Lesson 2

The purpose of this warm-up is to elicit the idea that many different questions could be asked about a situation, which will be useful when students solve problems in a later activity. 

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• If not mentioned in students’ responses, ask: “What mathematical questions could we ask about this picture?” (How many apples are in each box? Are there more apples in the boxes than on the trees? How many apples are in the boxes altogether?)

The purpose of this activity is for students to represent and solve “how many in each group?” problems using whatever strategy and visual representation make sense to them. Students create a poster of their solution to the first problem with a partner. In the next activity, they participate in a gallery walk of the posters.

Monitor for students who represent the situation with:

• concrete objects: putting 20 cubes into 4 groups one by one
• drawings of objects: drawing 20 apples and then splitting them into 4 groups
• arrays: drawing 4 rows with one apple in each row to reach 20

• Groups of 2
• Give students access to connecting cubes and counters.
• “Turn and talk to your partner about how you might solve these problems.”
• 1–2 minutes: partner discussion

• “Solve these problems and show your thinking using objects, a drawing, or a diagram.”
• 5–7 minutes: independent work time
• As student work, consider asking:
  • “How can you represent what you are thinking?”
  • “Where can you see the boxes in your work?”
  • “Where can you see how many apples are in each box 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 creating a visual display.
• 5–7 minutes: partner work time

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.

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 in each group?” 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 there are in each group. Select them to share in the next activity.

• 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.”
• 5–7 minutes: gallery walk

• 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?”

The purpose of this activity is for students to consider what is the same and what is different about the “how many groups?” and “how many in each group?” problems they solved in a previous lesson and in this lesson. The discussion should highlight that in “how many groups?” problems we know the size of each group and in “how many in each group?” problems we know how many groups there are. In order to describe how the problems are the same and how they are different, students attend to the structure of the problems, that is what is given in each situation and what is unknown (MP7).

• Gather the 2–3 posters  from the previous lesson and this lesson that highlight counting the groups in a “how many groups?” problem and finding how many in each group in a “how many in each group?” problem.

• Groups of 2
• Display the problems.
• Display the 2-3 previously selected posters for each problem.

• “Here are two problems we’ve worked on. Yesterday we made posters for the first one and today we made posters for the second one.”
• “Here are a few posters for each problem.”
• “Talk to your partner about how these problems are alike and how they are different. Also talk about what is alike and what is different about how the problems are represented and solved.”
• 3-5 minutes: partner discussion

• “What did you and your partner notice was alike?”
• “What did you and your partner notice was different?”
• Share and record responses.
• As students share, encourage them to use the posters to show examples of what they notice.