1728mm^{3}  3375mm^{3}  19683mm^{3}  103823mm^{3} 
27cm^{3}  5.832cm^{3}  9.261cm^{3}  13.824cm^{3} 
Topics: Starter  Roots  Xmas
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Note to teacher:
Doing this activity once with a class helps students develop strategies. It is
only when they do this activity a second time that they will have the
opportunity to practise those strategies. That is when the learning is
consolidated. Click the button above to regenerate another version of this
starter from random numbers.
Teacher, do your students have
access to computers? 

Here is the URL for a concise version of this page without comments or answers.
Transum.org/go/?Start=December26
Here is the URL which will take them to a fun Christmas activity.
Does your calculator have a cube root key?
Launch the calculator on your computer.
There is a way of calculating the "cube root" on a calculator.
Can anyone in your class work it out?
Interesting fact for the Teacher:
There is a simple method to compute the cube roots using a nonscientific calculator, which requires only the multiplication and square root buttons. No memory is required. The following method is used:
This process is continued until the number does not change when the multiplication button is pressed, since the repeated square root gives 1 (this means that the solution has been determined to as many significant digits as the calculator can handle). Then, press the square root button one last time. At this point an approximation of the cube root of the original number will be shown in the display.
A full explanation of why this works can be found on Wikipedia, the free online encyclopedia.
On the Windows calculator, switch to scientific mode, type in your number, the INV x^3 to get the cube root.