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Ratios & Percentages:

Proportional Numbers Aren't Cheesy

 

Today's snack: Try your favorite flavor of those individual cheese rounds they sell at the deli counter. Mmm! Does yours weigh one ounce? How many of them, together, would weigh a pound? (NOTE: there are 16 ounces in a pound) Wash down your cheese treat with cranberry-apple juice.

 

 

--------------------

 

Supplies:

2.5 pounds of individually-wrapped cheese rounds

(they are 1 oz. apiece, so that's 40 altogether)

Paper | Pencil

 

 

Proportional numbers help us understand relationships between things. You can figure out the proportions between numbers to see how much a food item would cost in the grocery store, or how far it is between cities on a map. It's a really useful tool, and it's easy to set up a proportional number comparison.

 

Let's do it with cheese! Everybody loves the little snack cheeses you can buy at the deli counter in the grocery store. They are a little expensive, but so full of nutrition.

 

Let's say that these little cheeses cost $6.32 per pound. So to buy one pound of the cheese, you would have to pay $6.32.

 

Lay out 16 of the little cheeses. There are 16 ounces in one pound, so those 16 little cheeses weigh one pound, all together. Since we are saying that one pound of cheese costs $6.32, how would you figure out how much each little one-ounce cheese costs? Divide $6.32 by 16. Answer: 39.5 cents.

 

You have 40 little cheeses laid out. How much would different quantities of them cost? To do that, using the power of proportional numbers, we can multiply.

 

Say, for example, that you want to know how much a pound and a half (1.5 pounds) of cheese would cost. Besides the 16 mini-cheeses you have already laid out on the table, add another eight, for a total of 24. That's a pound and half of cheese - 24 ounces.

 

How do you find out how much 1.5 pounds of cheese costs? Multiply 6.32 x 1.5. It comes to 9.48. Put a dollar sign in front of it, and you would know that a pound and a half of that cheese would cost $9.48. Remember how we figured out that each ounce of cheese costs 39.5 cents? We can use that proportion to check the result. Multiply 24 ounces x 39.5 cents. Answer: $9.48.

 

That's a proportional set of numbers!

 

Using this proportional concept, copy this chart on your paper. You can group the additional cheeses on the table to help you visualize each problem.

 

Do the multiplication needed to fill in the rest of this chart. You will show how much other amounts of this cheese would cost:

 

 

Weight of cheese 1 1.25 1.5 2 2.5

(in 1 lb.)

 

 

Price of cheese 6.32 9.48

(in $)

 

 

Now that you see how proportional numbers can help you figure things out, notice that you can add numbers quickly to get the same answer.

 

Once you figured out that one pound of cheese cost $6.32, and one and a half pounds cost $9.48, you could add those two to show how much two and a half pounds cost. Add $6.32 plus $9.48 = 2 pounds cost $15.80.

 

You can check that with your proportions - multiply 6.32 times 2.5, add a dollar sign, and bingo: it's $15.80.

 

Best of all, now it's time to eat the cheese! Groups of students can eat them, or if you are alone or have just a couple of kids doing this activity, brainstorm who you could share your cheese with. Keep it cold in the meantime! And don't forget to share your charts and what you learned about proportional numbers, too.

 

 

By Susan Darst Williams www.AfterSchoolTreats.com Math 2012

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