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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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. . . .
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?
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.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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. . . .
There are lots of different methods to find out what the shapes are worth - how many can you find?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
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.
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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 hidden squares?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you move the tiles around, can you make squares with different coloured edges?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
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?
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?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Which of these games would you play to give yourself the best possible chance of winning a prize?
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?
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
A jigsaw where pieces only go together if the fractions are equivalent.
Use the differences to find the solution to this Sudoku.
Is there an efficient way to work out how many factors a large number has?
Which set of numbers that add to 10 have the largest product?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you maximise the area available to a grazing goat?
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?