Can you find a way to prove the trig identities using a diagram?
A table has blocks of wood placed on and next to it. Can you work out how tall it is?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Can you find the sum of all of the numbers in the table?
How will you work out which numbers have been used to create this multiplication square?
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
This is a challenging game of strategy for two players with many interesting variations.
Weekly Problem 7 - 2014
The diagram shows a shaded shape bounded by circular arcs. What is the difference in area betweeen this and the equilateral triangle shown?
This article for teachers explains why geoboards are such an invaluable resource and introduces several tasks which make use of them.
These problems invite you to look again at ideas you may think you know inside-out.
An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?
A messenger runs from the rear to the head of a marching column and back. When he gets back, the rear is where the head was when he set off. What is the ratio of his speed to that of the column?
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
This article for primary teachers outlines how using counters can support mathematical teaching and learning.
In this article we outline how cubes can support children in working mathematically and draw attention to tasks which exemplify this.
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.
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?
Take Three From Five - December 2011
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?
Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Look at the advanced way of viewing sin and cos through their power series.
The first of two articles for teachers explaining how to include talk in maths presentations.
The second of two articles explaining how to include talk in maths presentations.
Weekly Problem 10 - 2017
Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?
A fun game for two. You'll need some counters.
Can you work out the equations of the trig graphs I used to make my pattern?
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
Twisting and turning with ropes can be encoded mathematically using fractions. Can you find a way to get back to zero?
Weekly Problem 29 - 2008
The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Use the tangram pieces to make our pictures, or to design some of your own!
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Can you make five differently sized squares from the tangram pieces?
A fun puzzle with tantrix tiles.
A simulation of target archery practice
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
This collection of tasks are for an adult and child working together.
Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.