Cost Comparison – What’s the better deal?Unit Rate Activity: What makes a bargain? How do you know which price is a better deal?
Many products, especially snack foods and cereal, are sold in different sizes. A great way to teach unit rate is by doing unit cost and price comparisons to find out which size gives you the most bang for your buck!
Through experience, I have learned that many times the larger sized package may cost more overall, but might have a lower unit rate. Sometimes, though, I have been surprised. I can’t guarantee that the larger sizes are the better deal unless I see the unit rate.
I like to present the lesson by playing a game, so I tell students they are going to explore rates through a game called Find the Better Deal. The challenge will be to look beyond the price tag to compare the unit rates!
For example:
For example (these prices were retrieved from walmart.com):
Start the class by asking the students about their experiences shopping:
Then tell the students that they are going to play a game called Find the Better Deal
Divide students into predetermined groups. They will play as a group, but every student must show their own work on the worksheet.
Tell the students that they will learn how to find the unit rate, and use it to compare prices. If they can find the better deal, they can win some of the snacks!
Write the word RATE on the board. Have students write it in their notebooks. Ask the students to think about the word rate and what they think it means. Have them think about the following questions and write their thoughts under the word RATE in their notebooks.
Give students time to write down some ideas. Then give a few minutes for them to discuss their ideas with their partner or group. Students should already have experience with what a ratio is and how to write it.
Supplement their ideas with other examples of rates if students didn’t come up with them on their own: heartbeats per second, miles per hour, cost per pound, 3 items for a dollar, shots per game, miles per gallon, steps per minute, price per pound, price per person.
Emphasize that with rates and ratios, we should always label each number with the correct units.
Define RATE as a special type of ratio that compares 2 different units. Review the definition of a ratio as a comparison of two amounts, and remind students that it can be written in three ways. Explain that we usually use the fraction form to show rates and help find unit rate.
Give this Unit Rate Example:
Guide the students towards rates that have to do with prices. Help them make a connection or think about rates in terms of shopping.
You can ask the students if they have ever seen the signs in the store that say “Two for a dollar”, or “3 packs for $12.00”, or even “Buy one get one free” ? Explain that these are rates, but they don’t always say how much one item costs. By finding unit rate, the costs are easier to compare.
Ask students to practice finding the unit rate, where it ends up being less than a dollar. A good example to show this is with fruit. Describe that someone might buy 12 ounces of blueberries for $2.94. If you have a photo or pint of blueberries, you can show it so students have a good idea of sizes. Ask students to find out what the unit price is, or the cost per ounce of blueberries.
Remind students not to forget to label the top and bottom values of the ratio, because RATE compares two different types of values. By labeling the values, they can understand the problem and talk through the situation.
Remind the students that in order to find the unit rate – they must find out how much it costs for 1 ounce. Since unit rates are expressed in terms of a quantity of 1, the bottom number or denominator must be set to 1 oz.
Set up the equivalent fractions and have the students solve.
Explain that they can divide the price by the number of ounces. Be sure to talk about the terms we use as well. Remember that math is like a language, so use the language with your students and explain how the words can help with setting up problems. Remember that the rate is also Price PER ounce. “Per” not only helps tell us how to set up the ratio but it also means, “divide by” – just like the fraction bar. So if per means divided by, then:
Students may get stuck, because the division results in a decimal, but remind them that we are talking about prices, and money goes to the hundredth place. It’s ok if the answer is less than 1, because money can be rounded to the nearest cent.
Share answers and show that the unit rate is $0.25/ 1 oz or 25 cents per ounce.
Tell students to get ready to shop! Let them know that it’s game time and they will have to Find the Better Deal!
Introduce and explain the game.
Show the students the snack stations and the price tags.
Explain where to find the number of ounces on the tag or on the bag itself.
The goal of the game is to find the package with the lowest unit price for each type of snack.
Explain that even if students have a guess for the better buy, they still must record their work on the Cost Comparisons Worksheets as follows:
After working through the example, send groups of students to each snack station. You can split up the groups and have them rotate through all of the snacks, or the groups can travel together. Just make sure that the students are evenly distributed throughout the room and there are enough snack samples to visit.
Remind the students that they need to record their data and come back together to discuss their ideas about which is the better deal.
Don’t forget to tell your students that if they find the better deal, they get to win the snack to eat!
Have each group write and share about which is the better buy. Groups should briefly present their data and reasoning to the class.
Talk about why stores have different unit rates for different sizes. Many times, the larger size has a higher price, but it has a lower unit rate. Why is this?
Also think about the benefits of buying the smaller size, even if it has a higher unit rate. The final overall price is often less, maybe the customer only has 5 dollars and can’t buy the larger size. Even if the large box of pretzels has the smaller unit rate, maybe someone can’t eat it all before it goes stale.
Ask: Can you pack the large bucket of pretzels in your lunch box? Why do small snack packs cost more per ounce and have a higher unit rate?
I have often had great discussions with these questions. It’s amazing how many ideas and explanations the students come up with. They have ideas about the snack packs needing more packaging material, or that they can easily fit in a lunchbox etc… Some talk about large families versus smaller families, or ways to share and save money. Others talk about how they like the packaging or just want their own bag. Unit price helps people find the best cost per ounce, but sometimes, the lower overall price or size is a factor as well.
All of these conversations help students realize the real world application of the math skill of finding rates!
Here are some fun ways to extend the learning of this lesson:
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