Math Accelerated Lesson

Proportional Relationships: Tables, Graphs, and Equations

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7th grade - honorsBTC Style / Thinking Classrooms50 min

Learning Objective

Students will identify, represent, and analyze proportional relationships using tables, graphs, and equations of the form $y = k x$ , and determine the constant of proportionality in context.

Lesson Overview

Students progress from identifying unit rates in tables to writing equations, graphing proportional relationships, and comparing multiple relationships across representations. Tasks change one variable at a time from reading a ratio to synthesizing across all three representations.

Materials

Vertical whiteboards or chart paper
Dry-erase markers
Pencil and paper for notes

Scaffolded Task Progression

1Task 1

The table shows the cost of apples at a farm stand.

Pounds ( $x$ )	Cost in dollars ( $y$ )
$1$	$2$
$3$	$6$
$5$	$10$
$8$	$16$

1. Find

\frac{y}{x}

for each row.
2. What do you notice?
3. What does this number mean in context?

2Task 2

Using the apple table from Task 1, write an equation that gives the cost

y

for any number of pounds

x

.

Then use your equation to find the cost of

12

pounds and

0

pounds.

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