DEVELOPING CONCEPTS
2.6
The Distributive Property
GOAL
Use reasoning to discover
how to use the distributive
property to write
equivalent expressions.
For use with
Lesson 2.6
Question
How can you model equivalent expressions using algebra tiles?
Each
represents 1 and each
represents x.
MATERIALS
• algebra tiles
Model 3(2 4).
Model 6 12.
Make 3 groups each consisting
of two plus four, or six, 1-tiles.
Make a group of six 1-tiles
and a group of twelve 1-tiles.
Student Help
LOOK BACK
For help with using
algebra tiles, see p. 77.
Complete: The models show that 3(2 4) ____
? .
This is an example of the distributive property.
Model 3(x 4).
Model 3x 12.
Make 3 groups each consisting
of one x-tile and four 1-tiles.
Make a group of three x-tiles
and a group of twelve 1-tiles.
Complete: The models show that 3(x 4) ____
? .
This is another example of the distributive property.
Think About It
Each equation illustrates the distributive property. Use algebra tiles to
model the equation. Draw a sketch of your models.
1. 5(1 2) 5 10
2. 2(4 3) 8 6
3. 7(1 1) 7 7
4. 6(x 2) 6x 12
5. 4(x 4) 4x 16
6. 3(x 5) 3x 15
7. 2(x 3) 2x 6
8. 5(x 1) 5x 5
9. 9(x 2) 9x 18
10. LOGICAL REASONING Use your own words to explain the distributive
property. Then use a, b, and c to represent the distributive property
algebraically.
Developing Concepts
99