GM Lesson 011 The Unit Cost Method

Learning Intentions

• Compare prices using the unit cost method.
• Calculate unit costs from different package sizes or quantities.
• Determine the better value option in practical contexts.

Prerequisites

Students should be able to:

• Divide decimals by whole numbers.
• Interpret rates such as “per kilogram”, “per litre” and “per item”.
• Compare decimal numbers representing money.
• Convert between common metric units such as grams and kilograms, or millilitres and litres.

Key Idea Summary

The unit cost method compares prices by finding the cost of one unit.

Common units include:

• cost per item
• cost per kilogram
• cost per gram
• cost per litre
• cost per millilitre
• cost per metre

The basic rule is:

The better value option is usually the option with the lower unit cost, provided that the quantity is useful and not wasted.

A low unit cost is not always the best decision if:

• the buyer cannot afford the larger package
• the product will expire before it is used
• the buyer does not need the extra quantity
• storage space is limited

Direct Instruction and Worked Examples

Lesson Timing

• Introduction and key idea: 5 minutes
• Direct instruction and worked examples: 20 minutes
• Understanding checks: 5 minutes
• Exercises: 15 minutes

Direct Instruction

When two products have different prices and different quantities, comparing the total price can be misleading.

For example, a larger packet may cost more overall but less per unit.

To compare fairly:

1. Identify the quantity and price of each option.
2. Choose a common unit.
3. Calculate the unit cost.
4. Compare the unit costs.
5. Choose the lower unit cost if it is practical.

Worked Example 1: Cost per Item

A pack of 6 muesli bars costs $ . A pack of 10 muesli bars costs $ .

Determine which pack is better value.

For the pack of 6:

So, the pack of 6 costs $ per muesli bar.

For the pack of 10:

So, the pack of 10 costs $ per muesli bar.

Since:

the pack of 10 is better value.

Worked Example 2: Cost per Kilogram

A box of cereal costs $ . A box costs $ .

Determine which box is better value.

First convert to kilograms:

For the box:

So, the box costs $ per kilogram.

For the box:

So, the box costs $ per kilogram.

Since:

the box is better value.

Worked Example 3: Cost per Litre

A bottle of juice costs $ . A bottle costs $ .

Determine which bottle is better value.

Convert to litres:

For the bottle:

So, the bottle costs $ per litre.

For the bottle:

So, the bottle costs $ per litre.

Since:

the bottle is better value.

Worked Example 4: Special Offer

A supermarket sells tuna in two ways:

• Single can: $ for
• Special offer: 4 cans for $ , each can is

Determine which option is better value per can.

For a single can, the cost per can is:

For the special offer:

The special offer costs $ per can.

Since:

the special offer is better value per can.

Worked Example 5: Better Value May Not Always Be Better Choice

A student needs about of grated cheese for one recipe.

Option A: for $

Option B: for $

Find the unit cost of each option, then decide which option may be more practical.

For Option A:

So, Option A costs $ per kilogram.

For Option B:

So, Option B costs $ per kilogram.

Option B has the lower unit cost, so it is better value mathematically. However, Option A may be more practical if the student only needs and the remaining cheese would be wasted.

Understanding Checks

Check 1

A pack of 8 batteries costs $ .

Calculate the cost per battery.

Check 2

A bag of rice costs $ .

Calculate the cost per kilogram.

Check 3

A bottle of detergent costs $ .

Calculate the cost per litre.

Check 4

Two options are available:

• Option A: rolls for $
• Option B: rolls for $

Which option has the lower cost per roll?

Check 5

Explain why the option with the lowest unit cost may not always be the best choice.

Exercises

Simple Familiar Exercises

Exercise 1

A pack of 5 pens costs $ .

Calculate the cost per pen.

Exercise 2

A pack of 12 cans of soft drink costs $ .

Calculate the cost per can.

Exercise 3

A bag of flour costs $ .

Calculate the cost per kilogram.

Exercise 4

A bottle of cordial costs $ .

Calculate the cost per litre.

Exercise 5

A packet of biscuits costs $ .

Calculate the cost per .

Complex Familiar Exercises

Exercise 6

A supermarket sells apples in two bags:

• Bag A: for $
• Bag B: for $

Use the unit cost method to determine the better value option.

Exercise 7

A brand of shampoo is sold in two sizes:

• Size A: for $
• Size B: for $

Calculate the cost per litre for each size and determine the better value option.

Exercise 8

A bakery sells bread rolls in two ways:

• Single roll: $
• Pack of 6 rolls: $

Determine which option is cheaper per roll.

Exercise 9

A student is comparing two internet prepaid plans:

• Plan A: for $
• Plan B: for $

Calculate the cost per gigabyte for each plan and determine the better value option.

Exercise 10

A butcher sells mince in two pack sizes:

• Pack A: for $
• Pack B: for $

Calculate the cost per kilogram for each pack and determine which pack is better value.

Homework Problems

Problem 1

A pack of 4 toothbrushes costs $ .

Calculate the cost per toothbrush.

Problem 2

A bag of oranges costs $ .

Calculate the cost per kilogram.

Problem 3

A bottle of drink costs $ .

Calculate the cost per litre.

Problem 4

A shopper compares two boxes of crackers:

• Box A: for $
• Box B: for $

Calculate the cost per for each box and determine the better value option.

Problem 5

A pack of 18 toilet rolls costs $ . A pack of 24 toilet rolls costs $ .

Calculate the cost per roll for each pack and determine the better value option.

Problem 6

A bottle of olive oil is sold in two sizes:

• Size A: for $
• Size B: for $

Calculate the cost per litre for each size and determine the better value option.

Problem 7

A pet owner is comparing dog food:

• Bag A: for $
• Bag B: for $

Calculate the cost per kilogram for each bag and determine the better value option.

Problem 8

A family needs bottles of water for a sports day.

The water is sold as:

• Pack A: 6 bottles for $
• Pack B: 10 bottles for $
• Pack C: 24 bottles for $

Determine the cost per bottle for each option. Then decide which packs the family should buy to get at least bottles at a reasonable cost.

Problem 9

A student compares two printing options:

• Printer A: $ per page
• Printer B: $ for a pack of 80 prepaid pages

Find the cost per page for Printer B and decide which option is cheaper per page.

Problem 10

A supermarket sells laundry liquid in three options:

• Option A: for $
• Option B: for $
• Option C: for $

Calculate the cost per litre for each option and determine the best value option.

Next: GM Lesson 012 Percentage Increase and Decrease