Mixed Attainment Maths Conference - January 2019

Resources shared by Charlie and Alison at the fifth Mixed Attainment Maths Conference, January 25th 2019

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

Twenty 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 sets...

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

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

Poly Plug Rectangles

Age 5 to 14 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?


Age 7 to 14 Challenge Level:

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Reach 100

Age 7 to 14 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.

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?

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?

Polygon Rings

Age 11 to 14 Challenge Level:

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

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...

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?

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?

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?

Hollow Squares

Age 14 to 16 Challenge Level:

Which armies can be arranged in hollow square fighting formations?

Pair Products

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?

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?

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.