What’s geo-dotting?  I have no clue but that’s what I’m calling this lesson.

We started by asking, “What do you notice?”

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Our favorites:

  • Looks like Pac-man
  • I see dots and they make a “Y”
  • Looks like someone went crazy with a hole punch

We needed to wrangle in student thinking a bit so we gave them some information…

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Unanimous vote. “I see a square and a triangle.”

We asked students to explain their reasoning and one said:

I know there are 7 corners, I mean “vertexeses”, and 4 of them make up a square which leaves 3. I can’t make a shape with less than 3 dots because then it’s not a shape. So the only shape I can make with 3 dots is a triangle.

We have a winner…

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Now that students had the hang of it, we went here next…

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What do you notice?

We let them play, talk, and share for a couple minutes and triangles seemed to be the shape of choice.  Then we revealed the mystery polygons.

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By now we felt students were ready to tackle the opening slide again.

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On our second time around there was no Pac-man or letters, only shapes.  But this time instead of just talking about the dots, students were encouraged to put their thinking on paper.

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Students used only the top three boxes for about 5 minutes. This allowed them to flush out each other’s misconceptions.

This helped students construct their own understanding.

After about 5 minutes we slow-released the following criteria, giving them one new nugget every 3 minutes:

  • Total of 5 shapes
  • No dots left over and each dot can only serve as 1 vertex for 1 shape
  • Shapes can overlap
  • Only 2 triangles
  • One square and one rectangle
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Students compared work to ensure the criteria was met.  “Looks like you have 2 rectangles in the bottom corner. Try again.”

As we wrapped things up, students came to the board and shared their solutions.

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My takeaways:

  • Talking about the shapes and their properties before moving to paper really allowed for students to engage in SMP#3 once we made the leap.
  • The slow release of information allowed students the opportunity to build problem-solving stamina.

If you want to give the lesson a try here’s the slides in a pdf file and student work mat. Please report back and let us know how it goes.  I’m wondering what takeaways you can share.

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