In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Understand (Functions are rules)
2 - Understand (Graphing functions)
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2 - I understand that a function is a rule that assigns each input exactly one output.
2 - I understand that the graph of a function is the set of ordered pairs consisting of the corresponding input and output.
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A. A function is a rule that assigns each input with exactly one corresponding output, which gives you the set of ordered pairs that forms the graph of the function.
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A.1 How does one find the output of a function when given an input value?
A.2 How many output are there for each input?
A.3 What is an ordered pair?
A.4 How does one graph a function?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Properties
Representations
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4 - Compare (Properties of two functions)
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4 - I can compare the properties of two functions represented in different ways (algebraically, graphically, numerically in tables or by verbal descriptions.
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A. The properties of two functions that are represented in different ways can be compared.
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A.1 How does one represent a function algebraically?
A.2 How does one represent a function graphically?
A.3 How does one represent a function numerically in a table?
A.4 How does one represent a function by verbal description?
A.5 How does one compare the properties of two function represented differently?
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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 = s 2 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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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y = mx + b
Examples
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2 - Interpret (Equation y = mx + b as a linear function)
3 - Give (Examples of non linear functions)
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2 - I can interpret the equation y = mx + b as defining a linear function whose graph is a straight line.
3 - I can give examples of function that are not linear.
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A. One can interpret the equation y = mx + b as being a linear function, and all other equation forms as not linear.
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A.1 When one graphs corresponding input and output for the equation y = mx + b, what does the graph look like?
A.2 When one graphs corresponding input and output for equations that do not have the form y = mx + b, does it make a straight line?
A.3 What does the term linear function mean?
A.4 How does one give examples of functions that are not linear?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Function
Relationship
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6 - Construct (Function to model a linear relationship between two quantities)
4 - Determine (Rate of change from a description of the relationship)
4 - Determine (Rate of change from a table of values)
4 - Determine (Rate of change from a graph)
4 - Determine (Initial value from a description of the relationship)
4 - Determine (Initial value from a table of values)
4 - Determine (Initial value from a graph)
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6 - I can construct a function to model a linear relationship between two quantities.
4 - I can determine the rate of change from a description of the relationship.
4 - I can determine the rate of change from a table of values)
4 - I can determine the rate of change from a graph.
4 - I can determine the initial value from a description of the relationship.
4 - I can determine the initial value from a table of values.
4 - I can determine the initial value from a graph.
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A. The rate of change, the initial value and a function to model a linear relationship can be determined if given two points, a table, a graph or a verbal description of a situation.
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A.1 How does one construct a function to model a linear relationship between two quantities?
A.2 What is the rate of change?
A.3 What is the initial value?
A.4 How does one determine the rate of change from a description of a situation?
A.5 How does one determine the rate of change from a table of values?
A.6 How does one determine the rate of change from a graph?
A.7 How does one determine the initial value from the description of a situation?
A.8 How does one determine the initial value from a table of values?
A.9 How does one determine the initial value from a graph?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Relationship
Graph
Features
Description
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2 - Describe (Functional relationship between two quantities)
4 - Analyze (Graph)
3 - Sketch (Graph)
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2 - I can describe qualitatively the functional relationship between two quantities.
4 - I can analyze a graph to see if the function is increasing, decreasing, linear or non linear.
3 - I can sketch a graph that exhibits the qualitative features of a function the has been described verbally.
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A. One can convert between a graph and a verbal description of the functional relationship between two quantities.
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A.1 What are qualitative features of a function?
A.2 How does one determine if a function is increasing or decreasing?
A.3 How does one determine if a function is linear or non linear?
A.4 How does one describe the qualitative features of a function?
A.5 How does one sketch a graph that exhibits the qualitative features that have been described verbally?
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