Warm-up: How Many Do You See: Apples (10 minutes)
The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see.
- Groups of 2
- “How many do you see? How do you see them?”
- Flash the image.
- 30 seconds: quiet think time
- Display the image.
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
How many do you see? How do you see them?
- “How did the organization of the apples help you see how many there were?” (I saw 2 rows of 4 which I knew was 8, then I doubled that to find how many apples were in the crate. I saw groups of 4 so I multiplied \(4 \times 4\) then added the other apples.)
- Consider asking:
- “Who can restate the way ___ saw the apples in different words?”
- “Did anyone see the apples the same way but would explain it differently?”
- “Does anyone want to add an observation to the way ____ saw the apples?”
Activity 1: How Many Apples? (20 minutes)
The purpose of this activity is for students to represent and solve “how many groups?” problems. Encourage students to use whatever strategy and visual representation that make sense to them. Students create a poster of their solution to the first problem with a partner. In the next activity, students participate in a gallery walk of the posters.
Monitor for students who represent the situation with:
- concrete objects: putting 24 cubes into groups of 8
- drawings of objects: drawing 24 apples and then splitting them into groups of 8 or circling groups of 8
- arrays: drawing 3 rows of 8 apples in each to reach 24
When students represent the situation with objects, concrete drawings, or abstract drawings they are reasoning abstractly and quantitatively (MP2).
Supports accessibility for: Social-Emotional Functioning
- Groups of 2
- Give students access to connecting cubes or counters.
- “Solve these problems and show your thinking using objects, a drawing, or a diagram.”
- 6–8 minutes: independent work time
- As student work, consider asking:
- “How can you represent what you are thinking?”
- “Where can we see the apples in your work?”
- “Where can we see how many boxes there are in your work?”
- Monitor for students who solve the first problem in the same way. Arrange them into groups of 2 to create a poster together.
- “Now you are going to create a poster to show your thinking on the first problem.”
- “You are going to work with a partner who solved the problem in the same way you did.”
- Give each group tools for making a visual display.
- 6–8 minutes: partner work time
Solve each problem. Show your thinking using objects, a drawing, or a diagram.
- If 24 apples are put into boxes with 8 apples in each box, how many boxes are there?
- If 42 apples are put into boxes with 6 apples in each box, how many boxes are there?
- If 32 apples are put into boxes with 4 apples in each box, how many boxes are there?
Advancing Student Thinking
If students don’t find a solution to the problems, consider asking: “What is this problem about?” and “How could you represent the problem?”
- Display posters around the room.
Activity 2: Gallery Walk: Apples in Boxes (15 minutes)
The purpose of this activity is for students to consider what is the same and what is different about the ways that they solved a “how many groups?” problem in the previous activity.
As students visit the posters, identify 2–3 students who show particularly well that this problem is about finding how many groups are made. Select them to share their explanations in the next lesson.
Advances: Writing, Speaking
- Groups of 2
- “As you visit the posters with your partner, discuss what is the same and what is different about the thinking shown on each poster.”
- 8–10 minutes: gallery walk
- Visit the posters around the room with your partner. Discuss what is the same and what is different about the thinking shown on each poster.
- Reflect on what you saw. Write down one thing that was the same and one thing that was different about the thinking shown on each poster.
- Give students a chance to ask questions they have about any posters.
- “What is the same about the thinking shown on the posters?”
- “What is different about the thinking shown on the posters?”
“Today we solved problems about putting apples into boxes. How were these problems the same as multiplication? How were they different?” (These problems had groups of equal size. In multiplication we counted how many things were altogether. In these problems we knew that already. We were trying to find how many groups we could make.)
“The problems we solved today are division problems. How would you define division based on the problems we saw today?” (Division is about putting into groups of equal size. I would say it’s about finding how many groups you can make.)
Cool-down: How Many Bags? (5 minutes)
Teachers with a valid work email address can click here to register or sign in for free access to Cool-Downs.