Green Olives

My 7th graders are working on "percentages of" problems currently, and late last night, I saw this problem on one of Don Steward's handouts.

There are 75 olives, 40% of which are green. I eat some of the green olives until 10% of the olives that remain are green. How many green olives did I eat?

How would you solve this? I solved it using algebra. Then, immediately, I thought, Fawnzie, since when do you use algebra to solve stuff like this. C'mon, do your rectangles.

I think of 40% as 2 of 5 boxes.

So, 75 olives must split into 5 groups of 15, so there are 30 green olives.

Then, I ate some olives to end up with only 10% of the remaining olives are green.

Well, since I didn't eat any of the 45 black olives, so these 45 must make up 90% of the olives remaining [in the 9 boxes], so 45 must split into 9 groups of 5.

Oh, look! I began with 30 green olives, I now only have 5 green ones left, so I must have eaten 25 of them.Okay, your turn.

There are 80 olives, 75% of which are green. I eat some of the green olives until 20% of the remaining olives are green. How many green olives did I eat?

I’d rather use the drawings than show them my work below.

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