Stimulating Understanding of Computational science through Collaboration, Exploration, Experiment, and Discovery for students with Hearing Impairments
a collaboration of the Shodor Education Foundation, Inc., Eastern North Carolina School for the Deaf, Barton College, the National Technical Institute for the Deaf, and Interpreters, Inc.

For Teachers!

Modular Mathematics 

Answer keys

Student worksheets

Additional practice worksheet

Answers to questions on Clock page:

Let's make our own clocks. Get a piece of circle paper from your teacher. In the first circle, draw the face of a normal clock. Now, erase the number 12 and put 0 there instead. Try the following problems using your clock. Write the problems and their answers on your own paper. 

1) 20 (mod 12) = ? 8
2) 5 (mod 12) = ? 5
3) 16 (mod 12) = ?4


Now, let's try different size clocks. Use your second circle to make a clock with only 7 numbers on it. 0 should be at the top. 1 through 6 should go in order around the outside. 

4) What is your new mod? Why?7 
5) What is 9 in mod 7? 2
6) What is 12 in mod 7?5


Try these other problems by drawing clocks in the other circles. 

7) What is 5 in mod 3? 2
8) What is 10 in mod 9? 1
9) What is 7 in mod 2?1

10) 8 (mod 3) = ? 2
11) 17 (mod 4) = ? 1
12) 25 (mod 9) = ?7

16) -2 (mod 4) = ? 2
17) -5 (mod 8) = ? 3
18) -10 (mod 6) = ?2

19) -3 (mod 7) = ? 4
20) -10 (mod 8) = ? 6
21) -18 (mod 5) = ?2

Addition 

1) 3 + 7 (mod 6) = ? 4
2) 6 + 13 (mod 7) = ? 5
3) 14 + 10 (mod 3) = ? 0
4) 8 + 5 (mod 4) = ? 1
5) 6 + 14 (mod 5) = ? 0

Subtraction 

7) 50 - 23 (mod 5) = ? 2
8) 10 - 8 (mod 2) = ? 0
9) 41 - 31 (mod 3) = ? 1
10) 100 - 64 (mod 7) = ?1

Try the following problems. Solve each equation for the X value listed. Write your answers on your own paper. 

1) Y = 7 X - 4 (mod 3) if X = 4 0
2) Y = X + 9 (mod 5) if X = 11 0
3) Y = 6 X + 1 (mod 4) if X = 3 3
4) Y = 2 X + 7 (mod 2) if X = 1 1
5) Y = 3 X - 8 (mod 7) if X = 2 5 

Developed by
The Shodor Education Foundation, Inc.

Copyright © 1999-2001 by The Shodor Education Foundation, Inc.

This project is supported, in part, by the National Science Foundation Opinions expressed are those of the authors and not necessarily those of the National Science Foundation.