Lesson 18Subtraction in Equivalent Expressions
Learning Goal
Let’s find ways to work with subtraction in expressions.
Learning Targets
I can organize my work when I use the distributive property.
I can re-write subtraction as adding the opposite and then rearrange terms in an expression.
Lesson Terms
- term
Warm Up: Number Talk: Additive Inverses
Problem 1
Find each sum or difference mentally.
Activity 1: A Helpful Observation
Problem 1
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?
Write an expression that is equivalent to
that uses addition instead of subtraction. If you wrote the terms of your new expression in a different order, would it still be equivalent? Explain your reasoning.
Activity 2: Organizing Work
Problem 1
Write two expressions for the area of the big rectangle.
Problem 2
Use the distributive property to write an expression that is equivalent to
Problem 3
Use the distributive property to write an expression that is equivalent to
Are you ready for more?
Problem 1
Here is a calendar for April 2017.
Let’s choose a date: the 10th. Look at the numbers above, below, and to either side of the 10th: 3, 17, 9, 11.
Average these four numbers. What do you notice?
Choose a different date that is in a location where it has a date above, below, and to either side. Average these four numbers. What do you notice?
Explain why the same thing will happen for any date in a location where it has a date above, below, and to either side.
Lesson Summary
Working with subtraction and signed numbers can sometimes get tricky. We can apply what we know about the relationship between addition and subtraction—that subtracting a number gives the same result as adding its opposite—to our work with expressions. 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. For 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: