### GOT IT Now

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

### 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?

### Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

# Picturing Square Numbers

##### Stage: 3 Challenge Level:

The sum of consecutive odd numbers can be represented as square arrays.

Full Screen Interactivity

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?

Have you a method for working this out quickly?

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

What is the sum of $1 + 3 + ... + 149 + 151 + 153$?

What is the value of $83 + 81+ ... + 5 + 3 + 1$?

What is the value of $51 + 53 + 55 + ... + 149 + 151 + 153$?

What is the sum of $2 + 4 + ... + 150 + 152 + 154$?

What is the sum of $2 + 6+ ... + 298+ 302+ 306$?

Explain how you worked these out.