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Learning Outcomes
Students will be able to

• use a visual model for comparing and subtracting fractions with unlike denominators
• solve story problems involving subtracting fractions with unlike denominators
• define the mathematical terms below

Common Core State Standards: 4.NF.B.3a, 4.NF.B.3d, 5.NF.A.1, 5.NF.A.2

Vocabulary: Equivalent fractions, common denominator

Materials: For the class: computer with large monitor; per student: paper, pencil; Fraction Diagram handout 

Procedure
1. Introduction (1–10 minutes, whole group)
Distribute the materials, including the handout. If students are familiar with the diagram on the handout from a prior lesson, skip or abbreviate this introduction.

Ask students to use the diagram to solve several problems:

How could you use this diagram to:

• show that 2/4 and 1/2 are equivalent fractions?
• show that 1/3 is larger than 1/4?
• solve 3/8 – 1/8?

Then ask, Is there a fraction equivalent to 3/8 on the diagram? How do you know?

After each question, ask volunteers to demonstrate their solution strategies.

2. Video  (10 minutes, whole group) 
Pose the following for students to solve using the diagram:

1/2 – 1/8

• Gather solution strategies. If students do not suggest these approaches, do so yourself: First, determine that 1/2 is equivalent to 4/8. Then, subtract 1/8 to get 3/8.
• Mark 1/2 on an edge of paper. Then, starting where 1/2 ends, mark 1/8 less. Next, determine that the entire segment fits across the three 1/8s. 

Now, pose this problem and give students a moment to solve it:

1/3 – 1/4

Show students the video, pausing at 0:50 to check their understanding of the term common denominator.

When the video is over, ask, Did anyone solve the problem the way Ms. Sheffield did? What other ways did you find to solve the problem? 

3. Fraction Subtraction (10 minutes, pairs) 
Introduce the following problem: Tina finds 1/2 of a jug of orange juice in the refrigerator. She drinks some, leaving 1/4 of the jug full. How much does she drink? How would you write that as an equation?

If no one suggests 1/2 – 1/4 = 1/4, do so yourself and record it on the board.

Then, pose a problem that students will work on in pairs:

Tina finds 1/2 of a jug of orange juice in the refrigerator. She drinks some and leaves some for her brother. What combinations of fractions could show how much she drinks and how much she leaves? 

Students should use the fraction diagram and record (as 1/2 – one fraction = another fraction) as many solutions as they can in the next 5 minutes.

If students are uncertain of how to proceed, talk through one or two possibilities and ask students for ideas on how to record them (e.g., 1/2 – 1/3 = 1/6).  

4. Conclusion (5 minutes, whole group)
Assemble students. As a class, discuss their solutions, their strategies, and what they learned about addition of fractions with unlike denominators.

Activity Extension: Have students find as many solutions as they can to a more challenging version of the in-class problem: Angelo finds 3/4 of a jug of orange juice in the refrigerator. He drinks some and leaves some for his sister. What combinations of fractions could show how much he drinks and how much he leaves?

This activity is based on work developed at TERC.