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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
A game in which players take it in turns to choose a number. Can you block your opponent?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Use the interactivities to complete these Venn diagrams.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A game that tests your understanding of remainders.
If you have only four weights, where could you place them in order to balance this equaliser?
Can you complete this jigsaw of the multiplication square?
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
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.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
What is the smallest number with exactly 14 divisors?
Given the products of diagonally opposite cells - can you complete this Sudoku?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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.
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Can you find a way to identify times tables after they have been shifted up?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.