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Math lesson plan · 6th grade (Year 7 in England) · 45 minutes

Reason about fraction division: method and size of the answer

Fractions

CCSS 6.NS.A.1England: KS3 Number

Objective and success criteria

Students will: Reason about fraction division: method and size of the answer.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Divide fractions by fractions

Leads to: the next skill in this area.

Materials: Fraction strips or a fraction wall, Paper strips to fold, Number lines, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Divide fractions by fractions). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. 1/2 ÷ 1/2 = ? Give your answer in simplest form. → 1Prompt: Dividing by a fraction is the same as multiplying by its reciprocal.
  2. Sofia has 4 cups of flour. Each batch of pancakes needs 2/4 cup. How many batches can Sofia make? → 8Prompt: How many groups of the batch size fit into the total? That is division.
  3. 3 3/4 ÷ 1/2 = ? (Simplest form; an improper fraction is fine.) → 15/2 (7 1/2)Prompt: Change the mixed number into an improper fraction first.

Hook · 5 min

  • Cut a pizza or a strip of paper unevenly and ask whether the pieces are really halves or quarters.
  • Share the objective: Reason about fraction division: method and size of the answer. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Which calculation gives the same answer as 1/4 ÷ 4/9?
  • Step 1: 1/4 ÷ 4/9 = 1/4 × 9/4
  • Answer: 1/4 × 9/4
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Which calculation gives the same answer as 1/2 ÷ 4/9? (2/1 × 4/9 / 2/1 × 9/4 / 1/2 × 4/9 / 1/2 × 9/4) → 1/2 × 9/4Prompt: Keep the first fraction as it is.
  2. Without calculating: is 19 ÷ 3/8 greater than or less than 19? (Greater than 19 / Less than 19) → Greater than 19Prompt: Is the divisor less than 1 or greater than 1?

You do: independent practice · 10 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Without calculating: is 17 ÷ 4/3 greater than or less than 17? (Greater than 17 / Less than 17) → Less than 17Prompt: Is the divisor less than 1 or greater than 1?
  2. Which calculation gives the same answer as 1/4 ÷ 1/7? (4/1 × 7/1 / 1/4 × 1/7 / 4/1 × 1/7 / 1/4 × 7/1) → 1/4 × 7/1Prompt: Keep the first fraction as it is.

Watch out for

  • Thinking a bigger denominator means a bigger fraction (1/8 > 1/4).
  • Adding the denominators when adding fractions (1/2 + 1/3 = 2/5).

Support and stretch

Support

  • Review first: Divide fractions by fractions.
  • Use concrete materials: fraction strips or a fraction wall.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-6.

Free lesson plan from eurekami.com/lesson-plan-builder

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Reason about fraction division: method and size of the answer

Name

Date

Score/ 8

  1. Question 1

    Without calculating: is 7 ÷ 3/2 greater than or less than 7?

    • A. Greater than 7
    • B. Less than 7

  2. Question 2

    Which calculation gives the same answer as 1/7 ÷ 3/4?

    • A. 1/7 × 3/4
    • B. 1/7 × 4/3
    • C. 7/1 × 4/3
    • D. 7/1 × 3/4

  3. Question 3

    Sofia worked out 2/3 ÷ 1/2 by flipping the first fraction: 3/2 × 1/2. What is the correct answer? Give a fraction in simplest form.

    Answer(as a fraction)

  4. Question 4

    Without calculating: is 8 ÷ 2/5 greater than or less than 8?

    • A. Greater than 8
    • B. Less than 8

  5. Question 5

    Which calculation gives the same answer as 4/5 ÷ 1/6?

    • A. 5/4 × 1/6
    • B. 4/5 × 6/1
    • C. 5/4 × 6/1
    • D. 4/5 × 1/6

  6. Question 6

    Kai worked out 1/7 ÷ 1/4 by flipping the first fraction: 7/1 × 1/4. What is the correct answer? Give a fraction in simplest form.

    Answer(as a fraction)

  7. Question 7

    Without calculating: is 3 ÷ 1/4 greater than or less than 3?

    • A. Greater than 3
    • B. Less than 3

  8. Question 8

    Which calculation gives the same answer as 2/5 ÷ 6/7?

    • A. 2/5 × 7/6
    • B. 5/2 × 7/6
    • C. 5/2 × 6/7
    • D. 2/5 × 6/7

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Answer key: Reason about fraction division: method and size of the answer

  1. 1. B. Less than 7

  2. 2. B. 1/7 × 4/3

  3. 3. 4/3

  4. 4. A. Greater than 8

  5. 5. B. 4/5 × 6/1

  6. 6. 4/7

  7. 7. A. Greater than 3

  8. 8. A. 2/5 × 7/6