About This Module Printable Material Module Trifold Math Night Modules

Make a Modular Bead Bracelet

Make a mod 8 bracelet:

Choose a color to represent numbers 0 through 7.

Choose a number between 0 and 7.

Start your bracelet with a zero bead. Add your number to this, find the equivalent mod 8, and put on the next bead.

Add your number to the previous number, find the equivalent mod 8, and put on the next bead. Continue until you have enough beads to make a bracelet.



Here's how it works if you choose 5 for your number:

5+5=2??? It's equivalent to 2 in mod 8, because 5+5=10 and 10 - 8 = 2.



Experiment with some variations:

1. Try choosing different numbers to add, maybe 4 instead of 5, and see what happens to the pattern.

2. Make a mod 10 or a mod 12 bracelet.

3. Make a mod 10 Fibonacci bracelet. Start your bracelet with any two bead colors. Add the two numbers which go with those colors and find the equivalent mod 10. Put that color bead on the string. Continue adding the numbers of the last two beads on the string to get the next color until you have enough beads on the string to make a bracelet.

CLOCK ARITHMETIC

Suppose your family is going on a long distance trip to visit a relative who lives about 500 miles away. Your mom tells you to pack plenty to do in the car because the trip will take 10 hours. If you leave at 9 in the morning, what time will it be when you get there? You can easily figure out that you will get there at 7 in the evening, becuae it's 3 hours from 9 until noon and then you have 7 hours of travelling left.

This is a clock arithmetic problem. Clock arithmetic is also called modular arithmetic. In modular arithmetic there is a number called the modulus. Every number is equivalent to a number between 0 and the modulus minus 1. For any number you choose you can figure out what the equivalent number is by subtracting the modulus over and over again until you have a number which is between 0 and one less than the modulus. When you are answering questions involving time, the modulus is 12 because there are 12 hours on a clock.

Pascal's Triangle in Modular Color

Choose a modulus and color Pascal's triangle to make an interesting pattern. Choose a color for each number you will use. For instance, if you choose 4 as your modulus you will need 4 colors, one for 0, one for 1, one for 2, and one for 3. Figure out what each entry in the triangle is equivalent to in your modulus, and color it.

Play Mancala

Play starts with 4 seeds in each hole. This picture shows the player with the blue holes starting first and picking up the seeds in the hole 2 away from his/her mancala.

Rules:

Each player has six small cups (the ones closest to that player) and the mancala (large cup) to the right.

Begin the game with four seeds in each of the twelve small cups. Each player always picks up seeds from one of the six cups on his/her side. Seeds are dropped into the mancalas but never taken out.

Player A picks up all of the seeds in one of his/her small cups and puts one seed in each cup to the right until all the seeds are gone. If there are enough to reach Player A's mancala, one seed gets dropped in. Player A does not put a seed into Player B's mancala.

If Player A's last seed goes into Player A's mancala then Player A gets anotyher turn. If the last seed goes into an empty hole on Player A's side of the board then Player A puts that seed plus any seeds in the hole oppposite this one into his/her mancala.

When one player runs out of seeds the game ends. The other player puts all the remaining seeds into his/her mancala. They player with the most seeds wins.

Mancala and modular arithmetic

Suppose you have 15 seeds in hole number 3. If you sow the seeds in hole number 3, in which hole will your last seed land? Don't forget the seed for your mancala.