Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Recognise equivalent expressions
Algebra
CCSS 6.EE.A.3CCSS 6.EE.A.4England: KS3 Algebra
Objective and success criteria
Students will: Recognise equivalent expressions.
- 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: Simplify expressions: like terms
Leads to: Expand brackets with positive terms
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 (Simplify expressions: like terms). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify 2x − 6x. → -4xPrompt: These are like terms: they both have x.
- Simplify 4x − 1 − x − 6. → 3x-7Prompt: Group the x terms together and the numbers together.
- Simplify 2x + 5y − 2x + y. → 6yPrompt: x terms and y terms are different kinds; collect each kind separately.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Recognise equivalent expressions. 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: Which expression is equivalent to 7(x + 3)?
- Step 1: 7(x + 3) = 7x + 21
- Answer: 7x + 21
- 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.
- Which expression is equivalent to 6(x + 5)? (6x + 11 / 6x + 30 / x + 30 / 6x + 5) → 6x + 30Prompt: The number outside multiplies EVERY term inside the brackets.
- Which expression is equivalent to y + 7 + 7y? (8y + 7 / 7y + 7 / 15y / 9y + 7) → 8y + 7Prompt: Like terms have exactly the same variable part.
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.
- Are 4(x + 7) and 4x + 28 equivalent? (Hint: test x = 2.) (Yes / No) → YesPrompt: Equivalent expressions give the same value for EVERY x.
- Which expression is equivalent to 7y + 2 + 5y? (13y + 2 / 12y² + 2 / 14y / 12y + 2) → 12y + 2Prompt: Like terms have exactly the same variable part.
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: Simplify expressions: like terms.
- 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: Expand brackets with positive terms.
- 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