Algebra 1 Lesson

From Tiles to Tables to Terms: Writing Algebraic Expressions from Visual Patterns

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8th-9th GradeThin-SlicingCCSS.MATH.CONTENT.8.F.B.4, CCSS.MATH.CONTENT.6.EE.A.2a, CCSS.MATH.CONTENT.7.EE.A.260 min

Learning Objective

Students will be able to identify the rate of change and starting value in a visual or numeric pattern and write a variable expression of the form $an + b$ that represents the $n$ th term.

Lesson Overview

Students progress from counting tiles in visual patterns to building tables of values, identifying rate of change and starting value, and writing algebraic expressions. Contexts include growing tile figures, toothpick patterns, and taxi cab fares.

Materials

Vertical whiteboards or chart paper
Dry-erase markers (multiple colors)
Random grouping tool
Printed tile pattern reference cards (optional)
Rulers or straightedges

Scaffolded Task Progression

1Task 1

Here are the first three figures of a tile pattern.

[ Interactive graph / diagram — available in the full lesson ]

Count the tiles in each figure and complete the table:

Figure number ( $n$ )	Number of tiles
1	?
2	?
3	?
4	?

How many tiles are added each time you go from one figure to the next?

2Task 2

Here are the first three figures of a tile pattern.

[ Interactive graph / diagram — available in the full lesson ]

1. Count the tiles in Figure

1

.
2. Count the tiles in Figure

2

.
3. Count the tiles in Figure

3

.
4. Complete the table for Figure

4

Figure number ( $n$ )	Number of tiles
$1$	?
$2$	?
$3$	?
$4$	?

5. How many tiles are added each time you go from one figure to the next?

3Task 3

Using the same tile pattern from Task 1, extend the table to Figure 6.

$n$	Tiles
1	3
2	5
3	7
4	?
5	?
6	?

Then answer: How many tiles would Figure 20 have? How did you figure that out WITHOUT drawing it?

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