Lesson 10
What’s the Question?
Warmup: Notice and Wonder: A Day in the Park (10 minutes)
Narrative
The purpose of this Notice and Wonder is to elicit different questions from students about a story to prepare them for writing their own questions for a math story in an upcoming activity. Although students may notice and wonder many things, the most important discussion point will be the types of mathematical questions that can be asked about the story.
Launch
 Groups of 2
 Display the questionless story problem.
 “What do you notice? What do you wonder?”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Share and record responses.
Student Facing
In the park, there are 37 kids on the soccer field, 18 kids on the tennis courts, and 25 kids at the picnic tables.
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
 “What are some mathematical questions that could be asked about this situation?”
 Record responses.
 “What do these questions have in common? How are they different?”
Activity 1: Asked and Answered (20 minutes)
Narrative
The purpose of this activity is for students to ask a question that can be answered with the given information and then answer the question. There are many different questions students can ask including:
 Who picked the most apples?
 How many apples did they pick together?
 Did Elena or Diego pick more apples?
 How many apples did Diego pick?
These questions require all the given information to solve. Students may also ask questions which require only some of the information to solve, such as, “How many apples did Han pick?” The activity synthesis focuses on sharing different questions students asked and how they found the answer, with a focus on the multistep problem “How many apples did they pick altogether?” Images are provided for display, however, student work should be used as much as possible in the synthesis.
Launch
 Groups of 2
 “Sometimes people buy apples at the market or grocery store, but sometimes people go to an apple orchard to pick apples.”
 “Each person gets a basket to collect the apples they pick, and then they pay for the apples.”
 “Apple picking can be a fun outing for families and friends.”
 “You will be reading a story and asking questions about friends who went apple picking together.”
Activity
 Read the problem.
 “Think about the questions you could ask someone that this story could help them answer.”
 5 minutes: independent work time
 “Switch questions with your partner and find the answer.”
 “Share your thinking and check to see if you agree about the answer.”
 5 minutes: partner work time
 Monitor for students who represent how many apples Han picked and students who represent how many apples Diego picked compared to Han to share in the synthesis as shown.
Student Facing
Elena picked 29 apples. Elena picked 14 fewer apples than Han. Han picked 15 more apples than Diego.
 Write a question someone could answer based on this information.
 Answer your question. Show your thinking using diagrams, symbols, or other representations.
Student Response
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Advancing Student Thinking
 “What is the story about?”
 “What can be counted in the story?”
 “What quantities do you know? What is unknown?”
Activity Synthesis
 Invite students to share their questions.
 Display a diagram that represents the number of apples Han picked, such as:
 “What does the diagram represent?” (The number of apples Han picked since he picked 14 more than Elena.)
 “How did you find how many apples Han picked?” (I added 30 to 14 to get 44 and then took away 1 to get 43.)
 Display a diagram that represents the number of apples Diego picked compared to Han, such as:
 “What does the diagram represent?” (How many apples Diego picked compared to Han.)
 “How did you find how many apples Diego picked?” (I took 15 away from 43.)
 “How did you find how many apples Elena, Han, and Diego picked altogether?” (I added 29, 43, and 28. I put all the tens together to get 80 and all the ones together to get 20 then added 80 and 20.)
Activity 2: What is the Question? (15 minutes)
Narrative
The purpose of this activity is to interpret student work with given numbers and use a story context to determine what question was answered. The first problem shows a tape diagram which puts together the three quantities in the story. The second problem shows a compare tape diagram with the three given quantities and an unknown. In each case, students need to reason about the representations and the given given information to determine what question the work could answer (MP2). Determining the relationships between quantities and using them to ask questions and solve problems is an aspect of modeling with mathematics (MP4).
The goal of the activity synthesis is to identify questions, especially for the second problem, and discuss strategies for performing the calculations.
.Advances: Speaking,, Conversing, Representing
Supports accessibility for: Conceptual Processing, Attention
Launch
 Groups of 2
Activity
 “You are going to look at some student work and figure out what question the student is trying to answer.”
 Read the problem.
 5 minutes: independent work time
 5 minutes: partner discussion
Student Facing
Clare picked 51 apples. Lin picked 18 apples and Andre picked 19 apples.
Here is some student work showing the answer to a question about the apples.

\(51 + 19 = 70\)
\(70 + 18 = 88\)
What’s the question?
Explain how you know.

\(19 + 18 = 37\)
\(51  37 = 14\)
What’s the question?
Explain how you know.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
 “What do you notice about the student work?”
 “How do you think the student work connects to the story?”
Activity Synthesis
 Invite 1–2 students to share questions for the first problem.
 “How did you know the student was trying to find a total amount?” (The tape diagram and student work shows addition.)
 “Why do you think the student added 51 and 19 rather than 51 and 18?” (They make 70 together. That way, there is no need to make a ten when you add the third number.)
 Invite 1–2 students to share questions for the second problem.
 “How did you know the question might be about comparing? Why not a question about taking away?” (The operation is subtraction but Lin’s apples and Andre’s apples aren’t taken away from Clare’s apples. The diagram helps see that it is a comparison.)
 “What strategies can you use to calculate \(51  19  18\)?” (Use the number line. Make a drawing. Subtract 20 and add 1, subtract 20 more and add 2.)
Lesson Synthesis
Lesson Synthesis
“Today we wrote questions for story problems and used diagrams and equations to figure out what questions might have been answered.”
“What do you need to know to be able to write a math question for a story?” (You need to know some numbers or amounts of things. You need something you can count or measure. You might need to know what people are doing, like putting things together or taking things away.)
“What clues in diagrams or equations can help you figure out what math question someone might be trying to figure out for a story?” (It helped to see what kind of diagram people were using. The question mark to show what was unknown was a good clue. We needed to know some parts of the story, like what was being counted or measured.)
Cooldown: Ask It and Answer It (5 minutes)
CoolDown
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