Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Multiply monomials using exponent laws
Algebra
CCSS HSA.APR.A.1CCSS 8.EE.A.1England: GCSE Foundation Algebra
Objective and success criteria
Students will: Multiply monomials using exponent laws.
- 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: Laws of exponents (indices)
Leads to: Divide monomials using exponent laws; Raise a monomial to a power; Multiply a polynomial by a monomial
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 (Laws of exponents (indices)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify a¹⁰ ÷ a⁵ and write it as a to a single power. What is the power? → 5Prompt: Dividing powers of the same base: subtract the exponents.
- Evaluate 2⁻³ as a fraction. → 1/8Prompt: A negative exponent means 'one over' the positive power.
- Simplify 2⁴ × 2³ ÷ 2⁶, then evaluate. Give your answer as a number (a fraction is fine). → 2Prompt: Add exponents when multiplying, subtract when dividing.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Multiply monomials using exponent laws. 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: Simplify: (2x⁴)(2x)
- Step 1: 2 × 2 = 4
- Step 2: x⁴ × x = x⁵
- Step 3: 4x⁵
- Answer: 4x^5
- 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.
- Simplify: (3x⁴)(6x⁵) → 18x^9Prompt: Multiply the numbers.
- Simplify: (3x⁵y)(−5x³y²) → -15x^8y^3Prompt: Deal with numbers, then each letter separately.
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.
- x⁸ × x⁹ × x⁻¹ = xᵏ. Find k. → 16Prompt: Multiplying powers of the same base: add the exponents.
- Simplify: (4x⁵)(−5x²y) → -20x^7yPrompt: Deal with numbers, then each letter separately.
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: Laws of exponents (indices).
- 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: Divide monomials using exponent laws; Raise a monomial to a power; Multiply a polynomial by a monomial.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder