Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
When are two plans equal? Equations from real comparisons
Algebra
CCSS 8.EE.C.7.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: When are two plans equal? Equations from real comparisons.
- 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: −5x − 5 = 6x − 27 → x = 2Prompt: Add 5x to both sides so the x-term stays positive.
- Amara solved 4x + 2 = 2x + 18 by adding 2x to both sides. Explain the mistake by finding the correct value of x. → x = 8Prompt: To remove 2x from the right, you must SUBTRACT 2x.
- Solve: −x + 4 = 3x − 28 → x = 8Prompt: Add 1x 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: When are two plans equal? Equations from real comparisons. 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: Gym A charges $33 to join plus $3 per visit. Gym B charges $6 to join plus $6 per visit. For how many visits do they cost the same?
- Step 1: 33 − 6 = 6n − 3n
- Step 2: 27 = 3n
- Step 3: n = 9
- Answer: 9
- 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.
- Gym A charges $27 to join plus $3 per visit. Gym B charges $12 to join plus $8 per visit. For how many visits do they cost the same? → 3Prompt: Write each cost for n visits/films and set them equal.
- Elena has $8 and saves $6 a week. Nia has nothing yet and saves $10 a week. After how many weeks will they have the same amount? → 2Prompt: Write each person's total after w weeks and set them equal.
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.
- Candle A is 39 cm tall and burns 5 cm per hour. Candle B is 25 cm tall and burns 3 cm per hour. After how many hours are they the same height? → 7Prompt: Write each candle's height after h hours and set them equal.
- Streaming plan A costs $35 up front plus $3 per film. Plan B costs $15 up front plus $5 per film. For how many films do they cost the same? → 10Prompt: Write each cost for n visits/films and set them equal.
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