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**Thought for the day**: Creative Math Prompts are great tools for differentiation, because students respond at their own level of thinking.

**Concepts**: polygons; segments; lengths and angles; parallel segments; (possibly tiling (tessellations), symmetry, area)

**Beginning**

*I notice *that the polygon has 6 sides. (It is a hexagon.)*I notice *that it looks different than the hexagons I usually see.*I notice *that the hexagon has three different side lengths.*I notice *that opposite sides are the same length.*I wonder *how the lengths compare to each other.*I wonder *if I could find a shape like this in real life.*I notice *that opposite sides are parallel.*I notice *that I can split the hexagon into two quadrilaterals (or pentagons) that look the same.

**Exploring**

*I wonder*how many ways there are to split the hexagon into two congruent parts.

*I wonder*if I could make this shape from equilateral triangles.

*I wonder*if I can make other hexagons with just three different sides lengths.

*if I can make all 6 sides different lengths without changing the angles.*

I wonder

I wonder

*that the (interior) angles in the hexagon are all the same size (1-third of a circle, or 120°).*

I notice

I notice

*I wonder*if the opposite sides have to be parallel whenever the hexagon's angles are all the same.

*I notice*that the hexagon looks the same if I turn it upside-down.

*I wonder*if this is always true when I make a hexagon with opposite sides parallel and congruent.

**Creating**

As they notice and wonder, students may create their own polygons satisfying various conditions. Many of their creations will flow from things that they have wondered about. For example, they may

Create other hexagons whose angles are all congruent but whose sides are not.

Try to create other kinds of polygons whose angles are all congruent but whose sides are not.

Put the hexagons together to create *tessellations *(by joining them to create patterns with no gaps or overlaps).

Create other patterned designs by combining their hexagons in different ways.

**Reflecting and Extending**

*I notice*a connection between parallel opposite sides and congruent opposite sides.

*I wonder*if the hexagons would fit together to make a "honeycomb" pattern.

*I wonder*if I can make heptagons or octagons whose angles are the same but whose sides are not.

*I notice*that it matters whether the polygon has an even or an odd number of sides.

*I wonder*if I can reverse the problem and create hexagons who sides are all congruent but whose angles are not.

If so,

*I wonder*if their opposite sides will be parallel.

*I wonder*what the area of the hexagon is. (Some students might try to measure it in

*triangular*units by asking how many equilateral triangles it would take to make it. Consider using pattern blocks!)

**Notes**

See Problem #4 in Problem Set 3 of the Intrepid Math series for a more structured problem on the same topic (or just for more information about it).

Pattern blocks are an excellent tool for exploring the ideas in this problem—for all ages, but especially for younger students.

Back to Creative Math Prompts Previous prompt for Early Grades Next prompt for Early Grades