We have had students change teams on the first day of each unit this year. Which is something, as I’ve always hesitated to change up teams that are working well together in the past. But since we are now on Unit 5, it’s the expectation.

For the Logic/Angles/Triangles unit, we gave students different conditional statements, along with their converses, inverses, contrapositives, and biconditionals. So, for example, the following five cards made a team:

If the sum of two angles is 90°, then the angles are complements of each other.

If two angles are complements of each other, then their sum is 90°.

If the sum of two angles is not 90°, then the angles are not complements of each other.

If two angles are not complements of each other, then their sum is not 90°.

The sum of two angles is 90˚ if and only if the angles are complements of each other.

Students learned during the first lesson about converse, inverse, etc., and each team had their own card set for discussion.

For the Polygons unit, we used different non-special rectangles, trapezoids, parallelograms, kites, rhombi, and squares. Which wasn’t totally easy, as students were unfamiliar with kites and don’t always distinguish rhombi from squares.

For the Dilations unit, we gave students cards such as the following:

3-4-5

32-60-68

18-80-82

9-40-41

12-16-20

Chaos ensued.

I overheard several comments:

11-60-61: November 60, 1961

Where is she?

We sorted a team by 2 digits – 2 digits – 3 digits

Is it a right triangle?

Is it a right triangle? Can you tell whether you have a right triangle?

Then they realized that they all had right triangles.

But they still didn’t know how to sort themselves into a team.

More chaos ensued.

And at some point, I realized that I would either have to intervene, or we would spend our entire first day of the new unit on Dilations sorting into new teams.

Does anyone know what our new unit is?

Dilations.

Oh. Dilations.

Can someone give me a card?

3-4-5.

How did I get so lucky?

5-12-13.

22-120-122.

11-60-61.

We wrote several of them on the board.

And then they found their Pythagorean families with the primitive patriarchs.

Another class sorted themselves by columns instead of rows (see card image below).

And another class sorted by rows correctly, thinking about scale factor, but had no idea that they were side lengths of right triangles.

Card sets are available at this link if you’re interested. Share them back with us if you improve them!

And let us know if you have any ideas for our remaining units, as we have a lot to live up to after the Dilations team sort.

6-Right Triangles

7-Circles

8-Coordinate Geometry

9-Geometric Measure & Dimension

10-Modeling with Geometry