Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Rational equations
Algebra
CCSS HSA.REI.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Rational equations.
- 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; Equations with the unknown on both sides
Leads to: Rational functions and asymptotes
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 (Algebraic fractions; Equations with the unknown on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify: (x² − 5x − 6) / (x − 6) (x − 1 / x − 5 / x − 6 / x + 1) → x + 1Prompt: Factorise the numerator first.
- Solve: 3x − 15 = 2x − 19 → x = -4Prompt: Collect the x terms on one side.
- Write as a single fraction: 2/(x + 6) + 5/(x + 2). Type the numerator over the factorised denominator, e.g. (3x+5)/((x+1)(x+2)). → (7x+34)/((x+6)(x+2))Prompt: The common denominator is the product of the two brackets.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Rational equations. 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: Solve: −66/x − 5 = 6
- Step 1: −66/x = 11
- Step 2: −66 = 11x
- Step 3: x = −6
- Answer: x = -6
- 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.
- Solve: 81/x + 4 = −5 → x = -9Prompt: Isolate the fraction first.
- Solve: (x + 5)/(x − 4) = 2 → x = 13Prompt: Multiply both sides by (x − 4).
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.
- Solve: −10/x − 4 = −2 → x = -5Prompt: Isolate the fraction first.
- Solve: (x + 4)/(x − 8) = 2 → x = 20Prompt: Multiply both sides by (x − 8).
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
- Move on to: Rational functions and asymptotes.
- 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