A proportional relationship can be described as a relationship between two variables in which the rate of change is constant. This is also called direct variation. The inputs or x-values (in this case, minutes) are called domains, and the outputs or y-values (in this case, feet) are called ranges. In the chart on the left above, we multiply the number of minutes by 3 to get the number of feet traveled. This rate of change remains constant in the chart on the left. The graph of a proportional relationship is a straight line through the origin.. The slope of the line is constant. Proportional relationships model a wide range of situations including measurement conversions (ex. feet to inches). The equation for a proportional relationship can be written in the form of *y=kx*, where *k* is the rate of change, slope, or constant of proportionality.

### Monday, November 20

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 graph, chart, or equation, I can determine if the relationship between the values is proportional.

Given a chart of values representing a proportional relationship, I can identify the pattern (the rate of change/constant of proportionality) between the outputs (x-values) and inputs (y-values).

Given a graph, chart, or equation, I can compare proportional relationships.

I can identify proportional and non-proportional relationships.

Bellwork

Students will complete *Math Minute 45*.

Lesson (Proportional Relationships Review)

1. Student exploration: Cafeteria Puzzle from Lure of the Labyrinth

2. Guided practice: unit rates

3. Guided review: proportional relationships bingo

4. Team/partner practice: Comparing Rates of Change War

5. Independent practice: proportional relationships review worksheet

Closing

Homework

Finish the proportional relationships review. Finish the IXL module 3 to-do list. Tomorrow, there will be a test over proportional relationships.

Links

Check out the instructional videos on my proportional relationships links page. You can locate this page by typing “proportional relationships” into the search box on any page of my website. Work on the IXL module 3 to-do list.

### Tuesday, November 21

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 graph, chart, or equation, I can determine if the relationship between the values is proportional.

Given a chart of values representing a proportional relationship, I can identify the rate of change.

Given a graph, chart, or equation, I can compare proportional relationships.

I can identify proportional and non-proportional relationships.

Bellwork

Students will complete *Math Minute 46*.

Lesson (Proportional Relationships Test)

1. Go over homework.

2. Test over proportional relationships

3. Lure of the Labyrinth

Closing

n/a

Homework

Have a wonderful Thanksgiving break!