This document outlines a lesson on solving two-step equations using all operations. The lesson introduces using tape diagrams to represent relationships between variables and develop equations. Students practice drawing tape diagrams and writing equations to solve word problems involving multiple steps. The lesson concludes with an activity where students work through practice problems in small groups, drawing tape diagrams and writing equations to find unknown values.

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Problem Set Lesson 27 Answers

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MODULE 4 Expressions and Equations
Topic G: Solving Equations
Lesson 28: Two‐Step Problems—All Operations
Student Outcomes
§ Students calculate the solution of one‐step equations by using their knowledge of order of operations and the
properties of equality for addition, subtraction, multiplication, and division. Students employ tape diagrams to determine
their answer.
§ Students check to determine if their solution makes the equation 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
Mathematical 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 equation to represent Juan’s tape diagram.
Write an equation to represent Rashod’s tape diagram.

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How can we use the final tape diagram or the equations above to answer the question
presented?
Calculate Diego’s weight.
We can use identities 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. Christina has $20 more than Marissa. If
Christina 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 Christina has.

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Which tape diagram provides enough information to determine the value of the
variable now?
Write and solve the equation.
The identities 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 information to find out how
much money Frank has?
Write an equation.
Solve the equation.
Once again, the identities can solidify that 2f ÷ 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 equations that you used to solve the problems?

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