Project B13 - The Base Five Arcade Project 13 - The Base Five Arcade

Every game or activity at Pete E. Pasta's Family Fun Center requires one or more tokens per play. The tokens come in the following denominations:

Token machines accept pennies, nickels, dimes, quarters, $1 bills, and $5 bills. When exchanging money for tokens, the machines always give the fewest number of tokens possible. The games give change in the same way, returning the fewest number of tokens possible.

  1. Use colored hexagons, base-five blocks, or money to represent the tokens. Obtain at least ten of each type of token. It may help to label the value of each token.
  2. Complete the following table showing the value of each token in terms of the other tokens.

    Red Blue Green Yellow
    1 Yellow 0 0 0 1
    1 Green 0 0 1 5
    1 Blue        
    1 Red        

  3. Josh has 3 red tokens and 2 green tokens.
    1. How much are they worth?

    2. Carefully explain how you obtained your answer?

  4. Suppose the token machine gave Sarah 1 red token, 3 blue tokens, and 2 green tokens.
    1. How much money did she put into the machine?

    2. Carefully explain how you obtained your answer?

  5. For this problem, an upper-case letter will denote the token color. For example,
    1R     2B     3G     4Y


    represents 1 red, 2 blue, 3 green, and 4 yellow tokens. What is the value of each collection of tokens? Show how you got your answer.
    1. 3B     0G     4Y

    2. 1R     0B     1G     0Y

    3. 4R     4B     1G     3Y

  6. Mary Beth placed $2.55 into a token machine.
    1. What tokens did she receive? Write your answer in RBGY order, using the notation of the previous problem.

    2. Carefully explain how you got your answer.

  7. Arthur knew the Jurassic Park game cost $1.65 to play. If he deposited this exact amount into the token machine, what tokens would he receive?

  8. Stan inserted one red token into a game that required 2 blue, 1 green, and 3 yellow tokens.
    1. What was his change?

    2. What was the value of his change?

  9. The Alpine Skiing game requires two red tokens. Lisa has 1 red, 4 blue, 3 green, and 4 yellow tokens. How much more money (not tokens) does she need to play the game?

Even though you may not be aware of it, throughout this activity you have been studying base-five numbers.

We typically use base-ten numbers: we use ten basic digits (0,1,2,3,4,5,6,7,8,9) with known face values and place value is based on powers of ten. For example, a base-ten number is expanded like so:

73425 = 7 ·104 + 3 ·103 + 4 ·102 + 2 ·101 + 5.
In base five, there are five basic digits (0,1,2,3,4, each with its usual face value, but we could use different symbols) and place value is based on powers of five. A number in base five is expanded in the following way:
43012five = 4 ·54 + 3 ·53 + 0 ·52 + 1 ·51 + 2.
The word five written next to the numeral lets us know we're working in base five. If you don't see such an indication, you should assume you're working in base ten.
  1. How could you use your tokens to represent the base-five number 231five?

  2. What base-five number does the following combination of tokens represent: 2R 0B 3G 3Y. Explain your reasoning.

  3. Use your tokens to model the addition problem 133five + 1214five. Carefully explain how you regrouped your tokens.

  4. Use your tokens to model the subtraction problem 3012five - 433five. Carefully explain how you regrouped your tokens.

  5. Referring to Pete E. Pasta's Family Fun Center and tokens, write a word problem involving addition of base five numbers.

  6. Referring to Pete E. Pasta's Family Fun Center and tokens, write a word problem involving multiplication of a base five number by 3.

  7. Since you don't have tokens of large enough denomination, you can't use them to model the base-five number 112320five. Nonetheless, write this number in expanded form.

File translated from TEX by TTH, version 1.98.
On 10 Nov 2001, 11:07.