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.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Use the differences to find the solution to this Sudoku.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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. . . .
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Can you describe this route to infinity? Where will the arrows take you next?
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Can you maximise the area available to a grazing goat?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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. . . .
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400. . . .
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?
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?
Can you work out the dimensions of the three cubes?
Explore the effect of reflecting in two parallel mirror lines.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G =
F and A-H represent the numbers from 0 to 7 Find the values of A,
B, C, D, E, F and H.
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .
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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Explore the effect of combining enlargements.
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?
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 all unit fractions be written as the sum of two unit fractions?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
Which has the greatest area, a circle or a square inscribed in an
isosceles, right angle triangle?
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?
A square of area 40 square cms is inscribed in a semicircle. Find
the area of the square that could be inscribed in a circle of the
A plastic funnel is used to pour liquids through narrow apertures.
What shape funnel would use the least amount of plastic to
manufacture for any specific volume ?
Can you find the area of a parallelogram defined by two vectors?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?