Lesson 3

Many Ways to Make a Hexagon

Est. Class Sessions: 1–2

Summarizing the Lesson

Conduct a class discussion about decomposing and composing hexagons.

Ask:

X
  • How did you decide which shapes to use? (Possible responses: I tried until I found pieces to fit. I tried to match sides on the hexagon with other blocks.)
  • Which shapes wouldn't work? (the skinny tan rhombus and the square)
  • Why couldn't you use the square? (The corners don't match but the sides do. If you match the sides you can't fill the hexagon with any other pieces if you use the square.)
  • Why couldn't you use the tan rhombus? (The corners don't match, but the sides do.)

Ask a pair of students to come to the front of the class to display one of their solutions. Have the pair briefly describe their solution. Post the solution so all can see it.

Ask:

X
  • Does anyone have another solution? Please come to the front of the class to share it.
  • Do we agree that this is a new solution?

As new solutions are posted, the class should compare all to verify that they are new to the display and not a new orientation for a solution already posted. Continue until all eight solutions have been presented and added to the display.

As students share their solutions, the rest of the class should look to see if they have the same solution and check off solutions on their own copies as they are discussed. Facilitate the discussion so that it is the students who check each time one of the combinations is presented and who verify that the new solution is indeed different, not just a previous solution with a new orientation.

After all possible solutions are displayed, compare various solutions.

The following example compares a solution using two trapezoids to one using three triangles and one trapezoid:

X
  • How are these two solutions alike? (They both use trapezoids.)
  • How are they different? (One has triangles, and the other one is just trapezoids.)
  • How was one changed to make the other? (Just take one trapezoid off of the first one and put three triangles there instead.)
  • How could we tell that would work before we tried it? (Because we found out three triangles fit on one trapezoid so we could just make the switch.)

End the lesson by comparing a few other solutions.

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