Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
The area of a square inscribed in a circle with a unit radius is,
satisfyingly, 2. What is the area of a regular hexagon inscribed in
a circle with a unit radius?
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.
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.
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
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?
Can you maximise the area available to a grazing goat?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
What is the smallest number with exactly 14 divisors?
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?
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?
Explore the effect of combining enlargements.
How many different symmetrical shapes can you make by shading triangles or squares?
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?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Explore the effect of reflecting in two parallel mirror lines.
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 describe this route to infinity? Where will the arrows take you next?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Is it always possible to combine two paints made up in the ratios
1:x and 1:y and turn them into paint made up in the ratio a:b ? Can
you find an efficent way of doing this?
A decorator can buy pink paint from two manufacturers. What is the
least number he would need of each type in order to produce
different shades of pink.
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the differences to find the solution to this Sudoku.
Can all unit fractions be written as the sum of two unit fractions?
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. . . .
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
Can you see how to build a harmonic triangle? Can you work out the next two rows?
A jigsaw where pieces only go together if the fractions are
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 ?
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...
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?