Place Value

# Exploration

### Problem 44

Jay decides to play with a system that follows a 1←1 rule. He puts one dot into the right-most box. What happens?

### Problem 45

Poindexter decides to play with a system that follows the rule 2←3.

1. Describe what this rule does when there are three dots in the right-most box.

2. Draw diagrams or use buttons or pennies to find the codes for the following numbers:

3. Can you find (and *explain*) any patterns?

### Problem 46

Repeat problem 45 for your own rule. Choose two numbers and . For each of the numbers

figure out the code. Look for patterns, and explain them if you can!