### Where did we start?

As we were exploring 2D shapes, we got some coloured card cut into rectangles.

First job was to rule a diagonal line across the rectangle as a cutting guide. After cutting down the line we produced 2 new shapes - a pair of triangles - Viola!

Some discussion ensued - What type of triangles were they? Were they both the same? What do you mean by same? What types of triangles are there? etc

Next challenge was to see what shapes we could make with the triangles. Here's a few pictures of our results.

We found that we could use all 4 triangles to make shapes from a quadrilateral up to a dodecagon.

- no overlapping allowed

- had to join at an edge not at a corner

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**4 Sides**

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**5 Sides**

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**6 Sides**

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**7 Sides**

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**8 Sides**

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**9 Sides**

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**10 Sides**

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**11 Sides**

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**12 Sides**

**Then we went backwards...**

**So we worked out that we could make a dodecagon if we had 4 triangles.**

What if we only had 3?

Hmm...so we took away one triangle and found - hey we can only make up to a nonagon!

And when we had two triangles, we could only get up to a hexagon!

**Amazing moment of understanding!**

"Hey! That's a pattern like the 3 times tables!" exclaimed one perceptive student.

"1 triangle makes a 3 sided shape.

2 triangles can make a 6 sided shape.

3 triangles can make a 9 sided shape.

4 triangles can make a 12 sided shape."

Get the pattern?

**Parting Words**

"So," I said to them at the end of the maths lesson. "What is we had started with quadrilaterals instead of triangles? What would be the pattern then?"

Or if we started with pentagons?

Or if we...?

Firstly, congratulations on topping 1000 page views. :)

ReplyDeleteThe exploration of shapes and how they interact when placed together can lead to many discoveries. The patterns made and shown above have been able to produce irregular shapes with up to twelve sides.

A question for the class...

Starting with quadrilateral, you can obviously make a four sided shape but can you use quadrilaterals to make shapes with an odd number of sides without overlaying them? (Hint: try using parallelograms without 90 degree angles)

An interesting post leaving the class with questions to keep them thinking of possibilities. :)

@RossMannell

Teacher, NSW, Australia