A Dot Can Be...

This morning, Bill and Robbie's kindergarten read Donald Crews's picture book Ten Black Dots. It's a lovely book showing imaginative ways of transforming static black dots into familiar objects...

...as in the children's responses pictured below.

One dot can make a Cyclops...



...or a squirrel hole...



...or a window in a house...



As for 2 dots, they make great eyes...



Stop by the kindergarten to see the whole series!

Fifteen Tires Were on Top of a Hill...

Robbie recently had her kindergarteners write story problems. They thought of a situation that involved plus ("joining") or minus ("taking away"), then wrote the story, wrote the number sentence for the problem, and finally made a box with clay figures and other decorations showing the problem. Today, they demonstrated their work for the class.

There were 15 tires on top of a hill...



Then five of them rolled down the hill....



How many were left at the top of the hill?

Hope you got 15 - 5 = 10!

Sally the snake sees 5 dragonflies. 2 fly away. How many are left?



Did everybody get 3? If not, ask your nearest kindergartener for help.

Other problems involved bats or butterflies flying off into the great big world, horses venturing out from the safety of barns, and wolves scaring away some (but not all) of a group of farm animals. I'm no psychologist, but it's pretty easy to tell that kindergarten is drawing to a close!

Fractions + Transformations = ?

This is a recipe.

Start with a small 4x4 square.

Sketch a continuous series of line segments (no curves) to divide the square neatly in half.
(Be interesting, please: no fair drawing a straight vertical or horizontal line or a simple diagonal.)

Prove that the two sections do indeed take up the same area.


Check to see if the figure has rotational symmetry. (That is, if it looks exactly the same when it's rotated any distance less than 360 degrees.)

Color the two sections contrasting colors.

Repeat the process 3 times. You may transform the original design by a) rotating (turning) the design 90, 180, or 270 degrees, or b) reflecting (flipping) the design as if it were appearing in a mirror. You may also keep the design oriented exactly the same as the original.


Arrange the four squares into a larger square.

Repeat this larger square four times. Place these together to create a sixteen-square unit.

Write a description of what you did.


The pictures show the results.

And the answer to the equation? Well, we could say "Fractions + Transformations = An Example of Applied Mathematics." Or, we could also say simply "Fractions + Transformations = Art." Your choice!