problem
Summing Consecutive Numbers
Age
11 to 14
Challenge level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
problem
Why 24?
Age
14 to 16
Challenge level
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
problem
CD Heaven
Age
14 to 16
Challenge level
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 each
price?
problem
Attractive Tablecloths
Age
14 to 16
Challenge level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
problem
What's it worth?
Age
11 to 16
Challenge level
There are lots of different methods to find out what the shapes are worth - how many can you find?
problem
Coordinate Patterns
Age
11 to 14
Challenge level
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
problem
Painted Cube
Age
14 to 16
Challenge level
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?
problem
Route to infinity
Age
11 to 14
Challenge level
Can you describe this route to infinity? Where will the arrows take you next?
problem
Reflecting Lines
Age
11 to 14
Challenge level
Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
problem
Translating Lines
Age
11 to 14
Challenge level
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
findings.
problem
Tower of Hanoi
Age
11 to 14
Challenge level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Partly Painted Cube
Age
14 to 16
Challenge level
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
problem
Which is bigger?
Age
14 to 16
Challenge level
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
problem
Fill Me Up
Age
11 to 14
Challenge level
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
problem
Factorising with Multilink
Age
14 to 16
Challenge level
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
What's that graph?
Age
14 to 18
Challenge level
Can you work out which processes are represented by the graphs?
problem
Steel Cables
Age
14 to 16
Challenge level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
What numbers can we make now?
Age
11 to 14
Challenge level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
problem
Quadratic Patterns
Age
11 to 14
Challenge level
Surprising numerical patterns can be explained using algebra and diagrams...
problem
Surprising Transformations
Age
14 to 16
Challenge level
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
problem
How far does it move?
Age
11 to 14
Challenge level
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
problem
Back fitter
Age
14 to 18
Challenge level
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?