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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Low Threshold High Ceiling

### Low Threshold High Ceiling - an Introduction

### Creating a Low Threshold High Ceiling Classroom

### Sizing Them Up

### Sort the Street

### Inside Triangles

### Noah

### How Many?

### Totality

### Four Triangles Puzzle

### Poly Plug Rectangles

### Tiling

### Nine-pin Triangles

### Neighbourly Addition

### Magic Crosses

### Reach 100

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Links to the NRICH website Home page

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30 April (Primary), 1 May (Secondary)

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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.

Age 5 to 18

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

Age 5 to 18

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

Age 5 to 7

Challenge Level

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

Age 5 to 7

Challenge Level

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

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?

Age 5 to 7

Challenge Level

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

Age 5 to 11

Challenge Level

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

Age 5 to 11

Challenge Level

This is an adding game for two players. Can you be the first to reach the target?

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 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?

Age 7 to 11

Challenge Level

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

Age 7 to 11

Challenge Level

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

Age 7 to 14

Challenge Level

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

Age 7 to 14

Challenge Level

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

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.