Math lesson plan · 11th grade (Year 12 in England) · 30 minutes
Complex numbers
Algebra
CCSS HSN.CN.A.1CCSS HSN.CN.A.2CCSS HSN.CN.C.7
Objective and success criteria
Students will: Complex numbers.
- 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); The quadratic formula
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 · 4 min
- Quick retrieval from earlier learning (Multiply binomials (expand double brackets); The quadratic formula). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Expand and simplify: (x + 7)(x + 4) → x^2+11x+28Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- Solve 2x² + 6x − 7 = 0 using the quadratic formula. Give the larger solution to 2 decimal places. → 0.9Prompt: x = (−b ± √(b² − 4ac)) / 2a.
- Expand and simplify: (3x + 6)(x − 1) → 3x^2+3x-6Prompt: Use a grid or FOIL: four multiplications.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Complex numbers. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Simplify (5 + 5i) + (8 − 7i). Write it as a + bi.
- Step 1: 13 − 2i
- Answer: 13-2i
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Simplify (8 − 3i) − (−9 + 9i). Write it as a + bi. → 17-12iPrompt: Combine real parts with real parts and imaginary parts with imaginary parts.
- Multiply (3 − 2i)(−3 + 2i). Write it as a + bi. → -5+12iPrompt: Expand like two binomials.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Multiply (3 + 4i)(4 − i). Write it as a + bi. → 16+13iPrompt: Expand like two binomials.
- Simplify i¹². (1 / i / −1 / −i) → 1Prompt: The powers of i repeat every 4: i, −1, −i, 1, …
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
- 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