Lesson 11
Different Ways to Subtract
Lesson Purpose
Lesson Narrative
In this lesson, students continue to find differences of fractions with a focus on mixed numbers. There are many ways to find these differences including
 finding equivalent fractions with a common denominator and finding their difference
 adding on, exploiting the whole number parts of the mixed numbers
 using equivalent expressions which help to find a common denominator and deal both with the whole number and fractional parts of the numbers
The second and third strategies have close analogies in arithmetic with whole numbers. One way to find a difference, such as \(135  28\), is to add on, first 2, then 5, then 100, finding that the difference is 107. For a fraction difference such as \(2 \frac{3}{8}  \frac{3}{4}\) the corresponding reasoning would be to add \(\frac{1}{4}\), then 1, then \(\frac{3}{8}\) and find that the difference is \(1\frac{5}{8}\). Students could also rewrite the expression \(135  28\) as \((100 + 20 + 15)  (20 + 8)\) and then find the differences \(100  0 = 100\), \(20  20 = 0\) and \(15  8 = 7\). With the fraction difference, they can rewrite \(2\frac{3}{8}\) as \(1 + \frac{11}{8}\) and then subtract \(\frac{3}{4}\) or \(\frac{6}{8}\) from \(\frac{11}{8}\), again getting a result of \(1\frac{5}{8}\). Students are not expected to bring out these connections but it is important to see that the techniques students used for finding whole number differences can also be used, with appropriate modification, for finding mixed number differences.
 Action and Expression
Learning Goals
Teacher Facing
 Subtract fractions and mixed numbers.
Student Facing
 Let’s subtract fractions and mixed numbers.
Required Preparation
CCSS Standards
Addressing
Lesson Timeline
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
Suggested Centers
 How Close? (1–5), Stage 9: Add Fractions to 5 (Addressing)
 Creating Line Plots (2–5), Stage 3: Eighth Inches, Add and Subtract (Supporting)
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