Answer quickly. These check you are ready for the topic.

1. 1.Fill in the missing number: 4/9 = □/54

   [1]

   Answer24

2. 2.Fill in the missing number: 5/6 = □/30

   [1]

   Answer25

Complete from memory. No calculator, no notes.

1. 1.Fill in the missing number: 5/10 = □/50

   [1]

   Answer25

2. 2.Fill in the missing number: 6/11 = □/44

   [1]

   Answer24

Work through each item. Show the step you used.

1. 1.Fill in the missing number: 3/4 = □/12

   [1]

   Answer9

2. 2.Fill in the missing number: 2/5 = □/20

   [1]

   Answer8

3. 3.Fill in the missing number: 1/4 = □/24

   [1]

   Answer6

The first step is given. Finish the reasoning.

1. 1.Write 30/60 in its simplest form, and state the factor you divided by.

   [2]

   Answer1/2 (divided by 30)

2. 2.Write 20/32 in its simplest form, and state the factor you divided by.

   [2]

   Answer5/8 (divided by 4)

No scaffolding. Set out your full method.

1. 1.Write 8/14 in its simplest form, and state the factor you divided by.

   [2]

   Answer4/7 (divided by 2)

2. 2.Write 30/40 in its simplest form, and state the factor you divided by.

   [2]

   Answer3/4 (divided by 10)

3. 3.Write 6/12 in its simplest form, and state the factor you divided by.

   [2]

   Answer1/2 (divided by 6)

Harder items. Attempt every one, even partially.

1. 1.Are 6/10 and 54/91 equivalent? Justify your answer with a calculation.

   [3]

   AnswerNo — the denominators were not scaled by the same factor.

2. 2.Are 1/6 and 8/49 equivalent? Justify your answer with a calculation.

   [3]

   AnswerNo — the denominators were not scaled by the same factor.

Use the skill in context. State units in your answer.

1. 1.A recipe uses 1/3 of a litre of milk. A baker makes 2 batches. Write the total as a fraction with denominator 6, then simplify it.

   [3]

   Answer2/3 litres = 2/3 (simplified where possible)

2. 2.A recipe uses 1/5 of a litre of milk. A baker makes 5 batches. Write the total as a fraction with denominator 25, then simplify it.

   [3]

   Answer5/5 litres = 5/5 (simplified where possible)

Explain your reasoning in full sentences.

1. 1.Compare and justify a student's method for equivalent fractions is or is not efficient.

   [4]

   AnswerAccept any correct response that applies the equivalent fractions rule accurately.

2. 2.Explain why a student's method for equivalent fractions is or is not efficient.

   [4]

   AnswerAccept any correct response that applies the equivalent fractions rule accurately.

Not marked. Answer honestly — this guides your next worksheet.

1. 1.Describe how confident you feel with equivalent fractions and what you will practise next.

   [—]

   AnswerStudent response — not marked.

2. 2.Reflect on how confident you feel with equivalent fractions and what you will practise next.

   [—]

   AnswerStudent response — not marked.

Warm-up

1. 1.24[1]

   1. 9 × 6 = 54, so the denominator was multiplied by 6.
   2. Multiply the numerator by the same factor: 4 × 6 = 24.

2. 2.25[1]

   1. 6 × 5 = 30, so the denominator was multiplied by 5.
   2. Multiply the numerator by the same factor: 5 × 5 = 25.

Recall

1. 1.25[1]

   1. 10 × 5 = 50, so the denominator was multiplied by 5.
   2. Multiply the numerator by the same factor: 5 × 5 = 25.

2. 2.24[1]

   1. 11 × 4 = 44, so the denominator was multiplied by 4.
   2. Multiply the numerator by the same factor: 6 × 4 = 24.

Basic Practice

1. 1.9[1]

   1. 4 × 3 = 12, so the denominator was multiplied by 3.
   2. Multiply the numerator by the same factor: 3 × 3 = 9.

2. 2.8[1]

   1. 5 × 4 = 20, so the denominator was multiplied by 4.
   2. Multiply the numerator by the same factor: 2 × 4 = 8.

3. 3.6[1]

   1. 4 × 6 = 24, so the denominator was multiplied by 6.
   2. Multiply the numerator by the same factor: 1 × 6 = 6.

Guided Practice

1. 1.1/2 (divided by 30)[2]

   1. Find the highest common factor of 30 and 60: HCF = 30.
   2. Divide both parts by 30 to get 1/2.

2. 2.5/8 (divided by 4)[2]

   1. Find the highest common factor of 20 and 32: HCF = 4.
   2. Divide both parts by 4 to get 5/8.

Independent Practice

1. 1.4/7 (divided by 2)[2]

   1. Find the highest common factor of 8 and 14: HCF = 2.
   2. Divide both parts by 2 to get 4/7.

2. 2.3/4 (divided by 10)[2]

   1. Find the highest common factor of 30 and 40: HCF = 10.
   2. Divide both parts by 10 to get 3/4.

3. 3.1/2 (divided by 6)[2]

   1. Find the highest common factor of 6 and 12: HCF = 6.
   2. Divide both parts by 6 to get 1/2.

Challenge Questions

1. 1.No — the denominators were not scaled by the same factor.[3]

   1. Numerator scale factor: 54 ÷ 6 = 9.
   2. Denominator scale factor: 91 ÷ 10 ≠ 9.
   3. Because the factors differ, the fractions are not equivalent.

2. 2.No — the denominators were not scaled by the same factor.[3]

   1. Numerator scale factor: 8 ÷ 1 = 8.
   2. Denominator scale factor: 49 ÷ 6 ≠ 8.
   3. Because the factors differ, the fractions are not equivalent.

Real-life Application

1. 1.2/3 litres = 2/3 (simplified where possible)[3]

   1. Each batch needs 1/3 l, so 2 batches need 1 × 2 = 2 lots of 1/3.
   2. That is 2/3 litres.
   3. Convert to a mixed number if the numerator exceeds the denominator.

2. 2.5/5 litres = 5/5 (simplified where possible)[3]

   1. Each batch needs 1/5 l, so 5 batches need 1 × 5 = 5 lots of 1/5.
   2. That is 5/5 litres.
   3. Convert to a mixed number if the numerator exceeds the denominator.

Critical Thinking

1. 1.Accept any correct response that applies the equivalent fractions rule accurately.[4]

   1. Recall the definition that underpins equivalent fractions.
   2. Apply it to the values or wording given in the question.
   3. State the final answer clearly, with units or terminology where relevant.

2. 2.Accept any correct response that applies the equivalent fractions rule accurately.[4]

   1. Recall the definition that underpins equivalent fractions.
   2. Apply it to the values or wording given in the question.
   3. State the final answer clearly, with units or terminology where relevant.

Reflection

1. 1.Student response — not marked.[0]

   1. Recall the definition that underpins equivalent fractions.
   2. Apply it to the values or wording given in the question.
   3. State the final answer clearly, with units or terminology where relevant.

2. 2.Student response — not marked.[0]

   1. Recall the definition that underpins equivalent fractions.
   2. Apply it to the values or wording given in the question.
   3. State the final answer clearly, with units or terminology where relevant.