Math lesson plan · 6th grade (Year 7 in England) · 60 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 · 6 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 6x + 3x. → 9xPrompt: These are like terms: they both have x.
- Simplify 2x + 9 − 5x − 5. → -3x+4Prompt: Group the x terms together and the numbers together.
- Simplify 4x + 8y − 5x − y. → -x+7yPrompt: x terms and y terms are different kinds; collect each kind separately.
Hook · 6 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 · 12 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 · 12 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 7(x + 1)? (7x + 8 / 7x + 7 / x + 7 / 8x) → 7x + 7Prompt: The number outside multiplies EVERY term inside the brackets.
- Which expression is equivalent to 6y + 7 + 2y? (12y + 7 / 9y + 7 / 8y + 7 / 15y) → 8y + 7Prompt: Like terms have exactly the same variable part.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Which expression is equivalent to 5y + 5 + y? (11y / 5y + 5 / 6y + 5 / 6y² + 5) → 6y + 5Prompt: Like terms have exactly the same variable part.
- Are 4(x + 9) and 4x + 9 equivalent? (Hint: test x = 4.) (Yes / No) → NoPrompt: Equivalent expressions give the same value for EVERY x.
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