Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Completing the square
Algebra
CCSS HSA.SSE.B.3.BCCSS HSA.REI.B.4.AEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Completing the square.
- 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: Multiply binomials (expand double brackets); Graphs of quadratics: roots, vertex, intercepts
Leads to: Equation of a circle; Quadratic functions in vertex form; Find the centre and radius from x² + y² + Dx + Ey + F = 0
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 (Multiply binomials (expand double brackets); Graphs of quadratics: roots, vertex, intercepts). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand and simplify: (x + 5)(x − 2) → x^2+3x-10Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- Expand and simplify: (2x + 6)(2x + 5) → 4x^2+22x+30Prompt: Use a grid or FOIL: four multiplications.
- Expand and simplify: (x + 3)(x − 4) → x^2-x-12Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Completing the square. 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 x² − 4x − 11 in the form (x + p)² + q. What is q?
- Step 1: p = −4 ÷ 2 = −2
- Step 2: (x − 2)² = x² − 4x + 4
- Step 3: q = −11 − 4 = −15
- Answer: -15
- 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 x² + 10x + 18 in the form (x + p)² + q. What is p? → 5Prompt: p is half of the coefficient of x.
- Find the turning point of y = x² − 12x + 32 by completing the square. Type it like (2, −1). → (6, −4)Prompt: Write it as (x − h)² + k.
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.
- Find the turning point of y = x² − 6x + 11 by completing the square. Type it like (2, −1). → (3, 2)Prompt: Write it as (x − h)² + k.
- Write x² + 4x + 1 in the form (x + p)² + q. What is p? → 2Prompt: p is half of the coefficient of x.
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: Multiply binomials (expand double brackets).
- 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: Equation of a circle; Quadratic functions in vertex form; Find the centre and radius from x² + y² + Dx + Ey + F = 0.
- 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