MS After School Intervention
Theme: Summer Vacation
Unit: Solving Equations and Inequalities
Day 4 Lesson
Objective
Students will solve multi-step equations for the unknown.
Common Core Standards:
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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Folders
Colored paper (optional)
“Send a Problem” resource sheet
“Day at the Races” resource sheet
“3-2-1 Closure” resource sheets (one per student)
Warm-Up Practice (10 minutes)
Have students solve the following problems individually. When finished, have students
compare answers with a partner and then go over as a class.
1. 8x  9  5x  6
2.  2 y  5  6 y  2  27
Solutions: 1. x = –3
2. y  6
Have students check their answer by substituting the solution into the original equation to
get a true statement.
Earning Money for Vacation – Part I (15 minutes)
Read and display the problem for students:
You have decided to go on vacation, but your parents aren’t willing to pay for it. This
means you must get a summer job. You would like to be on vacation for as many days as
you work. The vacation you have chosen is going to cost $40 per day for food and an
additional $200 in overall travel expenses. You have been offered a job baby-sitting and
will earn $60 per day. How many days must you work to receive an equal number of
vacation days?
Have students discuss how they would approach and solve the problem in small groups.
A possible solution may be an algebraic or visual representation of the equation
40x  200  60x . Some groups may derive the equation 60x  40x  200  0 (Students
may struggle with setting it equal to zero.) Another possibility may be that students
guess and check. If you see students trying to guess and check, encourage them to set up
a table of values. Have groups present their approach to the class. As a class, discuss the
pros and cons to each approach. (Solution: x = 10 days.)
Earning Money For Vacation -Part II (20 minutes)
Give each group a copy of the following scenario after the groups have presented their
solutions to Part I.
“Your vacation plans have changed. In addition to the $40 per day for food and $200 for
travel expenses, you have also decided to rent a beach umbrella for $10 each day in order
to prevent sunburn. Your babysitting job still pays $60 per day and you still want to
work the same number of days as your vacation. How does this change your vacation
from Part I?”
Have the groups rework their original approach to include the new information. Each
group should present their solution. A possible equation is 40x  10x  200  60x .
(Solution: x = 20 days.)
Follow this scenario up by giving each group the following additional information.
“On your birthday, your parents give you $100 for your vacation and your grandparents
give you $50. Your vacation will still cost the same for food, the beach umbrella and
travel expenses, and you will earn the same amount of money per day. How does this
change the problem?”
Have the class derive the problem together to include the new information. Solve the
problem together. A possible equation may be 40x  10x  200  60x  100  50 . If
students have combined some of the terms already from their previous work, be sure to
discuss where the terms came from. For example, students may have 50x on the vacation
side of the equation, so be sure to have them explain that $40 was for food and $10 was
for the umbrella. (Solution x = 5 days.)
Send-A-Problem (20 minutes)
Attach each problem to the front of a folder, and place the folders around the room. Have
each set of partners go to a folder and solve the problem together on a piece of paper.
After solving the problem, students should place their solution into the folder. Partner
sets should rotate at the same time and solve the problems at every folder.
Once the students have returned to their original problem, they can open the folder and
view all possible solutions. Students should be given a few minutes to review the
solutions in their folder and decide which solution seems correct. They will then present
their problem and solution to the class.
You may want each partner set to have different colored paper so you can see which
groups are getting the correct answers and which groups are struggling. If different
colored paper is not available, have students write their names on their papers. This will
allow you to determine groups for the differentiated activity.
A Day at the Races (20 minutes)
Assign students to small groups. Allow students access to QuietShape Algebra Tiles if
necessary. Distribute a picture of a car to each group and have them decide on a team
name. If time allows, have the groups decorate their cars. Draw vertical lines on the
chalkboard to cut it into 7 equal segments. Write “START” at the top of the first
chalkboard segment and “FINISH” at the top of the last segment. Students should tape
their cars in the start segment of the board. Once all of the cars have been taped to the
board, hand out the first problem to each group. Do not allow students to start the
problem until you say “GO.” Once you say, “GO,” groups are to work through the
problem they have. In order to get the next problem and move their car one segment
closer to the finish line, groups must show you their correct solution.
Continue the game until all cars make it to the finish line or until you run out of time. If a
group finishes all problems early, separate them and send them to the remaining groups
to help.
3-2-1 Closure (5 minutes)
On the 3-2-1 resource sheet, have students identify three things they have learned so far
in the course, two tools they can use to help them solve equations, and one question they
have regarding the lesson.
Send-A-Problem
 18  6k  6  18k
Solution: k = –1
8x  6  8  4  2 x
Solution: x = 3
p 1  5 p  3p  8
Solution: p = 1
5 p  14  8 p  4
Solution: p = –6
8x  2  9  7 x
Solution: x = –7
A Day at the Races
Source: http://www.abcteach.com/free/b/basicshaperacecarbw.jpg
A Day at the Races – Problems
PROBLEM 1: 13  5  20m  2m
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Solution: m = –1
PROBLEM 2:  11  5a  30a  24
Solution: a = –1
PROBLEM 3:  20x  10  6  12x
Solution: x = 2
PROBLEM 4: 10n  30  3n  20  8n
Solution: n = 10
PROBLEM 5:  8  8x  6  4  2x
Solution: x = 3
3-2-1 Closure
In the space below, write:
3 things you have learned so far in this program.
1.
2.
3.
2 tools available to help solve equations.
1.
2.
1 question you have regarding the lesson.
1.