Math lesson plan · 6th grade (Year 7 in England) · 60 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 · 6 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.
- 7/8 ÷ 1/2 = ? Give your answer in simplest form. → 7/4 (1 3/4)Prompt: Dividing by a fraction is the same as multiplying by its reciprocal.
- Ana has 3 cups of flour. Each batch of pancakes needs 1/3 cup. How many batches can Ana make? → 9Prompt: How many groups of the batch size fit into the total? That is division.
- 4 1/2 ÷ 2/3 = ? (Simplest form; an improper fraction is fine.) → 27/4 (6 3/4)Prompt: Change the mixed number into an improper fraction first.
Hook · 6 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 · 12 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 · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Which calculation gives the same answer as 1/4 ÷ 2/9? (4/1 × 2/9 / 1/4 × 9/2 / 1/4 × 2/9 / 4/1 × 9/2) → 1/4 × 9/2Prompt: Keep the first fraction as it is.
- Without calculating: is 14 ÷ 11/6 greater than or less than 14? (Greater than 14 / Less than 14) → Less than 14Prompt: Is the divisor less than 1 or greater than 1?
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Yuki worked out 1/8 ÷ 1/2 by flipping the first fraction: 8/1 × 1/2. What is the correct answer? Give a fraction in simplest form. → 1/4Prompt: Which fraction should be flipped?
- Without calculating: is 20 ÷ 1/4 greater than or less than 20? (Greater than 20 / Less than 20) → Greater than 20Prompt: Is the divisor less than 1 or greater than 1?
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