Thought for the day: Some noticing and wondering prompts work for learners of all ages!

Concepts (depending on age and experience): addition strategies and patterns; analyzing, justifying, and extending patterns; organizing data; sums of consecutive numbers; multiplication and division; symmetry; counting combinations; finding patterns and formulas for quadratic relations

Examples of noticing and wondering

I notice a triangle made of colored circles (with patterns in the colors).
I notice that the big triangle is made up of three small triangles, one at the top, the left, and the right.
I notice a trapezoid with a circle on top.
I notice a hexagon surrounded by three circles at the corners of the triangle.
I notice three overlapping rectangles in the picture.

I wonder why there is a circle missing in the middle.
I wonder how many circles would be missing if the triangle had 4, 5, or more circles on each side.
I wonder how many circles I would need to make triangles with 4, 5, ore more circles on each side.
I wonder how many parallelograms I could find in the picture.
I wonder what would happen if I filled the circles with numbers.

Notes

isn't it amazing how much there is to notice and wonder about such a simple picture? How many more ideas can you come up with? Do any of them lead to new problems to explore?

The final "wondering" about filling the circles with numbers is what I had in mind when I created the image, but I have learned so much from others' observations and questions! To see more about the original problem, visit Numbers and Operations under the ACCME Books menu, and look at the activity titled "Triangle Sums." You can download a complete activity based on this image this image for free.