Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Radical equations
Algebra
CCSS HSA.REI.A.2
Objective and success criteria
Students will: Radical equations.
- 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; Square roots and cube roots
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 (Solve quadratics by factorising; Square roots and cube roots). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x² − 16x + 63 = 0. Give both solutions, separated by a comma. → x = 7 or x = 9Prompt: Factorise: find two numbers that multiply to 63 and add to −16.
- What is ∛125? → 5Prompt: Which number, used three times in a multiplication, gives this?
- Solve: x² + 12x = 0. Give both solutions, separated by a comma. → x = -12 or x = 0Prompt: Take out the common factor x.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Radical equations. 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: √(x − 10) = 2
- Step 1: x − 10 = 4
- Step 2: x = 14
- Answer: x = 14
- 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: √(x + 6) = 2 → x = -2Prompt: Square both sides to remove the square root.
- Solve: √(x + 6) = x. Check for extraneous solutions. → x = 3Prompt: Square both sides, then solve the quadratic.
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: √(x − 6) = 8 → x = 70Prompt: Square both sides to remove the square root.
- Solve: √(x − 1) = x − 3. Check for extraneous solutions. → x = 5Prompt: Square both sides, then solve the quadratic.
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