1) The document provides materials and instructions for Module 4 Lesson 1 on the relationship between addition and subtraction. Students will use tape diagrams and variables to demonstrate that adding and then subtracting the same number results in the original number. 2) The lesson uses tape diagrams to show that adding a number and then subtracting the same number results in the original amount. Students represent these relationships with number sentences using variables. 3) Key ideas that students explore are identities such as x + x - x = w, which will always be true no matter the numbers used for the variables. Students demonstrate that the order of adding and subtracting does not change the final result.

1. Module 4 Lesson 1.notebook
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February 27, 2015
Feb 27­7:26 AM
Please collect your Mod 4 Materials:
• yellow exit tickets: front of the room
• white module notes: back table
• blue sprints: period baskets
• green terminology: math outbox

2. Module 4 Lesson 1.notebook
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Aug 26­5:45 PM
MODULE 4 Expressions and Equations
Topic A: Relationships of the Operations
Lesson 1: The Relationship of Addition &
Subtraction
Student Outcomes
§ Students build and clarify the relationship of addition and subtraction by evaluating
identities such as x – x + x = w and w + x – x = w.

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February 27, 2015
Nov 17­2:29 PM
Classwork
Opening Exercise
a. Draw a tape diagram to represent the following expression: 5 + 4
b. Write an expression for each tape diagram.

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Nov 17­2:29 PM
If each of the squares represents 1 unit, represent the number 3 using the squares provided.
Add two more squares to your tape diagram.
Write an expression to represent how we created a tape diagram with 5 squares.
Remove two squares from the tape diagram.
Alter our original expression 3 + 2 to create an expression that represents what we did with the tape diagram.
Evaluate the expression.

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Nov 17­2:28 PM
Let’s start a new diagram. This time, create a tape diagram with 6 squares.
Use your tiles to demonstrate 6 + 4
Remove 4 squares from the tape diagram.
Alter our original expression 6 + 4 to create an expression to represent the tape diagram.
How many tiles are left?
Evaluate the expression.
How many tiles did we start with?
What effect did adding four tiles then subtracting the four tiles have on the number of tiles?
ú Adding and then subtracting the same number of tiles resulted in the same number that we
started with.

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§ What if I asked you to add 215 tiles to the six tiles we started with and then
subtract 215 tiles? Do you need to actually add and remove these tiles to know
what the result will be? Why is that?
§ What do you notice about the expressions we created with the tape
diagrams?
ú When we add one number and then subtract the same number we get our
original number.

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Mar 6­7:12 PM
Write a number sentence, using variables, to represent what we just demonstrated with tape diagrams.
Remember that a variable is a letter that represents a number. Use the shapes provided to create tape
diagrams to demonstrate this number sentence.
Why is the number sentence x + x – x = w called an identity?
ú The number sentence is called an identity because the variables can be replaced with any numbers and the
sentence will always be true.
w + x – x = w

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Exercises
1. Predict what will happen when a tape diagram has a large number of squares, some
squares are removed, but then the same amount of squares are added back on.
2. Build a tape diagram with 10 squares.
a. Remove 6 of them. Write an expression to represent the tape diagram.
b. Add 6 squares onto the tape diagram. Alter the original expression to represent the
current tape diagram.
c. Evaluate the expression.
click

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3. Write a number sentence, using variables, to represent the identities we demonstrated with tape
diagrams.

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Closing
§ In every problem we did today, why did the final value of the expression equal the initial
expression?
§ Initially, we added an amount and then subtracted the same amount. Later in the
lesson, we subtracted an amount and then added the same amount. Did this alter the
outcome?
§ Why were we able to evaluate the final expression even when we did not know the
amount we were adding and subtracting?

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Mar 6­7:21 PM
White Board Exchange
Solve the following on
your white board and
hold up your answer
when you're done.

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Aug 26­8:21 PM
Closing
Please take out your exit ticket for Lesson 9, close your
binder, and complete the exit ticket. This will be collected.

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Mar 3­6:04 PM