MS After School Intervention
Unit: Solving Equations and Inequalities
Theme: Summer Vacation
Day 2 Lesson
Prior to the start of this lesson the teacher must review the Day 2 exit tickets to assess
each student’s mastery of solving two-step equations. The first activity will be
differentiated for students who need additional practice with manipulatives and students
who are ready for more challenging problems.
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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Overhead/document camera
Tape
Moving with Math: Algebra (MH5)
QuietShape algebra tiles
Paper cups
Two-color counters
“Challenge Problem Stations” resource sheet
“Placemat” resource sheet (one copy per group)
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. 4 x  3  15
2. 3d  6  18
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Solutions: 1. x = 3
2. d  4
Show students how to check their answer by substituting the solution into the original
equation to get a true statement.
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Differentiated Lessons
(25 minutes)
Students will be assigned one of two activities based on exit ticket performance:
For students needing additional support with two-step equations- Complete the
Introductory Activities on page 47 of Moving with Math: Algebra (MH5). Use the paper
cups and two-color counters. Once completed, write two or three additional examples on
the board and have students use the cups and two-color counters to complete the
additional practice (showing the model on the paper). Have students check their answers
using substitution.
For students who have mastered two-step equations: Place the challenge problems in
four locations in the room. Assign pairs and have pairs go do different stations, complete
the problems on their paper and rotate to the next station after 5 minutes. Collect when
finished. (Solutions: 1. 24 hours 2. 75 hours 3. 17.08 hours (a little over 17 hours)
4. 20 days)
Circulate between the two groups monitoring progress and providing support as needed.
Placemat Activity (15 minutes)
Place students in groups of four. Print one placemat for each group. Have each student
complete the solution to one of the problems on the placemat. When finished have each
group rotate the mat clockwise and instruct the students to check the work of the problem
that is now in front of them. When everyone has a chance to check the solution, the table
needs to take the four answers and find the sum. Place the sum in the center of the
placemat. Go around the room to check the sums.
(Solutions: m = 3, w = 9, x = 12, y = 8, Sum = 32)
If the sum is incorrect, have the group rotate the placemat clockwise again and check the
problem in front of them. Students should re-total with the new values to find a sum.
Remind them that they can use the substitution method to check to see if the answer is
correct. If some students are still struggling, call on students to present solutions to the
class.
Revisiting a Challenge Problem (10 minutes)
Reintroduce Station 4 from the Challenge problem to the entire class with the new
information.
“You have $500 to use on vacation. Each day you spend $15 on expenses. In order for
you to return home, you must have $200 for travel. How many days can you stay on
vacation?”
You decide to rent a Ski doo for $35 for transportation and fun and buy an ice cream cone
for $5. With the newly added spending, how many days can you stay on vacation?
Have students in pairs work on the new scenario. Have one pair who worked on this
problem come up to explain a general strategy they used to solve the problem (examples:
draw a picture, write an equation, add together the additional costs, etc.) Ask the class to
write an equation to represent this problem, using d to represent the days on vacation.
(15d + 200 + 5 + 35 = 500).
Have students compare the similarities and differences between this equation and the
other equations they have been solving. Ask students what would be a good strategy for
solving this equation. (Students should identify that they should add the additional costs
first to make the equation simpler: 15d + 240 = 500). Ask students if this equation will
give the same solution as the original equation. (Yes, because 240 is equivalent to
200 + 5 + 35). Now have students solve the equation. (d = 17 and 1/3 days) Have a
discussion about the decimal and not being able to stay a third of a day.
Solving by Combining Like Terms (20 minutes)
Distribute the QuietShape algebra tiles. Write this problem on the board:
3m + 2m + 5 = 20
Ask students to represent the problem using the QuietShape Algebra Tiles. When
students have the correct representation, ask if they can rewrite the equation. (Students
should write 5m + 5 = 20). Now have students solve the equation. (m = 3)
Write this problem on the board: 4n +3 – 2n – 6 = 5
Ask students to represent the problem using the QuietShape Algebra Tiles or by
drawing a pictorial representation. When students have the correct representation, ask if
they can rewrite the equation. (Students should write 2n – 3 = 5). Now have students
solve the equation. n = 4)
Write this problem on the board: –6n – 2n = 16.
Have students simplify and solve the equation, showing their work and checking the
solution. (Solution: n = –2)
Closure (10 minutes)
Lead a class discussion with the following questions:
1. How do we solve a two-step equation?
2. What can you do to simplify a complicated equation?
3. In what instances do you simply add terms?
4. In what instances do you perform operations to both sides of an equation?
Day 2 Challenge Problem Stations
Station 1:
Jonnie wants to earn $400 this summer. He must purchase a lawnmower for $200 and
will earn $25 an hour mowing lawns in the neighborhood. How many hours will he need
to work?
Station 2:
Kiana will be lifeguarding to earn spending money. She wants to make $600 this
summer. Kiana will earn $10 an hour but will also need to pay her mom $150 for the
transportation to the pool. How many hours will she need to work?
Station 3:
The Novak family is planning a vacation to Disney World in Florida. The total distance
to Disney is 950 miles. The family will also stop at a friend’s house, which will take
them off course for 160 miles. If the Novak family travels at a speed of 65 miles per
hour, how long will it take the family to arrive at Disney World?
Station 4:
You have $500 to use on vacation. Each day you spend $15 on expenses. In order for
you to return home you must have $200 for travel. How many days can you stay on
vacation?
-3m + 7 = -2
2.5y
31
13==38
1.5y++18
4w – 9 = 27