An environment which simulates working with Cuisenaire rods.
Can you work out which drink has the stronger flavour?
How much of the square is coloured blue? How will the pattern continue?
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.
Can all unit fractions be written as the sum of two unit fractions?
It would be nice to have a strategy for disentangling any tangled ropes...
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
Can you see how to build a harmonic triangle? Can you work out the next two rows?
An environment which simulates working with Cuisenaire rods.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
There are lots of ideas to explore in these sequences of ordered fractions.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?
Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
An activity for teachers to initiate that adds to learners' developing understanding of fractions.
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.
Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?
This article, written for primary teachers, links to rich tasks which will help develop the underlying concepts associated with fractions and offers some suggestions for models and images that help. . . .
Can you work out the parentage of the ancient hero Gilgamesh?
This article extends and investigates the ideas in the problem "Stretching Fractions".
I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?
Can you tangle yourself up and reach any fraction?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
A Sudoku with clues as ratios or fractions.
Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
This article, written by Nicky Goulder and Samantha Lodge, reveals how maths and marimbas can go hand-in-hand! Why not try out some of the musical maths activities in your own classroom?
Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?
Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?
In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?
Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!
Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?
Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?
Work out the fractions to match the cards with the same amount of money.
Match the halves.
Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
Who first used fractions? Were they always written in the same way? How did fractions reach us here? These are the sorts of questions which this article will answer for you.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
Investigate the successive areas of light blue in these diagrams.
We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?