Mixed Attainment Maths Conference - January 2019

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

Poly Plug Rectangles

Age 5 to 11
Challenge Level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Reach 100

Age 7 to 11
Challenge Level

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.

Dozens

Age 7 to 14
Challenge Level

Can you select the missing digit(s) to find the largest multiple?

Shifting Times Tables

Age 11 to 14
Challenge Level

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

Odds, Evens and More Evens

Age 11 to 14
Challenge Level

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

Magic Letters

Age 11 to 14
Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Polygon Rings

Age 11 to 14
Challenge Level

Join pentagons together edge to edge. Will they form a ring?

Tilted Squares

Age 11 to 14
Challenge Level

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

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?

Unequal Averages

Age 11 to 14
Challenge Level

Play around with sets of five numbers and see what you can discover about different types of average...

Charlie's Delightful Machine

Age 11 to 16
Challenge Level

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

Cyclic Quadrilaterals

Age 11 to 16
Challenge Level

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

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?

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?

Pair Productslive

Age 14 to 16
Challenge Level

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

Hollow Squares

Age 14 to 16
Challenge Level

Which armies can be arranged in hollow square fighting formations?

Odds and Evens Made Fair

Age 14 to 16
Challenge Level

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.