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

Transformation Tease

Age 7 to 11
Challenge Level Yellow starYellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Amy, David, Euan, Lewis and Robert at St. Nicolas School, Newbury tried solving this problem. They have explained their solution very clearly although it is quite long!

The shape ABCD is a trapezium. We think the coordinates are A (4,2) B (6,2) C(7,1) D (3,1)

After moving 3 squares left and 4 up the new coordinates are A (1,6) B (3,6) C (4,5) D (0,5). We noticed that the x coordinate of the new number was 3 less than the original coordinate and the y coordinate was 4 more than the original coordinate.

We reflected the shape in the x axis. The new coordinates are A (4,-2) B(6,-2) C (7,-1) D (3,-1). The x coordinate stayed the same but the y coordinate has got a minus in front of it. We predicted the new coordinates after reflecting in the y axis A (-4,2) B (-6,2) C (-7,1) D (-3,1)

We reflected the original shape in the line y = -x. The new coordinates we found were A (-2,-4) B (-2,-6) C (-1,-7) D (-1,-3). These coordinates are the ones we came up with when we predicted reflecting the 3 points in the line y = -x. (-4,-2) (4,-6) (5,5)

When we took the original shape and rotated it anticlockwise about the origin, we came up with these coordinates A (-2,4) B (-2,6) C (-1,7) D (-1,3)

Looking at the patterns we found, this transformation could also be described as reflecting in the line y = -x and then reflecting in the x axis.
Example A starts (4,2), after reflecting in the line y = -x it is (-2,-4), and then reflecting in the x axis it is (-2,4), which is the same as rotating through 90 degrees.

You may also like

Times

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

Penta Play

A shape and space game for 2, 3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board.

Clocks

These clocks have been reflected in a mirror. What times do they say?

  • 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