Grade 8 Math Activities

Numbers can form fascinating patterns. Exploring number patterns will give your child a sense of the power and wonder of mathematics. In this activity, your child explores the Fibonacci sequence, which can be found both in mathematics and in the natural world.

	Toothpicks

	Paper and pencil

The Fibonacci numbers are named after the thirteenth century Italian mathematician Leonardo da Pisa, who was better known as Fibonacci. This activity is a somewhat simplified version of Fibonacci’s famous rabbit problem.

After two months, a baby rabbit gives birth to a new baby rabbit. The rabbit gives birth to another rabbit every month after that. When each baby rabbit is two months old, it also gives birth to a new rabbit and continues to have a new baby each month after that. How many rabbits will there be in 4 months, 5 months, 6 months?

Above is a diagram of what is happening with the rabbits. The solid lines show that a new baby rabbit is born. The dotted lines show the same rabbit in the next month.

Here are some questions to ask your child as he works on the problem:

	What is the total number of rabbits for each month? Do you see a pattern in the numbers?

	How many rabbits do you think there will be in the 7th month? Can you continue the diagram to see?

	How many rabbits do you think there will be in the 8th month? 9th month? How could you describe the pattern that is developing? (You may want to encourage your child to use algebraic symbols to express the pattern.)

	Why do you think the pattern is occurring this way?

Another way to explore the Fibonacci sequence is to use toothpicks. Ask your child to place a toothpick horizontally on a table or floor. Then take another toothpick and put it at right angles with the first toothpick, making a backwards L-shape. Now going straight across, make a “roof” for this shape with 2 toothpicks, covering but stretching beyond the first toothpick, so that now there is a new, inverted L-shape. Next, take 3 toothpicks and make a “side” for this structure that stretches down to the first toothpick and makes a new backwards L.

	The next addition of toothpicks to make a “roof” and an inverted “L” will need 5 toothpicks. Do you see why?

	How many toothpicks will be needed for the next side?

	Do you see the same Fibonacci numbers appearing here? Why do you think they are showing up in this situation?

This activity is just the beginning of learning about where, why, and how Fibonacci numbers occur. Look for Fibonacci numbers in flower petals and the ways trees branch. Look for them in the numbers of spirals on pinecones and pineapples. If you want to find more information about them, look for books in the library and Internet resources on the Fibonacci numbers. Studying the Fibonacci numbers will give your child an appreciation for this special sequence and a stronger understanding of sequences generally.

 Grade 8 Math Activities