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### Advanced mathematics

# Factors and Multiples KS2

### Pebbles

### Sweets in a Box

### Round and Round the Circle

### Abundant Numbers

### Flashing Lights

### The Moons of Vuvv

### Mystery Matrix

### One Wasn't Square

### Multiplication Squares

### Factor Lines

### Two Primes Make One Square

### Cycling Squares

### Which Is Quicker?

### Up and Down Staircases

### Factors and Multiples Game

### Factor-multiple Chains

### Picture a Pyramid ...

### Three Dice

### Counting Cogs

### Factor Track

### Square Subtraction

### Dicey Array

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This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Age 7 to 11

Challenge Level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

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.

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Age 7 to 11

Challenge Level

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Age 7 to 11

Challenge Level

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Age 7 to 11

Challenge Level

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.

Age 7 to 14

Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Age 7 to 11

Challenge Level

Can you make square numbers by adding two prime numbers together?

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Age 7 to 11

Challenge Level

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?

Age 7 to 16

Challenge Level

This game can replace standard practice exercises on finding factors and multiples.

Age 7 to 11

Challenge Level

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Age 7 to 14

Challenge Level

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Age 7 to 11

Challenge Level

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.

Age 7 to 11

Challenge Level

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Age 5 to 11

Challenge Level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?