KS2 Mathematics: Coordinates, Translations and Reflections

In Year 6 the coordinate grid grows from one quadrant to four. The national curriculum asks pupils to describe positions on the full coordinate grid, to draw and translate simple shapes on the coordinate plane, and to reflect them in the axes. Negative numbers now appear in the coordinates, and that is exactly where most mistakes happen: a sign dropped, x and y swapped, or a point reflected in the wrong axis.

This material trains those skills without needing a picture: every point and every shape is given by its coordinates, written with the x-coordinate first. The twelve quiz questions ask you to name the quadrant of a point, write the coordinates of a point described from the origin, translate a point and a vertex of a triangle, describe the translation that takes one point to another, reflect points in the x-axis and in the y-axis, find the missing vertex of a square and of a rectangle whose corners lie in different quadrants, find the distance between two points on the same horizontal line on either side of the y-axis, and find the point halfway between two points on a vertical line. The wrong options are the classic slips, so each one points to a specific misunderstanding.

The flashcards give the rules in short form: which quadrant is which, x before y, what a translation does and does not change, how reflecting in each axis changes the signs of the coordinates, and how to describe a translation in words.

The printable written work has eight tasks to answer on paper, where you can sketch your own grid: naming quadrants and spotting a point that lies on an axis, translating a whole triangle, describing a translation and its reverse, reflecting a triangle in each axis, completing a rectangle and working out its perimeter and area, completing a square from two opposite corners, writing a translation in general terms, and explaining a pupil's mistake with a reflection. Each task asks for a reason or a method, which is what the reasoning papers of the Key Stage 2 tests look for.

In the oral exam an examiner gives you coordinates one question at a time and asks you to explain your moves, for example why a point that is 3 units below the x-axis ends up 3 units above it after a reflection.

The material is written for Year 6 pupils preparing for the end of Key Stage 2 tests. A sheet of squared paper is useful: drawing the axes and plotting the points is the surest way to check an answer.

• Describe positions on the full coordinate grid, including negative coordinates
• Identify the quadrant of a point, or recognise that it lies on an axis
• Translate points and simple shapes and describe a translation in words
• Reflect points and shapes in the x-axis and the y-axis
• Use the properties of rectangles and squares to find missing vertices
• Find distances between points on the same horizontal or vertical line

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): geometry, position and direction (the full coordinate grid, translations and reflections in the axes).