Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Give exact solutions with the quadratic formula
Algebra
CCSS HSA.REI.B.4.BEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Give exact solutions with 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: The quadratic formula; Simplify surds (radicals)
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 (The quadratic formula; Simplify surds (radicals)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve 3x² − 2x − 4 = 0 using the quadratic formula. Give the larger solution to 2 decimal places. → 1.54Prompt: x = (−b ± √(b² − 4ac)) / 2a.
- Simplify √108. It can be written as k√3. What is k? → 6Prompt: Look for the largest square number that divides it.
- How many real solutions does 5x² − 4x + 7 = 0 have? (Two / One (repeated) / None) → NonePrompt: Work out the discriminant b² − 4ac.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Give exact solutions with the quadratic formula. 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 2x² − 3 = 0. Give exact answers in the form (p ± √q)/r.
- Step 1: b² − 4ac = 24
- Step 2: x = (0 ± √24)/4
- Answer: x = (0 ± √24)/4
- 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 2x² + 6x + 1 = 0. Give exact answers in the form (p ± √q)/r. (x = (−6 ± √28)/2 / x = −6 ± √28/4 / x = (−6 ± √28)/4 / x = (−6 ± √44)/4) → x = (−6 ± √28)/4Prompt: x = (−b ± √(b² − 4ac))/(2a).
- Solve x² + 6x + 1 = 0 with the quadratic formula. Simplify fully. (x = 3 ± 2√2 / x = −3 ± 2√2 / x = −3 ± 4√2 / x = −6 ± 2√2) → x = −3 ± 2√2Prompt: The discriminant is 32: simplify √32.
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 − 2x − 23 = 0 with the quadratic formula. Simplify fully. (x = 1 ± 4√6 / x = 1 ± 2√6 / x = −1 ± 2√6 / x = 2 ± 2√6) → x = 1 ± 2√6Prompt: The discriminant is 96: simplify √96.
- Solve x² − 9x − 9 = 0. Give exact answers in the form (p ± √q)/r. (x = (9 ± √45)/2 / x = (−9 ± √117)/2 / x = (9 ± √117)/1 / x = (9 ± √117)/2) → x = (9 ± √117)/2Prompt: x = (−b ± √(b² − 4ac))/(2a).
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: The quadratic formula.
- 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