### LESSON 3

#### ACTIVITY 1 **ROCK-PAPER-SCISSORS…**

Play a few rounds of rock-paper-scissors with someone else. What sort of options do you have when you play? Isn’t there a sort of “hierarchy” of which option beats who? Draw this out, then explore what this looks like if we just applied abstract numbers to these options.

#### ACTIVITY 2 **DIFFERENT BASE NUMBER SYSTEMS: WHAT DO YOU NEED TO DO IN ORDER TO ADJUST NUMBERS?**

Research what it means to have a “different number system.” To give you an idea to start out with, the most common number system is **Base 10**, the number system that you’re used to:

**0, 1, 2, 3, 4, 5, 6, 7, 8, 9**

There are two reasons that we call this the Base 10 system. If you consider the list of possible digits above, there are only 10. As soon as you go outside of this list, you just start combining options:

10 is just a 1 and 0

75 is just a 7 and 5

But even more specifically, that second place value is the **tens** place.

10 is really 10 and 0

75 is really 70 and 5

There are other number systems out in the world though: Base 2 (binary), Base 8 (octal), Base 16 (hexadecimal). You can really do any base that you want. The key is that **second place value**. When we write numbers in a system that isn’t Base 10, we write a little subscript to indicate the base:

101Two means it’s the number 101 in Base 2

732Eight means it’s the number 732 in Base Eight

Explore this fun little website to see if you can figure out how numbers are translated across different base systems: http://www.cleavebooks.co.uk/scol/calnumba.htm

#### ACTIVITY 3: MATH **ARCHEOLOGY: DIFFERENT NUMBER SYSTEMS THROUGHOUT HISTORY**

In a group research one of the ancient number systems of our world. Your team will need to become “gurus” at this number system because you are going to bring everything you learned back to the rest of the class.

As a guide, try to find out the different symbols used, what sort of base system the culture used, and if there were any sort of weird rules that were needed in order to use the system appropriately. See the chart in the job aid to help you organize yourself for each of the systems.

#### ACTIVITY 4: **DIFFERENT WAYS OF MULTIPLYING NUMBERS, LARGE AND SMALL**

Humans haven’t always used a calculator. And not all cultures had an abacus either. So they had to use different arithmetic systems by hand, especially when it came to multiplication. Surprisingly enough, some primary schools are going back to some of these older methods of multiplication to teach our children so that they can be better 21st Century learners.

Research some of the allternate Multiplication Methods: **Egyptian Method, Russian Peasant Method, Lattice Method**

**Project Assignment: What is going on with the “numbers” in the game?**

The game that you have chosen most likely has something to do with numbers (otherwise why would you have picked it?)* This week’s task is to look into what are the “boundaries” of these numbers.

Specifically:

- If you are rolling dice in the game, what kind of outcomes can you get, or even expect to get?
- If you have cards in the game instead, what sort of expectations do you have for what you might get on a given card draw?
- Are there any impossibilities for the dice rolls and card draws?
- Anything that’s a guarantee?
- Are there player statistics that can go up and down throughout the gameplay?

If you do outside research on this task, please make sure that you only include content that you understand and can put into your own words.

*If you really did choose something that has nothing to do with numbers but you were able to complete the previous two Tasks successfully, you may choose a different game to analyze for this week.

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