Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve quadratics by taking square roots
Algebra
CCSS HSA.REI.B.4.BEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve quadratics by taking square 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: Square roots and cube roots; Two-step equations
Leads to: Choose an efficient method to solve a quadratic; Solve quadratics by completing the square (exact answers)
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 (Square roots and cube roots; Two-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is ∛1000? → 10Prompt: Which number, used three times in a multiplication, gives this?
- √10 lies between which two whole numbers? (4 and 5 / 2 and 3 / 3 and 4 / 1 and 2) → 3 and 4Prompt: List the square numbers near it.
- What is ∛512? → 8Prompt: Which number, used three times in a multiplication, gives this?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve quadratics by taking square roots. 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 − 17 = 15. Give both solutions, separated by a comma.
- Step 1: x² = 16
- Step 2: x = ±4
- Answer: x = -4 or x = 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: 5x² + 12 = 512. Give both solutions, separated by a comma. → x = -10 or x = 10Prompt: Get x² on its own first.
- Solve: (x + 6)² = 49. Give both solutions, separated by a comma. → x = -13 or x = 1Prompt: Square root both sides: don't forget ±.
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 + 7 = 56. Give both solutions, separated by a comma. → x = -7 or x = 7Prompt: Get x² on its own first.
- Solve (x − 2)² = 7, giving exact answers. (x = 2 ± √7 / x = 2 ± 7 / x = −2 ± √7 / x = ±√11) → x = 2 ± √7Prompt: Exact means leave the square root in the answer.
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: Square roots and cube 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
- Move on to: Choose an efficient method to solve a quadratic; Solve quadratics by completing the square (exact answers).
- 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