This document provides materials for a lesson on solving two-step equations involving all operations. It includes examples of word problems that are modeled with tape diagrams and translated into equations. Students complete problem sets, sprints, and an example modeling exercise involving creating tape diagrams and writing equations. The lesson concludes with an activity where students work through "stations" drawing tape diagrams on chart paper and an exit ticket to assess understanding of using tape diagrams to solve two-step equations.

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Problem Set Lesson 27 Answers

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MODULE 4 Expressions and Equaons
Topic G: Solving Equaons
Lesson 28: Two‐Step Problems—All Operaons
Student Outcomes
§ Students calculate the soluon of one‐step equaons by using their knowledge of order of operaons and the
properes of equality for addion, subtracon, mulplicaon, and division. Students employ tape diagrams to determine
their answer.
§ Students check to determine if their soluon makes the equaon true.

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Sprints Round 1 ~ Page 1

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Sprints Round 1 ~ Page 2

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Sprints Round 2 ~ Page 1

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Sprints Round 2 ~ Page 2

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Classwork
Mathemacal Modeling Exercise
Juan has gained 20 lb. since last year. He now weighs 120 lb. Rashod is 15 lb. heavier
than Diego. If Rashod and Juan weighed the same amount last year, how much does
Diego weigh? Allow j to be Juan’s weight last year (in lb.) and d to be Diego’s weight (in
lb.).
Draw a tape diagram to represent Juan’s weight.
Draw a tape diagram to represent Rashod’s weight.
Draw a tape diagram to represent Diego’s weight.

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What would combining all three tape diagrams look like?
Write an equaon to represent Juan’s tape diagram.
Write an equaon to represent Rashod’s tape diagram.

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How can we use the final tape diagram or the equaons above to answer the queson
presented?
Calculate Diego’s weight.
We can use idenes to defend our thought that d + 35 – 35 = d
Does your answer make sense?

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Example 1
Marissa has twice as much money as Frank. Chrisna has $20 more than Marissa. If
Chrisna has $100, how much money does Frank have? Let f represent the amount
of money Frank has in dollars and m represent the amount of money Marissa has in
dollars.
Draw a tape diagram to represent the amount of money Frank has.
Draw a tape diagram to represent the amount of money Marissa has.
Draw a tape diagram to represent the amount of money Chrisna has.

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Which tape diagram provides enough informaon to determine the value of the
variable now?
Write and solve the equaon.
The idenes we have discussed solidify that m + 20 – 20 = m.
What does the 80 represent?

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Now that we know Marissa has $80, how can we use this informaon to find out how
much money Frank has?
Write an equaon.
Solve the equaon.
Once again, the idenes can solidify that 2 f ÷ 2 = f
What does the 40 represent?
Does 40 make sense in the problem?

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"STATIONS"
At your table you will complete each "station"
one at time. Draw the tape diagram on the
chart paper. When everyone is done, we will
hold up our posters to compare. Then we will
move on to the next "station".

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Closing
Please take out your exit ticket for Lesson 28, close your
binder, and complete the exit ticket. This will be collected.
§ How did the tape diagrams help you create the expressions and equaons that you used to solve the problems?

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