Money Math · Lesson Plan

Discounts and Scalar Multiplication

The algebra extension of the discount cluster. A matrix is just an organized table of numbers — the way a business might lay out its prices — and scalar multiplication means multiplying every entry by the same number. This lesson uses that to reprice a whole matrix of fares at once: multiply by the fraction of the price still paid and a new price matrix falls out. Six problems with an answer key.

Grades 6–9 Lesson Plan 30–45 minutes Free Lesson Plan Lesson & Worksheet: Full Membership

For Teachers

Lesson at a glance

Topic: Money Math
Grade Level: Grades 6–9
Resource Type: Lesson + Worksheet
Estimated Time: 30–45 minutes
Format: Lesson + worksheet + answer key
Materials: Printable lesson, worksheet, answer key, calculator

What Students Learn

Learning objectives

Explain what a matrix is and why a business would organize prices in one
Multiply a matrix by a scalar by multiplying every entry
Write the new matrix that results from a scalar multiplication
Convert a percent discount into the scalar that gives the new price
Apply one discount to a whole set of prices in a single step

Materials

What you’ll need

Printed copies of the lesson and worksheet (one per student)
Calculators
Pencils
Whiteboard or projector for worked examples

Key Terms

Vocabulary

Matrix: A way of organizing data in a set of brackets, in rows and columns.
Scalar: A single number that a whole matrix is multiplied by.
Scalar multiplication: Multiplying every entry of a matrix by the same number.
Entry: One number inside a matrix.
Discount: A percentage taken off a price.
Sale price: The original price minus the discount.

For Teachers

Lesson plan

Estimated time: one 30–45 minute class period.

Lesson sequence

Introduction (5 min). Review what a discount is, then show a small table of prices and explain that a matrix is simply that table written in brackets — how a company might organize its pricing.
Scalar multiplication (10 min). Multiply a simple matrix by 2, entry by entry, and write the new matrix. Stress that every entry gets the same treatment.
Discount a whole matrix (12 min). Work the airline-fare example: a 20% discount means travelers pay 80%, so multiplying the fare matrix by 0.8 produces the new fare matrix in one step.
Worksheet (13 min). Students practice five scalar multiplications, then discount a matrix of fares.
Review (5 min). Check answers with the key; confirm each new matrix has the same shape as the original.

Assessment

Assess the completed worksheet against the included answer key.

Discussion

Discussion questions

Why does a company organize prices in a matrix instead of a list?
If a discount is 10%, what scalar do you multiply by to get the new prices?
Why does the new matrix have the same number of rows and columns as the original?
How is discounting a matrix faster than discounting each price one at a time?
What other business numbers could be organized in a matrix?

Printable Lesson, Worksheet & Answer Key