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(EE) Expressions and Equations

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MAT-08.EE

BPSS-MAT logoDomain (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.

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.

MAT-08.EE.01

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.

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

  • Power
  • Exponent
  • Base

 

PDF document MAT-08_EE_01 Proficiency Scale.pdf
Word 2007 document 8.EE.1 Proficiency Scale.docx

MAT-08.EE.02

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.

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

 

PDF document MAT-08_EE_02 Proficiency Scale.pdf
Word 2007 document Proficiency Scale 8.EE.2.docx

MAT-08.EE.03

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.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills Domain (Performance) Targets

  • I can

Product Targets

  • I can

Proficiency Scale

Link to PDF

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

Websites

  • Add resources with links, youtube or PDF

Vocabulary

  • List

 

MAT-08.EE.04

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.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
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 Standards
Domain (EE) Expressions and Equations
Cluster: 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.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • slope
  • y-intercept
  • linear equation
  • proportional

 

PDF document MAT-08_EE_05 Proficiency Scale.pdf

MAT-08.EE.06

8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

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

 

PDF document MAT-08_EE_06 Proficiency Scale.pdf

MAT-08.EE.07

8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can

Skills Domain (Performance) Targets

  • I can

Product Targets

  • I can

Proficiency Scale

Link to Proficiency Scale PDF

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

Websites

  • Add resources with links, youtube or PDF

Vocabulary

  • List

 

MAT-08.EE.07.a

8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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.

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

  • linear equation
  • solution
  • inverse 

 

PDF document MAT-08_EE_07a Proficiency Scale.pdf

MAT-08.EE.07b

8th Grade MAT Targeted Standards
Domain (EE) Expressions and Equations
Cluster: 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.

 

Proficiency Scale

Link to Proficiency Scale PDF

Resources

Websites

Vocabulary

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

 

PDF document MAT-08_EE_07b Proficiency Scale.pdf

MAT-08.EE.08

8th Grade MAT Targeted Standards
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:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
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

8th Grade MAT Targeted Standards
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:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
Rubric - Resources

MAT-08.EE.08b

8th Grade MAT Targeted Standards
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:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
Rubric - Resources

MAT-08.EE.08c

8th Grade MAT Targeted Standards
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:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills Domain (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can
Rubric - Resources

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