Little to Big: "Staircase" Models in Math

The Number Staircase

What does the number staircase look like for whole numbers, measurement statistics, place value models, and other units?

How does the staircase change from step to step (term to term)? Is the change exponential (times n, Xn) or is the change additive (+1, +2)?  How can we make “staircase” models that are proportionally correct? What would we include in these models? What tools will we use to make the “staircase” models accurate? How can these models help us to learn and remember the units of measurement and the values of numbers.

What words would you use for these models rather than staircase? What overarching concepts in math does this apply to? How do you think these visual models will affect student learning?

Proportional Thinking
Every staircase model can be turned into a number line. How does one "stair" or number compare to another:

• Which is greater and which is less?
• Is one number a factor of the other?
• Is one number a fraction of the other?
• Are factors and fractions the same, why or why not?
• How can I create one number by decomposing or composing the other number?
• Big/Little? Greater/Less? Fraction/Factor/Multiple (all or some)?

What other questions would you add to this list?

Note: Take a look at this SCRATCH staircase model animation.