Low Threshold High Ceiling

Low Threshold High Ceiling

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.

Sizing Them Up 

Age 5 to 7 Challenge Level:
Can you put these shapes in order of size? Start with the smallest.

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?

Inside Triangles 

Age 5 to 7 Challenge Level:
How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Noah 

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

How Many? 

Age 5 to 11 Challenge Level:
Have a look at these photos of different fruit. How many do you see? How did you count?

Totality 

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

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?

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?

Tiling 

Age 7 to 11 Challenge Level:
An investigation that gives you the opportunity to make and justify predictions.

Nine-pin Triangles 

Age 7 to 11 Challenge Level:
How many different triangles can you make on a circular pegboard that has nine pegs?

Neighbourly Addition 

Age 7 to 14 Challenge Level:
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Magic Crosses 

Age 7 to 14 Challenge Level:
Can you find examples of magic crosses? Can you find all the possibilities?

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.