Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Solve ax = b and x ÷ a = b, including fraction coefficients
Algebra
CCSS 6.EE.B.7England: KS3 Algebra
Objective and success criteria
Students will: Solve ax = b and x ÷ a = b, including fraction coefficients.
- 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: One-step equations
Leads to: Write and solve one-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 · 4 min
- Quick retrieval from earlier learning (One-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x/4 = −4 → x = -16Prompt: x is divided by 4. What undoes dividing?
- Solve: x/5 = 0 → x = 0Prompt: x is divided by 5. What undoes dividing?
- Solve: x/8 = 10 → x = 80Prompt: x is divided by 8. What undoes dividing?
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve ax = b and x ÷ a = b, including fraction coefficients. 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: Solve: x ÷ 9 = 15
- Step 1: x = 15 × 9
- Step 2: x = 135
- Answer: x = 135
- 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.
- Solve: x ÷ 5 = 4 → x = 20Prompt: What undoes dividing?
- Solve: (2/5)x = 14 → x = 35Prompt: Multiply both sides by the reciprocal of 2/5.
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.
- Solve: (2/3)x = 16 → x = 24Prompt: Multiply both sides by the reciprocal of 2/3.
- Solve: x ÷ 2 = 9 → x = 18Prompt: What undoes dividing?
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: One-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: Write and solve one-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-6.
Free lesson plan from eurekami.com/lesson-plan-builder