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Can you explain the strategy for winning this game with any target?

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Is There a Theorem?

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?

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Card Trick 2

Can you explain how this card trick works?

Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

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.