Unit 1, Lesson 20
The Commutative Property
Grade 3
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The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting 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 subtract, they look for and make use of structure (MP7).
Find the value of each expression mentally.
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The purpose of this activity is to introduce the commutative property. Students write array situations for a pair of arrays and discuss similarities and differences. While the situations will have the same total number of objects, how the objects are grouped should be different. Then students write equations to go with the arrays and situations, and make connections between the representations (MP2). Students notice that, while the order of the factors in the multiplication equation changes, the product does not change (MP7).
What do you notice? What do you wonder?
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Write a description of a situation for each array.
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Image B
How are the situations alike? How are they different?
Write a multiplication equation for each situation.
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How does your equation connect to the situation and array?
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MLR1 Stronger and Clearer Each Time
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The purpose of this activity is to reinforce the idea of the commutative property. In this activity, students write two equations to match an array to show again that reversing the order of the factors does not change the product. If students do not immediately see how they might write different equations for the array, encourage them to consider different ways of grouping the dots in the array, similar to the previous activity. Students use the vocabulary they have learned for describing arrays and multiplication to explain why both equations match an array with their partner. The Stronger and Clearer Each Time math language routine allows students to receive feedback and revise their explanation for clarity (MP3, MP6).
If students finish early, consider drawing another array. Have students write two equations for the array and consider how they can think of the rows or columns as equal groups.
This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing.
Write 2 multiplication equations that represent the array.
MLR1 Stronger and Clearer Each Time
We learned how equal groups are related to arrays and how to represent arrays with multiplication expressions and equations.
Equal groups:
Array:
Expression:
Equation:
We also learned that we can multiply numbers in any order and get the same product.
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