Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Multiply and divide negative fractions and decimals
Number sense
CCSS 7.NS.A.2.ACCSS 7.NS.A.2.BCCSS 7.NS.A.2.CEngland: KS3 Number
Objective and success criteria
Students will: Multiply and divide negative fractions and decimals.
- 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 integers, including three factors and powers; Divide fractions by fractions
Leads to: Multi-step problems with positive and negative numbers
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Multiply integers, including three factors and powers; Divide fractions by fractions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- −7 × (−12) = ? → 84Prompt: Multiply the sizes first.
- 1/6 ÷ 1/6 = ? Give your answer in simplest form. → 1Prompt: Dividing by a fraction is the same as multiplying by its reciprocal.
- 5 × (−2) × 4 = ? → -40Prompt: Count the negative factors.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Multiply and divide negative fractions and decimals. 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: Work out (−6/7) × (−5/7). Give a fraction in simplest form.
- Step 1: 30/49
- Answer: 30/49
- 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.
- Work out (−2/3) × (−1/2). Give a fraction in simplest form. → 1/3Prompt: Multiply the numerators and the denominators.
- −0.4 × (−5.5) = ? → 2.2Prompt: Multiply as if both were positive.
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.
- Work out (−1/3) ÷ (−1/6). Give a fraction in simplest form (or a whole number). → 2Prompt: Multiply by the reciprocal of the second fraction.
- Work out (−4/9) × (4/7). Give a fraction in simplest form. → -16/63Prompt: Multiply the numerators and the denominators.
Watch out for
- Reading 1,045 as one thousand four hundred five: point to each place and say its value.
- Thinking a longer number is always bigger, even with decimals (0.45 vs 0.5).
Support and stretch
Support
- Review first: Multiply integers, including three factors and powers.
- Use concrete materials: place value chart.
- 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: Multi-step problems with positive and negative numbers.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder