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### Number and algebra

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# Being Collaborative - Algebra

### Summing Consecutive Numbers

### Why 24?

### CD Heaven

### Attractive Tablecloths

### What's it Worth?

### Coordinate Patterns

### Painted Cube

### How Far Does it Move?

### Route to Infinity

### Diamond Collector

### Reflecting Lines

### Back Fitter

### Translating Lines

### Surprising TransformationsLive

### Tower of Hanoi

### Partly Painted Cube

### Which Is Bigger?

### Fill Me Up

### Factorising with Multilink

### What's That Graph?Live

### Steel Cables

### What Numbers Can We Make Now?

### Quadratic Patterns

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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?

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.

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?

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?

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?

Age 11 to 14

Challenge Level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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?

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.

Age 11 to 14

Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

Age 11 to 16

Challenge Level

Collect as many diamonds as you can by drawing three straight 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.

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?

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.

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?

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.

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?

Age 14 to 16

Challenge Level

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

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?

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?

Age 14 to 18

Challenge Level

Can you work out which processes are represented by the graphs?

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?

Age 11 to 14

Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Age 11 to 14

Challenge Level

Surprising numerical patterns can be explained using algebra and diagrams...