Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Add and subtract algebraic fractions
Algebra
CCSS HSA.APR.D.7England: GCSE Higher Algebra
Objective and success criteria
Students will: Add and subtract 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: Algebraic fractions
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 · 4 min
- Quick retrieval from earlier learning (Algebraic fractions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify: (x² + 2x − 15) / (x − 3) (x + 5 / x − 15 / x − 5 / x + 2) → x + 5Prompt: Factorise the numerator first.
- Write as a single fraction: 5/(x + 6) + 2/(x + 5). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)). → (7x+37)/((x+6)(x+5))Prompt: The common denominator is the product of the two brackets.
- Simplify: (x² + 9x + 14) / (x + 2) (x + 9 / x + 2 / x + 7 / x − 7) → x + 7Prompt: Factorise the numerator first.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Add and subtract algebraic fractions. 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: Write as a single fraction: 4/(x − 2) + 4/(x + 1)
- Step 1: (4(x + 1) + 4(x − 2))/((x − 2)(x + 1))
- Step 2: (8x − 4)/((x − 2)(x + 1))
- Answer: (8x − 4)/((x − 2)(x + 1))
- 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.
- Write as a single fraction: 4/(x + 1) + 4/(x − 3) ((8x − 16)/((x + 1)(x − 3)) / (8x − 8)/((x + 1)(x − 3)) / 8/((x + 1)(x − 3)) / (8x − 8)/((x + 1) + (x − 3))) → (8x − 8)/((x + 1)(x − 3))Prompt: Use the common denominator (x + 1)(x − 3).
- Simplify: 3/(x + 6) + (x − 6)/(x² − 36) (4/(x − 6) / (x − 9)/(x² − 36) / 3/(x + 6) / 4/(x + 6)) → 4/(x + 6)Prompt: Factorise x² − 36 first.
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: 1/(x + 5) + (x − 5)/(x² − 25) (2/(x² − 25) / 1/(x + 5) / 2/(x − 5) / 2/(x + 5)) → 2/(x + 5)Prompt: Factorise x² − 25 first.
- Write as a single fraction: 1/(x − 4) + 5/(x + 5) (6/((x − 4)(x + 5)) / (6x − 15)/((x − 4) + (x + 5)) / (6x + 25)/((x − 4)(x + 5)) / (6x − 15)/((x − 4)(x + 5))) → (6x − 15)/((x − 4)(x + 5))Prompt: Use the common denominator (x − 4)(x + 5).
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: Algebraic fractions.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder