![Summing Consecutive Numbers](/sites/default/files/styles/medium/public/thumbnails/content-97-05-six4-icon.png?itok=qriTyABd)
problem
Summing Consecutive Numbers
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?
![Why 24?](/sites/default/files/styles/medium/public/thumbnails/content-00-12-six2-icon.png?itok=IDw_MNsq)
problem
Why 24?
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.
![CD Heaven](/sites/default/files/styles/medium/public/thumbnails/content-02-06-six4-icon.jpg?itok=fsB1RXyP)
problem
CD Heaven
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?
![Attractive Tablecloths](/sites/default/files/styles/medium/public/thumbnails/content-03-03-six1-icon.gif?itok=SiNNF02K)
problem
Attractive Tablecloths
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?
![What's it worth?](/sites/default/files/styles/medium/public/thumbnails/content-01-04-penta5-icon.gif?itok=gGcp640G)
problem
What's it worth?
There are lots of different methods to find out what the shapes are worth - how many can you find?
![Coordinate Patterns](/sites/default/files/styles/medium/public/thumbnails/content-id-2292-icon.png?itok=tWsgfytK)
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Coordinate Patterns
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
![Painted Cube](/sites/default/files/styles/medium/public/thumbnails/content-id-2322-icon.png?itok=r3fcelpR)
problem
Painted Cube
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?
![Route to infinity](/sites/default/files/styles/medium/public/thumbnails/content-id-5469-icon.png?itok=277vYUz4)
problem
Route to infinity
Can you describe this route to infinity? Where will the arrows take you next?
![Reflecting Lines](/sites/default/files/styles/medium/public/thumbnails/content-id-6471-icon.jpg?itok=_vqW58fF)
problem
Reflecting Lines
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.
![Translating Lines](/sites/default/files/styles/medium/public/thumbnails/translating-lines.jpg?itok=_v1DZ7lJ)
problem
Translating Lines
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
findings.
![Tower of Hanoi](/sites/default/files/styles/medium/public/thumbnails/content-id-6690-icon.png?itok=VXO_iBIu)
problem
Tower of Hanoi
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
![Partly Painted Cube](/sites/default/files/styles/medium/public/thumbnails/content-id-6903-icon.png?itok=30VqrbOD)
problem
Partly Painted Cube
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?
![Which is bigger?](/sites/default/files/styles/medium/public/thumbnails/content-id-7344-icon.png?itok=Dq9q7UTS)
problem
Which is bigger?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
![Fill Me Up](/sites/default/files/styles/medium/public/thumbnails/content-id-7419-icon.jpg?itok=oU7VFjD1)
problem
Fill Me Up
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
![Factorising with Multilink](/sites/default/files/styles/medium/public/thumbnails/content-id-7490-icon.png?itok=JmNdK-Pw)
problem
Factorising with Multilink
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
![What's that graph?](/sites/default/files/styles/medium/public/thumbnails/content-id-7502-icon.jpg?itok=LHizmXXB)
![Steel Cables](/sites/default/files/styles/medium/public/thumbnails/content-id-7760-icon.png?itok=iTS5VCIy)
problem
Steel Cables
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
![What numbers can we make now?](/sites/default/files/styles/medium/public/thumbnails/content-id-8280-icon.jpg?itok=ba4RvjmQ)
problem
What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
![Quadratic Patterns](/sites/default/files/styles/medium/public/thumbnails/content-id-11011-icon.png?itok=Gz1WPuzi)
problem
Quadratic Patterns
Surprising numerical patterns can be explained using algebra and diagrams...
![Surprising Transformations](/sites/default/files/styles/medium/public/thumbnails/content-id-6544-icon.jpg?itok=48Xkr569)
problem
Surprising Transformations
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?
![How far does it move?](/sites/default/files/styles/medium/public/thumbnails/content-id-4808-icon.png?itok=lRYsUuCi)
problem
How far does it move?
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.
![Back fitter](/sites/default/files/styles/medium/public/thumbnails/content-id-6506-icon.gif?itok=gbCv-A6B)
problem
Back fitter
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?