# 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

Warm-up | 10 min |

Activity 1 | 20 min |

Activity 2 | 15 min |

Lesson Synthesis | 10 min |

Cool-down | 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)