Math lesson plan · 10th grade (Year 11 in England) · 45 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 · 5 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 − 6)/(x² − 1) ((x − 6)/(x − 1) / (x − 6)/(x + 1) / (x − 5)/(x − 1) / (x + 1)/(x − 1)) → (x − 6)/(x − 1)Prompt: Factorise the top and the bottom.
- Zoe simplified (x + 8)/x by crossing out the x's and got 1 + 8 = 9. 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 + 8)/x. Do you get 9? Try x = 2.
- Simplify: (x² + 4x + 3)/(x + 3) ((x + 1) / (x + 4) / (x + 1)/(x + 3) / (x + 3)) → (x + 1)Prompt: Factorise the numerator.
Hook · 5 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 · 10 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 · 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: (x² − 25)/(x − 3) × (x − 3)/(x − 5) ((x + 5) / (x + 5)/(x − 3) / (x − 5) / x² − 25) → (x + 5)Prompt: Factorise everything first.
- Simplify: (x² − 8x + 12)/x ÷ (x − 2)/(2x²) (2(x − 6) / 2x(x − 2) / 2x(x − 6) / (x − 6)/(2x)) → 2x(x − 6)Prompt: Dividing by a fraction = multiplying by its reciprocal.
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.
- Simplify: (x² − 10x + 24)/x ÷ (x − 4)/(4x²) (4x(x − 6) / (x − 6)/(4x) / 4x²(x − 6) / 4(x − 6)) → 4x(x − 6)Prompt: Dividing by a fraction = multiplying by its reciprocal.
- Simplify: (x² − 16)/(x + 3) × (x + 3)/(x − 4) ((x + 4) / 1 / x² − 16 / (x + 4)/(x + 3)) → (x + 4)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