Unit 4, Lesson 1
Subtraction in Equivalent Expressions
Accelerated 7
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This Math Talk focuses on adding and subtracting signed numbers. It encourages students to think about rewriting subtracting as adding and to rely on the properties of operations to mentally solve problems. The fluency elicited here will be helpful later in the lesson when students need to rewrite subtraction as adding the opposite.
To rewrite expressions using a different operation, students need to look for and make use of structure (MP7).
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
Keep all previous problems and work displayed throughout the talk.
Find the value of each expression mentally.
To involve more students in the conversation, consider asking:
Emphasize that “Subtract 10” can be rewritten as “Add negative 10” and that addition is commutative, but subtraction is not. Mention these points even if students do not bring them up.
MLR8: Discussion Supports
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In this activity, students express the area of a rectangle in different ways using the distributive property. Students learn that even when the terms are negative, we can still organize our work with the distributive property in a way that is similar to using area diagrams.
Students must notice and make use of structure to rewrite an expression in different ways (MP7).
Display the image, and ask students to write an expression for the area of the big rectangle in at least three different ways.
Collect responses. If students simply say “16,” ask them to explain how they calculated 16 and record these processes for all to see. Remind students that thinking about area gives us a way to understand the distributive property. This diagram can be used to show that
Tell students that when we are working with negative numbers, thinking about area doesn’t work so well, but the distributive property still holds when there are negative numbers. The expressions involved still have the same structure, and we can still organize our work the same way.
Write two expressions for the area of the big rectangle.
Use the distributive property to write an expression that is equivalent to
The purpose of this discussion is to recognize and justify different, valid ways to write equivalent expressions.
Solicit responses to the second question and demonstrate thinking about one product at a time:
Then ask students to share how they approached the last question. Highlight responses where students noticed that
In previous lessons, we learned that subtracting a number gives the same result as adding its opposite. We can apply this relationship to rewrite an expression with subtraction so it uses only addition. Then we can make use of the properties of addition that allow us to add and group in any order. This can make calculations simpler. Example:
We can also organize the work of multiplying signed numbers in expressions. The product
Multiply
Reassemble the parts to get the expanded version of the original expression:
Help us improve by sharing suggestions or reporting issues.
Lin and Kiran are trying to calculate
Lin: “I plan to first add
Kiran: “It would be a lot easier if we could start by working with the
Lin: “You can’t switch the order of numbers in a subtraction problem like you can with addition.
Kiran: “That’s true, but do you remember what we learned about rewriting subtraction expressions using addition?