Exploring Pascal's Triangle
Coloring Even and Odd Numbers
This activity can be done with or without a computer. Here are two possibilities:
Print a copy of the balloon worksheet and color the balloons using crayons, markers or colored pencils. Choose one color for the even-numbered balloons and a different color for the odd-numbered balloons.
Use the ClarisWorks paint program to color the balloons:
- Download a copy of the (compressed) balloons worksheet. The file will automatically unpack with Stuffit Expander. If you don't have Stuffit Expander, you can download a copy from the Math Forum Software page.
- Open the file in ClarisWorks.
- Select your favorite color from the paint palette.
- Use the paint bucket tool to pour the chosen color into all the odd-numbered balloons.
- Select a second color from the paint palette and color all the even-numbered balloons.
The Mathematics in the Patterns
Students practice the concept of even and odd numbers by coloring odd-numbered balloons red. They should see that the triangle is outlined in red balloons because the number 1 is an odd number.
The Commutative Property of Addition
This property, together with the structure of Pascal's Triangle, explains the symmetry that can be observed in the colors of each row of balloons. It is not necessary for students to know or understand this property to be able to appreciate the symmetry in the coloring: if the triangle is folded through its center, balloons of the same color will fall on top of each other.
The sum of two odd numbers is an even number. When two red balloons are next to each other, the balloon below will be white.
The sum of two even numbers is an even number. When two white balloons are next to each other, the balloon below will be white.
The sum of an odd number and an even number is an odd number. When a red balloon is next to a white balloon, the balloon below will be red.
Use one of the numbered Pascal student worksheets to repeat the activity. Six identically colored triangles can be joined to form a hexagon. These constructions make great classroom or hall decorations. Looking at the center point gives the optical illusion of a cube in three dimensions.
For more ideas, see Coloring Multiples (Intermediate Level).
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