collegemathforelementaryeducation.files.wordpress.com… · Web viewProject 1: Numeration Systems Please write all answers directly below each question (not on separate paper). You

Name:____________________________

Project 1: Numeration SystemsPlease write all answers directly below each question (not on separate paper).

You may type or write by hand, whichever you prefer.

In this project, you will make up your own symbols for your own numeration system!Your system will be additive, in base 8 or base 6, your choice. Neither one is harder or easier than the other. 😊

You will need symbols for every power of your base. If you choose base 8, you will need a symbol for 80, 81, 82, etc., up to about

85. If you choose base 6, you will need a symbol for 60, 61, 62, etc., up to about

65. Do not copy the symbols from any of the systems we have studied.

1. Describe your system (3 points each)a.)Write the symbols of your system and what each symbol is equal to.

Base and exponent (base 8 or base 6, your choice)

80

or60

Your symbols(If the table is too small for your symbols, make your own chart.)

What each symbol equals, using the

powers of base 6 or 8.

b.)What principle or design connects your symbols? For example, the Mayan system is made from a pattern of lines and dots; the Egyptian system uses pictures of objects that had significance to them. Where did you get your symbols and why?

c.) How many times are you allowed to repeat a symbol? Why? (Hint: in Egyptian, which is a base ten additive system, you should only repeat a symbol 9 times before you change to a new place; in Mayan, base 20, you can only have up to 19 before you use a higher place value)

2. Create Numbers (7 points each)Show how to write the following numbers in your system, and clearly show how you know that you have the correct answer (does not have to be in words, but show the math):

a.)50 Show your work.

b.)148 Show your work.

c.) 12,437 Show your work.

10 points3. Make two more numbers of your own choosing (not two more symbols, two more

numbers made up of your symbols). Show your work.

CAUTION: for questions 2 and 3, show how you got the value of each number or you will not get credit.

20 points4. Adding

a.)Show an example of adding two large numbers in your system, without translating into Hindu Arabic (our system). This will be similar to how Egyptian numbers were added (see Section 1.3), but now you are in base 6 or 8, so the trading will be different. Your example must show at least two carries/trades – circle what you are trading and show what you are trading for!

+

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b.)Explain in words the carrying or trading up you had to do, along with how much was leftover each time and why.

c.) What is the general principle behind how you trade to add in your system? Write something like this, “Generally, I have to trade ____ objects for _____. I know I have to trade whenever ______________.”

20 points5. Subtracting

a.)Show an example of subtracting two large numbers in your system, without translating into Hindu Arabic (our system). This will be similar to how Egyptian numbers were subtracted (see Section 1.3), but now you are in base 6 or 8, so the trading will be different. Your example must show at least two carries/trades – circle what you are trading and show what you are trading for!

______________________________________________________

b.)Explain in words the carrying or trading up you had to do, along with how much was leftover each time and why.

c.) What is the general principle behind how you trade to add in your system? Write something like this, “Generally, I have to trade ____ objects for _____. I know I have to trade whenever ______________.”

8 points6. Using all the symbols you have made up, what is the largest number you can

make in your system? Explain how you know.

Caution: be sure to follow all the rules of your system, including the largest number of times you can repeat a number. When you explain how you know, explain using the rules of your system.

7. A multiplicative number system

6 points eacha.)On the previous page is a description of a multiplicative system, created by

student Catherine Sayaman. Decode the number below using her explanations of how to do it. Show your work.

b.)Write the number 162 in Catherine’s system. Show your work.