Education Technology

Expressions and Equations / Visualizing Linear Expressions

Activity 9 of 18
In this lesson students will use the distributive property to rewrite expressions for a given context in order to make connections between the scenario and the expression(s) that describe it.

Planning and Resources

Objectives
Students should be able to find equivalent expressions using the distributive property and interpret visual representations of the distributive property, i.e., ax+bx = (a+b)x and a(b+c) = ab+ac

Vocabulary
linear expressions
distributive property

Standard:

Lesson Snapshot

Understanding

Students develop an understanding of how the distributive property connects the operation of multiplication to the operation of addition.

What to look for

Students can use the distributive property to write equivalent expressions involving the operations of multiplication and addition.

Sample Assessment

Select all the expressions that are equivalent to $$8(t+4)$$.

a. $$2(4t+2)$$
b. $$t+32$$
c. $$4t+4+4t$$
d. $$(8+t)+(8+4)$$
e. (8 x $$t)$$ + (8 x 4)

Answer: b and e

The Big Idea

The distributive property relates the addition and multiplication of real numbers and is central in creating equivalent expressions involving those operations.

What are the students doing?

Students use different visual models to make connections between the distributive property and the order of operations when creating equivalent expressions.

What is the teacher doing?

Encourage students to explore the visual models and look for the connections between the representation and the application of the distributive property.