Thought for the day: Be equally interested in all ideas that your students produce, even when they don't take you in a desired direction (which they often won't)!

Concepts: polygons; lengths and angles; parallel; parallelograms (possibly symmetry)


Examples of noticing and wondering

I notice that the bottom isn't flat.
I notice that the whole shape is tilted.
I notice that the shape has four sides.
I notice that it looks like a "squashed" rectangle.
I notice that the opposite sides look the same length.

I wonder why it looks so tall.
I wonder if (or how) I could make the shape into a rectangle.
I wonder if the shape has a name.
I wonder if the some of the sides are parallel.
I wonder if some of the angles are the same.



Your students'  (and your own) ideas will be far more creative than the examples I showed above! Enjoy their inventiveness, and take the opportunity to learn about what they are seeing and thinking. These observations can inform your instruction.

Even the simplest images can lead to wonderful, rich conversations. If you look through your teaching manual and other materials, you will probably find countless images that you could use effectively as prompts. It's simply a matter of approaching them from a new perspective: begin by listening rather than telling.

You can use the image above with students of many different ages. Younger students will see more general features of the shape. You might eventually have them compare and contrast it with more familiar shapes such as rectangles. Older students may focus more on particulars such as side lengths, angles, parallelism, etc. For them, you might use the prompt to study the properties or develop possible definitions of a parallelogram.

It is very useful for students to see plenty of examples of geometric figures in "non-standard" positions or orientations. For example, none of the sides of this shape are vertical or horizontal. I once had a teacher in a professional development session exclaim that she wanted to "just squash it flat"! You can be sure that unusual orientations are bothersome to many students as well. They are not used to them, because textbooks often show such a limited range of possibilities. In fact, this can be a leading cause of misconceptions in identifying and analyzing geometric figures. 

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