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

Star Find

Age 5 to 7
Challenge Level Yellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Star Find


Here is a grid made up of $9$ squares. All of them are the same except for one. Can you find the odd one out?

Grid of 9 squares, with patterns.

The basic tile from the design above looks like this:

Basic tile design.

In the star design, the tile has been turned around, or rotated , into different positions.
Below is a wall of $16$ blank tiles. Using the basic tile, can you make a repeating pattern to decorate our wall? Try making more designs by rotating the tile and using it in more than one position.

Grid of 16 squares.


Why do this problem?

This problem gives learners a chance to talk about similarities and differences, and also rotations and, in particular, quarter turns. These sheets may be useful to give to pairs or individuals:this sheet has $16$ copes of the basic tile and this sheet has a $4$ by $4$ grid which is the same size as the tiles.

Key questions

What can you tell me about this pattern?
What is the same about these two tiles?
What is different about these two tiles?
How can we make this tile look the same as that one?
How will you arrange the tiles to make your own pattern?

Possible extension

Challenge children to make different repeating patterns using the tiles, or they could design their basic tile.

Possible support

Learners could try the Turning Man problem first.
 

You may also like

Hexpentas

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Exploded Squares

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

  • 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