Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Solve two-step equations with negative numbers
Algebra
CCSS 7.EE.B.4.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve two-step equations with 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: Two-step equations; Divide integers and find missing factors
Leads to: Solve equations of the form p(x + q) = r; Solve two-step equations with a division; Write and solve two-step equations from real situations
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Two-step equations; Divide integers and find missing factors). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- −120 ÷ 12 = ? → -10Prompt: Divide the sizes.
- Solve: −8x − 5 = 35 → x = -5Prompt: Add 5 to both sides.
- 7 ÷ (−7) = ? → -1Prompt: Divide the sizes.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve two-step equations with negative numbers. 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: Solve: x − 11 = −17
- Step 1: x = −17 + 11 = −6
- Step 2: x = −6 ÷ 1 = −6
- Answer: x = -6
- 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.
- Solve: −6x + 2 = −58 → x = 10Prompt: First undo the addition: subtract 2 on both sides.
- Solve: 12 − 8x = −60 → x = 9Prompt: Subtract 12 from both sides.
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.
- Solve: −3x + 19 = 52 → x = -11Prompt: First undo the addition: subtract 19 on both sides.
- Zoe solved 5x − 15 = −30 and got x = −9. Check by substituting, then give the correct solution. → x = -3Prompt: To undo − 15, do the opposite.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Two-step equations.
- Use concrete materials: balance scales or a balance drawing.
- 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: Solve equations of the form p(x + q) = r; Solve two-step equations with a division; Write and solve two-step equations from real situations.
- 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