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; tiling (tessellations);
Examples of noticing and wondering
I notice that the polygon has 6 sides. (It is a hexagon.)
I notice that opposite sides are the same length.
I notice that the hexagon has three different side lengths.
I notice that opposite sides are parallel.
I notice that the (interior) angles in the hexagon are all the same size (120°).
I wonder if I could make this shape by joining equilateral triangles.
I wonder if it is possible to make all 6 sides different lengths without changing the angles.
I wonder if the opposite sides must always be parallel when all of the hexagon's angles are 120°.
I wonder if the hexagons would fit together to make a "honeycomb" pattern.
I wonder if I can make a heptagon or octagon whose angles are the same but whose sides are not.
This Creative Math Prompt appears as a problem in which students try to create their own example of an image like this. See Problem #4 of Intrepid Math Set 3 on the Intrepid Math page of this site.
Students' responses may vary a lot based on age and experience. For example, younger students who are just beginning to understand the concept of lengths or angles may trace sides or angles in order to compare them. They may also make "looks like" observations: the shape looks like a parallelogram with two corners chopped off, or it looks like part of a bee's honeycomb, except that it is "stretched out."
Older or more advanced students may measure the angles or explore what happens to other measurements when they change certain sides and angles. Seeing that it is possible to create a hexagon whose angles are congruent but whose sides are not, they may check if it is possible to create a hexagon whose sides are the same length but whose angles are not all congruent. (It is!) They may also explore related patterns with other types of polygons.
Pattern blocks make a great tool for exploring shapes like the one shown in this prompt.