Lesson 4 Same Size, Related Sizes

- Let’s find some fractions that are the same size.

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

What do you notice? What do you wonder?

diagram on top of number line, equal lengths. Diagram, 12 equal parts. Number line from 0 to 1. 5 evenly spaced tick marks.

Activity 1 Same Size, Different Numbers

Problem 1

Here’s a diagram of fraction strips, with two strips added for tenths and twelfths.

Use a blank strip to show tenths. Label the parts. How did you partition the strip?
Use a blank strip to show twelfths. Label the parts. How did you partition the strip?

Problem 2

Jada says, “I noticed that one part of $\frac{1}{2}$ is the same size as two parts of $\frac{1}{4}$ and three parts of $\frac{1}{6}$ . So $\frac{1}{2}$ , $\frac{2}{4}$ , and $\frac{3}{6}$ must be equivalent.”

Find a fraction that is equivalent to each of the following fractions. Be prepared to explain your reasoning.

$\frac{1}{6}$
$\frac{2}{10}$
$\frac{3}{3}$

Activity 2 Fractions on Number Lines

Problem 1

Here are some number lines. The point on this number line shows the fraction $\frac{1}{2}$ .

Number Line. Scale 0 to 1. There are 5 evenly spaced tick marks. First tick mark, 0. Third tick mark, one half. Fifth tick mark, 1. A Point is labeled at 1 half.

Label the tick marks on each number line.

Number line from 0 to 1. 4 evenly spaced tick marks. First tick mark 0. Last tick mark, 1.

number line from 0 to 1. 5 evenly spaced tick marks.

number line from 0 to 1. 6 evenly spaced tick marks. First tick mark, 0. Last tick mark, 1.

Problem 2

Suppose you are to locate $\frac{1}{6}$ , $\frac{1}{8}$ , and $\frac{1}{10}$ on one of the number lines.

Which number line would you use for each fraction? Be prepared to explain your reasoning.
Locate and label each fraction ( $\frac{1}{6}$ , $\frac{1}{8}$ , and $\frac{1}{10}$ ) on a different number line.

Problem 3

Locate and label each of the following fractions on one of the number lines.

$\frac{2}{3}$

$\frac{2}{8}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{4}{6}$

$\frac{4}{8}$

$\frac{4}{10}$

$\frac{6}{6}$

$\frac{6}{10}$

$\frac{8}{8}$

Practice Problem

Problem 1

Use the fraction strips to name three pairs of equivalent fractions. Explain how you know the fractions are equivalent.

Two diagrams of equal length. Top diagram, 12 equal parts, each labeled 1 twelfth. Bottom diagram, 6 equal parts, each labeled 1 sixth.