Geometry Tools

Geometry naturally lends itself to fun tools. Compasses, protractors, and rulers, just to name a few, are staples in math classrooms. Traditional math tools are important, and there are easy, inexpensive ways for students to make some of their own tools. You can also create some new tools out of everyday objects.

Math is not a spectator sport; it should be experienced. People understand math better when they touch it. So let's make some tools to help us learn geometry.

Pencil Compass

Use two pencils, rubber bands, and scrap cardboard to create perfect small circles.

Geometry Concepts: Compasses, circles, radius, and diameter

From the Junk Drawer:

* 2 sharpened pencils
* 2 rubber bands
* Scissors
* Scrap corrugated cardboard
* Scrap paper
* Pushpin or thumbtack

Step 1: Wrap a rubber band several times around the eraser end of two sharpened pencils that are the same length, binding the pencils together. You should be able to pull the sharpened ends of the pencils apart.

Step 2: Cut a piece of scrap corrugated cardboard approximately ½ inch wide by 1½ inches long. Cut a small v out of each short end of the scrap as shown.

Step 3: Slide the notched cardboard between the two pencils. The rubber band should be loose enough that you can move the cardboard up and down. Loosen or tighten the rubber band as needed.

Step 4: Wrap the second rubber band around the two pencils directly below the notched cardboard piece. This rubber band will keep the cardboard from sliding. Your compass is ready to use now.

Step 5: Place a sheet of paper on top of a larger scrap of corrugated cardboard. Use a pushpin or thumbtack to punch a small hole through the paper and cardboard. Put one pencil point in this hole — you want this pencil to remain in place. Hold the top of your Pencil Compass with one hand, then use your other hand to spin the second pencil 360 degrees to draw a circle.

Step 6: Move the notched cardboard piece up or down between the pencils to create different-sized circles. With practice, you can stop using the pushpin and the scrap cardboard under the paper and draw simple circles all day long with your Pencil Compass.

The Math Behind It

Compasses are one of the most useful tools around (pun intended). Compasses allow you to draw circles. Store-bought compasses are a staple in most math classes, but there are several ways to make your own. The distance between the two pencil points is the radius of your circle. The diameter is the complete width of your circle.

Math for the Ages

This activity is suitable for all ages. Younger students should use the scrap corrugated cardboard beneath the paper when drawing circles to help steady their hands.

World's Simplest Compass

A strip of paper, a pencil, and a thumbtack are all you need to draw circles.

Geometry Concepts: Concentric circles, radius, and diameter

From the Junk Drawer:

* Strip of heavy paper (like old holiday cards or recycled
magazine covers)
* Thumbtack or pushpin
* Scrap corrugated cardboard
* Ruler
* Pencil

Step 1: Cut a 1-by-6-inch strip of heavy paper. Use a thumbtack or pushpin to poke a hole through one end of the paper. The hole should be centered. Mark that point C for center with a pencil.

Step 2: Using a ruler, mark every inch from the hole to the other end of the paper, as shown. At each mark use the thumbtack to poke a hole big enough for the pencil's lead to go through.

Step 3: Put your sheet of paper on top of the corrugated cardboard. Push the thumbtack through the C point and leave the tack in, but loose enough so the paper spins. This is your compass! Place your pencil lead through one of the holes and simply spin it (and the paper with it) around to draw a circle.

Step 4: Try drawing a bigger or smaller circle by putting your pencil in a new hole. The circles you draw are called concentric circles.

The Math Behind It

Concentric circles are circles with a common center and different radii. The distance from the center hole to the hole with the pencil lead is the radius of the circle. The diameter is the entire distance across the circle, or twice the radius.

Math for the Ages

This is a safe activity for all ages, especially if you use pushpins. Another option is to have elementary and middle school students draw six different-sized circles and then calculate the area of each. Middle and high school students could graph area on the y-axis and radius on the x-axis for each circle they drew. The shape of the graph will be a parabola, which reinforces that area equals pi times the radius of a circle squared (A = p × r2).

Magnetic Triangle Flash Cards

Create large triangles of all the different types — equilateral, isosceles, scalene, acute, obtuse, and right — for Triangle Flash Cards.

Geometry Concepts: Different types of triangles

From the Junk Drawer:

* Scissors
* Old cereal boxes, file folders, or construction paper
* Marker
* Glue or glue sticks
* Magnets or magnet tape
* Magnetic surface

Step 1: Use scissors to cut out different types of triangles from old cereal boxes, file folders, or construction paper. Write the type of triangle on one side with a marker. The common types of triangles are:

Equilateral: each side equal length (and all angles equal)

Isosceles: two sides equal length (and two angles equal)

Scalene: all sides of different lengths

Right: one...