Lesson 10
Drawings, Situations, and Diagrams, Oh My!
Warmup: Notice and Wonder: Socks (10 minutes)
Narrative
The purpose of this warmup is to elicit different strategies for counting objects arranged in groups of 2, which will be useful when students multiply by 2 in a later activity. While students may notice and wonder many things about these images, flexible ways of seeing the groups and strategies for finding the total number of objects are the important discussion points.
When students see the socks are grouped by 2 and use that to find the total, they are looking for and making use of structure (MP7).
Launch
 Groups of 2
 Display the image.
 “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
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
 “How does this problem relate to what we know about multiplication?” (There are equal groups of socks, we can say there are 6 groups of 2.)
Activity 1: Scaled Picture Graph to Diagram (15 minutes)
Narrative
The purpose of this activity is for students to build on the work they have done with scaled picture graphs to use the tape diagram as a new representation of multiplication. The scale of the picture graph will be used to help students think about a category of the graph as a situation involving equal groups.
To add movement to this activity, students could find someone in the class who represented a different category than they did or represented the same category in a different way. When they find a person, they can describe what is the same and what is different about their representations.
Advances: Speaking, Representing
Launch
 Groups of 2
 Display the picture graph and tape diagram.
 “What do you notice? What do you wonder?” (The key says each square represents 2 signs. The diagram shows 3 groups of 2. I wonder whether they represent the same thing.)
 1 minute: quiet think time
 1 minute: partner discussion time
 “How does the diagram show the speed limit signs that Elena saw on the way home?”
 Share responses.
Activity
 “Now independently represent the data from another category in the graph with your own drawing or diagram.”
 12 minutes: independent work time
 “Share how you represented the data in your drawing or diagram with your partner.”
 2–3 minutes: partner discussion
 Monitor for students who create a tape diagram to represent one of the other categories to use during the synthesis.
Student Facing
 How does the diagram show the speed limit signs that Elena saw on the way home?
 Represent the data from another category in the graph with your own drawing or diagram.
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Have students share different ways they represented a category in the graph.
 Display a student created tape diagram or make a quick sketch of one to represent the street signs Elena saw on the way home.
 “Which category does this tape diagram represent? How do you know?”
 “How is the diagram the same as the scaled picture graph?” (Each picture and each part of the tape diagram represents 2 signs.)
 “How is the diagram different than the scaled picture graph?” (In the graph, you have to read the key to know that each picture shows two signs. In the diagram, each part is labeled with a 2.)
Activity 2: Card Sort: Equal Groups (20 minutes)
Narrative
The purpose of this activity is for students to connect situations involving equal groups to drawings and tape diagrams. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7). Students explain why two cards match and have opportunities to critique and question their peers' reasoning (MP3). When explaining, students have opportunities to revise their language to make their explanations more precise and clear (MP6). After sorting and describing their sort, students notice that all of the representations reinforce the meaning of multiplication as a way to express equal groups.
Students will spend all of the next lesson working with expressions. Keep the equal groups cards for the next lesson.
Supports accessibility for: Attention, Organization
Required Materials
Materials to Copy
 Card Sort Equal Groups
Required Preparation
Launch
 Groups of 2
 Give each group of 2 students a set of cards.
 “This set of cards includes drawings, situations, and diagrams. Take a little time to think about how some of the cards could match.”
 1 minute: quiet think time
 “Find the cards that match. Work with your partner to justify your choices. Be ready to explain your reasoning.”
 5 minutes: partner work time
 Have students share the matches they made and how they know those cards go together.
 Listen for the language students use to describe their match. If students only reference the numbers that match, consider asking:
 “What do you mean when you say _____?”
 “How could you use the words ‘equal groups’ to explain?”
Activity
 “Now you’re going to create a drawing or diagram to represent two different situations.”
 3–5 minutes: independent work time
 Monitor for the students who draw equal groups and students who draw a tape diagram.
Student Facing
 Your teacher will give you a set of cards that show drawings, situations, and diagrams. Find the cards that match. Be ready to explain your reasoning.

Create a drawing or diagram for each situation.
 There are 4 bags. Each bag has 2 strawberries.
 There are 4 hands. Each hand has 5 fingers.
Student Response
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Advancing Student Thinking
If students create representations that do not match the number of groups or size of the groups in the situations, consider asking:
 “How did you represent the situation?”
 “How could you show the groups in the situation? How could you show the objects in each group?”
Activity Synthesis
 For each situation in the last 2 problems, display 2–3 student representations, at least one drawing of equal groups and one tape diagram. Leave them displayed.
 “What do all these representations have in common?” (They all show equal groups. They all have groups. Each group has the same amount.)
 “Where are the 4 bags and 2 strawberries in each drawing or diagram?”
 “Where are the 4 hands and 5 fingers in each drawing or diagram?”
Lesson Synthesis
Lesson Synthesis
Display the tape diagram.
“Today’s lesson was all about multiplication. How can a diagram show multiplication?” (A diagram can show multiplication because you can draw the number of groups and write how many are in each group. You can see that there are 4 parts in this diagram, so there are 4 groups and the 5 tells you there are 5 things in each group.
Display:
4 groups and 5 in each group
\(4\times5\)
“You may remember that an expression has at least 2 numbers and at least one math operation. A multiplication expression is how we represent the number of groups and number in each group in a situation. For example, the multiplication expression \(4\times5\) would represent this diagram because we have 4 groups and 5 in each group.” Point to the 4 and 5 in the diagram and the expression as you explain.
“The symbol in the middle of the expression is the multiplication symbol. \(4\times5\) can be read as ‘4 groups of 5.’”
Cooldown: Boxes of Shirts (5 minutes)
CoolDown
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