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# Picturing Square Numbers

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### Is There a Theorem?

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Age 11 to 14

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*Picturing Square Numbers printable worksheet*

The diagram shows that 1 + 3 + 5 + 7 = 16.

What is the sum of the first $30$ odd numbers?

What is the sum of the first $60$ odd numbers?

Can you describe a method for working these out quickly?

Can you make $3249$ by adding odd numbers in this way?

What is the value of:

$1 + 3 + ... + 149 + 151 + 153$?

$83 + 81+ ... + 5 + 3 + 1$?

$51 + 53 + 55 + ... + 149 + 151 + 153$?

$2 + 4 + ... + 150 + 152 + 154$?

$2 + 6+ ... + 298+ 302+ 306$?

Explain how you worked these out.

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?