Prioritized Standards Categories All categories Not categorized Prioritized Standards (EE) Expressions and Equations (F) Functions (G) Geometry (NS) The Number System (SP) Statistics and Probability

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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.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

# 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

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