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 − 10x + 16 ((x − 8)(x − 2) / (x + 16)(x + 1) / (x − 8)(x + 2) / (x − 10)(x + 1)) → (x − 8)(x − 2)Prompt: Find two numbers that multiply to 16 and add to −10.
- Factorise: 25x² − 121 ((5x + 11)² / (5x − 11)² / (5x + 11)(5x − 11) / 5(x + 11)(x − 11)) → (5x + 11)(5x − 11)Prompt: This is a difference of two squares: A² − B² = (A + B)(A − B).
- Factorise fully: x² + 10x + 21 → (x+7)(x+3)Prompt: Two numbers: product 21, 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 − 4x + 3)/(x − 1) ((x − 3) / (x − 3)/(x − 1) / (x + 3) / (x − 4)) → (x − 3)Prompt: Factorise the numerator.
- Kofi simplified (x + 9)/x by crossing out the x's and got 1 + 9 = 10. 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 + 9)/x. Do you get 10? 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.
- Luis simplified (x + 7)/x by crossing out the x's and got 1 + 7 = 8. 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 + 7)/x. Do you get 8? Try x = 2.
- Simplify: (x² + 12x + 35)/(x + 7) ((x + 35) / (x + 12) / (x + 5) / (x + 5)/(x + 7)) → (x + 5)Prompt: Factorise the numerator.
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