Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Evaluate expressions with powers and two variables
Algebra
CCSS 6.EE.A.2.CEngland: KS3 Algebra
Objective and success criteria
Students will: Evaluate expressions with powers and two variables.
- 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: Evaluate expressions; Order of operations with exponents
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 · 4 min
- Quick retrieval from earlier learning (Evaluate expressions; Order of operations with exponents). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the value of 7x + 11 when x = 10. → 81Prompt: Replace x with 10.
- Work out 17 + 2 × 6². → 89Prompt: Powers first, then multiplication, then addition.
- Evaluate x² + 4y when x = 6 and y = 3. → 48Prompt: Substitute each letter, using brackets around negative numbers.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Evaluate expressions with powers and two variables. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Evaluate 5x² + 20 when x = 9.
- Step 1: 9² = 81
- Step 2: 5 × 81 = 405
- Step 3: 405 + 20 = 425
- Answer: 425
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Evaluate 6x² + 20 when x = 9. → 506Prompt: Square x first, then multiply by the coefficient.
- Evaluate a² + 5b when a = 2 and b = 3. → 19Prompt: Replace each letter with its value.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Evaluate (x + y)² ÷ 2 when x = 5 and y = 3. → 32Prompt: Add inside the brackets first.
- Evaluate a² + 5b when a = 3 and b = 6. → 39Prompt: Replace each letter with its value.
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: Evaluate expressions.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder