Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Solve equations with fractions or decimals on both sides
Algebra
CCSS 8.EE.C.7.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve equations with fractions or decimals on both sides.
- 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: Solve equations with x 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 (Solve equations with x on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: −x − 3 = 5x − 51 → x = 8Prompt: Add 1x to both sides so the x-term stays positive.
- Mateo solved 7x − 8 = 6x − 13 by adding 6x to both sides. Explain the mistake by finding the correct value of x. → x = -5Prompt: To remove 6x from the right, you must SUBTRACT 6x.
- Solve: −4x + 9 = 5x − 36 → x = 5Prompt: Add 4x to both sides so the x-term stays positive.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve equations with fractions or decimals on both sides. 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/5 − 5 = x/10 − 4
- Step 1: 2x − 50 = x − 40
- Step 2: x = 10
- Step 3: x = 10
- Answer: x = 10
- 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/3 + 9 = x/6 + 10 → x = 6Prompt: Multiply every term by 6 to clear the fractions.
- Solve: 0.4x − 2.1 = 0.1x − 4.2 → x = -7Prompt: Multiply every term by 10 (or 100) to remove the decimals.
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: 0.6x − 1.1 = 0.5x − 0.9 → x = 2Prompt: Multiply every term by 10 (or 100) to remove the decimals.
- Solve: x/4 + 0 = x/6 + 4 → x = 48Prompt: Multiply every term by 12 to clear the fractions.
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: Solve equations with x 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder