Low Threshold High Ceiling Resources for Primary Teachers

This feature focuses on using those tasks which most children can access, because the mathematical content is relatively simple, yet which offer opportunities for children to extend their thinking and reasoning skills through the choices they make.

LTHC was a feature several years ago and so we thought it was about time to update it, particularly in line with the new mathematics National Curriculum (DfE, 2013). We have reflected on what it means to call a task LTHC as well as adding some new thinking to this feature.


This article explores what LTHC tasks are and why they are a firm favourite here at NRICH. We recommend that you start by reading the article to understand what makes a task LTHC and then delve into some of the activities we have selected.

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?

Magic Vs 

Age 7 to 11 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Sort the Street 

Age 5 to 7 Challenge Level:
Sort the houses in my street into different groups. Can you do it in any other ways?

Number Differences 

Age 7 to 11 Challenge Level:
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?


Age 5 to 11 Challenge Level:
This is an adding game for two players.

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.

Four Triangles Puzzle 

Age 5 to 11 Challenge Level:
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?


Age 5 to 7 Challenge Level:
Noah saw 12 legs walk by into the Ark. How many creatures did he see?


Age 7 to 11 Challenge Level:
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?