In the recent Math Fundamentals problem *Count the Discount*, students calculated the price of a jacket after it had been on the sale rack for five days. Each day on the sale rack, the price was discounted an additional 20%. Submitters used four different methods to figure out the new price each day.

The most common method by far was to multiply the current price by 0.2 to find the amount of the discount, and then subtract that from the current price to get the new price. (Many students also knew that 20% of 100 is 20, without doing any arithmetic.)

Charlotte C, Steele Elementary SchoolOn the first day the jacket is $100.

Percent means out of a hundred, since it was 20% of 100, It was obviously $20. To make sure I multiplied 100 by 0.20 to figure out the percent. On the first day $20 was taken off of the jacket. 100-20=80

On the second day the jacket costs $80. Since The jacket isn’t $100 anymore My first method is harder so I will stick to the second method. 80 multiplied by 0.20=16. Now the jacket costs $64 because the discount was $16. 80-16=64

Breanna C, East Middle SchoolIf the coat is originally $100, and you are taking 20% off the item, then you will use multiplication. To make the equation, you will end up having to convert the percent into a decimal. The equation will be $100 times .20 which equals $20.00. Then you will subtract that amount from the total.

Some students calculated the 20% by first finding 10% and then doubling the result. I wonder if the students who used this method didn’t have a calculator and thought this would be a little easier to do in their heads.

Natalie V, Seminary Hill School

- I found 10% of $100.00 ($10.00), and multiplied it by 2.($10.00 x 2=$20.00)
- I subtracted the first day’s discount ($20.00) from $100.00, and the answer was $80.00.( $100.00 – $20.00= $80.00.)
- I found 10% of $80.00 ($8.00) and multiplied it by 2. ($8.00 x 2 =$16.00) That is the second day’s discount.
- I subtracted $16.00 from $80.00 and the answer was $64.00. ($80.00 – $16.00 = $64.00)

Ria D., Laurel SchoolThe steps i used to find the percents were

- first i divided the numbers by 10

- next i multiplied that # by 2 to get 20%

-then i subtracted the 20% from the original #

Another method to find 20% is to divide by 5, which this next student did because he wasn’t sure how else to figure it out. *(Aside: What experiences do we need to provide students so that they develop the understanding that multiplying by 0.2 and dividing by 5 are the same thing? I don’t mean teaching procedures for converting from percents to decimals to fractions, but really developing true understanding.)*

Praeek D, Highlands Elementary SchoolI subtracted $20 from $100, because the text said the price would go down 20% every day, and 20% of $100 is $20. I got $80, so I put it down under price, and beside 1st day, because it was the price on the first sale day.

Next I divided $80 by 5, because I didn’t know how to get 20% of $80, but I knew 100% dived by 5= 20 %. I got $16.00, so I subtracted $16.00 from $80, because the price had to go down 20%, and 20% of $80 was $16.

The last method we saw is the one that I would use, since it involves one step instead of two to find the new price each day.

Zoe B, Birch Wathen Lenox SchoolTo solve the problem, I multiplied the total by .8 each ‘day.’ I did this because after the 20% discount, the item would be 80% of the price.

Developing facility with percents gets a lot of emphasis in elementary school, and it would be super if kids could use all these methods equally well and decide which one they like best, or which is best suited for a specific situation. If your students tended to use one of these methods, what would they think of the others? Did you have any conversations with them about different methods and how they’re related? What method is most popular in your classroom?

Some ** Count the Discount** links in case you are interested:

- The problem [requires a Math Forum PoW Membership].
- Information about accessing “Count the Discount” (and a selection of all our PoWs) for 21 days with a free Math Forum trial account.
- Information about becoming a Math Forum Problems of the Week Member. Consider starting with a $25 membership, which gives you access to all of this year’s Current PoWs — and now you can create 36 student logins as well!