How Many Squares?
Class 5 · Mathematics
5 ideas in Class 5 Mathematics, explained in plain words, with games and quizzes to practise.
Area by Counting Squares
Part of: Measuring the space a shape covers
Area tells us how much flat surface a shape covers. We find it by counting squares of side 1 cm. If a shape covers 15 such squares, its area is 15 square cm. Two shapes that look very different can still cover the same number of squares.
Why it matters. Children often mix up how long something is with how much space it covers. Counting squares builds a real feel for area before any formula is used.
Try it in two minutes
- Draw a 1 cm grid on paper, or use a squared notebook page.
- Place a leaf or a postage stamp on it and trace around it.
- Ask: about how many full squares does it cover? How many half squares?
- Ask your child to say the area using the words square cm.
Try at home. Trace two different leaves on squared paper and ask your child which has the bigger area and by how many squares.
Area and Perimeter Are Different
Part of: Measuring the space a shape covers
Perimeter is the length of the boundary of a shape, like a fence around a field. Area is the space inside. Take 12 squares: laid in a single row they make a long thin rectangle with a long boundary, but laid as 3 rows of 4 they make a compact rectangle with a shorter boundary. The area is 12 square cm both times.
Why it matters. Children often use one number for both ideas. Knowing the difference helps in everyday jobs like fencing, framing and tiling.
Try it in two minutes
- Give your child 12 small square coins, buttons or sticky notes.
- Ask them to make a rectangle, and then a different rectangle with all 12.
- Walk a finger around the outside of each and count the edges.
- Ask: did the space inside change? Did the boundary change?
Try at home. Ask your child to make three rectangles from 16 squares and say which has the shortest boundary.
Area of Triangles as Halves of Rectangles
Part of: Triangles and halves
A straight cut from one corner of a rectangle to the opposite corner makes two triangles that are exactly the same size. So each triangle has half the area of the rectangle. A triangle whose base is a full side of the rectangle and whose tip touches the opposite side is also half the rectangle, even when it looks quite different.
Why it matters. Children learn that a tricky shape can be understood by relating it to a simple one. This habit helps in many later topics.
Try it in two minutes
- Cut a rectangle out of paper and ask for its area in squares.
- Fold it along the corner-to-corner line and cut. Place one piece on top of the other.
- Ask: are they the same? What is the area of each piece?
- Try a tip placed in the middle of one side and see how it splits the rectangle.
Try at home. Ask your child to draw three different triangles inside one rectangle on squared paper, each with half the area of the rectangle.
Shapes Made from Five Squares
Part of: Shapes from squares and tiles
Join 5 equal squares edge to edge and you get a shape. There are 12 different ways to do it, if turning or flipping a shape does not count as new. All of them have the same area, 5 squares, but their boundaries can be different lengths. A straight row of 5 has a long boundary, while a chunkier shape has a shorter one.
Why it matters. Building shapes from squares trains children to see space, to be patient and to check their own work. It also shows once more that area and perimeter are separate ideas.
Try it in two minutes
- Give your child 5 small squares such as sticky notes or square biscuits.
- Ask them to make a shape where every square touches another along a full edge.
- Ask for a second, different shape. Count the squares again and say the area.
- Compare the two boundaries. Which looks longer?
Try at home. Ask your child to make as many different shapes as possible from 5 squares and draw each one on squared paper.
Tiles and Patterns
Part of: Shapes from squares and tiles
A tile is a shape that can be repeated to cover a floor with no gaps. You can make a new tile from a square by cutting a piece from one side and fixing it to another side. The tile looks different, but its area is the same as the square you began with. Copies of the tile can then fill a floor, and the floor area is the tile area times the number of tiles.
Why it matters. It joins area, shapes and patterns in a creative task. Children see that cutting and moving a piece does not add or remove any area.
Try it in two minutes
- Cut a square from thick paper. Cut a small triangle from one edge.
- Stick the triangle on the opposite edge with tape. This is your new tile.
- Trace the tile again and again on paper to cover a page without gaps.
- Ask: what is the area of one tile? How many tiles are on the page?
Try at home. Ask your child to design a tile from a 4 cm square, trace it six times without gaps, and work out the total area.
What your child will practise
- Area and Perimeter Are Different: Space Sort (Sort It Out)
- Area by Counting Squares: Number Quest (Collect the Answer)
- Area of Triangles as Halves of Rectangles: Jungle Quick Fire (Quick Fire)
- Shapes Made from Five Squares: Jungle Puzzle (Clue Puzzle)
- Tiles and Patterns: Desert Quick Fire (Quick Fire)
- Quiz: Area and Perimeter Are Different (8 questions)
- Quiz: Area by Counting Squares (8 questions)
- Quiz: Area of Triangles as Halves of Rectangles (8 questions)
- Quiz: Shapes Made from Five Squares (8 questions)