### 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.

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.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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