What is the smallest number with exactly 14 divisors?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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...
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Think of two whole numbers under 10. Take one of them and add 1. Multiply by 5. Add 1 again. Double your answer. Subract 1. Add your second number. Add 2. Double again. Subtract 8. Halve this number. . . .
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 different methods to find out what the shapes are worth - how many can you find?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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.
Use the differences to find the solution to this Sudoku.
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
There is a particular value of x, and a value of y to go with it,
which make all five expressions equal in value, can you find that
x, y pair ?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .
Explore the effect of combining enlargements.
A game for 2 or more people, based on the traditional card game
Rummy. Players aim to make two `tricks', where each trick has to
consist of a picture of a shape, a name that describes that shape,
and. . . .
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Explore the effect of reflecting in two parallel mirror lines.
Can you maximise the area available to a grazing goat?
Can you describe this route to infinity? Where will the arrows take you next?
How many different symmetrical shapes can you make by shading triangles or squares?
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?