Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Equation of a circle
Geometry
CCSS HSG.GPE.A.1England: GCSE Higher Algebra
Objective and success criteria
Students will: Equation of a circle.
- 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: Distance and midpoint between points; Completing the square
Leads to: Write the equation of a circle from its centre and radius
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Distance and midpoint between points; Completing the square). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write x² − 2x + 9 in the form (x + p)² + q. What is q? → 8Prompt: p is half of the coefficient of x.
- Find the midpoint of (−4, 3) and (−4, −7). Type it like (2, −1). → (−4, −2)Prompt: The midpoint is the average of the coordinates.
- Write x² − 10x + 22 in the form (x + p)² + q. What is p? → -5Prompt: p is half of the coefficient of x.
Hook · 6 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Equation of a circle. 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: What is the centre of the circle (x + 6)² + (y − 5)² = 16? Type it like (2, −1).
- Step 1: (−6, 5)
- Answer: (−6, 5)
- 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.
- What is the radius of the circle (x − 2)² + (y + 2)² = 36? → 6Prompt: The form is (x − a)² + (y − b)² = r².
- The circle x² + y² = r² passes through (0, −5). What is r? → 5Prompt: Substitute the point into x² + y².
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.
- The circle x² + y² = r² passes through (−7, 24). What is r? → 25Prompt: Substitute the point into x² + y².
- What is the centre of the circle (x − 5)² + (y − 1)² = 4? Type it like (2, −1). → (5, 1)Prompt: The form is (x − a)² + (y − b)² = r², with centre (a, b).
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Distance and midpoint between points.
- Use concrete materials: rulers and protractors.
- 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: Write the equation of a circle from its centre and radius.
- 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