Year 4: Area: counting squares
Part of the Year 4 perimeter, area and measures chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Area: counting squares
The area of a shape is the amount of flat space inside it. To find the area, we cover the shape with squares that are all the same size and count them. If each square is 1 cm by 1 cm, then each square has an area of 1 square centimetre, written 1 cm².
Count in rows. Counting row by row is neat. In the shape above there are 4 + 4 + 4 + 2 + 2 = 16 squares.
Rectangles: rows and columns. In a rectangle every row has the same number of squares. So we can multiply: number of rows × squares in each row. This is an array, like in your times tables.
Area is not perimeter. Perimeter is the distance round the edge (in cm). Area is the space inside (in cm²). A shape can have a big area and a small perimeter, or the other way round.
Splitting shapes. To find the area of an L-shape, split it into rectangles, find the area of each one, and add. In the picture each rectangle has its own colour.
Key words. Area is the space inside a shape. A square centimetre (cm²) is the area of a square with sides of 1 cm. A row goes across and a column goes down.
Key ideas
- Area = the number of squares that cover a shape. Units: cm² (or m²).
- Count carefully: row by row.
- Rectangle: rows × squares in each row (length × width).
- Split L-shapes into rectangles. Find each area and add.
- Area is the space inside. Perimeter is the distance round the edge. They are different!
- A bigger perimeter does not always mean a bigger area.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 4 squares
Row 2: 4 squares
Row 3: 4 squares
Row 4: 2 squares
Row 5: 2 squares - Add the rows. 4 + 4 = 8
8 + 4 = 12
12 + 2 = 14
14 + 2 = 16 - Write the area with its unit. Area is measured in square units.Area = 16 cm²
Check. Count in columns instead: 5 + 5 + 3 + 3 = 16. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 6 squares
Row 2: 6 squares
Row 3: 6 squares
Row 4: 6 squares - Add the rows. 6 + 6 = 12
12 + 6 = 18
18 + 6 = 24 - Use rows and columns as a quick way. This is a rectangle, so every row has the same number of squares.4 rows of 6 = 4 × 6 = 24
- Write the area with its unit. Area is measured in square units.Area = 24 cm²
Check. Count in columns instead: 4 + 4 + 4 + 4 + 4 + 4 = 24. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 7 cm long, so one row has 7 squares. It is 5 cm tall, so there are 5 rows.5 rows of 7 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.5 × 7 = 35
- Write the area with its unit. Area = 35 cm²
Check. Swap them: 7 × 5 = 35. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Split the shape into rectangles. Find the area of each one, then add the areas.
- Split the shape into rectangles. Rectangles are easy: area = rows × columns. We colour each rectangle so we do not mix them up.
- Find the area of each rectangle. Multiply the squares in a row by the number of rows.Rectangle A: 8 cm by 3 cm, area = 8 × 3 = 24 cm²
Rectangle B: 4 cm by 3 cm, area = 4 × 3 = 12 cm² - Add the areas together. 24 + 12 = 36
- Write the area with its unit. Area = 36 cm²
Check. Count the squares one by one: there are 36. ✓
Watch out. Make sure the rectangles do not overlap and nothing is left out.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 1 square
Row 2: 2 squares
Row 3: 3 squares
Row 4: 4 squares - Add the rows. 1 + 2 = 3
3 + 3 = 6
6 + 4 = 10 - Write the area with its unit. Area is measured in square units.Area = 10 cm²
Check. Count in columns instead: 4 + 3 + 2 + 1 = 10. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Find the area and the perimeter of each shape. Then compare.
- Find the area of shape A. Count the squares: 2 rows of 6.2 × 6 = 12 cm²
- Find the area of shape B. 3 rows of 4.3 × 4 = 12 cm²
- Find the perimeter of each shape. Add the sides.A: 6 + 2 + 6 + 2 = 16 cm
B: 4 + 3 + 4 + 3 = 14 cm - Compare. The areas are equal, but the perimeters are not.Same area (12 cm²), but different perimeters (16 cm and 14 cm).
Check. A: 2 × (6 + 2) = 16. B: 2 × (4 + 3) = 14. ✓
Watch out. Shapes with the same area can have different perimeters.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area = length × width, so divide the area by the side you know.
- Write what we know. Area = rows × columns, so the area is made from the two side lengths.9 × ? = 36
- Divide the area by the side we know. Division is the opposite of multiplication.36 ÷ 9 = 4
- Write the length with its unit. The answer is a length, so it is in cm (not cm²).The other side is 4 cm.
Check. 9 × 4 = 36. ✓
Watch out. The answer is a length in cm, not an area in cm².
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 6 m long, so one row has 6 squares. It is 4 m tall, so there are 4 rows.4 rows of 6 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.4 × 6 = 24
- Write the area with its unit. Area = 24 m²
Check. Swap them: 6 × 4 = 24. The answer is the same. ✓
Watch out. Area is in square units (m²). The perimeter is the distance round the edge, in m. Do not mix them up.
Watch out
Area is in squares, perimeter is in lengths. Do not add the sides to find the area, and do not multiply the sides to find the perimeter. Count every square once only. For an L-shape, make sure your rectangles do not overlap.Exercise 7I Area
Non-calculatorKey words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 1 square
Row 2: 2 squares
Row 3: 3 squares
Row 4: 4 squares - Add the rows. 1 + 2 = 3
3 + 3 = 6
6 + 4 = 10 - Write the area with its unit. Area is measured in square units.Area = 10 cm²
Check. Count in columns instead: 4 + 3 + 2 + 1 = 10. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 1 square
Row 2: 3 squares
Row 3: 1 square - Add the rows. 1 + 3 = 4
4 + 1 = 5 - Write the area with its unit. Area is measured in square units.Area = 5 cm²
Check. Count in columns instead: 1 + 3 + 1 = 5. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 2 squares
Row 2: 3 squares - Add the rows. 2 + 3 = 5
- Write the area with its unit. Area is measured in square units.Area = 5 cm²
Check. Count in columns instead: 2 + 1 + 2 = 5. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 4 cm long, so one row has 4 squares. It is 3 cm tall, so there are 3 rows.3 rows of 4 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.3 × 4 = 12
- Write the area with its unit. Area = 12 cm²
Check. Swap them: 4 × 3 = 12. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 7 cm long, so one row has 7 squares. It is 2 cm tall, so there are 2 rows.2 rows of 7 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.2 × 7 = 14
- Write the area with its unit. Area = 14 cm²
Check. Swap them: 7 × 2 = 14. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 5 cm long, so one row has 5 squares. It is 5 cm tall, so there are 5 rows.5 rows of 5 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.5 × 5 = 25
- Write the area with its unit. Area = 25 cm²
Check. Swap them: 5 × 5 = 25. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 8 cm long, so one row has 8 squares. It is 3 cm tall, so there are 3 rows.3 rows of 8 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.3 × 8 = 24
- Write the area with its unit. Area = 24 cm²
Check. Swap them: 8 × 3 = 24. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 9 cm long, so one row has 9 squares. It is 6 cm tall, so there are 6 rows.6 rows of 9 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.6 × 9 = 54
- Write the area with its unit. Area = 54 cm²
Check. Swap them: 9 × 6 = 54. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 12 cm long, so one row has 12 squares. It is 5 cm tall, so there are 5 rows.5 rows of 12 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.5 × 12 = 60
- Write the area with its unit. Area = 60 cm²
Check. Swap them: 12 × 5 = 60. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area of a rectangle: the number of squares in one row times the number of rows. (length × width)
- Picture the squares. The rectangle is 10 cm long, so one row has 10 squares. It is 10 cm tall, so there are 10 rows.10 rows of 10 squares
- Multiply the rows by the squares in each row. This is quicker than counting every square. It is an array, like in the times tables.10 × 10 = 100
- Write the area with its unit. Area = 100 cm²
Check. Swap them: 10 × 10 = 100. The answer is the same. ✓
Watch out. Area is in square units (cm²). The perimeter is the distance round the edge, in cm. Do not mix them up.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Split the shape into rectangles. Find the area of each one, then add the areas.
- Split the shape into rectangles. Rectangles are easy: area = rows × columns. We colour each rectangle so we do not mix them up.
- Find the area of each rectangle. Multiply the squares in a row by the number of rows.Rectangle A: 6 cm by 2 cm, area = 6 × 2 = 12 cm²
Rectangle B: 3 cm by 3 cm, area = 3 × 3 = 9 cm² - Add the areas together. 12 + 9 = 21
- Write the area with its unit. Area = 21 cm²
Check. Count the squares one by one: there are 21. ✓
Watch out. Make sure the rectangles do not overlap and nothing is left out.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Split the shape into rectangles. Find the area of each one, then add the areas.
- Split the shape into rectangles. Rectangles are easy: area = rows × columns. We colour each rectangle so we do not mix them up.
- Find the area of each rectangle. Multiply the squares in a row by the number of rows.Rectangle A: 5 cm by 4 cm, area = 5 × 4 = 20 cm²
Rectangle B: 2 cm by 2 cm, area = 2 × 2 = 4 cm² - Add the areas together. 20 + 4 = 24
- Write the area with its unit. Area = 24 cm²
Check. Count the squares one by one: there are 24. ✓
Watch out. Make sure the rectangles do not overlap and nothing is left out.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 4 squares
Row 2: 4 squares
Row 3: 4 squares - Add the rows. 4 + 4 = 8
8 + 4 = 12 - Use rows and columns as a quick way. This is a rectangle, so every row has the same number of squares.3 rows of 4 = 3 × 4 = 12
- Write the area with its unit. Area is measured in square units.Area = 12 cm²
Check. Count in columns instead: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 5 squares
Row 2: 5 squares
Row 3: 3 squares - Add the rows. 5 + 5 = 10
10 + 3 = 13 - Write the area with its unit. Area is measured in square units.Area = 13 cm²
Check. Count in columns instead: 3 + 3 + 3 + 2 + 2 = 13. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Compare the two areas. The bigger number of squares is the bigger area.
- Look at the two areas. We found them in parts (a) and (b).A = 12 cm² B = 13 cm²
- Compare and find the difference. 13 is more than 12.13 − 12 = 1. Shape B is bigger by 1 cm².
Check. 12 + 1 = 13. ✓
Watch out. Compare the areas, not how the shapes look.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.
- Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.Each square has an area of 1 cm² (one square centimetre).
- Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.Row 1: 4 squares
Row 2: 4 squares
Row 3: 4 squares
Row 4: 2 squares
Row 5: 2 squares - Add the rows. 4 + 4 = 8
8 + 4 = 12
12 + 2 = 14
14 + 2 = 16 - Write the area with its unit. Area is measured in square units.Area = 16 cm²
Check. Count in columns instead: 5 + 5 + 3 + 3 = 16. ✓
Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.
Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.
Method. The perimeter is the distance round the outside. Count the edges of the squares on the outside of the shape.
- Each side of a square is 1 cm long. So the perimeter is the number of square edges round the outside of the shape.Count only the edges on the OUTSIDE.
- Count the edges on each side of the shape. Counting the top, right, bottom and left separately helps you not to miss any.Top: 4
Right: 5
Bottom: 4
Left: 5 - Add them. 4 + 5 = 9
9 + 4 = 13
13 + 5 = 18 - Write the perimeter with its unit. Perimeter = 18 cm
Check. The top (4) matches the bottom (4), and the left (5) matches the right (5). That is a good sign. 2 × (4 + 5) = 18. ✓
Watch out. Do not count the lines inside the shape. Only the outside edges are part of the perimeter.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area = length × width, so divide the area by the side you know.
- Write what we know. Area = rows × columns, so the area is made from the two side lengths.9 × ? = 36
- Divide the area by the side we know. Division is the opposite of multiplication.36 ÷ 9 = 4
- Write the length with its unit. The answer is a length, so it is in cm (not cm²).The other side is 4 cm.
Check. 9 × 4 = 36. ✓
Watch out. The answer is a length in cm, not an area in cm².
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area = length × width, so divide the area by the side you know.
- Write what we know. Area = rows × columns, so the area is made from the two side lengths.6 × ? = 48
- Divide the area by the side we know. Division is the opposite of multiplication.48 ÷ 6 = 8
- Write the length with its unit. The answer is a length, so it is in cm (not cm²).The other side is 8 cm.
Check. 6 × 8 = 48. ✓
Watch out. The answer is a length in cm, not an area in cm².
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Area = length × width, so divide the area by the side you know.
- Write what we know. Area = rows × columns, so the area is made from the two side lengths.5 × ? = 30
- Divide the area by the side we know. Division is the opposite of multiplication.30 ÷ 5 = 6
- Write the length with its unit. The answer is a length, so it is in cm (not cm²).The other side is 6 cm.
Check. 5 × 6 = 30. ✓
Watch out. The answer is a length in cm, not an area in cm².
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. The number of tiles is the area. Multiply the rows by the number of tiles in each row.
- Picture the tiles. The room is 9 m long, so one row has 9 tiles. It is 6 m wide, so there are 6 rows.6 rows of 9 tiles
- Multiply. Rows × tiles in each row.6 × 9 = 54
- Write the answer. 54 tiles are needed.
Check. 9 × 6 = 54. ✓
Watch out. The number of 1 m tiles is the same as the area in m².
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. A sheet of stamps is an array. Multiply the number of rows by the number in each row.
- Picture the sheet. 5 rows of stamps with 8 stamps in each row.5 rows of 8
- Multiply. 5 × 8 = 40
- Write the answer. 40 stamps
Check. 8 × 5 = 40. ✓
Watch out. Rows times the number in each row.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. The number of stickers is the area of the card. Multiply the rows by the stickers in each row.
- Picture the stickers. One row has 12 stickers and there are 7 rows.7 rows of 12
- Multiply. Use the distributive law: 7 × 12 = 7 × 10 + 7 × 2.70 + 14 = 84
- Write the answer. 84 stickers
Check. 12 × 7 = 84. ✓
Watch out. Split 12 into 10 and 2 to multiply easily.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Split the shape into rectangles. Find the area of each one, then add the areas.
- Split the shape into rectangles. Rectangles are easy: area = rows × columns. We colour each rectangle so we do not mix them up.
- Find the area of each rectangle. Multiply the squares in a row by the number of rows.Rectangle A: 7 m by 3 m, area = 7 × 3 = 21 m²
Rectangle B: 4 m by 3 m, area = 4 × 3 = 12 m² - Add the areas together. 21 + 12 = 33
- Write the area with its unit. Area = 33 m²
Check. Count the squares one by one: there are 33. ✓
Watch out. Make sure the rectangles do not overlap and nothing is left out.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Work out the area correctly, and see what Mei did.
- Look at what Mei did. Mei added the sides: 4 + 5 + 4 + 5.4 + 5 + 4 + 5 = 18
- Find the mistake. Adding the sides gives the perimeter (the distance round the edge). The area is the number of squares inside.Mei found the perimeter.
- Work out the area. 4 rows of 5 squares.4 × 5 = 20 cm²
Check. Count the squares: 4 rows of 5 = 20. ✓
Watch out. Area: multiply. Perimeter: add the sides.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. List the pairs of whole numbers that multiply to make 12. Each pair is the length and width of a rectangle.
- Find the factor pairs of 12. The length and width multiply to make the area, 12.1 × 12, 2 × 6, 3 × 4
- Write each rectangle. The length is the longer side.12 cm by 1 cm: area 12 × 1 = 12 cm², perimeter = 26 cm
6 cm by 2 cm: area 6 × 2 = 12 cm², perimeter = 16 cm
4 cm by 3 cm: area 4 × 3 = 12 cm², perimeter = 14 cm - Count them. 3 different rectangles.
Check. There are no more factor pairs of 12. ✓
Watch out. A 2 by 6 rectangle is the same as a 6 by 2 rectangle turned round.
Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.
Method. Try some rectangles to see if a bigger perimeter always means a bigger area.
- Try a long, thin rectangle. 12 cm by 1 cm.Area = 12 cm². Perimeter = 26 cm.
- Try a square. 4 cm by 4 cm.Area = 16 cm². Perimeter = 16 cm.
- Compare. The thin rectangle has the bigger perimeter (26 cm > 16 cm) but the smaller area (12 cm² < 16 cm²).Sometimes it is true and sometimes it is not: sometimes.
Check. We found a case where it is false. ✓
Watch out. Area and perimeter measure different things.