Cubic Steps - Team A

Autor:Susanne Digel

Surely Sarah and Max ask themselves whether they can discover a correlation between number of steps and the number of cubes needed. But they do not have a sharp idea so far.... Hence, take a look at the simulation. You can alter the number of steps and observe building the steps with the cubes needed through pulling the slider in the simulation Staircase.

Staircase

Now increase the number of steps from 1 to 6 and observe how many cubes are needed. Repeat this and turn your attention to the number of cubes that are added each time you increase the number of steps by 1. Take notes of your first impressions.

Not an easy bit! Max ponders: how many cubes are needed to build a staircase with 4 steps from one with three steps. Help him!

Now complete these sentences When extending the staircase from 4 onto 5 steps, _____________ more cubes are needed.

When extending the staircase from 5 onto 6 steps, _____________ more cubes are needed.

Max thinks out loud: "For each stair that is added we need... hm..." Help him to complete the statement.

Given a certain number of steps now write down a sample calculation, how to estimate the number of cubes needed:

Compare this correlation with the one that you discovered with the cirular discs. What do they have in commom, what is different?

Cubic Steps - Team A

Staircase

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