The Shoe Sale

This problem is from Peter Liljedahl's site.

The Shoe Sale
You decide to take advantage of a buy 2 pair get 1 pair of equal or lesser value for free sale at the local shoe store. The problem is that you only want to get two pairs of shoes. So, you bring your best friend with you to the store. After much deliberation you settle on two pairs of shoes – a sporty red pair for $20 and a dressy black pair for $55. You friend finds a practical cross trainer for $35. When you proceed to the check out desk the cashier tells you that your bill is $90 plus tax (the $20 pair are for free). How much should each of you pay? Justify your decision.

Peter lists this problem under "Senior High School (10-12)." I give it to both my 6th and 8th graders. I like this problem because I like hearing how kids think about "fair sharing." A few 6th graders think each person should pay $45. I don't think these kids have too many friends. (That was mean.)

One of my 6th graders says one person should pay 2/3 of the $90 and the friend pays 1/3. But her answers are $59.40 and $29.60, respectively. My math says 2/3 of 90 is 60, so I call her up to explain. She has her calculator in hand, and I see her punch in .66 while mouthing "two thirds."

It was an opportunity for me to yell and scream at the children for turning a perfectly good number of 2/3 into mush.

4/22/14 4/22/14

Discount and Sales Tax

Instead of doing the above exercises in our textbook, I had my 6th graders do this:

Shopping Contest at Target

Let’s pretend Target has a contest. The contest is for shoppers to find merchandise from their online store.

Contest rules

You must choose at least 10 different items.
The items must come from at least 5 different departments, such as footwear, kitchen, clothing, toys, etc.
You may buy more than 1 same item — you can buy 2 or more packs of athletic socks.

The winner

The winner is the shopper whose merchandise receipt totals exactly $500 or closest to it — without going over. They get to keep all the merchandise!

Your task

Phase 1: Go to Target’s website and find some items that you’ll want to get for yourself and your family. List the items and their original prices in the table provided separately.

Phase 2: The store manager (really, it’s your teacher) then announces the percent discounts for different categories of merchandise. Write these down below. Apply these discounts to your items and calculate the new sale prices.

Phase 3: The current tax rate for our city is 8%, so you must add this to your total. In this phase, you get to add or remove items on your shopping list to reach the target goal of $500 without going over.

I only did Phase 1 with the kids, my sub supposedly did Phases 2 and 3 with them. (I wanted to do the rest of the lesson with them when I return from NCTM — and after spring break — but they voted to continue the lesson with the sub as they were really into the task. I'll find out tomorrow when class resumes.)

Why this task

You can change everything about it. Shop somewhere else instead of Target.
Change the rules depending on time available and access to computers. Are there enough computers for each kid or do they need to work in groups of 2 or 3? My kids were in pairs. (We have enough laptops, but at least 30% of them have issues.)
I like the idea of not going over a certain amount — $500 in this case — instead of "whoever is closest to the target price" because I think it keeps the kids more reserved in their shopping spree. Students understand that if there were only 2 contestants, then the one with a final receipt total of $154 would win over the other with a $501 total.
Kids don't know what the exact discounts are until Phase 2, so this makes it a fun temporary secret. But they know to go over budget in Phase 1 because there will be discounts — not all departments have to have discounts either. Their totals in Phase 1 were in the $600 to $700 range because they also know that it'd be easier (faster) to remove items than add them later in Phase 3. They were also told that the discounts would be somewhat realistic, meaning Electronics will get a smaller percent discount, if any, than Clothing.
They'll become more aware of how much things cost — and how quickly they add up in the shopping cart.

Handout Discount and Sales Tax