Math lesson plan · 11th grade (Year 12 in England) · 45 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 · 5 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 + 3)(x − 7) → x^2-4x-21Prompt: Multiply each term in the first bracket by each term in the second (FOIL).
- Solve x² + 5x − 7 = 0 using the quadratic formula. Give the larger solution to 2 decimal places. → 1.14Prompt: x = (−b ± √(b² − 4ac)) / 2a.
- Expand and simplify: (5x − 1)(x + 5) → 5x^2+24x-5Prompt: Use a grid or FOIL: four multiplications.
Hook · 5 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 · 10 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 · 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.
- Simplify (−8 − 5i) + (8 + 7i). Write it as a + bi. → 2iPrompt: Combine real parts with real parts and imaginary parts with imaginary parts.
- Multiply (1 − 4i)(−4 + 4i). Write it as a + bi. → 12+20iPrompt: Expand like two binomials.
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.
- Simplify i²². (1 / i / −1 / −i) → −1Prompt: The powers of i repeat every 4: i, −1, −i, 1, …
- Multiply (4 − 5i)(3 + 3i). Write it as a + bi. → 27-3iPrompt: Expand like two binomials.
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