It's May. You've finished your math book. Now what do you do? The answer is math, of course. Explore the world of application and games and problems designed to make you learn through the process of finding the answer. Here are three ideas:
 

1. Play with tangrams.
Did you know you can make all 26 letters in the alphabet and the 10 digits? (6 and 9 are the same solution.) See how many your children can make. Can they spell their name or even just make their initials?
The tangram is seven pieces cut from a single square. The pieces are 5 triangles of 3 different sizes, a square, and a parallelogram. Use cardboard or glue the pieces to cardboard for a more durable game. There are hundreds of pictures you can make using all seven pieces.

Follow these instructions to make the tangram.

 

 

 

 

Begin with a square of any size. Fold the square in half along the diagonal. Cut. That makes 2 triangles.

 

Fold a triangle in half from the top point to the midpoint of the hypotenuse, the long side. Cut. That makes 2 triangles. These are two of the seven tangram pieces. Set them aside.

 

Take the other triangle from the first step. Fold the tip down to touch the hypotenuse. This will create a set of parallel lines. Cut along the fold. This will make a triangle and a trapezoid. The triangle is another piece for the tangram. Set it aside.

Fold the trapezoid in half. Cut. That makes 2 trapezoids. Each of these two pieces will make 2 pieces.

Fold the long side in half. This will form a triangle and a square. Cut. These are two more pieces for the tangram. Set them aside.

The last two pieces are formed by folding the long side of the trapezoid in half on the diagonal to the upper right angle corner. Imagine the square you just created in this piece. Fold along its diagonal. Cut. These two pieces, triangle and parallelogram, are your final tangram pieces.

 

2. Try your hand at string art.
Make a large square, triangle, circle, lines, or other geometric shapes. Divide each side of your shape into pieces. These can be evenly spaced or randomly (unevenly) spaced. You must put the same number of dots on the each side. Number the dots and connect the dots in order from one side to another. Connect the dots from side to side in different ways. Watch for the hole (or lack of a hole) to develop. When connecting dots from one adjacent side to another (sides next to each other) you will see a hole develop. If you connect opposite sides, will you see the hole? Organize your thoughts and observations. Create your own pictures. Look at the book String Art: Step-by-Step available through Brookline Library for more ideas.
 

 

3. Try your hand at simple calculus. Explore the limit.
Cut a sheet of paper in half repetitively. This is the infinite sequence 2-n or (1/2)n. It is 1/2 , 1/4 , 1/8 , 1/16 , 1/32 and so on. The early grades can do this activity by starting with a whole number like 32 or 16 and dividing it in half. To help the child learn use the analogy of sharing with a friend. Ask the question 'How many should you and your friend each get?' Your objective is to see the student notice that the number is getting smaller and smaller. Each time we divide the paper in half the two new pieces are smaller. Will you every divide the paper into such small pieces that the paper disappears? The theoretical answer is no. The practical answer is yes. This phenomena is called the limit. Mathematically we say:


Look at what all those repetitive halves add up to. Answer the question 'Can you ever get more than 1 sheet of paper doing this procedure'? Take one of each of the halves you create and color and paste it on another sheet of paper. Use only the halves. Do not use any whole numbers you used in the sequence. When a sequence of numbers is added together like this we call the summing of the sequence a series. It is expressed mathematically like this

The courageous and older kids can try this with other fractions. The answer will always be less than 1 but you can get a better answer than simply less than 1.

Copyright Notice

The entire contents of this website, including images and text, are protected under U.S. and international
copyright law. It is unlawful to copy or reproduce any of the content of this website.

Unauthorized commercial use of text or images from this website, is specifically not permitted and is illegal.

Copyright 1998 by Janette Duvall

Feel free to email with questions, comments or just because you are looking for more ideas.
Janette Duvall force5@jlc.net