# Lesson 10

The Numbers in Subtraction

### Lesson Purpose

The purpose of this lesson is for students to recognize that a fraction can be subtracted from a whole number by writing an equivalent fraction for the whole number. It can also be done by decomposing the whole number, the fraction, or both, into a sum of fractions with the same denominator.

### Lesson Narrative

In earlier lessons, students explored addition and subtraction of fractions in context and out of context. They used diagrams to represent and find the values of sums and differences, and they also reasoned numerically. Students learned that a non-unit fraction can be decomposed—in at least one way—into a sum of other fractions with the same denominator. They recognized adding and subtracting fractions as joining and removing parts that refer to the same whole.

In this lesson, students apply these insights, as well as their knowledge of equivalent fractions from an earlier unit and from grade 3, to find differences of a whole number and a fraction.

• Representation

Activity 1: What’s Left?

### Learning Goals

Teacher Facing

• Subtract a fraction from a whole number by decomposing the whole number and reasoning about equivalence.

### Student Facing

• Let’s subtract fractions from whole numbers.

### Required Materials

Materials to Copy

• Card Sort: Twelfths

### Required Preparation

Activity 2:

• Create a set of cards for each group of 2.

Building On

### 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

How did the student work that you selected impact the direction of class discussion? How would you adjust your selection if you teach the lesson again?