# The Relationship of Addition and Subtraction

Videos and solutions to help Grade 6 students learn how to build and clarify the relationship of addition and subtraction by evaluating identities.

New York State Common Core Math Grade 6, Module 4, Lesson 1

Related Topics:
Lesson Plans and Worksheets for Grade 6
Lesson Plans and Worksheets for all Grades

Lesson 1 Student Outcomes

Students build and clarify the relationship of addition and subtraction by evaluating identities such as
w + x - x = w and w + x - x = w

Opening Exercises

a. Draw a tape diagram to represent the following expression: 5 + 4.

b. Write an expression for each tape diagram.

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.

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

4. Using your knowledge of identities, fill in each of the blanks.
a. 5 + 5 - ___ = 4
b. 25 - ___ + 10 = 25
c. ___ + 16 - 16 = 24
d. 56 - 20 + 20 = ___

5. Using your knowledge of identities, fill in each of the blanks.
a) a + b - ___ = a
b) c - d + d = ____
c) e + ___ - f = e
d) ___ - h + h = g

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? A review of the relationship between addition and subtraction and the relationship between multiplication and division.

Problem Set
1. Fill in each blank.
a. _____ + 15-15 = 21
b. 450-230+230 = _____
c. 1289- ______ + 856 = 1289

2. Why are the equations w-x+x = w and w+x-x = w called identities?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.