Home›Lesson Plans›Mathematics›Algebra · Grade 12

Matrices: Grids of Numbers

Twelfth graders are introduced to matrices — rectangular grids of numbers — learning scalar multiplication, the determinant, and how matrices organize data and solve systems, a gateway to linear algebra.

Grade 12Matrices55 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Read a matrix.
  • ✓Perform scalar multiplication.
  • ✓Compute a 2×2 determinant.
  • ✓Understand what matrices represent.
Essential Question

A matrix is just a grid of numbers — but it’s a surprisingly powerful one. How do we operate on matrices, and what does a determinant tell us about one?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

The Matrix Tool

Project this and change the entries and scalar. Watch scalar multiplication scale every entry — and see the determinant update!

🔲 Explore scalar multiplication & the determinantTry it
A
→ 2A
2A
a: 2
b: 1
c: 3
d: 4
k: 2

The Lesson · Gradual Release (I Do · We Do · You Do)

55 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — A Grid of Numbers

5 min

A matrix is just a grid of numbers — but what can it do?

👩‍🏫 Teacher Moves

  • Show a 2×2 matrix.
  • Ask what operations apply.
  • Set the goal: matrices.

🎒 Student Actions

  • See the matrix.
  • Wonder the operations.
  • Predict them.
2

I Do — Scalar & Determinant

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Scalar multiplication scales every entry.
  • Compute the determinant ad − bc.
  • Explain what it means.

🎒 Student Actions

  • Learn scalar mult.
  • Compute the determinant.
  • See the meaning.
3

We Do — Explore Together

13 min

Class uses the Matrix Tool.

👩‍🏫 Teacher Moves

  • Change entries and scalar.
  • Read kA.
  • Read the determinant.

🎒 Student Actions

  • Set values.
  • Read kA.
  • Read det.
4

You Do — On Your Own

12 min

Students operate.

👩‍🏫 Teacher Moves

  • Do scalar multiplication.
  • Compute determinants.
  • Add matrices.

🎒 Student Actions

  • Scale them.
  • Find det.
  • Add them.
5

Close — Close

5 min

One matrix.

👩‍🏫 Teacher Moves

  • Give a matrix.
  • Find kA and det.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find kA.
  • Find det.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School · Precalculus).

CCSS
N-VM.7

Multiply matrices by scalars.

CCSS
N-VM.8

Add, subtract, and multiply matrices of appropriate dimensions.

CCSS
N-VM.6

Use matrices to represent and manipulate data.

CCSS
N-VM.10

Understand the role of the determinant.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Label rows and columns.
  • Sentence frame: “Scalar mult scales ___.”
  • Use a data-table example.

Support & Access

IEP / 504
  • Start with scalar multiplication.
  • Use a small 2×2 matrix.
  • Compute step by step.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Multiply two matrices.
  • Use the determinant to find an inverse.
  • Solve a system with matrices.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Calculators
  • 💻The Matrix Tool
  • 📄Data tables
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

matrixa rectangular grid of numbersentrya single number in a matrixrowa horizontal line of entriescolumna vertical line of entriesscalara single number multiplierscalar multiplicationmultiplying every entry by a scalardeterminantad − bc for a 2×2 matrixdimensionsthe number of rows × columns
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
If A = [[2, 1], [3, 4]], what is 2A?
[[4, 2], [6, 8]] (every entry doubled).
QUESTION 2
What is the determinant of [[2, 1], [3, 4]]?
5 (2×4 − 1×3 = 8 − 3).
QUESTION 3
What does scalar multiplication do to a matrix?
Multiplies every entry by the scalar.

Going deeper? Solve a system.

Have students use a matrix and its determinant to solve a 2×2 system of equations (Cramer’s rule). A printable matrices sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 MatricesFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 MatricesQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ MatricesPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: column, determinant, dimensions, entry, matrix, row, scalar, scalar multiplication
  1. a single number multiplier
  2. a vertical line of entries
  3. a single number in a matrix
  4. the number of rows × columns
  5. a rectangular grid of numbers
  6. multiplying every entry by a scalar
  7. ad − bc for a 2×2 matrix
  8. a horizontal line of entries

Part B · Show what you learned

  1. If A = [[2, 1], [3, 4]], what is 2A?
  2. What is the determinant of [[2, 1], [3, 4]]?
  3. What does scalar multiplication do to a matrix?
Answer key — Part A: 1) scalar · 2) column · 3) entry · 4) dimensions · 5) matrix · 6) scalar multiplication · 7) determinant · 8) row
Part B: 1) [[4, 2], [6, 8]] (every entry doubled). 2) 5 (2×4 − 1×3 = 8 − 3). 3) Multiplies every entry by the scalar.