Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Low Threshold High Ceiling Tasks

Low Threshold High Ceiling Tasks

We hope that you find you can easily get started on the activities in this feature but that you can also take the mathematics to great heights!

Sort the Street 
Age 5 to 7
Challenge Level Yellow star

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 Yellow star

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

Sizing Them Up 
Age 5 to 7
Challenge Level Yellow star

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

Noah 
Age 5 to 7
Challenge Level Yellow starYellow star

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

Totality 
Age 5 to 11
Challenge Level Yellow star

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

Four Triangles Puzzle 
Age 5 to 11
Challenge Level Yellow star

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 11
Challenge Level Yellow star

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?

How Many? 
Age 5 to 11
Challenge Level Yellow star

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

Nine-pin Triangles 
Age 7 to 11
Challenge Level Yellow star

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

Tiling 
Age 7 to 11
Challenge Level Yellow star

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

Reach 100 
Age 7 to 11
Challenge Level Yellow starYellow star

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.

Magic Crosses 
Age 7 to 14
Challenge Level Yellow star

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

Neighbourly Addition 
Age 7 to 14
Challenge Level Yellow star

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

Related

  • More Low Threshold High Ceiling Tasks

You may also like

Digging Into Geometry

Dig deeply into geometrical ideas by having a go at the tasks in this Primary student feature.

Past Features

Past Features for LP

Lower Primary Related Content Low Threshold High Ceiling Tasks

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo