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**When NRICH started out, the resources were created for, and used mainly by, the highest achieving students.**

Twenty five years on, our site has grown and changed, and our target audience is now teachers and students working at all levels. And yet we are still working to shake off the commonly held belief that NRICH is just for top set students...

For many years now, our aim has been, wherever possible, to publish "low threshold high ceiling" tasks that whole classes can work on together. With these tasks, everyone can get started, and everyone can get stuck!

**Here are some resources which you might find useful:**

Secondary Curriculum

Enriching the Secondary Curriculum

What we think and why we think it

Thinking Mathematically

Posters for the classroom.

Teachers can Register for the NRICH email newsletter to be kept up to date with our latest news.

**Below are some of our favourite "low threshold high ceiling" tasks for secondary students.**

### Poly Plug Rectangles

### Reach 100

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

### Cyclic Quadrilaterals

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Shifting Times Tables

Can you find a way to identify times tables after they have been shifted up or down?

### Charlie's delightful machine

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### Odds, Evens and More Evens

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

### Magic Letters

### 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?

### Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

### Unequal Averages

### Factorising with Multilink

### Steel Cables

### Pair Products

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?