MAT-08.F.02
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8th Grade MAT Targeted Standards
Domain (F) Functions
Cluster: 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.
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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.
Proficiency Scale
Link to Proficiency Scale PDF
Resources
Websites
Vocabulary
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MAT-08.G
 Domain (G)
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.
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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. |
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MAT-08.G.07
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8th Grade MAT Targeted Standards
Domain (G) Geometry
Cluster: 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.
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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.
Proficiency Scale
Link to Proficiency Scale PDF
Resources
Websites
Vocabulary
- Pythagorean Theorem
- Leg
- Hypotenuse
- Right Triangle
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MAT-08.NS
 Domain (NS)
The Number System
- Know that there are numbers that are not rational, and approximate them by rational numbers.
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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. |
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MAT-08.SP
 Domain (SP)
Statistics and Probability
- Investigate patterns of association in bivariate data.
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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. |
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MAT-08.EE
 Domain (EE)
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.
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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 formx² = 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.
- 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. |
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MAT-08.EE.01
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8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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.
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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.
Proficiency Scale
Link to Proficiency Scale PDF
Resources
Websites
Vocabulary
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MAT-08.EE.02
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8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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.
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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.
Proficiency Scale
Link to Proficiency Scale PDF
Link to Proficiency Scale Google Doc
Resources
Websites
Vocabulary
- square root
- cube root
- radical
- radicand
- perfect square
- perfect cube
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MAT-08.EE.03
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8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills Domain (Performance) Targets
Product Targets
Proficiency Scale
Link to PDF
| Score |
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Description |
Sample Activity
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| 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. |
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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. |
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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). |
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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). |
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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. |
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Resources
Websites
- Add resources with links, youtube or PDF
Vocabulary
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MAT-08.EE.04
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8th Grade MAT Targeted Standards
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.
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Student Learning Targets:
Knowledge Targets
Reasoning Targets
Skills Domain (Performance) Targets
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
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