Lesson 8 Addition of Fractions

- Let’s explore sums of fractions on a number line.

Warm-up Notice and Wonder: A Fraction on a Number Line

What do you notice? What do you wonder?

Number line. Evenly spaced tick marks. First tick mark, 0. Sixth tick mark, 5 thirds.

Activity 1 Sum of Jumps

Problem 1

On each number line, draw two “jumps” to show how to use sixths to make a sum of $\frac{8}{6}$ . Then, write an equation to represent each combination of jumps.
Noah draws the following diagram and writes: $\frac{8}{6} = \frac{6}{6} + \frac{2}{6}$ and $\frac{8}{6} = 1 + \frac{2}{6}$ . Which equation is correct? Explain your reasoning.

Problem 2

On each number line, draw “jumps” to show how to use thirds to make a sum of $\frac{7}{3}$ . Then, write an equation to represent each combination of jumps.
Write $\frac{7}{3}$ as a sum of a whole number and a fraction.

Activity 2 What is the Sum?

Problem 1

Use a number line to represent each addition expression and to find its value.

$\frac{5}{8} + \frac{2}{8}$
$\frac{1}{8} + \frac{9}{8}$
$\frac{11}{8} + \frac{9}{8}$
$2 \frac{1}{8} + \frac{4}{8}$

Problem 2

Priya says the sum of $1 \frac{2}{5}$ and $\frac{4}{5}$ is $1 \frac{6}{5}$ . Kiran says the sum is $\frac{11}{5}$ . Tyler says it is $2 \frac{1}{5}$ . Do you agree with any of them? Explain or show your reasoning. Use one or more number lines if you find them helpful.

Number line. 16 evenly spaced tick marks. First tick mark, 0. Sixth tick mark, 1.

Activity 3 Make Two Jumps

Here are four number lines, each with a point on it.

For each number line, label the point. This is your target. Make two forward jumps to get from 0 to the target.

Pick a card from the set given to you. Use the fraction on it for your first jump. Draw the jump and label it with the fraction.
From there, draw the second jump to reach the target. What fraction do you need to add? Label the jump with the fraction.
Write an equation to represent the sum of your two fractions.

Practice Problem

Problem 1

Draw “jumps” on the number lines to show two ways to use fourths to make a sum of $\frac{7}{4}$ .
Represent each combination of jumps as an equation.