Lesson 4 Build Fractions from Unit Fractions

- Let’s build other fractions from unit fractions.

Warm-up Number Talk: 3 and Another Factor

Find the value of each expression mentally.

$3 \times 3$
$7 \times 3$
$10 \times 3$
$3 \times 17$

Activity 1 Introduce Secret Fraction

The goal of the game is to be the first to build 2 secret fractions with unit fractions.

Make two stacks: one for secret fractions and one for unit fractions. Place all cards face down.
Each player draws 2 secret fraction cards. These are the fractions you are trying to make with your unit fractions.
On your turn, you can make one of these moves:
- Pick up 1 unit fraction card.
- Trade both of your secret fractions for 2 new secret fractions from the stack.
When you have enough unit fractions to make one of your secret fractions, shade your gameboard to represent your secret fraction. Then, pick a new secret fraction.
The first player to make 2 secret fractions wins.

Diagram of game board that shows wholes and fractions of halves, thirds, quarters, sixths, and eighths. — Gameboard

Activity 2 Represent Fraction Situations

Children in Ghana playing a game of Pilolo.

Here are four situations about playing Pilolo and four diagrams. Each diagram represents the length of a street where the game is played.

Represent each situation on a diagram. Be prepared to explain your reasoning.

A student walks $\frac{4}{8}$ the length of the street and hides a rock.
A student walks $\frac{2}{3}$ the length of the street and hides a penny.
A student walks $\frac{3}{4}$ the length of the street and hides a stick.
A student walks $\frac{5}{6}$ the length of the street and hides a penny.
This diagram represents the location of a hidden stick.
About what fraction of the length of the street did the student walk to hide it? Be prepared to explain how you know.

Practice Problem

Problem 1

Jada walks across the street at a stoplight $\frac{5}{6}$ of her way from home to school. Represent the situation on the fraction strip. Explain your reasoning.