Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
The quadratic formula
Algebra
CCSS HSA.REI.B.4.BEngland: GCSE Higher Algebra
Objective and success criteria
Students will: The quadratic formula.
- 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; Simplify surds (radicals)
Leads to: Complex numbers; Use the discriminant to find unknown coefficients; Give exact solutions with the quadratic formula
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 (Solve quadratics by factorising; Simplify surds (radicals)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x² + 14x + 45 = 0. Give both solutions, separated by a comma. → x = -9 or x = -5Prompt: Factorise: find two numbers that multiply to 45 and add to 14.
- Simplify √24. It can be written as k√6. What is k? → 2Prompt: Look for the largest square number that divides it.
- Solve: x² − 6x = 0. Give both solutions, separated by a comma. → x = 0 or x = 6Prompt: Take out the common factor x.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: The quadratic formula. 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: Solve 3x² − 6x − 3 = 0 using the quadratic formula. Give the larger solution to 2 decimal places.
- Step 1: b² − 4ac = 36 − (−36) = 72
- Step 2: x = (6 ± √72) / 6
- Step 3: x ≈ 2.41 or x ≈ −0.41
- Answer: 2.41
- 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.
- Solve 2x² − 5x − 9 = 0 using the quadratic formula. Give the smaller solution to 2 decimal places. → -1.21Prompt: x = (−b ± √(b² − 4ac)) / 2a.
- How many real solutions does 4x² + 7x − 5 = 0 have? (Two / One (repeated) / None) → TwoPrompt: Work out the discriminant b² − 4ac.
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.
- Solve: 2x² − 7x + 3 = 0. Give both solutions, separated by a comma. → x = 0.5 or x = 3Prompt: Use the quadratic formula with a = 2, b = −7, c = 3.
- How many real solutions does x² − x + 5 = 0 have? (Two / One (repeated) / None) → NonePrompt: Work out the discriminant b² − 4ac.
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
- Move on to: Complex numbers; Use the discriminant to find unknown coefficients; Give exact solutions with the quadratic formula.
- 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