Due to the 2-hour delay and school closing last week, the unit test over linear equations was postponed. Students will take the test on Wednesday. It will be the last test for this grading period. It will cover proportional relationships, non-proportional relationships, constant of proportionality, unit rate, slope, y-intercept, slope-intercept form, graphing lines, and writing linear equations from graphs, tables, and scenarios. Use the links pages in the following folders of our Schoology course to review: “Proportional Relationships,” “Non-Proportional Relationships,” and “Writing Linear Equations.” IXL and this website also offer opportunities to review for Tuesday’s test.

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.

### Tuesday, January 16

**School closed due to inclement weather**

Common Core Standards and Extended Standards

8.EE.6 Understand the connections between proportional relationships, lines, and linear equations.

Create and solve ratios.

Represent proportional relationships.

Use ratios to solve real-world problems.

Ratios and proportional relationships can be used to determine unknown quantities.

8.F.4 Use functions to model relationships between quantities.

Specific input will yield specific output.

Compare/contrast two different input/output relationships.

Equations of linear and non-linear functions

Construct a linear graph using a table or equation.

Construct a linear graph as described verbally.

Student Objectives

Given a graphed line, an input/output table, or two ordered pairs, I can use a coordinate graph to determine slope.

I can classify positive, negative, zero, and undefined slopes.

I can write a linear equation to represent a graph, an input-output table, or a written scenario.

Bellwork

Students will complete *Math Minute 61*.

Flashcard Machine challenge

Lesson (Linear Equations Review)

1. Go over homework: “Linear Equations Review” worksheet

2. Linear equations card sort in teams of 3: equations, graphs, word problems, and tables

3. Linear equations review trashketball including IXL trouble spots items

4. Other: Pass back papers. Pass out IXL module 6 to-do list. Work on homework.

5. Independent practice and homework if not completed in class: Linear equations review, Google form

6. Independent practice: IXL IEP to-do list

Closing

Essential questions:

What does the slope of a line indicate about the line?

What information does the equation of a line give you?

How are equations and graphs related?

Homework

There will also be an organization quiz and a journal check on Wednesday. Work on any incomplete items from the IXL module 7, IXL module 3, and IXL modules 4/5 to-do lists. There will be a unit test over linear equations on tomorrow. Finish the “Linear Equations Review” Google form. It is due tomorrow.

Links

Use the links in the Schoology proportional relationships and non-proportional relationships folders to review linear equations.

### Wednesday, January 17

Common Core Standards and Extended Standards

8.EE.6 Understand the connections between proportional relationships, lines, and linear equations.

Create and solve ratios.

Represent proportional relationships.

Use ratios to solve real-world problems.

Ratios and proportional relationships can be used to determine unknown quantities.

8.F.4 Use functions to model relationships between quantities.

Specific input will yield specific output.

Compare/contrast two different input/output relationships.

Equations of linear and non-linear functions

Construct a linear graph using a table or equation.

Construct a linear graph as described verbally.

Student Objectives

Given a graphed line, an input/output table, or two ordered pairs, I can use a coordinate graph to determine slope.

I can classify positive, negative, zero, and undefined slopes.

I can write a linear equation to represent a graph, an input-output table, or a written scenario.

Bellwork

Students will complete *Math Minute 62*.

XtraMath challenge

Lesson (Linear Equations Test)

1. Go over homework: Share correct answers for Linear equations review and share class results in Google forms.

2. Collect math journals.

3. Linear equations unit test

4. Organization quiz

5. Math Minutes points for the quarter

6. Independent practice: IEP IXL to-do list

Closing

Discussion: Respond to essential questions prompt in Schoology “Functions” folder

Homework

Work on IXL module 6 to-do list. Work on any incomplete items from the IXL module 7, IXL module 3, IXL mods 4/5 to-do lists. Work on and turn in all missing work. The quarter ends on Friday. Respond to discussion question in Schoology “Functions” folder if you did not do so in class.

### Thursday, January 18

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

IXL IEP to-do list

Lesson (Introduction to Functions/HRW 6.1)

1. Essential questions:

How do you use functions to model relationships between quantities?

How do you define, evaluate, and compare functions

2. Introduction to functions guided notes: examples and nonexamples (concept attainment method)

3. Guided practice: odd numbered problems on “Identifying Functions” worksheet

4. STAR math test without calculators

5. Independent practice: finish “Identifying Functions” worksheet

Closing

Exit ticket:

Homework

Finish the “Identifying Functions” worksheet. Work on IXL module 6 to-do list: Z.1.

### Friday, January 19

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*.

Lesson (More Functions/HRW 6.2)

1. XtraMath challenge

2. Go over homework: “Identifying Functions” worksheet

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. Independent practice: IXL module 6 to-do list

Closing

Exit ticket:

Homework

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