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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 Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s.

What numbers can we make? Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true. 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? Using the digits 1 to 9, the number can be written as the product of two numbers. Can you find the factors? Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand. The items in the shopping basket add and multiply to give the same amount.

What could their prices be? Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses? What is the largest number which, when divided into , , , and in turn, leaves the same remainder each time? Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Factors, Multiples and Primes. Statement Snap Age 7 to 14 Challenge Level: Dozens Age 7 to 14 Challenge Level: Do you know a quick way to check if a number is a multiple of two? How about three, four or six? A game in which players take it in turns to choose a number. Can you block your opponent? How Much Can We Spend? Age 11 to 14 Challenge Level: Number Families Age 11 to 14 Challenge Level: How many different number families can you find?

Diminishing Returns live Age 11 to 14 Challenge Level: How much of the square is coloured blue? How will the pattern continue? Using your knowledge of the properties of numbers, can you fill all the squares on the board? American Billions Age 11 to 14 Challenge Level: On the planet Vuv there are two sorts of creatures.

The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there? Can you find some more abundant numbers? 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? Can you fill in this table square? The numbers 2 were used to generate it with just one number used twice.

Use the information to find out what the three numbers were. 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. Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line. Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down? 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? How about when a friend begins a new rhythm at the same time? This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers? Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube? Investigate the sum of the numbers on the top and bottom faces of a line of three dice.

What do you notice? Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Factor track is not a race but a game of skill.

The idea is to go round the track in as few moves as possible, keeping to the rules. Look at what happens when you take a number, square it and subtract your answer.

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Short homework tasks on integers, where students are asked to: create a factors web; and answer a few questions on factors and multiples. Large type is used so that the page can be printed out A5 size. /5(6).

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