Fishtank Learning

4th Grade Math
Unit 5: Fraction Operations
Lesson 7

Objective

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Anchor Tasks - Problem 1

Act 1: Watch the video Black box - Act 1.

a. What do you notice? What do you wonder?

b. What will the sum $$\frac{1}{2} + \frac{1}{4}$$ be? Make a prediction.

Anchor Tasks - Problem 2

Act 2: Use the following information to determine what the sum $$\frac{1}{2}+\frac{1}{4}$$ is.

Anchor Tasks - Problem 3

Act 3: Watch Black box - Act 3 to see the solution.

Was your prediction correct? Why or why not?

Anchor Tasks - Problem 4

Solve. Show or explain your work.

a. $${{1\over2}+{1\over8}}$$

b. $${{1\over5}+{3\over10}}$$

c. $${{2\over3}+{1\over6}}$$

d. $${{3\over4}+{5\over12}}$$

Guiding Questions

Before adding, do you expect the sum to be greater than or less than one half? One whole? Why?
What is 1 apple + 1 orange? How can we create like units to be able to find the sum of these quantities?
How can we create like units? What can we draw that might help us?
Can we rewrite our solution using larger units? Can we write any of them as mixed numbers?

Notes

Examples of a tape diagram and number line used to solve Part (a) are shown below.

Notice that this shows the addition with one tape rather than 2, as done in Anchor Tasks 1-3, to show the connection to the number line more clearly. Either way of representing the tape diagrams is valid and might be worth discussing if students are still unsure of their equivalence.
While Anchor Task #4 after a 3-Act task is typically an optional “sequel,” this task should not be considered such, since students will benefit from additional examples of adding fractions where one denominator is a multiple of the other denominator, including cases where the multiple is 3 or 4 times as large as the other denominator, as well as cases where the sum is greater than 1.
Since it is possible to overemphasize the importance of simplifying fractions, the question regarding writing the solution using larger units is optional.

Problem Set

View Problem Set

Discussion of Problem Set

How did you determine which amounts could have been what Jake added to the jug in #1?
In #2c, did you use sixths as the common denominator? Explain how thirds could be used as the common denominator.
For #5, what strategies did you use to estimate if the sum would be between 0 and 1 or 1 and 2?
Why is it important to have common denominators when adding fractions?
How can you find the sum of two fractions without using a model?
What benefit can you see in expressing a fraction as a mixed number or a mixed number as a fraction?

Target Task