standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: 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).
MLR8 Discussion Supports.
Prior to solving the problem, invite students to make sense of the situation and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
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 4-liter jugs.
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Use the information about the lemonade stand to write a question that could be answered with the mathematical work shown.
\(132 - 90 = 42\)
Question:
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Question:
Student Response
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Advancing Student Thinking
If students don’t write a question that could be solved with the given work, consider asking:
“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?”


aligns: no