Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve linear equations by clearing fractions
Algebra
CCSS HSA.REI.B.3England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve linear equations by clearing fractions.
- 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: Equations with the unknown on both sides
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Equations with the unknown on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 6x + 14 = 5x + 12 → x = -2Prompt: Collect the x terms on one side.
- Solve: 6(x + 7) = 3(x + 7) + 18 → x = -1Prompt: Expand the brackets on both sides first.
- How many solutions does 3x + 4 = 3x + 6 have? (No solution / Infinitely many solutions / Exactly one solution) → No solutionPrompt: Subtract the x terms from both sides. What is left?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve linear equations by clearing fractions. 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: Solve: x/4 + 4 = 10
- Step 1: x/4 = 6
- Step 2: x = 6 × 4
- Step 3: x = 24
- Answer: x = 24
- 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.
- Solve: x/6 + 4 = 13 → x = 54Prompt: First undo the + 4.
- Solve: (x + 6)/7 = 2 → x = 8Prompt: Multiply both sides by 7 to clear the 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.
- Solve: x/9 − 6 = −11 → x = -45Prompt: First undo the − 6.
- Solve: (x + 3)/6 = 0 → x = -3Prompt: Multiply both sides by 6 to clear the fraction.
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: Equations with the unknown on both sides.
- 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
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder