Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Use the discriminant to find unknown coefficients
Algebra
CCSS HSA.REI.B.4.BEngland: GCSE Higher AlgebraEngland: A-level Pure Mathematics
Objective and success criteria
Students will: Use the discriminant to find unknown coefficients.
- 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
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve 3x² − 4x − 8 = 0 using the quadratic formula. Give the larger solution to 2 decimal places. → 2.43Prompt: x = (−b ± √(b² − 4ac)) / 2a.
- How many real solutions does 2x² − 3x + 3 = 0 have? (Two / One (repeated) / None) → NonePrompt: Work out the discriminant b² − 4ac.
- Solve: 2x² − 5x + 3 = 0. Give both solutions (fractions allowed), separated by a comma. → x = 1 or x = 1.5Prompt: Use the formula, or factorise into (px + q)(x + r).
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Use the discriminant to find unknown coefficients. 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: Work out the discriminant of 2x² + 8x + 6 = 0.
- Step 1: 8² − 4 × 2 × 6
- Step 2: = 16
- Answer: 16
- 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.
- Work out the discriminant of 5x² + 9x + 5 = 0. → -19Prompt: The discriminant is b² − 4ac.
- x² + kx + 49 = 0 has equal roots and k is positive. Find k. → 14Prompt: Equal roots: discriminant = 0.
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.
- For which values of k does x² + 4x + k = 0 have two distinct real roots? (k < 4 / k > 4 / k > −4 / k = 4) → k < 4Prompt: Two distinct real roots: b² − 4ac > 0.
- Work out the discriminant of 5x² − 9x − 2 = 0. → 121Prompt: The discriminant is 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: 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