Activity 3.1a

Math Activity 3.1a: Making Change

Purpose: To explore and understand place-value numeration systems

Materials: 1 die, 3 quarters, 6 nickels, 6 pennies
Although this is BEST done with real coins, here is an online coin app Links to an external site.. Also, if you can't find a die, virtual die Links to an external site., and more virtual dice Links to an external site..

Welcome to a base-five world.

In base-five, we group by five instead of ten. We have only five digits {0, 1, 2, 3, 4} and place-values are powers of five.

1. List the first ten counting numerals in base-five.
2. Play Make 2 Quarters
   Using only pennies, nickels and quarters, you will start with nothing, then roll the dice, collecting pennies matching your roll. Always trade up, so never have more than five pennies or nickels.
   Make a table keeping track of the value rolled, and the quarters, nickels, and pennies at each stage, as shown in the example below.
   Keep playing until you have at least 2 quarters.
   

   Roll	Quarters	Nickels	Pennies
   6		1	1
   4		2	0

3. Play Lose 3 Quarters
   Using only pennies, nickels and quarters, you will start with 3 quarters, then roll the dice. Remove pennies matching your roll.
   Make a table keeping track of the value rolled, and the quarters, nickels, and pennies at each stage, as shown in the table below.
   Keep playing until all of your money is gone.
   

   Roll	Quarters	Nickels	Pennies
   	3
   6	2	3	4
   4	2	3	0

4. List the first 30 counting numerals in base 5.
5. What comes next in base-five?
   1. 44, ____, ____
   2. 443, 444, ____, ____
6. What came before?
   1. ____, ____, 100, 101
   2. ____, ____, 344, 400