Read and write fraction notation

What you will learn

• Read and write fraction notation

Models used: number sentences, stories, diagrams.

Before you start

• Represent a fraction as part of a whole

Name the part we have chosen

This strip stands for one whole sandwich. Cut it into four equal pieces.

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

   This strip stands for one whole sandwich. Cut it into four equal pieces.

   A fraction describes part of a chosen whole. Equal pieces let us give every piece the same name.

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

   Choose one piece. It is one of the four equal pieces: one quarter.

   1/4

   The bottom number, 4, tells us how many equal pieces make the whole. We call it the denominator.

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

   Now choose three of those pieces. We have three quarters.

   3/4

   The top number, 3, counts the pieces we chose. We call it the numerator. The pieces are still quarters.

   Why is the bottom number still 4 when only three pieces are shaded?

   The bottom number counts every equal part of the whole, including the unshaded part.

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

   Point to the three shaded pieces, then to all four pieces. That is what the two numbers tell us.

   3 chosen parts / 4 equal parts in the whole

   Read 3/4 as “three quarters”: three selected pieces, each one a quarter of the whole.

Worked example: A new example, together

What fraction of this whole is shaded?

1. Point to the whole. Count all its equal parts.

   The numerator counts selected parts and the denominator counts all equal parts of the whole.

2. Count all 12 equal parts: this is the denominator.

   What fraction of this whole is shaded?

   2/12

3. Count the 2 shaded parts: this is the numerator.

4. The fraction is 2/12.

5. Check the result against the question we started with.

   2 selected + 10 unselected = 12 equal parts.

   We found 2/12. The numerator counts selected parts and the denominator counts all equal parts of the whole.

Common mistakes to discuss

• Reading the two numbers the wrong way round. The lower number counts all the equal parts of the whole; the upper number counts the chosen parts. Two of five parts is 2/5.

Check your understanding

• Read and write fraction notation
• name a fraction using all parts and chosen parts
• check the answer against the original quantities and units

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.