Thank you 101qs.com

This past week was a humbling reminder that I still have a long way to go before I'm satisfied with my ability to be an effective teacher.

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.  

Making "Real World" Problems Feel More Real

Third week of school, and I am feeling more and more satisfied with the amount of problems on which students have been working. Starting with my Geometry classes working on the great transversal tape and sticky activity that I found on the wonderful problem based learning curriculum maps (that I adore exploring). The activity didn't go quite as planned because I wasn't able to make copies of the handouts, but the students worked well none the less.

Those Geometry classes also had fun tackling some logic puzzles as we started talking about forming proofs and deductive reasoning. I was very thankful that my wife and I were able to visit her grandparents last weekend, and while there her grandmother gave me a book titled "The Brain Game." The book has 27 intelligence tests "that will reveal your unique abilities" like an IQ test. 

When I first saw it, I instantly thought of the possible problems and tasks I could pull from for the students, and thinking about the proof lessons coming up, I was look at the logic tests for some gems. One of the puzzles involved blue wombats, and it was a nice starter before we started proving angle relationships.

Moving to the Algebra 1 classes, I tried my hand at implementing a 3 Act task today with a Pepsi Points task  that I also found using those wonderful curriculum maps. I am looking forward to talking with the kids on Monday about the court case involving the person who tried to redeem pepsi points for a jet, and today they were really into estimating how much things cost and starting to figure out how many points it would take to get the jet. This was also a fun task because I got to talk about my experience with my dad riding in his van and stopping on the side of the rode to pick up pepsi bottles for the caps, so that he could redeem the points for stuff.

The fun did not end with Algebra, thankfully, as my seventh graders got to work on a problem about designing a model of the solar system, a problem about McDonalds, and a problem about the Curiosity Rover. They were working with exponent properties and scientific notation, and problems about space and the McDonald's serving 1% of the world's population seemed to fit. I loved showing them pictures of some really cool planets and stars, and they were really interested in how the Curiosity Rover landed. Infecting kids with the wonders of space explorations is my favorite past time. The fun again came in when I was able to relate the problems to experiences from my life. They seemed to enjoy some funny stories from my childhood when my mom worked as a manager at McDonald's, and I would play around the store in the freezer, in the drive through (scrounging for dropped change for a small fry), and wearing the headsets listening to the drive through orders. One particular group of girls found the idea of a car coming through the drive through while I was looking for change quite funny.

I started thinking after having the chance to share the stories about myself to my students that being able to connect these problems to my life really seemed to help make the work we were doing more meaningful. The students weren't just working through problems from some foreign book, or even good problems that aren't related to anything. Not only were students given an opportunity to work on interesting and challenging problems, they were able to see these problems as something more than just a math problem. Through telling my little stories, I felt that I was able to make these "real world problems" more real.

Ordering Pizza

Once again, a problem idea comes from West Virginia. While I was waiting in line at a general store, I noticed the store's menu for pizza. Unfortunately, I forgot to snap a picture, but I did write the prices down.

Pepperoni and Cheese is $10.99

Each additional topping is $1.59

Toppings
Sausage, Onions, Green Peppers, Ham, Mushrooms, Bacon, Banana Peppers, Olives, Sardines.

A pizza with everything is ???

The problem is straightforward for a student. Multiply 1.59 by nine, and add that to 10.99. However, the resulting price is not what the store advertised. Once students found the obvious answer, I plan on showing them that the store is selling an everything pizza for $17.99.

Now the question is, why would they sell an everything pizza for $17.99, when it would make sense to sell it for $25.30?

Why they would charge $1.59 for each topping when their everything price indicates that they can afford to only charge about $0.78 cents for each topping?

I am glad that I found this problem because I'm not sure of the answer, and it would be interesting to see what students came up with with regards to the possible reasons for the stores pricing. I would be interested to find out what they would charge for an everything pizza, and it would be interesting to see how they support their decisions.

This would also be extended to other businesses and how they go about deciding on their prices, and I could see a connection to systems of equations and tall about weighing cost versus revenue.

What do you think about this problem? Have you seen stores price items in perplexing ways?

Train Speed

While working next to the train tracks in West Virginia, I was lucky enough to see three trains go by. It's possible that it was the same train going by three times.

At any rate, I was wondering, how fast was the train moving, so I took a video as it went down the tracks. 

That would be my Act 1, and from here the students would go about figuring out how fast the train was moving.

I could see this problem being used in a unit about rates and unit co versions. I think it could seve as a nice quick activity to get students thinking and working. 

There are a lot of angles to solving this problem. They could find the carts per second and convert to miles per hour, or they could see how long the driveway is and find out how long it takes a cart to travel that distance.

I might try to give them the original video file and let them manipulate to find the time from there.  

What would you do with this video, and what else have you done that's similar? 

Octagon Table

While visiting family in West Virginia, I came across this table at their river lot. I'm wondering the angle at which the wood was cut. 

I can see this as being a good problem for getting into polygons and how they're built from triangles, and I like the link to carpentry. 

I can see having the students build their own table top with a varying number of sides, and figuring out what angle to cut the wood cross sections.

I'm thinking that this would fall under common core standard G-MG-A.1 or G-SRT-B.5. What do you think, and what would do with this problem?