Math lesson plan · 12th grade (Year 13 in England) · 30 minutes
Matrices: operations and determinants
Algebra
CCSS HSN.VM.C.8CCSS HSN.VM.C.10CCSS HSN.VM.C.12
Objective and success criteria
Students will: Matrices: operations and determinants.
- 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: Systems of linear equations (simultaneous equations); Multiply and divide integers
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 (Systems of linear equations (simultaneous equations); Multiply and divide integers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve the system: y = 4x + 2 and 3x + y = −19. Find x. → x = -3Prompt: Substitute the first equation into the second.
- −3 × (−1) = ? → 3Prompt: First multiply the sizes, ignoring the signs.
- Solve: 3x + 5y = −7 and 5x − 5y = −25. Find y. → 1Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Matrices: operations and determinants. 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: Find the determinant of the matrix [[8, −1], [−2, 3]].
- Step 1: 8 × 3 − (−1) × (−2)
- Step 2: = 24 − 2 = 22
- Answer: 22
- 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.
- Find the determinant of the matrix [[3, 3], [2, −1]]. → -9Prompt: For [[a, b], [c, d]] the determinant is ad − bc.
- A = [[1, 2], [5, −4]] and B = [[−3, 1], [4, 0]]. What is the top-left entry of AB? → 5Prompt: Use row 1 of A and column 1 of B.
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.
- A = [[5, 3], [−1, 5]] and B = [[5, 5], [3, 0]]. What is the top-left entry of AB? → 34Prompt: Use row 1 of A and column 1 of B.
- Find the determinant of the matrix [[−1, 6], [2, 9]]. → -21Prompt: For [[a, b], [c, d]] the determinant is ad − bc.
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: Systems of linear equations (simultaneous equations).
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder