Math lesson plan · 11th grade (Year 12 in England) · 60 minutes
Build a quadratic from its roots; sum and product of roots
Algebra
CCSS HSA.APR.B.3CCSS HSA.SSE.A.1.BEngland: A-level Pure Mathematics
Objective and success criteria
Students will: Build a quadratic from its roots; sum and product of roots.
- 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
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 · 6 min
- Quick retrieval from earlier learning (Solve quadratics by factorising). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x² + 3x − 54 = 0. Give both solutions, separated by a comma. → x = -9 or x = 6Prompt: Factorise: find two numbers that multiply to −54 and add to 3.
- Solve: x² − 12x = 0. Give both solutions, separated by a comma. → x = 0 or x = 12Prompt: Take out the common factor x.
- Solve: x² + x = 6. Give both solutions, separated by a comma. → x = -3 or x = 2Prompt: First rearrange so that one side is 0.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Build a quadratic from its roots; sum and product of roots. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Write a quadratic x² + bx + c with roots −5 and −7. Type it.
- Step 1: (x + 5)(x + 7)
- Step 2: x² + 12x + 35
- Answer: x^2+12x+35
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Write a quadratic x² + bx + c with roots 6 and 0. Type it. → x^2-6xPrompt: If x = 6 is a root, then (x − 6) is a factor.
- Without solving, find the product of the roots of 5x² − 11x + 8 = 0. Give a fraction if needed. → 8/5 (1 3/5)Prompt: For ax² + bx + c = 0: sum = −b/a and product = c/a.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Without solving, find the product of the roots of 3x² + 4x + 1 = 0. Give a fraction if needed. → 1/3Prompt: For ax² + bx + c = 0: sum = −b/a and product = c/a.
- Write a quadratic x² + bx + c with roots 7 and 1. Type it. → x^2-8x+7Prompt: If x = 7 is a root, then (x − 7) is a factor.
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-11.
Free lesson plan from eurekami.com/lesson-plan-builder