This week students will continue to explore functions and relations. Students will identify, describe, compare and analyze functions presented in tables, sets of ordered pairs, graphs, word problems and mapping diagrams (arrays). Several key characteristics differentiate linear and nonlinear functions. The graph of a linear function is a straight line, and its equation has no exponents. The equation can be written in slope-intercept form, y=mx+b. The graph of a nonlinear function is curved, and its equation has an exponent on the input (x-value).

Exponents also help us differentiate between relations (ordered pairs that are not functions) and functions. If an equation has an exponent on the output (y-value), it is not a function; and its graph will be nonlinear. It will also fail the vertical line test when graphed. If an equation has an exponent on the input (x-value), it may be a function; but its graph will be nonlinear.

### Monday, January 29

Common Core Standards and Extended Standards

8.F.1 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.

8.F.2 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.

8.F. 3 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 squared 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.

8.F.4 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.

8.F.5 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.

Student Objectives

I can identify functions using sets of ordered pairs, tables, mappings, and graphs.

I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.

I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.

I can analyze and interpret graphs.

I can compare functions using rate of change and y-intercept.

Bellwork

Students will complete *Math Minute 64*.

Lesson (Comparing Linear Functions/Linear vs. Nonlinear Functions/Comparing Functions)

1. IXL Z.4: “Rate of Change” and Z.5 “Constant Rate of Change”

2. IXL Z.11 “Compare linear functions”

3. Go over results of identifying functions quiz: Google form portion

4. Comparing functions solve & color packet

5. Demonstration: Desmos graphing calculator & Interactivate Simple Plot

6. Guided practice: linear vs. nonlinear discovery worksheet

7. Demonstration and guided practice: Function Machine & function rules packet

8. Cooperative practice: functions task cards

9. Independent practice: IXL module 6 to-do list & linear vs. nonlinear worksheet

Closing

IXL trouble spots

Homework

There will be a test over functions on Friday. The IXL module 6 to-do list will be due Friday. Finish the linear vs. nonlinear worksheet.

### Tuesday, January 30

Common Core Standards and Extended Standards

8.F.1 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.

8.F.2 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.

8.F. 3 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 squared 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.

8.F.4 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.

8.F.5 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.

Student Objectives

I can identify functions using sets of ordered pairs, tables, mappings, and graphs.

I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.

I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.

I can analyze and interpret graphs.

I can compare functions using rate of change and y-intercept.

Bellwork

Students will complete *Math Minute 65*.

Lesson (Functions/Analyzing Graphs)

1. IXL

2. Go over homework.

3. Go over results of identifying functions quiz: paper portion

4. Review: comparing functions

5. Functions task cards with a partner(s)

6. Analyzing graphs discovery worksheet

7. Cooperative practice: matching verbal descriptions to graphs from Math Tales from the Spring Blog

Use corresponding Powerpoint slides to go over and discuss answers.

8. Independent practice: IXL module 6 to-do list

Closing

IXL trouble spots

Homework

There will be a test over functions on Friday. The IXL module 6 to-do list is due Friday. The functions review packet is due Thursday. The functions review worksheet is due Friday.

### Wednesday, January 31

Common Core Standards and Extended Standards

8.F.1 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.

8.F.2 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.

8.F. 3 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 squared 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.

8.F.4 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.

8.F.5 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.

Student Objectives

I can identify functions using sets of ordered pairs, tables, mappings, and graphs.

I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.

I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.

I can analyze and interpret graphs.

I can compare functions using rate of change and y-intercept.

Bellwork

Students will complete *Math Minute 66*.

IXL trouble spots

Lesson (Functions/Analyzing Graphs)

1. Go over homework.

2. Identifying and comparing functions hot seat review game

3. Modified interpreting distance-time graphs lesson (from Mathematics Assessment Resource Service

University of Nottingham & UC Berkeley)

4. Independent practice: IXL module 6 to-do list and functions review packet

Closing

Exit ticket in Google forms

Homework

There will be a test over functions on Friday. The IXL module 6 to-do list is due on Friday. The functions review worksheet is due tomorrow. The functions review worksheet is due Friday.

### Thursday, February 1

Shortened class due to awards assembly

8.F.1 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.

8.F.2 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.

8.F. 3 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 squared 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.

8.F.4 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.

8.F.5 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.

Student Objectives

I can identify functions using sets of ordered pairs, tables, mappings, and graphs.

I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.

I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.

I can analyze and interpret graphs.

Bellwork

Students will complete *Math Minute 67*.

Lesson (Functions Review)

1. Review key ideas

2. Trashketball-functions review

3. Independent practice: functions review packet and IXL module 6 to-do list

Closing

Summarize key ideas with a venn diagram: functions vs. relations (not functions)

Homework

The functions review worksheet and the IXL module 6 to-do list are due tomorrow. The unit test over functions is tomorrow.

### Friday, February 2

Shortened class due to pep rally

8.F.1 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.

8.F.2 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.

8.F. 3 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 squared 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.

8.F.4 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.

8.F.5 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.

Student Objectives

I can identify functions using sets of ordered pairs, tables, mappings, and graphs.

I can identify examples of proportional and nonproportional functions that arise from mathematical and real-world problems.

I can distinguish between proportional and nonproportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0.

I can analyze and interpret graphs.

Bellwork

Students will complete *Math Minute 68*.

Lesson (Functions Test)

1. XtraMath challenge

2. Collect IXL module 6 to-do list

3. Review key ideas

4. Functions test

5. Common core math vocabulary: bingo, Quizlet Live or Pictionary (student choice-majority rules)

6. Independent practice: Just for You IXL To-Do List

Closing

Homework

There is no homework. Enjoy your weekend!