Represent a fraction as part of a whole

What you will learn

• Represent a fraction as part of a whole

Models used: number sentences, stories, diagrams.

Before you start

• Equal groups become multiplication

Give the share a name

One sandwich is cut into 4 equal pieces. Mei chooses 3. How do we name her share?

1. One strip is the whole. Each of its four pieces has the same size.

   We will draw Mei’s chosen pieces together to make them easy to count. Replay the sharing from the start. This strip is one whole sandwich, with four equal pieces.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   One chosen piece is one of four equal parts. We call it one quarter.

   1/4

   The bottom number counts all four equal parts. The top counts the one chosen part.

3. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Mei chooses three of those pieces. We call her share three quarters.

   3/4

   Only the chosen count changed. The whole still has four equal parts.

4. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Read the two numbers together: three chosen parts out of four equal parts in the whole.

   3 chosen / 4 in the whole

   The white piece counts in the bottom number too. The bottom does not count only what is left.

Worked example: Name a new share together

What fraction of this whole strip is blue?

1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   This is a new whole, cut into five equal parts. We use the same idea: all parts at the bottom, chosen parts at the top.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   How many equal parts make this whole?

   5

2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Two parts are blue. Keep the bottom number five and write the chosen count above it.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   What fraction of this whole strip is blue?

   2/5

3. The whole includes the three white parts as well as the two blue parts.

   Two blue parts and three white parts make all five. The blue share is two fifths.

   2/5

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

Common mistakes to discuss

• Parts that are not equal. A fraction needs equal-sized parts. Three pieces of a strip only show thirds when the three pieces match exactly.

Check your understanding

• identify the whole and its equal parts
• name the chosen share in a strip or circle
• explain why unequal pieces cannot be called halves

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.