Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Multi-step problems with positive and negative numbers
Number sense
CCSS 7.NS.A.3CCSS 7.EE.B.3England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Multi-step problems with positive and negative 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 and divide negative fractions and decimals; Add and subtract negative decimals
Leads to: the next skill in this area.
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 and divide negative fractions and decimals; Add and subtract negative decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Work out (2/9) × (3/8). Give a fraction in simplest form. → 1/12Prompt: Multiply the numerators and the denominators.
- 0.1 + (−6) = ? → -5.9Prompt: Use the same sign rules as for integers.
- −0.4 × (−3.5) = ? → 1.4Prompt: Multiply as if both were positive.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Multi-step problems with positive and negative 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: A diver is at −3 m. She descends 0.75 m every second for 4 seconds. What is her new depth, in m? (Give a negative number.)
- Step 1: 4 × (−0.75) = −3
- Step 2: −3 + (−3) = −6
- Answer: -6
- 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.
- A diver is at −2 m. She descends 0.75 m every second for 6 seconds. What is her new depth, in m? (Give a negative number.) → -6.5Prompt: Each second the depth changes by −0.75 m.
- The temperature was −2 °C and fell steadily to −14.5 °C over 5 hours. What was the change in temperature per hour? (Give a negative number.) → -2.5Prompt: Total change = final − start.
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.
- A diver is at −4 m. She descends 0.75 m every second for 10 seconds. What is her new depth, in m? (Give a negative number.) → -11.5Prompt: Each second the depth changes by −0.75 m.
- The temperature was 11 °C and fell steadily to 2 °C over 3 hours. What was the change in temperature per hour? (Give a negative number.) → -3Prompt: Total change = final − start.
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 and divide negative fractions and decimals.
- 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
- 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