Nonetheless, I am feeling more comfortable with my ability to implement problem solving tasks with my students. I am very grateful for the wonderful community of resources that exists through the twitters and all of the blogs, and one in particular that I am excited to have started using is http://www.101qs.com/.
I had started my seventh graders working on representing percentage using equivalent expressions, when I came across a picture that led to a really interesting question about deciding between two coupons. The picture led to students noticing and wondering, which led to them thinking.
Which coupons is better, 30% off the entire purchase or 40% off one regular item?
Their first inclination was that, "it depends." Now came for the fun part, because they realized that they would be figuring out on what it would depend. What prices would cause you to choose one coupon over another? Does it matter how many items are in your cart?
They were split up into groups of three, and most every group started working through different purchase situations. Most began to find that the 30% off coupon consistently won out, and this led to a prompt for them to find a situation when the 30% off coupon would not be the better deal.
As groups worked through this portion, I could see the wheels really start turning. They were noticing different patterns, they were being strategic in the prices that they assigned to the one item on which the 40% off coupon would be used, they were thinking about the problem in creative and insightful ways.
When a student first gave me his answer, I didn't quite know how to respond. I expected that the groups would find an answer, but I anticipated solutions to start popping up later based on the progress they were making at the time. For several of the groups to start noticing that the one item had to be more than 75% of the total purchase in order for the 40% off coupon to be a better deal, really impressed me.
I was excited, and I was very proud to see them start with no more than a picture and some questions only to end with a powerful solution.
The best part of the solution was the extension afterwards. Having the conclusion that the one item had to be worth more than three fourths of the total in order for the 40% off coupon to be worth using, led to students observing that 30/40 reduces to three fourths. Their problem now became one of verifying whether that result would continue for other combinations of discounts, or if it was merely a coincidence.
All in all the problem was rich with great thinking and exploration, and so far it served as one of my best class sessions this year.
I am still struggling to present the problems more consistently and effectively, but I won't be able to improve if I don't try new things. Here is to my own exploration and discovery.
Which coupons is better, 30% off the entire purchase or 40% off one regular item?
Their first inclination was that, "it depends." Now came for the fun part, because they realized that they would be figuring out on what it would depend. What prices would cause you to choose one coupon over another? Does it matter how many items are in your cart?
They were split up into groups of three, and most every group started working through different purchase situations. Most began to find that the 30% off coupon consistently won out, and this led to a prompt for them to find a situation when the 30% off coupon would not be the better deal.
As groups worked through this portion, I could see the wheels really start turning. They were noticing different patterns, they were being strategic in the prices that they assigned to the one item on which the 40% off coupon would be used, they were thinking about the problem in creative and insightful ways.
When a student first gave me his answer, I didn't quite know how to respond. I expected that the groups would find an answer, but I anticipated solutions to start popping up later based on the progress they were making at the time. For several of the groups to start noticing that the one item had to be more than 75% of the total purchase in order for the 40% off coupon to be a better deal, really impressed me.
I was excited, and I was very proud to see them start with no more than a picture and some questions only to end with a powerful solution.
The best part of the solution was the extension afterwards. Having the conclusion that the one item had to be worth more than three fourths of the total in order for the 40% off coupon to be worth using, led to students observing that 30/40 reduces to three fourths. Their problem now became one of verifying whether that result would continue for other combinations of discounts, or if it was merely a coincidence.
All in all the problem was rich with great thinking and exploration, and so far it served as one of my best class sessions this year.
I am still struggling to present the problems more consistently and effectively, but I won't be able to improve if I don't try new things. Here is to my own exploration and discovery.
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