Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Quadratic inequalities
Algebra
CCSS HSA.REI.B.4England: GCSE Higher Algebra
Objective and success criteria
Students will: Quadratic inequalities.
- 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: Solve quadratics by factorising; Solve linear inequalities
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 · 5 min
- Quick retrieval from earlier learning (Solve quadratics by factorising; Solve linear inequalities). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x² + x − 72 = 0. Give both solutions, separated by a comma. → x = -9 or x = 8Prompt: Factorise: find two numbers that multiply to −72 and add to 1.
- Solve: 8x + 15 ≥ 55 (x ≤ 5 / x ≥ 6 / x ≥ 5 / x ≥ 40) → x ≥ 5Prompt: Solve it like an equation, keeping the inequality sign.
- Solve: x² − 3x = 0. Give both solutions, separated by a comma. → x = 0 or x = 3Prompt: Take out the common factor x.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Quadratic inequalities. 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: x² − 8x + 12 > 0
- Step 1: (x − 2)(x − 6) > 0
- Step 2: x < 2 or x > 6
- Answer: x < 2 or 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: x² − 9x + 18 < 0 (3 < x < 6 / −6 < x < −3 / x < −6 or x > −3 / x < 3 or x > 6) → 3 < x < 6Prompt: Find the roots by factorising.
- Solve: x² + 5x + 4 < 0 (x < 1 or x > 4 / 1 < x < 4 / −4 < x < −1 / x < −4 or x > −1) → −4 < x < −1Prompt: Find the roots by factorising.
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: x² + 7x + 12 < 0 (3 < x < 4 / x < −4 or x > −3 / x < 3 or x > 4 / −4 < x < −3) → −4 < x < −3Prompt: Find the roots by factorising.
- Solve: x² + x − 12 > 0 (x < −3 or x > 4 / −3 < x < 4 / x < −4 or x > 3 / −4 < x < 3) → x < −4 or x > 3Prompt: Find the roots by factorising.
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: Solve quadratics by factorising.
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder