Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Find reciprocals of fractions, mixed numbers and whole numbers
Fractions
CCSS 6.NS.A.1England: KS3 Number
Objective and success criteria
Students will: Find reciprocals of fractions, mixed numbers and whole numbers.
- 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: Multiply fractions
Leads to: Divide a whole number by a fraction; Divide a fraction by a whole number
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 (Multiply fractions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Arjun has 4 metres of ribbon and uses 1/2 of it. How many metres is that? → 2Prompt: "Of" means multiply: 1/2 × 4.
- Ethan has 32 metres of ribbon and uses 7/8 of it. How many metres is that? → 28Prompt: "Of" means multiply: 7/8 × 32.
- Fatima has 18 metres of ribbon and uses 2/3 of it. How many metres is that? → 12Prompt: "Of" means multiply: 2/3 × 18.
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: Find reciprocals of fractions, mixed numbers and whole numbers. 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: What is the reciprocal of 1/3?
- Step 1: 1/3 × 3 = 1
- Step 2: The reciprocal is 3.
- Answer: 3
- 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.
- What is the reciprocal of 7/9? → 9/7 (1 2/7)Prompt: The reciprocal is what you multiply by to get 1.
- What is the reciprocal of 1 2/3? Give a fraction. → 3/5Prompt: First write the mixed number as an improper fraction.
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.
- What is the reciprocal of 5/11? → 11/5 (2 1/5)Prompt: The reciprocal is what you multiply by to get 1.
- 3/4 × □ = 1. What fraction goes in the box? → 4/3 (1 1/3)Prompt: A number times its reciprocal is 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: Multiply 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
- Move on to: Divide a whole number by a fraction; Divide a fraction by a whole number.
- 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