Compare unit fractions with denominators up to 12

What you will learn

• Compare unit fractions with denominators up to 12

Models used: number sentences, stories, fraction strips.

Before you start

• Read and write fraction notation

Same whole, different-sized pieces

Imagine sharing two identical cakes. Cut the first cake into two equal pieces and the second into four.

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

   Imagine sharing two identical cakes. Cut the first cake into two equal pieces and the second into four.

   We must start with equal-sized cakes. Otherwise, comparing the fractions would not compare equal wholes.

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

   Take one piece from each cake. Which piece would you rather have?

   More cuts make smaller pieces. A quarter is one of four equal pieces; a half is one of two.

   Is one quarter larger than one half because 4 is larger than 2?

   No. Four tells us how many pieces share the whole cake. Each of those pieces is smaller.

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

   One half covers more of the same whole than one quarter.

   1/2 > 1/4

   With unit fractions, the numerator stays at one. So compare the size of that one piece.

Worked example: A new example, together

Compare 1/4 □ 1/10.

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

   Check the wholes are the same size. Compare one piece from each.

   With the same whole, fewer equal parts make each unit fraction larger.

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

   Use two wholes of the same size.

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

   Compare 1/4 □ 1/10.

   >

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

   Each whole is cut into 4 or 10 equal parts. Fewer parts make each piece larger.

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

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

   1/4 > 1/10.

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

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

   Check the result against the question we started with.

   Compare the shaded lengths on equal-sized wholes.

   We found >. With the same whole, fewer equal parts make each unit fraction larger.

Common mistakes to discuss

• A bigger denominator means a bigger fraction. More parts means smaller parts. One eighth is less than one third, because the whole is cut into more pieces.

Check your understanding

• Compare unit fractions with denominators up to 12
• compare unit fractions
• 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.