Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Choose an efficient method to solve a quadratic
Algebra
CCSS HSA.REI.B.4.BEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Choose an efficient method to solve a quadratic.
- 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 taking square roots; Solve quadratics by factorising
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 taking square roots; Solve quadratics by factorising). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 2x² + 6 = 134. Give both solutions, separated by a comma. → x = -8 or x = 8Prompt: Get x² on its own first.
- Solve: x² − x − 6 = 0. Give both solutions, separated by a comma. → x = -2 or x = 3Prompt: Factorise: find two numbers that multiply to −6 and add to −1.
- Solve: (x − 7)² = 81. Give both solutions, separated by a comma. → x = -2 or x = 16Prompt: Square root both sides: don't forget ±.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Choose an efficient method to solve a quadratic. 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: Which method is the most efficient way to solve (x + 6)² = 10?
- Step 1: Take square roots
- Answer: Take square roots
- 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.
- Without solving, how many real solutions does (x − 6)² = 0 have? → 1Prompt: A square of a real number is never negative.
- Which method is the most efficient way to solve 5x² + 2x − 6 = 0? (Take square roots / Factorise / Use the quadratic formula) → Use the quadratic formulaPrompt: Is there an x term? If not, square roots are quickest.
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.
- Without solving, how many real solutions does (x + 3)² = 19 have? → 2Prompt: A square of a real number is never negative.
- Which method is the most efficient way to solve x² − 6x − 16 = 0? (Take square roots / Factorise / Use the quadratic formula) → FactorisePrompt: Is there an x term? If not, square roots are quickest.
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 taking square roots.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder