
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Use the interactivity to sort these numbers into sets. Can you give each set a name?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Use the interactivities to complete these Venn diagrams.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Which of these sets of numbered balls will give the most even totals when two balls are chosen from them?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Can you find the chosen number from the grid using the clues?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

How many different sets of numbers with at least four members can you find in the numbers in this box?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Read all about Pythagoras' mathematical discoveries in this article written for students.