Support Identifying & Representing Proportional Relationships

Support Identifying & Representing Proportional Relationships Materials

Activity Name Carnegie Course 3 Lesson 6.1: Proportional Situations, Part 1

Carnegie Course 3 Lesson 6.2: Proportional Situations, Part 2

Reinforcing Activity: Part Time Jobs

Carnegie Course 3 Lesson 6.3: Proportional vs. Non-

proportional Relationships

Performance Task: Card Sort

Supporting Activity: Stations

Carnegie Course 3 Lesson 6.4: Proportional Applications

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Quick Check

Table of Contents

TEKS

Description

This lesson explores linear proportional

8.4B

situations and direct variation with

8.5A

different representations. Questions ask

8.5E

students to analyze and compare proportional

situations in tables and graphs.

8.4B

This lesson introduces the distinction between

8.5A

proportional and non-proportional relationships.

8.5E

Students will identify examples of proportional

8.5F

and non-proportional situations by comparing

8.5H

tables, graphs, and equations for proportional and

non-proportional relationships.

This lesson analyzes and compares

8.5A

proportional and non-proportional situations.

8.5B

Questions ask students to use tables, graphs,

8.5F

and equations to describe proportional and

non-proportional relationships.

Students will identify examples of proportional

8.5F

and non-proportional situations by comparing

8.5H

tables, graphs, and equations for proportional and

non-proportional functions.

Students will rotate through station activities

8.5F

determining whether situations are representing

8.5H

proportional or non-proportional relationships.

8.4B

This lesson presents problem situations using

8.4C

either proportional or non-proportional

8.5A

relationships. Questions ask students to

8.5B

distinguish between proportional and non-

8.5F

proportional applications in context.

Students create anchor with explanations of the

8.5F 8.5H

characteristics of proportion and non-proportional relationships

8.5A

Students create their own proportional or non-

8.5B

proportional situations within given guidelines.

This activity can be repeated through the unit to

Austin ISD

Middle School Math

Support Identifying & Representing Proportional Relationships Materials

check for understanding.

Austin ISD

Middle School Math

Performance Task

Identify Proportional &

Non-Prop. Relationships

Standards

Content

ELPS

8.5F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form of y= kx or y = mx + b, where b 0

8.5H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problem situations

3(E) share information in cooperative learning interactions

5(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary

Objectives

Content Objective: Identify examples of proportional and non-proportional situations by comparing tables, graphs, and equations for proportional and non-proportional relationships.

Language Objective: Students will explain the characteristics of proportional and nonproportional relationships.

A graph is showing a proportional relationship when the line goes through the ____. (origin)

An equation representing a ______________ relationship is in the form of y = mx + b. (non-proportional)

An equation representing a relationship is in the form of y = kx. (proportional)

Another term for proportional is _______. (direct variation)

Middle School Math

Performance Task

Identify Proportional &

Non-Prop. Relationships

Vocabulary function, proportional, non-proportional, direct variation, origin, table, equation Vocabulary Activity: FACT OR FIB 1. Give each student two index cards labeled "FACT" and "FIB." (I would laminate these so that they can be reused in class throughout the year.)

2. Read a true or false statement about a word from the Word Wall (examples provided below). 3. On the count of three, the students must slap down either the "fact" or "fib" card.

4. Repeat.

* Remember to give "think time" BEFORE counting to 3.

FACT

FIB

Fact or Fib Questions A proportional line on a graph will go through the origin. (Fact) An equation that reflects a direct variation would be in the form of y = mx + b (Fib) Another term for non-proportional is direct variation. (Fib) A table with the values (0, 0) tells me there is a proportional relationship. (Fact) An equation that reflects a direct variation would be in the form of y = kx + c (Fib) If a table has point (0, 8) and the rate of change is constant, that is non-proportional. (Fact)

Middle School Math

Performance Task

Identify Proportional &

Non-Prop. Relationships

Non-proportional relationships vary directly. (Fib)

Guiding Questions

? How can you determine if a relationship is proportional or non-proportional? ? What are the characteristics of a graph representing a proportional relationship? A table?

An equation? ? What are the characteristics of a graph representing a non-proportional relationship? A

table? An equation?

Differentiation

Provide sentence stem quick notes to guide them through the activity:

I know an equation is proportional when it is in the format _______________. I know an equation is non-proportional when it is in the format _______________. I know a table is proportional when __________________________________________. I know a table is non-proportional when ___________________________________. I know a graph is proportional when _______________. I know a graph is non-proportional _______________.

Implementation

? Students cut out the three sheets containing proportional and non-proportional relationships attached below.

? Students categorize as proportional or non-proportional in partners/groups. ? For each graph and table card require students to write the equation that it represents. ? Once the card sort is verified for correctness, students can glue it in their interactive

notebook OR on butcher paper/poster and explain why they categorized each item as they did.

Middle School Math

Performance Task

Identify Proportional &

Non-Prop. Relationships

Middle School Math

Performance Task

Identify Proportional &

Non-Prop. Relationships

Middle School Math

Performance Task

Identify Proportional &

Non-Prop. Relationships

Middle School Math

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