Warm Up: “Not A Half”
Print copies of the following template.
Use a curve, zig-zag, or scribble to divide squares into two as-close-to-equal pieces as you can get. Color one or both parts in different colors.
Unless you are a computer-powered super-genius, you will not produce two mathematically exact halves. Why not? Are these fractions? Why or why not?
Look closely. The sizes and shapes of resulting pieces are different. The areas of the resulting pieces are not equal... unless you’re some sort of math-art savant!
Activity: Playing with Halves
Let’s repeat the warm up, working from another copy of the same printout from above. This time divide the squares with straight lines. To start, use guide marks and rulers to divide squares into mathematically equal parts.
Using only horizontal, vertical, and diagonal lines, you can generate simple symmetrical shapes. Once each square is divided, color either one or both halves.
How are these shapes similar? Different? Equal?
Continue this exploration to make new halves in different shapes. Create divisions that combine horizontal, vertical, and diagonal lines. How did I create the halves below?
Challenge yourself to create new and different halves.
Study your halves. What makes each piece a half?
Notice the wide variety of halves that can be generated. Each of the primary-colored shapes above are very distinct from each other. What quality or qualities must these shapes share to be considered equal halves?
Do more! Can your halves be divided into equal fourths? Eighths? Sixteenths? If yes, how so? If no, why not?
Identify 1/4s, 1/8s, and 1/16ths in the squares below. Can you name any other fractions?
What’s going on in the squares below? Do they show the concept of 1/2? If yes, how? If no, why not?
Make further representations of 1/2. Figure out ways to describe how your shape is divided into equal halves of different colors.
Enjoy the infinity of one half!
Math concepts: fractions (definitions and examples), shapes and shape qualities, area
Art concepts: positive/negative space, shapes, symmetry/asymmetry
Use as an Introduction to Fractions and as a math/art activity for special dates, for example March 6 (3/6) or April 15 (15/30).
This may be done as a collage cut-out activity, using pre-cut squares on a different colored background paper.
Challenge students to divide squares, using the greatest possible variety of shapes for a specific fraction (example, 1/8).
Have students identify the fraction of each shape division as they draw them. Once completed have students find/compare/contrast with other examples of the same fraction by their classmates.
Please post pics of you and your students’ halves to CoTA's Facebook page or tweet us @cotaprogram!