Lesson 14
What Makes Sense in the Problem?
Warmup: Number Talk: Give and Take (10 minutes)
Narrative
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(306 + 199\)
 \(318 + 297\)
 \(275 + 325\)
 \(275 + 329\)
Student Response
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Activity Synthesis
 “How do you decide how much to add to one addend and take away from the other addend?”
Activity 1: Carnival Time Number Choice (20 minutes)
Narrative
The purpose of this activity is for students to consider numbers that make sense in situations involving elapsed time. Then students solve the problems. While a variety of times and answers make sense for each situation, students focus on justifying why their choices make sense to them (MP3).
Consider preparing and displaying images of roller coasters and Ferris wheels for students who may be unfamiliar with carnival attractions.
Supports accessibility for: Memory, Conceptual Processing
Launch
 Groups of 3
 “What are some rides that you might see at a fair or a carnival?”
 “What are some situations at a carnival that could involve time?” (Time spent waiting in line for a ride or waiting for someone. Time spent on a ride. Opening or closing times.)
 30 seconds: quiet think time
 Share responses.
 “Here are some problems about time at the carnival. They are missing some information.”
 “Each person in your group is going to think of numbers or times that make sense in one of the situations. Explain your choices to your group and work together to solve all three problems.”
 “Decide which problem each member of your group will work on.”
Activity
 1 minute: independent work time
 8–10 minutes: group work time
 Monitor for different number choices and justifications.
Student Facing
Here are three problems about time at the carnival. They are missing some information.

In the blanks, write numbers or times that make sense for the situation in the problem assigned to you.
 Clare waited for Tyler to ride the Ferris wheel. Tyler left at \(\underline{\hspace{3 cm}}\) and got back at \(\underline{\hspace{3 cm}}\). How long did Clare wait for Tyler?
 When Tyler got back, he and Clare got in line to ride the roller coaster. They waited \(\underline{\hspace{1 cm}}\) minutes. At \(\underline{\hspace{3 cm}}\), they got on the ride. What time did they get in line?
 Clare and Tyler got to the carnival at \(\underline{\hspace{3 cm}}\). After \(\underline{\hspace{1 cm}}\) minutes, they took a break to buy lemonade. What time did they take their lemonade break?
 Share the numbers and times you chose with your group and explain why they make sense.

Work with your group to solve each problem. Be prepared to explain your reasoning.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
 “What is the problem about?”
 “How long do you think it would make sense to wait in line (or wait for a friend, or go on rides without breaks)? What time do you think would make sense to arrive at the fair (or to be in line for a ride)?”
Activity Synthesis
 Select 2–3 students to share the numbers they chose for each problem.
 As students share, ask:
 “How did you decide what numbers (or times) to choose for each problem?”
 Ask the class:
 “Why do these numbers (or times) make sense for this situation?”
 “What numbers (or times) would not make sense in this situation?”
Activity 2: Lemonade Break (15 minutes)
Narrative
The purpose of this activity is for students to write a question that could be answered by given mathematical work and that would make sense in the given situation. When students interpret given student work in terms of the supplied information and decide what question the work might answer, they identify important quantities and their relationships in context (MP4).
Advances: Reading, Representing
Launch
 Groups of 2
 “Clare and Tyler took a break at the lemonade stand. Here’s what it might look like.”
 Display the image.
 “What do you notice? What do you wonder?” (Students may notice: The stand is close to the carnival. There are lemons hanging in baskets. Students may wonder: How much lemonade do they make each day? What size can you buy? How much does the lemonade cost?)
 1 minute: quiet think time
 Share and record responses.
Activity
 Read the information about the lemonade stand as a class.
 “What mathematical questions could we ask about this situation?”
 1–2 minutes: partner discussion
 Share and record responses.
 “Now, look at the mathematical work in each problem. Work with your partner to write a question that could be answered by that work.”
 5–7 minutes: partner work time
 Monitor for groups that accurately write questions that the work could represent.
Student Facing
A lemonade stand at the fair makes 132 liters of lemonade a day. When Clare and Tyler stopped by the stand, there were 90 liters left.
At the end of the day, there were 56 liters of lemonade left, which the vendor put on sale in 4liter jugs.
Use the information about the lemonade stand to write a question that could be answered with the mathematical work shown.

\(132  90 = 42\)
Question:

Question:
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
 “What numbers from the work do you see in the information about the lemonade stand?”
 “What would the work represent in the lemonade stand situation? What question would lead up to this work?”
Activity Synthesis
 For each problem, invite a group to read the question they wrote.
 Ask the class:
 “How does their question make sense with this mathematical work and what we know about the situation?”
 Consider asking:
 “What did you like about writing the questions to match the mathematical work?”
 “What was challenging about writing the questions to match the mathematical work?”
Lesson Synthesis
Lesson Synthesis
Display the image of the Ferris wheel from the activity about time at the carnival.
“Today we solved a variety of problems that came up at the carnival or lemonade stand at the fair. Work with your partner to write a situation that represents this image and involves multiplication or division.” (The ride lasts 4 minutes. Diego rode the Ferris wheel 5 times. How long was he on the Ferris wheel? There are 12 cars on the Ferris wheel. Each car holds 2 people. How many people can ride the Ferris wheel at one time? Six tickets are needed to ride the Ferris wheel. If 42 tickets were collected from a group of riders, how many people were in the group?)
If time allows, invite students to share and solve some of the problems they wrote.
Cooldown: A Show at the Carnival (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.