Earlier I posted a list of sources for math data to use with your gifted students. Here’s an example of how my class will be practicing percentages using some real data (inspired by the amazing math work by Dan Meyer).
With our state testing around the corner, I certainly have a responsibility to my students to give them opportunities to practice state standards. So naturally, I frame my project around some 6th grade California standards:
Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b). – Number Sense 1.2 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. – Number Sense 1.4. And a whole slew of math reasoning standards.
I’m also upleveling the standard by working with percents greater than 100% – always a bit tricky for students.
Since we are in review mode, I do a few “practice problems” just to test the waters. We’ll solve a few simple percent problems (What is 25% of 300? 50 is what percent of 450?). This does two things for me:
- Let’s me orient my students towards the skill they’ll need to utilize in the upcoming problem.
- Identifies the students who don’t have the basic skill down… I’ll park next to them during the rest of the activity.
The post “Should I Have Bought That Apple Product” provides some outstanding information regarding the price of Apple products and the increase in Apple stock. For example, if you bought an original iPhone in January of 2007, you dropped $499. If you bought Apple stock instead, that stock would be worth $1,460 or an increase of about 293%!
Again, borrowing from Dan Meyer’s rules for creating an intriguing and challenging problem, I begin with a visual of the original iPod (courtesy of Wikipedia) and throw out a bunch of questions to get the class talking.
- “What is this thing?” (first generation iPod)
- “How’s it different from the one you have now?” (black and white screen, buttons along the wheel, smaller hard drive, etc)
- “When did this iPod come out?” (October 23, 2001)
- “How much did it cost?” ($499)
Pose The Big Question
“Let’s say that instead of buying this iPod, you spent the same amount of money on Apple stock. How much would that stock be worth now?”
I then open up a round of inquiry (using the language of Melanie Montgomery’s Math Icons). During this time, students get thirty seconds to consider what information they need. Then I answer as many of those questions as I feel necessary. In this case, I’ll answer the following questions (oh, and I try to answer them all visually – I used screenshots from Yahoo’s finance webpage for example):
- How much did the iPod cost when it came out?
- How much did Apple stock cost on that day?
- How much is Apple stock worth now?
I then allow students to partner up and take a crack at the big question. Why partners?
- Collaboration is awesome.
- But too many cooks in the kitchen leads to chit chat and free-riders.
- I also leave the solo option available for reasons explained here.
- This frees me up to sit with students who I identified earlier as lacking pieces of the base skill.
I’m also emphasizing organization of work in these activities. If their work requires any interpretation on my part, I send them back to relabel, restructure, and reorganize. Students are utilizing both depth and complexity and some of the math icons to make their work clear.
We wrap it back up at the end and see who got the closest to the correct percentage. I’ll ask for some of the 6th grade skills students used to answer the question. We talk through their thinking a bunch too.
It’s always fun to leave them with a question (perhaps an assignment for home?). In this case, I uncovered an ebay auction selling a first generation iPod (new in box!). It sold for $325. Students then determined the percent that they would have lost by selling the iPod. Students could also investigate the percent difference between the stock option and the iPod’s
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