Warm-up: Which One Doesn’t Belong: Representations (10 minutes)
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 each is the same or different (MP6). Listen to the language students use to describe the different characteristics of each expression and equation and connect students' language to the new terms, factor and product, that are introduced in the synthesis.
- Groups of 2
- Display the image, expression, and equations.
- “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
- 1 minute: quiet think time
- “Discuss your thinking with your partner.”
- 2-3 minutes: partner discussion
- Share and record responses.
Which one doesn't belong?
\(7 + 8 = 15\)
- “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: Multiplication Equation Match (20 minutes)
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 or the number of objects in each group and between the product and the total number of objects. These connections are brought out explicitly during the synthesis. When students make explicit connections between multiplication situations and equations, they are reasoning abstractly and quantitatively (MP2).
- Groups of 2 and 4
- “Think about how you might match these equations to a situation or diagram.”
- 1 minute: quiet think time
- “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 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, diagram, or drawing. Record the equation. Be prepared to explain your reasoning.
- \(3\times5 = 15\)
- \(4\times10 = 40\)
- \(2\times10 = 20\)
- \(10 = 5\times2\)
- \(30 = 6\times5\)
- \(4\times2 = 8\)
- \(16 = 8\times2\)
- \(4\times5 = 20\)
- \(50 = 5\times10\)
Andre had 5 pairs of socks.
6 hands were on the table. Each hand had 5 fingers.
There were 4 boxes of markers. Each box had 10 markers.
- “Were there any matches you disagreed on? How did you come to an agreement?” (We went back and recounted the dots together.)
- For the first, fourth, and seventh pairs that match 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: Write Multiplication Equations (15 minutes)
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.
Advances: Representing, Conversing
Supports accessibility for: Social-Emotional Functioning
- Groups of 2
- “Work with your partner to write an equation that represents each situation 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 an 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.
- For each problem have a student 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?”
Equation: \(3\times5 = 15\)
“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. 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. Equations are helpful if you are trying to find the product.)