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(EE) EXPRESSIONS AND EQUATIONS

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

(F) FUNCTIONS

MAT-08.F

BPSS-MAT logoDomain (F)

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.

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