A low threshold high ceiling task is one which is designed to be mathematically accessible, and to have built-in extension opportunities. In other words, everyone can get started and everyone can get stuck. In this updated feature, we bring together our favourite low threshold high ceiling tasks, as well as two articles which will support you in creating a low threshold high ceiling
classroom.

The last day for submitting solutions to our live problems is Monday 9 December.

In this article for teachers, we explain what is meant by Low Threshold High Ceiling tasks, and why we like them.

This article explores the key features of a Low Threshold High Ceiling classroom.

Can you put these shapes in order of size? Start with the smallest.

Sort the houses in my street into different groups. Can you do it in any other ways?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Have a look at these photos of different fruit. How many do you see? How did you count?

This is an adding game for two players.

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?

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?

An investigation that gives you the opportunity to make and justify predictions.

How many different triangles can you make on a circular pegboard that has nine pegs?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Can you find examples of magic crosses? Can you find all the possibilities?

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.