Figure It Out: Stick Arithmetic

Question 1

Using sticks (Method 1), give a method for adding, subtracting, multiplying, and dividing.

Solution:

1. Addition: Combine the two bundles of sticks into one large bundle. The total count is the sum.
2. Subtraction: To subtract collection B from collection A, remove one stick from A for every stick in B. The remaining sticks in A are the result.
3. Multiplication: To multiply a collection of $N$ sticks by $M$, create $M$ identical piles of $N$ sticks each. Combine them all to get the product.
4. Division: To divide $N$ sticks by $M$, distribute the sticks one by one into $M$ separate piles until you run out. The size of one pile is the quotient.

Question 2

Extending the ‘aa’ (base-26 letters) system.

Solution: This works like a spreadsheet column system (A, B… Z, AA, AB… AZ, BA…).

• After ‘z’, we start with two letters: ‘aa’, ‘ab’, … ‘az’.
• Then ‘ba’, ‘bb’ … ‘bz’.
• This creates a base-26 bijective system (where there is no zero symbol).

Question 3

Make your own number system.

• Student Activity: Try using shapes like $\triangle$ for 1 and $\square$ for 5.