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Can you see how to build a harmonic triangle? Can you work out the next two rows?
Can all unit fractions be written as the sum of two unit fractions?
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
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.
A jigsaw where pieces only go together if the fractions are equivalent.
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.
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.
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?
Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
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?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
What is the smallest number with exactly 14 divisors?
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. . . .
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?
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 find rectangles where the value of the area is the same as the value of the perimeter?
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
The sums of the squares of three related numbers is also a perfect square - can you explain why?
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?
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.
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Explore the effect of reflecting in two parallel mirror lines.
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 find the area of a parallelogram defined by two vectors?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
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?
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. . . .
Explore the effect of combining enlargements.
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
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?
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?
According to an old Indian myth, Sissa ben Dahir was a courtier for a king. The king decided to reward Sissa for his dedication and Sissa asked for one grain of rice to be put on the first square. . . .
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?
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.
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?