This Warm-up prompts students to carefully analyze and compare features of expressions and equations. When students compare the drawing, expression, and equations, they must use language precisely to describe how the representations are alike (MP6). Listen to the language students use to describe the different characteristics of the multiplication expression and equation. After the new terms “factor” and “product” are introduced in the Synthesis, connect students’ descriptions to those terms.
This is the first time students experience the Which Three Go Together? routine in IM Grade 3. Students should be familiar with this routine from a previous grade. However, they may benefit from a brief review of the steps involved.
Launch
Groups of 2
Display the image, expression, and equations.
“Pick 3 that go together. Be ready to share why they go together.”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
2–3 minutes: partner discussion
Share and record responses.
Which 3 go together?
A
B
C
D
Student Response
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Advancing Student Thinking
Activity Synthesis
“How is C different from the other ways we’ve represented equal groups before?” (It has an equal sign. It’s an equation.)
“C is a multiplication equation because it contains a multiplication symbol and the equal sign.”
“There are words that help us talk about different parts of the multiplication equation. The factors are the numbers being multiplied. The product is the result of multiplying some numbers. In the equation in C, the numbers 2 and 5 are the factors. The product is 10. Keep these words in mind today as we work with other multiplication equations.”
Activity 1
Standards Alignment
Building On
Addressing
3.OA.A.1
Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as .
The purpose of this activity is for students to match multiplication equations to situations and representations. Students make explicit connections between the factors and the number of groups and the number of objects in each group and between the product and the total number of objects. These connections are discussed explicitly during the Activity Synthesis. When students make explicit connections between multiplication situations and equations, they are reasoning abstractly and quantitatively (MP2).
Launch
Groups of 2 and 4
“Think about how you might match these equations to a situation or diagram.”
1 minute: quiet think time
Activity
“Take turns finding a situation or diagram that matches each equation. Explain your reasoning to your partner.”
5–7 minutes: partner discussion
Monitor for students who make direct connections between each factor representing the number in each group or the number of groups and the product representing the total number of objects to share during the Activity Synthesis.
“Get together with another group to discuss the matches you made.”
3–5 minutes: small-group discussion
Find an equation from the list that can represent each situation, drawing, or diagram. Record the equation. Be prepared to explain your reasoning.
Andre has 5 pairs of socks.
There are 6 hands on the table. Each hand has 5 fingers.
There are 4 boxes of markers. Each box has 10 markers.
Student Response
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Advancing Student Thinking
Activity Synthesis
“Were there any matches you disagreed on? How did you come to an agreement?” (We went back and recounted the dots together.)
For the , , and matches ask, “How does the equation represent the situation (or diagram)?” (The 2 represents the 2 parts in the diagram. The 5 represents the 5 fingers on each hand. The 50 represents how many dots were in the groups altogether.)
Activity 2
Standards Alignment
Building On
Addressing
3.OA.A.1
Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as .
The purpose of this activity is for students to write equations that match situations and diagrams. Students use what they learned in the last activity to use multiplication equations to represent situations and diagrams. In the Lesson Synthesis, use the words “factor” and “product” to help students connect the vocabulary to the concepts.
MLR7 Compare and Connect. Synthesis: Invite groups to prepare a visual display that shows their reasoning for one of the equations using details, such as different colors, arrows, labels, diagrams or drawings. Give students time to investigate each others’ work. Ask, “Which details or language helped you understand the displays?” “Did anyone create the same equation, but would explain it differently?” Advances: Representing, Conversing
Engagement: Provide Access by Recruiting Interest. Provide choice. Invite students to decide which problem to start with or decide the order to complete the task. Supports accessibility for: Social-Emotional Functioning
Launch
Groups of 2
Activity
“Work with your partner to write an equation that represents each situation, drawing, and diagram.”
5–7 minutes: partner work time
Monitor for students who can justify the equations they wrote by explaining the meaning of the factors and products in their equations.
Write a multiplication equation that represents each situation, drawing, or diagram. Be prepared to explain your reasoning.
A package has 6 pairs of socks.
Diego has 7 sections in his notebook. Each section has 10 pages.
Elena has 4 bags of oranges. Each bag has 5 oranges in it.
Student Response
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Advancing Student Thinking
Activity Synthesis
For each problem, invite a student to share their equation. Consider asking:
“How does this equation make sense for this situation, drawing, or diagram?”
“What parts of the situation, drawing, or diagram were especially helpful as you wrote the equation?”
Lesson Synthesis
Display:
Expression:
Equation:
“Today we learned about equations and how we can use them to represent multiplication. In this equation, 3 and 5 are the factors and 15 is the product.”
“How are multiplication expressions and equations alike?” (They both use the multiplication symbol. They both have factors.)
“How are multiplication expressions and equations different?” (Equations have an equal sign and a product. Multiplication equations have numbers on both sides of the equal sign.)
“When would each be helpful?” (Expressions are helpful when you want to describe a situation with equal groups. Equations are helpful if you are trying to find the total number of objects, or the product.)
Standards Alignment
Building On
Addressing
3.OA.A.1
Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as .
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 2.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 2.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 2.