The Price is Right: Unit Rates

SALE! SALE! SALE!

Besides my curly hair and my singing, one thing I am infamous for (at least to my friends and family) is my frugality and ability to sniff out the best sale I can find. I rarely buy anything full price (including groceries) and whenever I come home after a shopping trip, my family has to play the Price is Right as I show off my deals. Comedian Steve Trevino highlighted this ordeal perfectly:

(Disclaimer: He uses the S Word a couple times, so NSFW)  

“Guess how much the regular price for this dress was? What do you think I paid for it? No, it was way cheaper! I saved [insert grand amount here]!”

Sure, they get tired of it, but I never do! Shopping and sales are the only maths that spoke to my heart. It's more exhilarating than most things I do. 

Shop Smart, Love

To my husband’s dismay, I am currently teaching him how to shop smart when we go grocery shopping. He will grab any bag of chips he wants, without looking at the best deal, and it ends up costing more for 1 bag than it might for 2 or even 3. This is also true when we go to Costco. Sometimes the deals are not as good as they seem because they are in bulk. That pack of 5 antiperspirant sticks for $12.99 might seem like a great deal and it’s easy to just throw it in the cart because it’s a good price and you will always need more antiperspirant. 

That's the Best You can Do?

But is it really the best deal you can get? What I am trying to teach my husband is to look at the price of one and compare that to another brand's price, or another store’s sale. Those antiperspirant sticks costs $2.60 per stick. That’s not a bad price, but I also know I can usually find a sale for $2.50/each or even $1.99/each. It’s better to stock up when I see those sales and get 5 sticks for $12.50 or better yet, $9.95.

There's Not Enough Chocolate

Another trick I am teaching my husband is to look at the amount in a product compared to the price. The other day while grocery shopping, we decided to get some chocolate. They had a sale for smaller bars, 2 for $3.99 and then they had a giant chocolate bar on sale for $4.99. My husband reached for the smaller bars first, seeing the smaller price so assuming that was the better deal. I stopped him and told him to look at the amount in grams first. So we looked at the smaller chocolate bars. They were 100 grams each. Then I looked at the giant bar, which was 300 grams.

So I did a little “mental” math.

Two chocolate bars are $3.99.

$3.99 / 2 = $1.99 per 1 chocolate bar.

1 big chocolate bar is $4.99.

$4.99 per chocolate bar.

Okay so at this rudimentary point, the $3.99 price looks cheaper.

How much per gram?

Each smaller chocolate bar is 100 grams.

The big chocolate bar is 300 grams.

 $1.99 / 100 grams = $0.0199 per 1 gram

$4.99 / 300 grams = $0.0167 per 1 gram

So by a less than cent, the larger chocolate bar is the better deal by amount of chocolate per gram.

This comparison down to the single gram unit is called finding the Unit Rate.    

Okay, to be honest, I didn’t actually mentally calculate down to the fraction of a cent. I used 100 grams as my unit rather than 1 gram, and I just used the smaller chocolate bar as my Unit Rate, and counted up from there.

100 grams (1 chocolate bar) is $1.99

200 grams (2 chocolate bars) is $3.99

300 grams (3 chocolate bars) is $5.97

300 grams (1 lg chocolate bar) is $4.99!

Well, now it looks like I’m saving a dollar!

The Price is Right: Home Edition

So remember my shopping Price is Right game with my family? So while I couldn’t break down the unit rate for my dress, I certainly could (and do) for my accessories or bundle prices. Recently I got a shirt and two pairs of leggings for $20. That would be 3 items for $20, or $6.67 per item. Considering each item was over $10 regular price, that’s a good deal.  

Price is Right: Classroom Edition

Why not bring the Price is Right to your classroom when teaching unit rates? This teacher does a wonderful job introducing the concept of unit rates to her classroom, using a modified version of Price is Right.

Ask students to find the better deal between a pack of 12 pens compared to a 48 box full of pens.

Have them figure out if 1 t-shirt costs $____ from this company, and 5 shirts cost $____ from that company, what’s the better choice.

You can add the complexity by adding in more choices to figure out, or adding an additional step beyond the unit rate. I modified a question from an activity in Chapter 14 of Small's Making Math Meaningful to Canadian Students, K-8:

For example:

Bookstore 1 has a sale: 3 books for $14.25

Bookstore 2 has a sale: 7 books for $37.98

Bookstore 3 has a sale: 9 for $42.73

What is the best price for 5 books?

Students need to find the lowest unit rate, and then find the price for 5 books at that cost.

A tool to help track the proportional relationship between the unit rate and the quantity amounts is an Equivalency Chart:

We can chart the unit rate, and what the corresponding rates might be.

Bookstore #1 = $4.75/book      
Bookstore #2 = $4.43   
Bookstore #3 = $4.75

$$$ Price	$4.43	$8.86	$13.29	$17.72	$21.15	$25.58
# of Books	1	2	3	4	5	6

As we can see on the chart, 5 books at Bookstore 2 would cost $21.15.

Having the concrete chart helps students see the relationships between the numbers and their values, and will better understand what their calculations are representing. 

Think Before You Buy

So remember when you go shopping for a jar of salsa and there are two different sizes, or looking at big “value” pack of gum at Costco, look at the unit rate and see if you are really getting the best bang for your buck!