Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Algebraic fractions
Algebra
CCSS HSA.APR.D.6CCSS HSA.APR.D.7England: GCSE Higher Algebra
Objective and success criteria
Students will: 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: Factorise quadratics x² + bx + c; Add and subtract fractions with unlike denominators
Leads to: Rational equations; Add and subtract algebraic fractions
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 (Factorise quadratics x² + bx + c; Add and subtract fractions with unlike denominators). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Factorise: x² + 13x + 40 ((x − 5)(x − 8) / (x + 5)(x − 8) / (x + 5)(x + 8) / (x + 40)(x + 1)) → (x + 5)(x + 8)Prompt: Find two numbers that multiply to 40 and add to 13.
- 3/5 + 7/8 = ? Give your answer in simplest form. → 59/40 (1 19/40)Prompt: You need a common denominator first.
- Factorise fully: x² + 5x − 14 → (x+7)(x-2)Prompt: Two numbers: product −14, sum 5.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: 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 − 12x + 35) / (x − 7)
- Step 1: (x − 7)(x − 5) / (x − 7)
- Step 2: x − 5
- Answer: x − 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: (x² − x − 30) / (x + 5) (x − 1 / x − 6 / x + 6 / x − 30) → x − 6Prompt: Factorise the numerator first.
- Write as a single fraction: 4/(x + 5) + 2/(x + 1). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)). → (6x+14)/((x+5)(x+1))Prompt: The common denominator is the product of the two brackets.
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.
- Write as a single fraction: 4/(x + 4) + 2/(x + 6). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)). → (6x+32)/((x+4)(x+6))Prompt: The common denominator is the product of the two brackets.
- Simplify: (x² + 5x + 4) / (x + 4) (x + 4 / x + 5 / x + 1 / x − 1) → x + 1Prompt: Factorise the numerator 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: 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: Rational equations; Add and subtract algebraic fractions.
- 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