Lesson 15 An Assortment of Fractions

- Let’s find the heights of some stacked objects.

Warm-up Which One Doesn’t Belong: Halves, Fourths, Sixths, and Eighths

Which one doesn’t belong?

$1 \frac{1}{2}$
$\frac{4}{4} + \frac{2}{4}$
$\frac{12}{8}$
$\frac{4}{6}$

Activity 1 All the Way to the Top

Priya, Kiran, and Lin are using large playing bricks to make towers. Here are the heights of their towers so far:

Priya: $21 \frac{1}{4}$ inches
Kiran: $32 \frac{3}{8}$ inches
Lin : $55 \frac{1}{2}$ inches

tower of playing bricks 21 and 1 fourth inches high.

Problem 1

For each question, show your reasoning.
How much taller is Lin’s tower compared to:

Priya’s tower?
Kiran’s tower?

Problem 2

They are playing in a room that is 109 inches tall. Priya says that if they combine their towers to make a super tall tower, it would be too tall for the room and they’ll have to remove one brick.

Do you agree with Priya? Explain your reasoning.

Activity 2 Stacks of Blocks

Andre is building a tower out of foam blocks. The blocks come in three different thicknesses: $\frac{1}{2}$ foot, $\frac{1}{3}$ foot, and $\frac{1}{6}$ foot.

Andre stacks one block of each size. Will that stack be more than 1 foot tall? Explain or show how you know.
Can Andre use only the $\frac{1}{6}$ -foot and $\frac{1}{3}$ -foot blocks to make a stack that is $1 \frac{1}{2}$ feet tall? If you think so, show one or more ways. If not, explain why not.
Can Andre use only the $\frac{1}{6}$ -foot and $\frac{1}{2}$ -foot blocks to make a stack that is $1 \frac{1}{3}$ feet tall? If so, show one or more ways. If not, explain why not.

Practice Problem

Problem 1

Andre is building a tower out of different foam blocks. These blocks come in three different thicknesses: $\frac{1}{2}$ -foot, $\frac{1}{4}$ -foot, and $\frac{1}{8}$ -foot.

Andre stacks two $\frac{1}{2}$ -foot blocks, two $\frac{1}{4}$ -foot blocks, and two $\frac{1}{8}$ -foot blocks to create a tower. What will the height of the tower be in feet? Explain or show how you know.