Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Expand two brackets and simplify
Algebra
CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Expand two brackets and simplify.
- 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: Expand brackets with a negative multiplier; Collect like terms with negative coefficients
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 (Expand brackets with a negative multiplier; Collect like terms with negative coefficients). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand −9(x + 3). → -9x-27Prompt: Multiply BOTH terms by −9.
- Simplify 8x + 6 − 7x + 11. → x+17Prompt: Group the x-terms and the number terms.
- Expand −(4x − 7). → -4x+7Prompt: A minus sign in front of brackets means × (−1).
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Expand two brackets and simplify. 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: Expand and simplify 5(x + 9) + 2(x + 4).
- Step 1: 5x + 45 + 2x + 8
- Step 2: 7x + 53
- Answer: 7x+53
- 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.
- Expand and simplify 6(x + 3) + 6(x + 9). → 12x+72Prompt: Expand each bracket separately.
- Expand and simplify 4(x − 2) − 3(x + 3). → x-17Prompt: The second bracket is multiplied by −3.
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.
- A rectangle is 5 cm wide and (3x + 1) cm long. Write and simplify an expression for its perimeter in cm, using brackets first: 2(5 + 3x + 1). → 6x+12Prompt: Simplify inside the brackets first.
- Expand and simplify 3(x + 5) − 5(x + 4). → -2x-5Prompt: The second bracket is multiplied by −5.
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: Expand brackets with a negative multiplier.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder