MS After School Intervention
Theme: Summer Vacation
Unit: Solving Equations and Inequalities
Day 7 Lesson
Objective
Students will solve equations involving rational numbers 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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Overhead projector or document camera
Whiteboards and markers
Chalk and chalkboard
“Seek and Solve Stations” resource sheets
“Seek and Solve Answer Sheet” resource sheet
Fraction squares and/or circles
“3-2-1 Closure” resource sheet (one per student)
Opener (10 minutes)
Megan brought home her paycheck from her summer life-guarding job. She needs
$650.00 for her rent. Unfortunately, her take home pay is 2/3 of her full salary as a result
of taxes. How much does her paycheck need to be in order to pay her rent?
2
x  650 . Allow students time to solve for the
3
answer. x =$975. Have students volunteer how they solved for the answer.
Have the students set up the equation
Inside-Outside Circle (20 minutes)
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Have students form two different circles: half of the group stands in a circle facing
outward while the other half forms a circle around them facing inward. Students
exchange information until the teacher signals the outer circle to move in one direction.
The students now have a different partner with whom to exchange.
The first question the inner circle will answer is “What are the steps needed to solve for
an unknown in an equation?”
For the second question, have the outside respond to “What is a way to check if your
answer is correct when solving for an unknown?”
For the third question use whiteboards and have the inner circle show and explain the
1
steps to solve the equation x  8  40. (The answer is x =128.)
4
For the fourth question, have the outer circle use the white boards to explain and show
1
the steps for the equation
 x 12  96 . (The answer is x = 168.)
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2
Relay Practice Game (20 minutes)
Divide the class
into teams. The students will be playing as a team to complete the multistep equations for the unknown. Use the blackboards to show the work. Each student
will complete one step for the problem. Each team will be awarded a point if their steps
are correct and they arrive at the correct answer.
The problems for the relay are listed below:
1.
2.
1
x  6  62 Solution: x = 224
4
3
 x  7  41 Solution: x = –64
4
2
2  x  32 Solution: x = –75
5
1
3
x  4   x  38 Solution x = 84
8
8
2
1
x  8  x  74 Solution x = 198
3
3
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3.
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4.
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5.
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Thumbs Check (10 minutes)
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Have the students return to their seats. Next, ask the students to show by using their
thumb how comfortable they feel with solving for an unknown with rational numbers.
Thumb up – in good shape and can do the problems. Thumb sideways – doing okay and
getting at least 60% correct. Thumb down – still having trouble and need more help.
Use the information from their thumb check to group the students for they next activity.
The thumbs up will complete a seek-n-solve, while the thumbs sideways and down will
be working with fraction practice and the teacher.
Differentiated Activities (15 minutes)
Assign the students to one of two groups. The students that struggled (thumbs down and
sideways) with representing and/or solving equations with variables on both sides should
be in one group with the instructor. The students who seem to understand (thumbs up)
how to approach equations with variables on both sides will be working on the Seek and
Solve activity around the room.
For the Seek and Solve, post each station around the room in alphabetical order. Students
may choose to start at any station. Students are to attempt the problem at the bottom of
the page, recording the letter of their station, the work, and their answer on their tracking
sheet. The answer they get should guide the student to the top of their next station. They
should continue to record each station letter in the order that they travel. Students have
finished all stations when their answer leads them back to their original problem. Note:
Students should arrive at the stations in the following sequence if they started at station
A: A, C, E, B, D, A. Students will all start at different letters, but they should cycle
through in the same order. (For example, a student that starts at station D will have the
answers D, A, C, E, B, D, if they have time to complete every problem.)
For the students having difficulty with this concept, bring out the fraction squares or
circles and work with fractions for a little bit together as a group. Next, have the student
discuss how to set up and solve the first problem from the seek and solve. As students
begin to gain a deeper understanding of the problems, send them to the Seek and Solve
activity to finish as many problems as they can. Check their understanding periodically
by projecting the next problem and having students attempt it individually before
discussing the solution. Note that students who continue to struggle may need to keep
working with the teacher the entire time, while others may be able to join the Seek and
Solve activity quickly.
3-2-1 Closure (5 minutes)
On the “3-2-1 Closure” resource sheet, have students identify three things they have
learned so far in the course, two topics they still need to practice, and one question they
have regarding the lesson.
Seek and Solve Stations
Station A
Answer
x  46
_________________________________________________________________
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Problem
2
x  6  22
3
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Station B
Answer
x  390
___________________________________________________________________
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Problem
1
 x  4  38
6
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Station C
Answer
x  42
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Problem
2
1
x  6   x  16
5
5
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Station D
Answer
x  240
_____________________________________________________________________
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Problem
1
1
 x  7  x  30
4
4
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Station E
Answer
2
x  16 or16.6
3
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Problem
3
1
x  6  x  45
5
2
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Seek and Solve Answer Sheet
Station Letter
Work
Answer
3-2-1 Closure
In the space below, write:
3 things I have learned so far in this program.
1.
2.
3.
2 topics I still need to practice.
1.
2.
1 question I have regarding the lesson.
1.