Crazy Twos (Two to the…s)

Updated for 2022!


Let your students practice manipulating exponents. Multiplication, division, roots, powers of powers.  This powerful activity asks them to do some impressive mathematics ... in their heads.

Powers of Two

We give students values of 2 to the exponents 1 through 30.  Powers of Two

     2^8 = 256
     2^{12} = 4,096
     2^{14} = 16,384
     2^{20} = 1,048,576
     2^{28} = 268,435,456

Then asked them to calculate all kinds of amazing math in their heads.  It's like magic!


\displaystyle \frac {1,048,576}{4,096}

or   \sqrt {268,435,456}



For members we have an editable Word doc and solutions.

two-to-thes.docx    two-to-thes-solution.pdf

More Mental Math

Multiply by 5, in your head - Let your students develop their own individual way of mentally multiplying by 0.5, 5, 50, 500, and so on.  We have a little practice and a requirement for students to make sense of and verbalize or draw a picture of their conclusions as to why this works.


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