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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?”

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…

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…

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

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.

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

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.

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

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.

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.