Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Divide a whole number by a fraction
Fractions
CCSS 6.NS.A.1England: KS3 Number
Objective and success criteria
Students will: Divide a whole number by a fraction.
- 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: Find reciprocals of fractions, mixed numbers and whole numbers; Divide unit fractions and whole numbers
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 · 4 min
- Quick retrieval from earlier learning (Find reciprocals of fractions, mixed numbers and whole numbers; Divide unit fractions and whole numbers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the reciprocal of 5/6? → 6/5 (1 1/5)Prompt: The reciprocal is what you multiply by to get 1.
- What is the reciprocal of 3 2/3? Give a fraction. → 3/11Prompt: First write the mixed number as an improper fraction.
- What is the reciprocal of 2/3? → 3/2 (1 1/2)Prompt: The reciprocal is what you multiply by to get 1.
Hook · 3 min
- Cut a pizza or a strip of paper unevenly and ask whether the pieces are really halves or quarters.
- Share the objective: Divide a whole number by a fraction. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Work out 3 ÷ 7/8. Give a whole number, or a fraction in simplest form.
- Step 1: 3 ÷ 7/8 = 3 × 8/7
- Step 2: = 24/7
- Answer: 24/7 (3 3/7)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Work out 8 ÷ 5/6. Give a whole number, or a fraction in simplest form. → 48/5 (9 3/5)Prompt: Dividing by a fraction is the same as multiplying by its reciprocal.
- A 14-litre water cooler fills bottles of 2/3 litre each. How many pieces or portions is that? → 21Prompt: How many 2/3s fit into 14? That is a division.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Work out 3 ÷ 1/3. Give a whole number, or a fraction in simplest form. → 9Prompt: Dividing by a fraction is the same as multiplying by its reciprocal.
- A 5-litre water cooler fills bottles of 1/2 litre each. How many pieces or portions is that? → 10Prompt: How many 1/2s fit into 5? That is a division.
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: Find reciprocals of fractions, mixed numbers and whole numbers.
- 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