Measurement, Space & Statistics

Geometry and Location: Symmetry, Maps and Grids

Year 3 · Year 4

✓Identify and describe symmetrical shapes and patterns in the environment and in two-dimensional shapes.
✓Draw lines of symmetry on two-dimensional shapes.
✓Interpret and create simple maps using symbols, legends (keys) and directional language.
✓Use grid references (coordinates) to describe locations on a grid and follow directions to move between locations.

Key concepts

Symmetry

A shape or object has symmetry if one half is a perfect mirror image of the other half. This means if you fold the shape along a special line, both halves will match up exactly.

Line of Symmetry (or Axis of Symmetry)

This is an imaginary line that divides a symmetrical shape or object into two identical halves. If you fold the shape along this line, the two halves will perfectly overlap.

Map

A map is a drawing that shows an area, like a park, a neighbourhood, or a country, from above. Maps help us find places and understand where things are located.

Legend (or Key)

The legend, also called a key, is a list of symbols used on a map and what each symbol means. It helps you understand what different pictures or colours on the map represent.

Grid

A grid is a pattern of lines that cross each other to form squares. Grids are often used on maps to help us find exact locations easily.

Grid Reference (or Coordinate)

A grid reference is a special 'address' that tells you the exact location of a square on a grid. It is usually made up of a letter (from the bottom or top) and a number (from the side), for example, A3 or B2. We always say the letter first, then the number.

Key facts to remember

1A shape is symmetrical if it can be folded in half so that both halves match exactly.
2The fold line that creates two identical halves is called a line of symmetry.
3Some shapes, like a square, can have more than one line of symmetry.
4Maps use symbols and a legend (or key) to represent different features and places.
5A grid uses a pattern of lines to form squares, helping to locate places precisely.
6A grid reference (or coordinate) uses a letter and a number (e.g., A4, C2) to pinpoint an exact square on a grid.
7When giving a grid reference, always say the letter first, then the number (e.g., 'B3', not '3B').

Worked examples

Example 1

Which of these shapes has a line of symmetry? Draw all lines of symmetry on the symmetrical shapes.

ILook at the first shape (a rectangle). Imagine folding it vertically down the middle. The halves match. Imagine folding it horizontally across the middle. The halves match. So, a rectangle has lines of symmetry.

IILook at the second shape (a heart). Imagine folding it vertically down the middle. The halves match. So, a heart has a line of symmetry.

IIILook at the third shape (a scalene triangle, where all sides are different lengths). Imagine folding it in any way. The halves do not match perfectly. So, this triangle does not have a line of symmetry.

IVDraw the lines where the shapes fold perfectly on the rectangle and the heart.

Answer

The rectangle and the heart shape have lines of symmetry. (The rectangle has two lines of symmetry: one vertical, one horizontal. The heart has one vertical line of symmetry).

Some shapes can have more than one line of symmetry!

Example 2

Draw all the lines of symmetry for a square.

IImagine folding the square in half from top to bottom (vertically). It matches. Draw this line.

IIImagine folding the square in half from left to right (horizontally). It matches. Draw this line.

IIIImagine folding the square from one corner to the opposite corner (diagonally). It matches. Draw this line.

IVImagine folding the square from the other corner to its opposite corner (diagonally). It matches. Draw this line.

Answer

A square has four lines of symmetry: one vertical, one horizontal, and two diagonal lines.

Always use a ruler to draw straight and accurate lines of symmetry.

Example 3

Look at the map grid below. \n\n[Imagine a 3x3 grid. Columns labelled A, B, C. Rows labelled 1, 2, 3.]\n[Symbols: Tree at A1, House at B2, Shop at C1, Park at A3, School at B1]\n\nLegend:\n🌳 = Tree\n🏠 = House\n🛒 = Shop\n🏞️ = Park\n🏫 = School\n\n1. What is at grid reference B2?\n2. What is the grid reference for the Park?\n3. Describe how to get from the Tree to the Shop.

I1. To find what is at B2: First, find the letter 'B' along the top of the grid. Then, move down to the row labelled '2'. The symbol at this location is a House (🏠).

II2. To find the grid reference for the Park: First, locate the Park symbol (🏞️) on the map. Then, look up to see the letter above it (A) and look across to see the number next to it (3). So, the grid reference is A3.

III3. To describe how to get from the Tree to the Shop: The Tree is at A1. The Shop is at C1. To move from A1 to C1, you need to move across the grid. Count how many squares you move to the right. From A to B is 1 square right, from B to C is another 1 square right. So, you move 2 squares to the right.

Answer

1. A House (🏠) is at grid reference B2.\n2. The grid reference for the Park is A3.\n3. To get from the Tree to the Shop, move 2 squares to the right.

Always refer to the legend (key) to understand the symbols on the map. Remember: 'along the corridor (letter), then up the stairs (number)' for grid references.

Common mistakes

✗Confusing a line of symmetry with any line that simply cuts a shape in half; the halves must be mirror images.
✗Missing some lines of symmetry for shapes that have multiple (e.g., only drawing two lines of symmetry for a square instead of four).
✗Not checking the legend (key) when reading a map, leading to misinterpreting symbols.
✗Mixing up the order of letters and numbers when giving grid references (e.g., saying '2A' instead of 'A2').
✗Not carefully following directional instructions on a grid, such as 'move 2 squares right' or 'move 1 square down'.

Exam tips

★For symmetry questions, imagine folding the shape along the line you draw. Do both sides match perfectly? If not, it's not a line of symmetry.
★Use a ruler to draw all lines of symmetry to ensure they are straight and accurate.
★Always look at the map's legend (key) first to understand what each symbol represents before answering questions about the map.
★When using a grid, remember the rule: 'along the corridor (letter), then up the stairs (number)' to correctly identify grid references.

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