Lessons excerpted fromMath Puzzles and Patterns for Kids

by Kristy Fulton

Copyright ©2007 Prufrock Press, Inc.

Grades2-4

K FK FK FK F

© Prufrock Press • Math Puzzles and Patterns for Kids This page may be photocopied or reproduced with permission for student use.6

Name: ___________________________________ Date: ______________

Fibonacci SequenceThe Fibonacci sequence is a series of numbers studied by Leonardo Pisano Fibonacci of Italy. The numbers form a pattern. It begins with the number 1 and each number after that is the sum of the two numbers that came before it. This pattern is often found in nature, such as the spirals of seashells, family trees, and the number of petals on a flower. Here’s an example of how it works:

1 1 2 3 51 + 1 = 2 1 + 2 = 3 2 + 3 = 5

1.) Can you figure out what comes next?

1 1 2 3 5 _____ _____ _____ _____

2.) Using the same idea as before, can you figure out what comes next?

21 34 55 _____ _____ _____ _____ _____

From Math Puzzles and Patterns for Kids by Kristy Fulton© 2007 Prufrock Press Inc. • Sample reproduced with the permission of Prufrock Press Inc. (http://www.prufrock.com)

7© Prufrock Press • Math Puzzles and Patterns for Kids

This page may be photocopied or reproduced with permission for student use.

Name: ___________________________________ Date: ______________

Other Fibonacci PatternsFibonacci’s sequence always starts with 1, but what if it started with a different number? Figure out what comes next in each of the problems below. Remember to add the two numbers that come right before each blank. You may use a calculator if needed.

1.) 2 2 4 _____ _____ _____ _____ _____

2.) 3 3 6 _____ _____ _____ _____ _____

3.) 4 4 8 _____ _____ _____ _____ _____

4.) 5 5 10 _____ _____ _____ _____ _____

5.) 6 6 12 _____ _____ _____ _____ _____

6.) 7 7 14 _____ _____ _____ _____ _____

7.) 8 8 16 _____ _____ _____ _____ _____

Try some more Fibonacci-style patterns.

8.) 10 10 20 _____ _____ _____ _____

9.) 15 15 _____ _____ _____ _____ _____

10.) 20 20 _____ _____ _____ _____ _____

11.) 99 99 _____ _____ _____ _____ _____

12.) 41 41 _____ _____ _____ _____ _____

13.) 23 23 _____ _____ _____ _____ _____

14.) 17 17 _____ _____ _____ _____ _____

15.) 150 150 _____ _____ _____ _____ _____

16.) 101 101 _____ _____ _____ _____ _____

17.) 1,000 1,000 _____ _____ _____ _____ _____

From Math Puzzles and Patterns for Kids by Kristy Fulton© 2007 Prufrock Press Inc. • Sample reproduced with the permission of Prufrock Press Inc. (http://www.prufrock.com)

From Math Puzzles and Patterns for Kids by Kristy Fulton© 2007 Prufrock Press Inc. • Sample reproduced with the permission of Prufrock Press Inc. (http://www.prufrock.com)

© Prufrock Press • Math Puzzles and Patterns for Kids This page may be photocopied or reproduced with permission for student use.8

Name: ___________________________________ Date: ______________

Other Fibonacci Patterns, Continued

Solve these Fibonacci-style patterns backward by using subtraction.

1.) 147 91 56 _____ _____ _____ 7 7

2.) 105 65 40 _____ _____ _____ _____ _____

3.) 42 26 _____ _____ _____ _____ _____ _____

4.) 210 130 _____ _____ _____ _____ _____ _____

5.) 84 52 _____ _____ _____ _____ _____ _____

6.) 168 104 _____ _____ _____ _____ _____ _____

7.) 252 156 _____ _____ _____ _____ _____ _____

8.) 189 117 _____ _____ _____ _____ _____ _____

9.) 63 39 _____ _____ _____ _____ _____ _____

10.) 21 13 _____ _____ _____ _____ _____ _____

From Math Puzzles and Patterns for Kids by Kristy Fulton© 2007 Prufrock Press Inc. • Sample reproduced with the permission of Prufrock Press Inc. (http://www.prufrock.com)

9© Prufrock Press • Math Puzzles and Patterns for Kids

This page may be photocopied or reproduced with permission for student use.

Name: ___________________________________ Date: ______________

Other Fibonacci Patterns, Continued

Now try multiplying numbers to finish the pattern. You may use a calculator, if needed.

1.) 2 2 4 _____ 32

2.) 3 3 _____ _____ _____

3.) 4 4 _____ _____ _____

4.) 5 5 _____ _____ _____

5.) 6 6 _____ _____ _____

6.) 7 7 _____ _____ _____

7.) 8 8 _____ _____ _____

8.) 9 9 _____ _____ _____

9.) 10 10 _____ _____ _____

Try dividing the first number by the second number to finish these patterns. You may use a calculator, if needed.

10.) 243 27 _____ _____ _____

11.) 3,125 125 _____ _____ _____

12.) 16,807 343 _____ _____ _____

13.) 1 1 _____ _____ _____

14.) 32 8 _____ _____ _____

15.) 1,024 64 _____ _____ _____

16.) 100,000 1,000 _____ _____ _____

17.) 59,049 729 _____ _____ _____

From Math Puzzles and Patterns for Kids by Kristy Fulton© 2007 Prufrock Press Inc. • Sample reproduced with the permission of Prufrock Press Inc. (http://www.prufrock.com)

From Math Puzzles and Patterns for Kids by Kristy Fulton© 2007 Prufrock Press Inc. • Sample reproduced with the permission of Prufrock Press Inc. (http://www.prufrock.com)