# Lesson 12 Sums and Differences of Fractions

Let’s add and subtract fractions and analyze our strategies.

## Warm-up Number Talk: Subtract Some Eighths

Find the value of each expression mentally.

## Activity 1 Make It True

## Problem 1

Find the number that makes each equation true. Show your reasoning.

## Problem 2

Write a sentence to describe your first step for finding the missing number in each equation in the first problem.

First step:

First step:

First step:

First step:

## Problem 3

Compare and reflect on your first steps with your group. Did you make the same moves?

Discuss why you might have chosen the same way or different ways to start finding the missing numbers.

## Activity 2 To Decompose or Not to Decompose

Here are some addition and subtraction expressions. Sort them into two groups based on whether you think it would be helpful to decompose a number to find the value of the expression. Be prepared to explain your reasoning.

Not necessary or not helpful to decompose any number:

Necessary or helpful to decompose one or more numbers:

Choose at least one expression from each group and find their values. Show your reasoning.

## Practice Problems

## Problem 1

For each of the expressions, explain whether you think it would be helpful to decompose one or more numbers to find the value of the expression.

## Problem 2

The lengths of the shoes of a dad and his two daughters are shown.

For each question, show your reasoning.

How much longer is the older daughter’s shoes than her sister’s?

Which is longer, the dad’s shoes or the combined lengths of his daughters’ shoes?