Lesson 9
Multiplication as Equal Groups
Warmup: Number Talk: More Addition (10 minutes)
Narrative
The purpose of this Number Talk is to elicit strategies and understandings students have for addition within 100. It also provides an opportunity to observe student strategies as they work toward becoming fluent in addition within 1,000.
When students use strategies based on place value to add they look for and make use of structure (MP7).
Launch
 Display one expression.
 “Give me a signal when you have an answer and can explain how you got it.”
 1 minute: quiet think time
Activity
 Record answers and strategy.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(40+35\)
 \(45+35\)
 \(45+36\)
 \(34+58\)
Student Response
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Activity Synthesis
 “How did you compose new tens as you solved these problems?” (In the second problem I composed a ten from the 2 fives. In the third problem I composed a new ten from the 5 and the 6 and still had 1 leftover.)
 Consider asking:
 “Who can restate _______ 's reasoning in a different way?”
 “Did anyone have the same strategy but would explain it differently?”
 “Did anyone approach the problem in a different way?”
 “Does anyone want to add on to____’s strategy?”
Activity 1: From Scaled Graphs to Equal Groups (15 minutes)
Narrative
The purpose of this activity is for students to connect scaled picture graphs to situations involving equal groups. 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.
The launch of the activity is an opportunity for students to share their experiences and ask questions about the graph to ensure each student has access to the context. If it is helpful, display a few images of different types of signs students may see in their community.
Supports accessibility for: VisualSpatial Processing
Required Materials
Materials to Gather
Required Preparation
Launch
 Groups of 2
 Give students access to connecting cubes or counters.
 “We’re going to look at a scaled picture graph about signs that Elena saw on the way home. What types of signs do you see in the community?” (stop signs, speed limit signs, street signs, billboards)
 30 seconds: quiet think time
 1 minute: partner discussion
 Share responses.
 Display the graph.
Activity
 “Work independently to represent the number of speed limit signs that Elena saw on the way home.”
 1 minute: independent work time.
 Monitor for students who create drawings of equal groups similar to the one shown in the last problem to display during the synthesis.
 1 minute: partner discussion
 “Work with your partner to complete the next problem.”
 1 minute: quiet think time
 2 minutes: partner discussion
 “How did you know which statement described the speed limit signs that Elena saw on the way home?” (There were 3 pictures on the graph. Each picture represents 2 signs.)
 Share responses.
 “Take a few minutes to complete the last problem on your own.”
 3 minutes: independent work time
 “Share your responses with your partner.”
 1 minute: partner discussion
Student Facing
Elena collected data about the kind of signs she saw on the way home. The data is shown in this picture graph:
 Represent the number of speed limit signs Elena saw on the way home.

Which statement describes the number of speed limit signs Elena saw? Explain your reasoning.
 There are 3 pictures and each picture represents 1 speed limit sign.
 There are 3 pictures and each picture represents 2 speed limit signs.
 There are 2 pictures and each picture represents 2 speed limit signs.
 How could this drawing represent the street signs Elena saw on the way home?
Student Response
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Activity Synthesis
 Display a studentcreated drawing of equal groups that represents the speed limit signs that Elena saw on the way home and the drawing in the last problem.
 “These drawings show equal groups. How did these drawings help you represent the data in the picture graph?” (The key told us that each picture represented 2 signs and the drawings helped us see the 2 signs. Each group showed 2 signs.)
Activity 2: Equal Group Situations (20 minutes)
Narrative
The purpose of this activity is for students to represent situations involving equal groups in a way that makes sense to them. Have connecting cubes available for students to use to represent the situation, if they would like. Students may also draw a picture. One partner could use the objects while one draws and then switch for each problem. The focus of the discussion is on the important quantities of each situation and how students used their representation to model each quantity (MP4).
In the launch of the activity, it may be helpful to ask students to tell their partner a quick story or ask any questions about the focus of each of the three contexts to ensure each student has access. It may also be helpful to display images for students to reference.
Advances: Representing, Listening
Required Materials
Materials to Gather
Required Preparation
Launch
 Groups of 2
 Give students access to connecting cubes or counters.
 “What are some places you see groups of 2 in the community? Groups of 5? Groups of 10?” (Shoes. Socks. Wings. Hands have 5 fingers. Flowers can have 5 petals. Markers come in packs of 10. Ten people on a bus.)
 30 seconds: quiet think time
 1 minute: partner discussion
 Share and record responses.
 Choose a studentgenerated example with small numbers or display this situation: “There are 3 flowers. Each flower has 5 petals.”
 “How could you represent this situation?”
 30 seconds: quiet think time
 12 minutes: partner work time
 Share and record responses. Focus on how the representation connects to the problem.
 Consider asking:
 “How did you represent the 3 flowers?”
 “How did you represent the 5 petals on each flower?”
 “Did someone represent this differently?”
Activity
 “Now you are going to represent some more situations involving equal groups with your partner.”
 5–7 minutes: partner work time
 If some students finish earlier than others, encourage them to write their own situation and trade with their partner.
Student Facing
Represent each situation.
 There are 4 people wearing shoes. Each person is wearing 2 shoes.
 There are 2 boxes of markers. Each box has 10 markers.
 There are 3 basketball teams. Each team has 5 players.
Student Response
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Activity Synthesis
 Ask 23 students to share their work for each problem. Be sure to share a variety of different representations.
 In each, ask how the numbers in the situation are represented in their work.
 “How do the representations help you picture the situation?” (I can pretend the objects are the things in the story like the shoes. The drawing is like a picture of what’s happening in the story.)
Lesson Synthesis
Lesson Synthesis
Display a representation of equal groups from the lesson.
“The situations we looked at today were all multiplication. Multiplication is how we represent the total number of objects when you have a certain number of equal groups. For example, in this picture, we would say we have 5 groups of 2.”
“Describe a situation with equal groups that you could represent as multiplication.” (Packs of pencils, bins or baskets with the same number of things in each one, pairs of shoes, rows of seats on the bus.)
Cooldown: Represent Equal Groups (5 minutes)
CoolDown
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