High-Five

This task is one I always started the year with. It’s a great task and enages students in a way that may involve physical modeling, initially (actual high-fives).

Opening

To introduce the task, ask for three student volunteers. Tell the class that these three students decided to high-five each other when they entered the classroom. And they wondered how many high-fives it would be if they each high-fived everyone in the group once. Let’s try it. Count the high-fives as the three volunteers act it out.

After students count all three high-fives, introduce the task of finding how many high-fives for 6 students. Send them to their groups and monitor student work. Look for students to physically model, draw diagrams, and make tables of values.

Work Session

As students solve, this problem, extend the task for groups who are ready by asking, What if it was 12 students? 16 students? 21 students? (these numbers can be adjusted to suit student needs). The goal, here is to keep students thinking and also provide opportunities for them to notice, explain, and use patterns to solve additional challenges you provide.

Take note of different strategies and representations student groups use to solve the task. Keep a record of these strategies and begin to think how these could be structured/sequenced in the closing to help make the mathematics they are doing visible. Many times, I select the least efficient strategy to go first. These usually include a lot of drawings and maybe some errors. Then, I move to a strategy/representation that builds nicely on the first, and so on.

Closing

To close this task, ask students to share their solutions. Be purposeful, here. Choose which groups share first, second, third, etc. Not all groups need to share, the sequence is what matters. You want the solutions and strategies used to build on each other – exposing more mathematics/mathematical structure as they go.

Facilitate discussions between groups sharing and the rest of the class by asking:

  • What patterns did you notice?
  • Explain your diagram/picture so we can follow your mathematical reasoning.
  • How does this representation/strategy relate to the previous group’s?
  • What mathematical rules did you come up with to explain the pattern and use to solve the problem?
  • What mathematical structures did you notice as you worked?