Exploring and noticing

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Ben's class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

There are lots of ideas to explore in these sequences of ordered fractions.

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?