 1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). 1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). - 0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). 0.0 Even with help, the student demonstrates no understanding or skill. -

## Resources

### Vocabulary

• List

#### MAT-08.EE.04

Domain (EE) Expressions and Equations
Cluster: Work with radicals and integer exponents

MAT-08.EE.04 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-9-10.1.1. Express numbers between one-billionth and one billion in fraction, decimal, and verbal form; express numbers of all magnitudes in scientific notation

**MAT-8.1.4 Represent large and small numbers using scientific notation

**MAT-9-10.1.1. Express numbers between one-billionth and one billion in fraction, decimal, and verbal form; express numbers of all magnitudes in scientific notation

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.EE.05

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Understand the connections between proportional relationships, lines, and linear equations. MAT-08.EE.05 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

## Student Learning Targets:

### Knowledge Targets

• I can graph proportional relationships in a coordinate plane.

### Reasoning Targets

• I can interpret the unit rate of a proportional relationship as the slope of the graph that intersects the origin.

### Skills Domain (Performance) Targets

• I can compare two different proportional relationships represented in different ways, such as tables, graphs, and equations.

## Resources

### Vocabulary

• slope
• y-intercept
• linear equation
• proportional

#### MAT-08.EE.06

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Understand the connections between proportional relationships, lines, and linear equations. MAT-08.EE.06 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

## Student Learning Targets:

### Knowledge Targets

• I can use right triangles to show why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.
• I can write an equation for a line in slope-intercept for (y = mx + b).

### Reasoning Targets

• I can justify the right triangles are similar by comparing the ratios of the lengths of the corresponding sides.

## Resources

### Vocabulary

• slope
• y-intercept
• slope-intercept form
• linear equation

#### MAT-08.EE.07

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Analyze and solve linear equations and pairs of simultaneous linear equations MAT-08.EE.07 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

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## Proficiency Scale

 Score Description Sample Activity 4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. - 2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). 2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). - 1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). 1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). - 0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). 0.0 Even with help, the student demonstrates no understanding or skill. -

## Resources

### Vocabulary

• List

#### MAT-08.EE.07.a

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Analyze and solve linear equations and pairs of simultaneous linear equations Solve linear equations in one variable. MAT-08.EE.07.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

## Student Learning Targets:

### Knowledge Targets

• I can use inverse operations and the properties of equality to solve linear equations in one variable.

### Reasoning Targets

• I can solve linear equations in one variable with one solution.
• I can solve linear equations in one variable with infinitely many solutions.
• I can solve linear equations in one variable with no solutions.

## Resources

### Vocabulary

• linear equation
• solution
• inverse

#### MAT-08.EE.07b

 8th Grade MAT Targeted StandardsDomain (EE) Expressions and EquationsCluster: Analyze and solve linear equations and pairs of simultaneous linear equations Solve linear equations in one variable. MAT-08.EE.07b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

## Student Learning Targets:

### Reasoning Targets

• I can solve linear equations with rational number coefficients and variables on both sides of the equation.
• I can solve linear equations involving the distributive property.
• I can solve linear equations involving combining like terms.

## Resources

### Vocabulary

• solution
• inverse
• coefficient
• distributive property
• like terms
• linear equation

#### MAT-08.EE.08

Domain (EE) Expressions and Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

MAT-08.EE.08 Analyze and solve pairs of simultaneous linear equations.

• a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
• b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
• c. Solve real-world and mathematical problems leading to two linear equations in two variables.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-9-10.5.9(A) Solve linear equations and inequalities, systems of two linear equations or inequalities, and quadratic equations having rational solutions; e.g., factoring, quadratic formula.

**MAT-9-10.5.9(A^) Solve linear equations and inequalities, systems of two linear equations or inequalities, and quadratic equations having rational solutions; e.g., factoring, quadratic formula.

**MAT-9-10.5.9(B) Solve linear equations and inequalities, systems of two linear equations or inequalities, and quadratic equations having rational solutions; e.g., factoring, quadratic formula.

**MAT-9-10.5.9(C) Solve linear equations and inequalities, systems of two linear equations or inequalities, and quadratic equations having rational solutions; e.g., factoring, quadratic formula

**MAT-9-10.5.9(D) Solve linear equations and inequalities, systems of two linear equations or inequalities, and quadratic equations having rational solutions; e.g., factoring, quadratic formula

**MAT-9-10.5.13 Interpret a graphical representation of a real-world situation

MAT-9-10.5.12 Graphically represent the solution or solutions to an equation, inequality, or system.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.EE.08a

Domain (EE) Expressions and Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

Analyze and solve pairs of simultaneous linear equations.

MAT-08.EE.08a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-08.EE.08b

Domain (EE) Expressions and Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

Analyze and solve pairs of simultaneous linear equations.

MAT-08.EE.08b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-08.EE.08c

Domain (EE) Expressions and Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations

Analyze and solve pairs of simultaneous linear equations.

MAT-08.EE.08c Solve real-world and mathematical problems leading to two linear equations in two variables.

For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

# Functions

• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.

## Domain Description

Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.

## Standards in this Domain

• MAT-08.F.01 - Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required for Grade 8)
• MAT-08.F.02 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
• MAT-08.F.03 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
• MAT-08.F.04 - Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
• MAT-08.F.05 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-08.F.01

 8th Grade MAT Targeted StandardsDomain (F) FunctionsCluster: Define, evaluate, and compare functions. MAT-08.F.01 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

## Student Learning Targets:

### Knowledge Targets

• I can understand that in a function, each input has only one output.

### Reasoning Targets

• I can evaluate a function.
• I can complete an input-output table accurately.
• I can describe the domain and the range of a function.
• I can determine whether a given graph or table represents a function.

### Skills Domain (Performance) Targets

• I can graph a function from a table.

## Resources

### Vocabulary

• function
• domain
• range
• input
• output
• discrete
• continuous
• linear
• nonlinear

#### MAT-08.F.02

 8th Grade MAT Targeted StandardsDomain (F) FunctionsCluster: Define, evaluate, and compare functions MAT-08.F.02 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

## Student Learning Targets:

### Reasoning Targets

• I can determine the properties of a function written in algebraic form (slope, y-intercept, linear, nonlinear).
• I can determine the properties of a function given the inputs and outputs in a table.
• I can determine the properties of a function represented as a graph.
• I can determine the properties of a function given verbally.

### Skills Domain (Performance) Targets

I can compare properties of two functions each represented in a different way.

## Resources

### Vocabulary

• rate of change

#### MAT-08.F.03

Domain (F) Functions
Cluster: Define, evaluate, and compare functions

MAT-08.F.03 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

*MAT-11-12.5.2 Generate graphs of a variety of functions (i.e., linear, quadratic, polynomial, absolute value, and exponential), using technology when appropriate.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.F.04

Domain (F) Functions
Cluster: Define, evaluate, and compare functions

MAT-08.F.04 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y)values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.F.05

Domain (F) Functions
Cluster: Define, evaluate, and compare functions.

MAT-08.F.05 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

*MAT-11-12.5.2 Generate graphs of a variety of functions (i.e., linear, quadratic, polynomial, absolute value, and exponential), using technology when appropriate.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

# Geometry

• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

## Domain Description

Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.

## Standards in this Domain

• MAT-08.G.01 - Verify experimentally the properties of rotations, reflections, and translations
• MAT-08.G.02 - Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
• MAT-08.G.03 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
• MAT-08.G.04 - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
• MAT-08.G.05 - Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
• MAT-08.G.06 - Explain a proof of the Pythagorean Theorem and its converse.
• MAT-08.G.07 - Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
• MAT-08.G.08 - Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
• MAT-08.G.09 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-08.G.01

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.01 Verify experimentally the properties of rotations, reflections, and translations.

• a. Lines are taken to lines, and line segments to line segments of the same length.
• b. Angles are taken to angles of the same measure.
• c. Parallel lines are taken to parallel lines.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

**MAT-7.2.5. Draw the result of a transformation in the coordinate plane; i.e., translation, reflection, and rotation

**MAT-8.2.6 Draw the results of a combination of transformations in the coordinate plane; i.e., reflections, rotations, and translations

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.01a

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

Verify experimentally the properties of rotations, reflections, and translations.

MAT-08.G.01a Lines are taken to lines, and line segments to line segments of the same length.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-08.G.01b

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

Verify experimentally the properties of rotations, reflections, and translations.

MAT-08.G.01b Angles are taken to angles of the same measure.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-08.G.01c

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

Verify experimentally the properties of rotations, reflections, and translations.

MAT-08.G.01c Parallel lines are taken to parallel lines.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

#### MAT-08.G.02

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.02 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-5.2.7 Describe properties of congruent (BPS: and similar figures with proportionality) figures and use them to solve problems

*MAT-7.2.4 Identify relationships between congruent figures and similar figures

*MAT-2.2.5. Identify congruent figures from a selection of similar figures

*MAT-4.2.4 Use motion geometry to show that shapes are congruent or similar

*MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.03

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.03 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

## Student Learning Targets:

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-9-10.4.2 Describe the effects of scalar change on the area and volume of a figure; eg., the effects of doubling one or more edges of a solid on its surface area and volume.

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.04

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.04 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

## Student Learning Targets:

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.2.5 Identify, describe, and model motion geometry; i.e., rotations, reflections, and translations

*MAT-7.2.4 Identify relationships between congruent figures and similar figures

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.05

Domain (G) Geometry
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software

MAT-08.G.05 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

## Student Learning Targets:

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

*MAT-8.2.3 Identify the angles formed and the relationships between the angles when parallel lines are intersected by a transversal

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.06

Domain (G) Geometry
Cluster: Understand and apply the Pythagorean Theorem.

MAT-08.G.06 Explain a proof of the Pythagorean Theorem and its converse.

## Student Learning Targets:

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.07

 8th Grade MAT Targeted StandardsDomain (G) GeometryCluster: Understand and apply the Pythagorean Theorem. MAT-08.G.07 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.

## Student Learning Targets:

### Reasoning Targets

• I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in mathematical problems in two and three dimensions.

### Skills Domain (Performance) Targets

• I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world problems in two and three dimensions.

## Resources

### Vocabulary

• Pythagorean Theorem
• Leg
• Hypotenuse
• Right Triangle

#### MAT-08.G.08

Domain (G) Geometry
Cluster: Understand and apply the Pythagorean Theorem

MAT-08.G.08 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

## Student Learning Targets:

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-8.2.4 Apply the Pythagorean Theorem to problems involving right triangles

**MAT-9-10-2.6 Use distance, midpoint, and slope to determine relationships between points, lines, and plane figures in the Cartesian coordinate system; e.g., determine whether a triangle is scalene, isosceles, or equilateral given the coordinates of its vertices.

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.G.09

Domain (G) Geometry
Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

MAT-08.G.09 Know the formulas for the volume of cones, cylinders and spheres and use them to solve real-world and mathematical problems.

## Student Learning Targets:

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-7.4.8. Use formulas to determine the volume of right cylinders

***MAT-8.4.3 Use formulas to determine the surface area and volume of right cones and spheres

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

# The Number System

• Know that there are numbers that are not rational, and approximate them by rational numbers.

## Standards in this Domain

• MAT-08.NS.01 - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
• MAT-08.NS.02 - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ∏²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-08.NS.01

Domain (NS) The Number System
Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers

MAT-08.NS.01 Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-6.1.3 Find the equivalent forms among fractions, decimals, and whole number percents

*MAT-8.1.1 Identify subsets of the real number system; i.e., natural and whole numbers, integers, rational and irrational numbers

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.NS.02

Domain (NS) The Number System
Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers

MAT-08.NS.02 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²).

For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

# Statistics and Probability

• Investigate patterns of association in bivariate data.

## Standards in this Domain

• MAT-08.SP.01 - Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
• MAT-08.SP.02 - Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
• MAT-08.SP.03 - Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
• MAT-08.SP.04 - Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-08.SP.01

Domain (SP) Statistics and Probability
Cluster: Investigate patterns of association in bivariate data

MAT-08.SP.01 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

***MAT-8.3.2 Collect, organize, and display data using scatter and stem-and-leaf plot

***MAT-9-10.3.2. Interpret a given visual representation (i.e., circle graphs, bar graphs, histograms, stem-and-leaf plots, box-and-whisker plots, and scatter plots) of a set of data

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.SP.02

Domain (SP) Statistics and Probability
Cluster: Investigate patterns of association in bivariate data

MAT-08.SP.02 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

## Student Learning Targets:

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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

**MAT-11-12.3.4 Given a set of data exhibiting a linear trend, approximate an equation for the line of best fit (with or without technology) and use that model to make predictions

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.SP.03

Domain (SP) Statistics and Probability
Cluster: Investigate patterns of association in bivariate data

MAT-08.SP.03 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

## Student Learning Targets:

• I can
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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark

• *** Indicates strong content alignment from Common Core Standards to North Dakota Content Standards
• ** Indicates partial content alignment from Common Core Standards to North Dakota Content Standards
• * Indicates weak content alignment from Common Core Standards to North Dakota Content Standards

#### MAT-08.SP.04

Domain (SP) Statistics and Probability
Cluster: Investigate patterns of association in bivariate data

MAT-08.SP.04 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

## Student Learning Targets:

• I can
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### Product Targets

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Rubric - Resources

Comparison to ND 2005 Mathematics Standards/Benchmark