Algebra Readiness Intervention Lesson
Theme: Summer Vacation
Unit: Solving Equations and Inequalities
Day 5 Lesson
Objective
Students will simplify expressions using the distributive property.
Common Core Standards:
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem,
and construct simple equations and inequalities to solve problems by reasoning about the
quantities.
7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) =
r, where p, q, and r are specific rational numbers. Solve equations of these forms
fluently. Compare an algebraic solution to an arithmetic solution, identifying the
sequence of the operations used in each approach. For example, the perimeter of a
rectangle is 54 cm. Its length is 6 cm. What is its width?
8.EE.7 Solve linear equations in one variable.
8.EE.7a Give examples of linear equations in one variable with one solution, infinitely
many solutions, or no solutions. Show which of these possibilities is the case by
successively transforming the given equation into simpler forms, until an equivalent
equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
8.EE.7b Solve linear equations with rational number coefficients, including equations
whose solutions require expanding expressions using the distributive property and
collecting like terms.
Materials
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Overhead or document camera
Moving with Math: Algebra (MH5)
Dimes and pennies (or use Moving with Math: Number Sense, Reasoning and
Data (MH1) Master 14)
QuietShape Base Ten Deluxe Set: Blue
QuietShape Algebra Tiles
“Mix-N-Match Cards” resource sheets
“Day 5 Exit ticket” resource sheets (one per student)
Whiteboards or sheet protector with white paper
Dry-erase markers
Opener (10 minutes)
“The Howard County Fair is in town! Today they are having a deal on ride tickets. The
price of the ticket books is discounted by $2 since it is Wacky Wednesday. You want to
purchase 10 books of tickets.”
Tell students to let p represent the price of ticket books. Have students brainstorm in
small groups how to write an expression to represent the situation. Allow a few minutes
to process the problem.
As a class, discuss the equations each group created and lead the students to the correct
expression: 10(p – 2)
The Distributive Property in Arithmetic and Algebra (25 minutes)
Complete the Introductory Activities on page 49 of Moving with Math: Algebra (MH5)
using dimes and pennies, QuietShape Base Ten Deluxe Set: Blue and QuietShape
Algebra Tiles. Once completed write a few additional examples with variables on the
board and have students use the QuietShape Algebra Tiles to demonstrate how to
simplify. Students should show the algebraic steps on a sheet of paper as well.
Have each student write his/her own problem that uses the distributive property.
(Students should simplify on their own paper.) Assign student to partners. On a
whiteboard, the pair should take turns writing their problem and challenging their partner
to simplify. (Have QuietShape Algebra Tiles available if needed.)
Simplifying Algebraic Expressions (20 minutes)
Complete the Introductory Activities on page 50 of Moving with Math: Algebra (MH5)
using the QuietShape Algebra Tiles. Once completed write a few additional examples
on the board and have students use the QuietShape Algebra Tiles to demonstrate how
to simplify. Students should show the algebraic steps on a sheet of paper as well.
Mix-N-Match Cards Practice (20 minutes)
Have the students practice simplifying expressions with the distributive property using
Mix-N-Match cards. Distribute one Mix-N-Match card to each student. Have students
move around the room, switching off their cards so that they don’t have the same one for
very long. Students should continue to trade cards until “freeze” is called.
Call “freeze” to have the students stop switching. Give the students a few minutes to
evaluate their card. Call “match” to have the students walk around the room and find the
student who has the answer card that corresponds to their problem. Have students hold
up their cards to confirm that they have matched correctly.
After students have found their matches, call “mix” and repeat the process.
Exit Ticket (10 minutes)
Have the students simplify the following expressions:
1. 6(y +3) – 2
2. 3(2x – 4) + 4x
3. –4(3n +5) + 8n – 4
Collect and grade. Use the results of the exit ticket to inform instruction for Day 6. Is
there any part of the simplification process that needs to be reviewed?
Solutions: 1. 6y + 16
2. 10x – 12
3. –4n – 24
Closure (5 minutes)
Have students answer the following questions. Call on multiple students for the same
questions.
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3.
What math concepts did we investigate today?
What is the distributive property?
How do you simplify expressions that have parentheses?
Mix-N-Match Cards
2(x  3)  x
3x  6
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5(x  3)
5x  15
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27  9x
9(3 x)
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4(x  3) 10
4x  2
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5(x  3)  4x
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x 15
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2x  4(x 1)
6x  4
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4(x 1)  (2)(3)
4x  2
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2(x  2)  3(x 1)
5x  1
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4(x  3)  2x
6x  12
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5(x  2)  3(x  5)
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2x  25
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Day 5 Exit Ticket
Simplify the following expressions:
1.
6(y +3) – 2
2.
3(2x – 4) + 4x
3.
–4(3n +5) +8n – 4