Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Multiply and divide algebraic fractions
Algebra
CCSS HSA.APR.D.7England: GCSE Higher Algebra
Objective and success criteria
Students will: Multiply and divide algebraic fractions.
- 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 algebraic fractions by factorising
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 · 6 min
- Quick retrieval from earlier learning (Simplify algebraic fractions by factorising). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify: (x² + 5x + 4)/(x + 4) ((x + 1)/(x + 4) / (x − 1) / (x + 4) / (x + 1)) → (x + 1)Prompt: Factorise the numerator.
- Aisha simplified (x + 4)/x by crossing out the x's and got 1 + 4 = 5. Is this right? (Right / Wrong: only common factors can be cancelled, not terms / Right, but only when x is positive) → Wrong: only common factors can be cancelled, not termsPrompt: Test it: put x = 1 into (x + 4)/x. Do you get 5? Try x = 2.
- Simplify: (x² + x − 42)/(x² − 49) ((x − 6)/(x + 7) / (x + 7)/(x − 7) / (x + 6)/(x − 7) / (x − 6)/(x − 7)) → (x − 6)/(x − 7)Prompt: Factorise the top and the bottom.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Multiply and divide algebraic fractions. 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: Simplify: (x² − 64)/(x − 7) × (x − 7)/(x − 8)
- Step 1: (x + 8)(x − 8)(x − 7)/((x − 7)(x − 8))
- Step 2: (x + 8)
- Answer: (x + 8)
- 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.
- Simplify: (x² − 16)/(x − 2) × (x − 2)/(x − 4) ((x + 4) / (x − 4) / 1 / x² − 16) → (x + 4)Prompt: Factorise everything first.
- Simplify: (x² − 3x + 2)/x ÷ (x − 1)/(4x²) ((x − 2)/(4x) / 4x(x − 2) / 4x(x − 1) / 4x²(x − 2)) → 4x(x − 2)Prompt: Dividing by a fraction = multiplying by its reciprocal.
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.
- Simplify: (x² + 7x + 6)/x ÷ (x + 6)/(2x²) (2x(x + 6) / (x + 1)/(2x) / 2x(x + 1) / 2x²(x + 1)) → 2x(x + 1)Prompt: Dividing by a fraction = multiplying by its reciprocal.
- Simplify: (x² − 64)/(x − 6) × (x − 6)/(x − 8) ((x − 8) / (x + 8)/(x − 6) / (x + 8) / x² − 64) → (x + 8)Prompt: Factorise everything first.
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 algebraic fractions by factorising.
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder