Compare unlike fractions with denominators up to 12

What you will learn

• Compare unlike fractions with denominators up to 12

Models used: number sentences, stories, fraction strips.

Before you start

• Simplest form

Keep the wholes the same size

These strips are equally long. One is split into thirds, the other into sixths.

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

   These strips are equally long. One is split into thirds, the other into sixths.

   A fraction describes a share of its whole. Equal-sized wholes make the lengths or areas comparable.

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

   Shade one piece on each strip. Which single piece is 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.

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

   A third is larger than a sixth: cutting a whole into more pieces makes each piece smaller.

   1/3 > 1/6

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

Worked example: A new example, together

Compare 1/3 □ 1/2.

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

   Check the wholes first. Then compare chosen amounts or rename the parts to the same size.

   Equal-sized wholes let us compare fractions by renaming them into equal-sized parts.

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 1/3 □ 1/2.

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3. 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.

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

   Rename with denominator 6: 2/6 and 3/6.

   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.

   1/3 < 1/2.

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

6. 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.

   The numerators at denominator 6 are 2 and 3.

   We found <. Equal-sized wholes let us compare fractions by renaming them into equal-sized parts.

Common mistakes to discuss

• Comparing the denominators. With the same whole, compare the numbers of equal parts. 3/5 is greater than 2/5; for unlike fractions, rename them to the same denominator first.

Check your understanding

• Compare unlike fractions with denominators up to 12
• justify a fraction comparison using a common whole
• 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.