I call these types of activities, "Numeracy Prompts". The term was inspired by Peter Liljedahl during one of his sessions at SUM 2010. The idea is to create a rich environment where students are required to make multiple mathematical decisions. The situation should be vague enough to provide freedom, but defined enough to allow mathematical modeling. A good numeracy prompt allows every student to begin by being accessible to elementary skills (a low floor). It also has a never-ending supply of mathematical depth (a high ceiling). These two attributes allow students to interpret the situation at a variety of skill levels. There are several reasons why I use numeracy prompts:
1) They are great formative tools at the beginning of the year.
2) They can be used over and over because answers and interpretations typically vary.
3) They are self-enriching. (the problem grows with the student's ability)
Some educators call these types of activities tasks, problems, or projects. I like the term "prompt" because is implies a vagueness that encourages play. A prompt may end in a product (much like a project) or give a list of requirements (much like a task) but leaves the process up to interpretation. The NHL Dream Team numeracy prompt can work skills like basic operations, percentage, unit conversion, and scientific notation. Again, the skills required to solve depend on the solution method chosen by the solver. The task is as follows:
NHL Commissioner Gary Betman has finally announced that the Winnipeg Jets are returning. In order to construct the team, he has enabled a fantasy draft. As the general manager, it is your job to put together a dream team. You can take any player from any team as long as you follow these rules:
1) No more than 65% of players can be from one conference
2) You can't take more than 2 players from a single team
3) You must chose 15 forwards, 8 defense, and 3 goalies
4) The total salary must be under 59.4 million dollars
5) No single player can be paid more than 10% of the salary cap
6) You cannot spend more than 50% of your money on one position (forward, defense, or goalie)
If you provide this question in the form of a memo to your class along with a list of every player and their salaries (available in any regular season edition of "The Hockey News" or online at www. nhlnumbers.com), they can begin right away. You may want to develop an alternative for those students who are not interested in hockey, or change the sport to fit your class' preference.
Mathematical discourse is best developed in groups, so pairs or groups of 3 would be effective. When groups begin to hammer down their final lists based on reputation of players, it may be interesting to extend the problem a little:
1) Get player stats for each of their picks. Whose team is statistically the "best"?
2) Fiddle with the rules to see if that would change any of their picks.
ie. Now a player can make 15% of the total salary cap
You can only have 6 players from any single country
The results are best reported in a chart format. I never miss an opportunity to model good statistical note-taking to my students. One of the options could look like this:
| Name | Position | Salary | % of Cap |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
Let the students work around in the mathematics. If they need a refresher on percent or make a calculation error, let their group members work through it with them. Don't deprive them of a calculator! The mathematics lies in the decision to make a calculation, not in the actually calculation itself. Let students struggle with mathematical give-and-take, not with the onerous task of carrying 1s.
Numeracy prompts are excellent ways to tie engagement to basic skills. They alleviate the constant pressure for right answers. The basic skills become masked because they are no longer the end--they are now a means to an end. That is how basic skills need to be approached. Prompt, task, project--whatever you call it, it is just one more way to open up math, set it before your students, and allow them to be curious.