P3 Area and Perimeter: Fence It, Cover It, Count It

An empty garden plot sits on a green lawn, a plain rectangle with nothing on it yet. "A garden plot. Two questions." Then the second line: "Round the edge. Inside the edge."

That is Garden Fence, a 30-second Primary 3 episode of our Topic Explainers series. A fence goes round the plot, one side at a time. Then squares of grass cover the inside, one row at a time. Then the same two questions are asked about a small square tile. Each shape gets two different answers with two different units. Watch it first, then read on.

Garden Fence: fence it, cover it, count it.

Area and perimeter arrive together in Primary 3 in the Singapore syllabus: the idea of each, measuring area in square centimetres (cm²) and square metres (m²), and finding the perimeter and area of a rectangle and a square. Children meet both at once, which is exactly why they mix them up. The video keeps them apart with one question each: are we going round the edge, or covering inside the edge?

The method

Perimeter: round the edge

The perimeter of a shape is the total length of its edge, the distance all the way round. A fence round a garden is a perimeter. So is a ribbon round a cake box, or the frame round a picture.

To find the perimeter, add the lengths of all the sides. A rectangle has 4 sides: two lengths and two widths. A square has 4 equal sides, so its perimeter is 4 times one side.

Perimeter is a length, so it is measured in m or cm.

Area: inside the edge

The area of a shape is the amount of flat surface inside its edge. The grass inside the fence is an area. So is the paper of a drawing, or the top of a table.

Area is measured by counting square units: squares that are 1 m on each side (1 m²) or 1 cm on each side (1 cm²). Cover the inside with squares, with no gaps and no overlaps, and count them.

For a rectangle, the squares always line up in equal rows, so there is no need to count one by one. Count the rows and how many squares are in each row, then multiply. That gives the rule your child will meet in school: the area of a rectangle is length × width.

Keep the units apart

Every answer needs its unit, and the unit says what kind of answer it is. A perimeter in m or cm is a length. An area in m² or cm² is a number of squares. "26 m" and "40 m²" can describe the same garden, but they answer different questions.

Worked examples

All the numbers below are the ones in the video.

Example 1: the fence round the garden

A garden plot is 8 m long and 5 m wide. How long is the fence round its edge?

Step 1: Name the question. A fence goes round the edge, so this is the perimeter.

Step 2: Go round the shape, one side at a time. Start at one corner and say each side as you pass it: top 8 m, right side 5 m, bottom 8 m, left side 5 m.

Step 3: Add the four sides. 8 + 5 + 8 + 5 = 26.

The fence is 26 m long.

The video shows the fence with a post at every metre, and when all four sides are up there are 26 posts. Counting posts is a nice way to see that perimeter really is a length all the way round. A quicker way, once your child is confident: one length and one width make half the way round, 8 + 5 = 13, so the whole way round is 2 × 13 = 26 m.

Example 2: the grass inside

The inside of the garden is covered with grass squares, each 1 m by 1 m. What is the area of the garden?

Step 1: Name the question. The grass covers the inside, so this is the area. Each square is 1 m².

Step 2: Count the squares in one row. The plot is 8 m long, so 8 squares fit along each row.

Step 3: Count the rows. The plot is 5 m wide, so there are 5 rows.

Step 4: Multiply. 5 rows of 8 squares: 5 × 8 = 40.

The area of the garden is 40 m².

Check: add the rows one at a time: 8, 16, 24, 32, 40. Same answer.

Example 3: the square tile

A square tile has sides of 7 cm. Find its perimeter and its area.

Perimeter. Round the edge: 4 sides of 7 cm. 4 × 7 = 28, so the perimeter is 28 cm. You can also add: 7 + 7 + 7 + 7 = 28.

Area. Inside: 1 cm squares fill the tile in 7 rows of 7. 7 × 7 = 49, so the area is 49 cm².

Notice that the tile is measured in centimetres, so its answers are in cm and cm², and the garden's answers are in m and m². Each shape keeps its own units.

Try one at home

A rectangle is 6 cm long and 4 cm wide. Find its perimeter and its area.

Round the edge: 6 + 4 + 6 + 4 = 20, so the perimeter is 20 cm. Inside: 4 rows of 6 squares, 4 × 6 = 24, so the area is 24 cm². If your child has squared paper, draw it and count the squares to check.

Common mistakes

Adding only two sides. 8 + 5 = 13 m is only half of the fence. Ask your child to trace the whole edge with a finger and say all four sides aloud before adding.
Adding for area, or multiplying for perimeter. 8 + 5 = 13 is not the area, and 8 × 5 = 40 is not the perimeter. Ask the video's question first: "Round the edge, or inside the edge?"
Leaving out the unit, or using the wrong one. "40" is not finished. "40 m" is a length, and the area is 40 m². Say the unit aloud with every answer.
Writing m2 instead of m². The small raised 2 is part of the unit. It tells you the answer counts squares.
For a square, multiplying the side by itself for the perimeter. 7 × 7 = 49 is the tile's area. Its perimeter is 4 sides of 7 cm, which is 28 cm.
Thinking a bigger perimeter always means a bigger area. A 9 m by 4 m plot has the same 26 m fence as the 8 m by 5 m garden, but only 36 m² of grass. Perimeter and area are different measures, so it is worth checking each one separately.

Parent tips

Walk the edge, then cover the inside. Pick a rectangle at home, such as a rug, a table top or a book cover. Run a finger round its edge for the perimeter, then lay flat hands or sticky notes on it for the area. The two actions feel different, which helps the two ideas feel different.
Use squared paper. Draw rectangles and squares on 1 cm squared paper. Count the squares inside for the area, and count the unit lengths round the edge for the perimeter.
Measure something real. Use a ruler to measure a placemat or a tile in centimetres, then work out both its perimeter and its area together.
Pace out a corridor or a corner. Use a metre ruler or a 1 m length of string to mark one metre on the floor, or tape out a 1 m by 1 m square. That square is one square metre, which helps your child picture m².
Ask "round or inside?" Before any area or perimeter question, at home or in schoolwork, ask that one question. Once your child answers it, the method usually follows.

For one more garden to try, our post on P3 math hide and seek has a 9 m by 6 m plot among its five everyday questions.

A step at a time, when your child needs it

Near the end of the video, a worked-solution page slides in and its rows unlock one by one, with a last row labelled "Worked solution". "Every question has a worked solution. Open a hint when you want a step."

That is how progressive hints and worked solutions work in Singapore Math Drills: every question can be opened up step by step, and every question has a full worked solution to read afterwards. A child who is stuck on whether to add or multiply can open one step and keep going, instead of giving up or guessing.

And practice stays calm by design: no guilt-tripping over a missed day and no dark patterns, with your child's progress only ever measured against their own. Fence it, cover it, count it.

Try a sample

Try a free interactive Primary 3 worksheet and see how calm practice feels, with no signup or credit card required.

Try a free Singapore math sample