Generate equivalent fractions

What you will learn

• Generate equivalent fractions

Models used: number sentences, stories, fraction strips.

Before you start

• Add and subtract like fractions within one whole

Connect the action to the maths

Half of a strip is coloured. We cut every half into two equal pieces. Did the coloured amount grow?

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

   Start with one of two equal parts coloured. The whole is the full strip, not just the coloured part.

   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.

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

   Cut every half into two. The whole now has four parts; the coloured half now contains two.

   1/2 = 2/4

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

   1/2 = 2/4: the same length, so the same amount.

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

   We multiplied both counts by two: one coloured part became two, and two parts in the whole became four.

   (1 × 2) / (2 × 2) = 2/4

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

   1/2 = 2/4: the same length, so the same amount.

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

   Cut each original half into three instead. Three sixths still reaches the same point. More pieces does not mean more strip.

   1/2 = 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.

   1/2 = 3/6: the same length, so the same amount.

Worked example: Split thirds into sixths

Two thirds of a strip is coloured. Each third is cut into two equal pieces. How many sixths are coloured?

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

   This time two of three equal parts are coloured. Both strips show the same whole and the same coloured length.

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

   2/3 = 4/6: the same length, so the same amount.

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

   Each coloured third becomes two sixths. Count the small coloured 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.

   Two thirds of a strip is coloured. Each third is cut into two equal pieces. How many sixths are coloured?

   4

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

   Four of six parts are coloured. Both counts doubled because every part was cut the same way.

   2/3 = 4/6

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

   2/3 = 4/6: the same length, so the same amount.

Common mistakes to discuss

• Adding instead of multiplying. Both numbers are multiplied or divided by the same amount. 1/2 = 4/8 because both were multiplied by 4; adding 3 to each would give 4/5, a different amount.

Check your understanding

• Make an equivalent fraction by cutting every part equally, while keeping the whole and the chosen amount unchanged.
• explain equivalent fractions as different names for the same share
• 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.