Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Simplify algebraic fractions by factorising
Algebra
CCSS HSA.APR.D.6CCSS HSA.SSE.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Simplify algebraic fractions by factorising.
- 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: Factorise quadratics x² + bx + c; Difference of two squares
Leads to: Multiply and divide algebraic fractions; Evaluate limits by substitution or by factorising
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 (Factorise quadratics x² + bx + c; Difference of two squares). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Factorise: x² + 7x + 6 ((x + 1)(x − 6) / (x + 6)(x + 1) / (x + 7)(x + 1) / (x + 1)(x + 6)) → (x + 1)(x + 6)Prompt: Find two numbers that multiply to 6 and add to 7.
- Factorise: x² − 121 ((x − 11)² / (x + 11)(x − 11) / (x + 121)(x − 1) / (x + 11)²) → (x + 11)(x − 11)Prompt: This is a difference of two squares: A² − B² = (A + B)(A − B).
- Factorise fully: x² + 10x + 16 → (x+8)(x+2)Prompt: Two numbers: product 16, sum 10.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Simplify algebraic fractions by factorising. 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: Simplify: (x² + 7x + 12)/(x + 3)
- Step 1: (x + 3)(x + 4)/(x + 3)
- Step 2: (x + 4)
- Answer: (x + 4)
- 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.
- Simplify: (x² + 10x + 24)/(x + 4) ((x + 6)/(x + 4) / (x − 6) / (x + 6) / (x + 24)) → (x + 6)Prompt: Factorise the numerator.
- Zara 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.
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.
- Simplify: (x² − 36)/(x + 6) (1/(x − 6) / (x + 6) / x − 36 / (x − 6)) → (x − 6)Prompt: Factorise the top: it is a difference of two squares.
- Ethan simplified (x + 6)/x by crossing out the x's and got 1 + 6 = 7. 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 + 6)/x. Do you get 7? Try x = 2.
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: Factorise quadratics x² + bx + c.
- 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: Multiply and divide algebraic fractions; Evaluate limits by substitution or by factorising.
- 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