Close encounters with shapes - teaching geometry

Activities that make real-world connections to geometry

My book The Greedy Triangle (Scholastic, 1994) is the story of a fun-loving triangle who gets bored and wistfully wishes for more sides and more angles. The plot prompts children to explore shapes and learn that geometry is part of the world around them.

ABOUT THE STORY

Always on the go, the triangle supports bridges, makes music in a symphony orchestra, catches wind for sailboats, becomes slices of pie, and more. But one day the triangle gets tired of doing the same old things and asks the shapeshifter to turn it into a quadrilateral. Still bored, it asks to change into a pentagon, a hexagon, and finally a shape with so many sides and angles that it can't tell which side is up. Eventually the triangle realizes that a triangle is a fine and useful shape to be, after all.

PRIMARY

Step #1

As you read, ask children to look at the illustrations of the triangle's mentioned pastimes and find others that are not mentioned. When you get to the line, "The triangle's favorite thing, however, was to slip into the place where people put their hands on their hips," ask students to put their hands on their hips and notice the shape of the triangle.

Step #2

At the point in the story where the triangle wishes for one more side, ask, "What would the triangle look like if its wish were granted? How many sides will the new shape have?" Introduce children to the word quadrilateral.

Step #3

Each time the shape is about to change, stop reading the story and have children imagine how the shape will turn out, and figure out how many sides and angles it will have. Introduce the names of the shapes.

Step #4

Cut out construction-paper triangles of different sizes and shapes. Ask each child to pick one, look at it from different angles, and figure out what other shapes it might be part of. Then give each child a sheet of paper, have him or her glue the triangle to it, draw a picture around it to show the new shape, and write a sentence about the picture.

Step #5

Ask, "What do you think the triangle might like to do if it visited our school?" Once students offer suggestions, divide them into pairs, give them notepads, and walk with them around the school to look for triangular shapes. Ask children to draw pictures of what they see and write a sentence to describe each picture.

Primary activity adapted from Math and Literature (K-3), Book Two by Stephanie Sheffield (Math Solutions Publications, 1994), distributed by Cuisenaire.

INTERMEDIATE

Step #1

Before reading the story, post a class chart with the following information:

Polygons are named for the number of sides they have:

3 sides = triangle 4 sides = quadrilateral 5 sides = pentagon 6 sides = hexagon 7 sides = heptagon 8 sides = octagon 9 sides = nonagon 10 sides = decagon 11 sides = undecagon 12 sides = dodecagon

Talk about the prefixes tri-, quad-, penta-, hexa-, and so on. Have students brainstorm other words that begin with them.

Step #2

After reading the story, ask students to look around the classroom and point out examples of each of the more common shapes mentioned--triangle, quadrilateral, pentagon, hexagon, and octagon. As homework, have kids look for other examples from their homes or neighborhoods and report their findings.

Step, #3

Tell students that all of the shapes in the book are called polygons. Ask them to work in pairs or small groups and write a one-sentence definition of a polygon. Have groups share their thoughts, then present the definition as "a closed plane figure bound by three or more straight line segments." (Closed means it encloses a space, like a fence around a corral; plane means it's on a flat surface. Check the dictionary for other definitions, too.)

Step #4

Initiate a class discussion around the following questions (remember that these ideas may be new for students; don't expect right answers, but aim to stimulate thinking):

* A circle isn't considered a polygon. Why do you think this is so?

* Why would a shape with many sides and many angles, like a dodecagon, roll more easily than a shape with fewer sides and angles?

* Regular polygons have sides all the same length and angles all the same size, like a square. As a regular polygon acquires more and more sides, mathematicians say it approaches being a circle. What do you think this means?

MARILYN BURNS is the creator of Math Solutions, inservice workshops offered throughout the country, and the author of numerous books and articles.

COPYRIGHT 1995 Scholastic, Inc.
COPYRIGHT 2004 Gale Group