Some colleagues recently told me about an activity they had used in class called "Math Market". I'm not sure who originally created it. The teacher who shared it with me learned it at a math conference several years ago. I decided to give it a try with a Calculus class that was just finishing up a unit on integration.
Here is how the activity is run. Students work in small groups (we had groups of three). Each group starts with $5 and selects a captain who can buy questions of different levels of difficulty from the market. Easier questions cost less and have a smaller profit. More difficult questions cost more and have a higher profit. The captain takes the purchased question back to their group to solve. Once they all agree on a correct solution, the captain returns to the market to sell the solution for a profit. The card is added back to the bottom of the market pile and some other group will have an opportunity to buy it. If their solution is correct, they buy a new question and continue working. If the solution is incorrect, they have to buy the question again to attempt a revised solution (or they can purchase a new question at a different level of difficulty). We decided to purchase the solution at a reduced price ($1 less) if they forgot to include the "+C" at the end for the constant of integration. The easiest questions were free so that if groups went bankrupt with an incorrect solution, they would still be able to "buy" another a problem.
I printed the questions on coloured card stock and cut them out. Each question was marked with its level of difficulty. I also added a letter to the card so that it would be easy to find its solution to check the answers.
How it Went
I like that students got immediate feedback on their work. If it was wrong, they had to work with their group to correct their mistake. This was a test review for the class so there were lots of different types of problems mixed together and students had to determine what strategy would be best to solve each problem. It is a nice way to introduce some interleaved practice. This activity could be done with nearly any topic but it worked really well for integration as the questions were challenging and took them some time to solve. This made the market area less crowded.
I'm sure there are lots of variations of this activity. If you have some suggestions, I'd love to hear about them.
My nephew visited me this summer during a family vacation. He will soon be starting grade 11 (junior) year. He is a hard working student and would like to study mathematics in university. He understands that this is the year when he needs to start thinking about university and scholarship applications. We started chatting about his post-secondary plans one evening and he asked me two questions. The first question was, "What can I do to make sure I have competitive university and scholarship applications?" The second question was, "What sorts of careers are possible with a mathematics degree?" Here is the advice that I offered him.
Break Out from the Pack
As a high school teacher, I have written a lot of reference letters. The hardest reference letters to write are for talented students who come to class every day and work hard but have nothing to set them apart from the other 30 or so students in class. Ask yourself, "What sets me apart or makes me different and special?" Here are some things I suggested to my nephew:
Careers for Mathematians
There are some great careers for mathematicians that don't get a lot of press. Here are some careers that I find really interesting:
So what advice would you give to a grade 11 student who is interested in a career in mathematics? I'd love to know what you think.
As a math teacher, I always love to see folks doing real math on television. Last week, on The Amazing Race Canada (Season 3, Episode 7), there was a 'tricky' mathematical challenge. Contestants were given a list of Air Canada flights and asked to create a flight plan using Air Canada destinations from around the world. They had to find a set of flights that had a total flight time of 25 hours (or 1500 minutes). They also had to ensure they used "a combination of routes that travel to at least three continents". Calculating the flight time was the first hurdle. Since arrival and departures are listed in local time and the vast majority of these flights crossed multiple time zones, contestants had to use the universal time code for each city to correct for time changes. A number of teams were confused right from the start (there was a lot of fixed mindset talk from the contestants). One team used an 'Express Pass' to skip this challenge while two other teams gave up and took a 2 hour time penalty instead of continuing with the challenge,
That is a lot of flights! There are 12 flights listed on the Europe board, 11 flights on the Asia Pacific board and 15 flights on The Americas board. If we use just one flight from each board (so that we visit three continents), there are a total of 1980 combinations (12*11*15=1980). The rules state that we have to visit at least three continents but it doesn't say how many flight to use so we could have a flight plan with more than three flights. If we add one additional flight to make a flight plan with four flights, now we have 69300 possible flight plans (12*11*15*35=69300... one flight from each board and any one of the remaining 35 flights). That is a LOT of trial and error. The two solutions shown on the episode contained 4 flights. Are there any 3 flight plans that would work? Here is what I did.
First I got some screen captures of the flight boards so I could read all the flight times. Then I put them all into an Excel spreadsheet to calculate the flight times in minutes. Next I played with Excel for about an hour to try to find an efficient way to calculate all the combinations of flights that I wanted to try and then gave up. Instead, I created a quick program in Python to calculate all the possible sets with just three flight plans. This turned out to be much easier than using Excel (just 8 lines of code).
for i in AList:
for j in BList:
for k in CList:
Now, assuming that I calculated the correct flight times in my Excel spreadsheet, this gave me three possible solutions:
1- AC025 Vancouver to Shanghai, AC824 Toronto to Amsterdam, AC541 Toronto to Seattle
731 + 453 + 361 = 1500 minutes
2- AC084 Toronto to Tel Aviv, AC898 Edmonton to London, AC962 Toronto to Bogota
635 + 522 + 343 = 1500 minutes
3- AC056 Toronto to Dubai, AC1904 Toronto to Edinburgh, AC1973 Halifax to Calgary
767 + 408 +325 = 1500 minutes
The two solutions that were shown on the episode using four flights are below:
AC480 Toronto to Montreal, AC918 Toronto to Miamai, AC882 Toronto to Copenhagen, AC007 Vancouver to Hong Kong
77 + 192 + 447 + 784 = 1500 minutes
AC230 Vancouver to Calgary, AC541 Vancouver to Seattle, AC1910 Montreal to Nice, AC009 Calgary to Tokyo
87 + 316 + 457 + 640 = 1500 minutes
There was a nice article posted online that interviewed the Air Canada captain that handed out the clue cards for the challenge. He mentions the factors that he said made this such a challenging competition.