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:

    \[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and } 39\]

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

 

Problem 46

Repeat problem 45 for your own rule. Choose two numbers a \neq 1 and b.  For each of the numbers

    \[1\text{ through }20, 24, 27, 30, 33, 36, \text{ and } 39,\]

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

 

License

Icon for the Creative Commons Attribution-ShareAlike 4.0 International License

Mathematics for Elementary Teachers by Michelle Manes is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.