A function is a mathematical relationship in which each input has exactly one output. It is like an input-output machine. For each number that goes into the machine, a unique output comes out. There are 3 parts to a function: the input (x-value), the relationship or rule, and the output (y-value). The rule determines how the input relates to the output. In the example below, the output is equal to the input cubed.

### Monday, January 22

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.

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 61*.

Blended learning: XtraMath & Flashcard Machine Vocabulary

Lesson (Introduction to Functions)

1. Pass back and go over linear equations test.

2. Generate interest: What does a blender and a function machine have in common?

3. Identifying functions notes & handout: examples and nonexamples (concept attainment method)

4. Function vocabulary journal entry

(taken from Math Tales from the Spring Blog)

5. Guided practice: “Functions Homework 1”

6. Independent practice: “Identifying Functions” homework paper

7. Blended learning: IXL, grade 8, Z.1 Identifying Functions

Closing

Exit ticket:

Homework

Finish the “Identifying Functions” worksheet. On Friday, there will be a quiz over identifying and comparing functions.

### Tuesday, January 23

There will be a substitute teacher. Plans will be left on teacher’s desk.

Homework

Work on your IXL module 6 to-do list. On Friday, there will be a quiz over identifying and comparing functions.

### Wednesday, January 24

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. 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.

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 63*.

Blended learning: XtraMath & Flashcard Machine Vocabulary

Lesson (Comparing Functions & Describing Functions)

1. Go over “Identifying Functions” homework from Monday.

2. Introduction to function rules: Function Machine

3. Review definition of a function: a rule that explains what to do with the input value to get the output value. The rule may involve one or more operations but each input value results in exactly one output, definition of input, definition of output

4. “Ins and Outs of Functions” lesson

5. Guided practice: identifying functions from graphs, tables, and ordered pairs

IXL-Identify functions

6. Cloze notes & guided practice: “Comparing Functions Student Handout 2”

7. Independent practice: “Comparing Functions Homework 2”

Closing

Exit ticket:

Homework

On Friday, there will be a brief quiz over identifying functions. Work on your IXL module 6 to-do list.

### Thursday, January 25

Common Core Standards and Extended Standards

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.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.

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 64*.

Blended learning: XtraMath & Flashcard Machine Vocabulary

Lesson (Linear vs. Non-Linear Functions)

1. Go over homework.

2. Review key ideas

3. Desmos graphing calculator demonstration & guided notes

3. Guided practice:

6. Cooperative practice: functions task cards footloose

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

Closing

Homework

There is no homework. Work on your IXL module 6 to-do list. It is due next Friday. The functions unit test will be next Friday. There will be a quiz over functions tomorrow.

Graphs can be used to model complex real-world situations. Graphs help us interpret situations more easily than information presented in an equation, a table, or a written scenario. The slope of a graphed line represents the rate of change of the function. A linear function increases or decreases at a constant rate, and its graph is a straight line. The rate of change is variable if the graph of the function is curved, and the function is called a nonlinear function.

### Friday, January 26

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.

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

Identifying functions worksheet

Blended learning: IXL module 6 to-do list

Lesson (Identifying and Comparing Functions Quiz/Describing Functions)

1. Demonstration: Interactivate Simple Plot (link in Schoology course)

2. Independent practice: functions sorting activity

3. Review: identifying and comparing functions

4. Identifying & comparing functions quiz: Google form & paper

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

Closing

Homework

There will be a unit test over functions next Friday. Work on your IXL module 6 to-do list. It is due next Friday.