F. Financial Literacy · Money and Finances: Moving Money, Sales Tax, Budgets, Credit and Best Value

Unit Rates: Finding the Best Value

F1.5 A1About 45 minutes

Learning goals

I can explain what a rate and a unit rate are.
I can calculate unit rates for goods, like the price per item, per kilogram, per litre or per 100 g.
I can calculate unit rates for services, like the price per lesson or per hour.
I can compare unit rates to find the best value, and decide whether the best value is the best choice for me.

Words to know

rate
A comparison of two different kinds of amounts, like $6 for 3 kg or 20 km in 2 hours.

unit rate
A rate for one unit: the price for 1 item, 1 kg, 1 L, 100 g, 1 lesson or 1 hour.

unit price
A unit rate for buying something, like $0.80 per granola bar.

per
For each. "$2 per kg" means $2 for each kilogram.

best value
The choice that gives you the most for your money, often the one with the lowest unit price.

Remember from Grade 4

In Grade 4 you used rates like 8 legs per spider, and you compared pack sizes by finding the cost of each item. In Grade 5 you will call this a unit rate, and you will use it with dollars and cents, kilograms, litres and hours.

Which box is the better deal?

At the grocery store, Nora's dad needs granola bars for school lunches.

Box A: 6 bars for $4.80
Box B: 8 bars for $6.00

Box A is cheaper. But Box B has more bars. Which one gives more for the money? To compare fairly, find the price for one bar. That is the unit rate.

Box A: 6 bars for $4.80, or 80¢ per bar. Box B: 8 bars for $6.00, or 75¢ per bar.

How to find a unit rate

Divide the price by the number of units.

Tip: change dollars to cents to divide with whole numbers. $4.80 = 480¢.

Box A: 480¢ ÷ 6 = 80¢ per bar
Box B: 600¢ ÷ 8 = 75¢ per bar

Box B is the better value: each bar costs 5¢ less.

Units can be different

You can find unit rates for many things:

per item: granola bars, pencils, tennis balls
per kilogram (kg): apples, potatoes, rice
per litre (L): milk, juice
per 100 grams (100 g): cereal, crackers, cheese
per lesson or per hour: services, like swimming lessons, renting a canoe, or a dog walker's pay

Worked example

Example 1: Price per litre

Apple juice comes in a 1 L bottle for $2.40 or a 2 L bottle for $4.20. Which is the better value?

The 1 L bottle is already a unit rate: $2.40 per L.
2 L bottle: 420¢ ÷ 2 = 210¢ = $2.10 per L.
$2.10 is less than $2.40.

The 2 L bottle is the better value. It saves 30¢ per litre.

Worked example

Example 2: Price per 100 g

Cereal comes in a 500 g box for $4.50 or an 800 g box for $6.40. Which is the better value?

Use 100 g as the unit for both boxes.
500 g is 5 groups of 100 g. 450¢ ÷ 5 = 90¢ per 100 g.
800 g is 8 groups of 100 g. 640¢ ÷ 8 = 80¢ per 100 g.
80¢ is less than 90¢.

The 800 g box is the better value: 80¢ per 100 g, compared with 90¢.

Cut each box into 100 g blocks. The 500 g box makes 5 blocks at 90¢ each; the 800 g box makes 8 blocks at 80¢ each, so the big box is the better value.

Worked example

Example 3: Services

Two clubs offer skating lessons. Club A: 8 lessons for $96. Club B: 5 lessons for $65. Which costs less per lesson?

Club A: $96 ÷ 8 = $12 per lesson.
Club B: $65 ÷ 5 = $13 per lesson.

Club A is the better value at $12 per lesson, $1 less than Club B. (A family might still pick Club B if its times or location work better.)

Worked example

Example 4: Best value is not always the best choice

Apples cost $2.50 for a 1 kg bag, or $6.00 for a 3 kg bag. Dev's family needs only about 1 kg this week, and apples go soft if they sit too long. Which should they buy?

1 kg bag: $2.50 per kg.
3 kg bag: $6.00 ÷ 3 = $2.00 per kg. It's the better value.
But if they only eat 1 kg, the other 2 kg could go to waste. Then they paid $6.00 for 1 kg of apples they ate!
The 1 kg bag costs $3.50 less today, and nothing is wasted.

The 1 kg bag is the smarter choice for Dev's family, even though the 3 kg bag has the lower unit price.

Think before you choose

The lowest unit price is the best value only if:

you will use it all before it spoils or you get tired of it,
you have room to store it,
you have enough money right now, and
the quality is the same.

Many store shelf labels in Canada show a unit price, like "$0.80 / 100 g". Look for it next time you shop!

Explain your thinking

When you compare, write both unit rates and say which is lower: "The big box is 75¢ per bar, and the small box is 80¢ per bar, so the big box is better value." Then add whether it is the best choice for you, and why.

Just for fun

Funny but true: the biggest box on the shelf isn't always the best deal. Sometimes a "JUMBO" box costs more per 100 g than the regular one. Unit rates don't care how loud the box is shouting!

Hands-on activity

Unit price hunt

You need: a grocery flyer (paper or online) or a trip to the store with a grown-up, paper, a pencil and a calculator.

Find three products that come in two sizes, like juice, yogurt, rice, crackers or granola bars.
For each, write the size and price of both choices.
Find the unit rate for each: price per item, per 100 g, per kg or per L.
Circle the better value.
Look for the unit price on the shelf label (if you're in the store). Does it match yours?
For each product, decide: is the better value also the better choice for your family? Why?

What to look for: the same unit used for both sizes (for example, both per 100 g), the correct division, and a reason for the final choice.

Your turn

4 juice boxes cost $3.00. What is the price per juice box?

10 pencils cost $2.50. What is the price per pencil?

Tennis balls: 3 for $4.50 or 4 for $5.60. Which is the better value?

A 2 kg bag of potatoes costs $3.80. What is the price per kg?

Swimming lessons cost $84 for 6 lessons. What is the price per lesson?

Milk: 500 mL for $1.75 or 1 L for $3.00. Which is the better value?

A dog walker earns $36 for 4 walks. What is her rate per walk?

More practice: warm-up

5 stickers for $5. Price per sticker?

2 muffins for $3. Price per muffin?

12 eggs for $3.60. Price per egg?

$20 for 4 hours of work. Rate per hour?

Which is a unit rate: "$6 for 3 kg" or "$2 per kg"?

More practice: on your own

Yogurt cups: 4 for $3.60 or 6 for $5.10. Which is the better value?

A single bus ride costs $3.50. A card with 10 rides costs $30. Which is the better value per ride? When is the card not a good choice?

Rice: 2 kg for $5.40 or 5 kg for $12.50. Find the price per kg of each.

Canoe rental: $18 per hour, or $60 for 4 hours. Which is cheaper for a 3-hour trip?

Raisins: 250 g for $2.00 or 1 kg for $7.00. Find the price per 100 g of each.

Challenge

Pasta comes in three sizes: 450 g for $1.80, 900 g for $3.15 and 2 kg for $7.20. Find the price per 100 g of each. Which is the best value?

A hockey team rents ice time for $240 per hour. If 12 players share the cost, what does each pay? What if 15 players share it?

A store sign says: "2 for $5, or $2.75 each." How much do you save per item with the deal? Should you always buy 2?

Check your understanding

Quiz

5 bars cost $4.00. What is the price per bar?

Which is the better value?

Skating lessons cost $45 for 3 lessons. What is the price per lesson?

Which bag of carrots has the lower price per kg?

When might the better-value big package not be the best choice?

Cheese costs $3.00 for 200 g. What is the price per 100 g?

For parents and teachers

What your child is learning: the Ontario curriculum (F1.5) asks Grade 5 students to calculate unit rates for various goods and services, and identify which rates offer the best value. In Grade 4 your child compared pack sizes by finding the cost of each item; Grade 5 extends this to unit rates per kg, per L, per 100 g, per lesson and per hour, using dollars and cents. Converting to cents ($4.80 = 480¢) lets them divide with whole numbers. Deciding whether the best value is the best choice, and explaining why, is part of A1.

Common difficulties:

Comparing different units, like price per 100 g for one box and per kg for the other. Both must use the same unit.
Dividing the wrong way (items ÷ price instead of price ÷ items). Ask, "What is the cost of one?"
Always choosing the biggest package. Spoilage, storage, and how much money is available now all matter.

How to help: Point out shelf unit-price labels at the grocery store. Ask your child to check one with a calculator. Let them choose between two sizes of something your family buys and explain their choice.