# IGCSE Mathematics Foundation: Perimeter, Area and Volume

## Scheme of work: IGCSE Foundation: Year 10: Term 3: Perimeter, Area and Volume

#### Prerequisite Knowledge

1. Know the Names of 2D Shapes
• Concept: Recognizing and naming common 2D shapes such as rectangles, triangles, parallelograms, trapezia, and compound shapes.
• Example: $\text{Common 2D shapes include: rectangle, triangle, parallelogram, trapezium, square, and circle.}$
• Concept: Understanding the properties of different quadrilaterals, including rectangles, parallelograms, and trapezia.
• Example: $\text{Rectangle: Opposite sides are equal and all angles are } 90^\circ.$ $\text{Parallelogram: Opposite sides are equal and opposite angles are equal.}$ $\text{Trapezium: Only one pair of opposite sides is parallel.}$

#### Success Criteria

1. Calculate the Perimeter of Rectangles, Triangles, Parallelograms, Trapezia, and Compound Shapes
• Objective: Accurately calculate the perimeter of various shapes by summing the lengths of their sides.
• Example: $\text{For a rectangle with length } l \text{ and width } w, \text{ the perimeter } P = 2l + 2w.$ $\text{For a triangle with sides } a, b, \text{ and } c, \text{ the perimeter } P = a + b + c.$ $\text{For a parallelogram with sides } a \text{ and } b, \text{ the perimeter } P = 2a + 2b.$ $\text{For a trapezium with sides } a, b, c, \text{ and } d, \text{ the perimeter } P = a + b + c + d.$ $\text{For compound shapes, add the lengths of all the outer sides.}$
2. Calculate the Area of Rectangles, Triangles, Parallelograms, Trapezia, and Compound Shapes
• Objective: Accurately calculate the area of various shapes using the appropriate formulas.
• Example: $\text{For a rectangle with length } l \text{ and width } w, \text{ the area } A = l \times w.$ $\text{For a triangle with base } b \text{ and height } h, \text{ the area } A = \frac{1}{2} b \times h.$ $\text{For a parallelogram with base } b \text{ and height } h, \text{ the area } A = b \times h.$ $\text{For a trapezium with parallel sides } a \text{ and } b \text{ and height } h, \text{ the area } A = \frac{1}{2} (a + b) \times h.$ $\text{For compound shapes, divide the shape into simpler shapes, calculate their areas, and sum them up.}$
3. Calculate the Volumes of Cubes and Cuboids
• Objective: Accurately calculate the volume of cubes and cuboids using the appropriate formulas.
• Example: $\text{For a cube with side length } s, \text{ the volume } V = s^3.$ $\text{For a cuboid with length } l, \text{ width } w, \text{ and height } h, \text{ the volume } V = l \times w \times h.$
4. Calculate the Surface Areas of Cubes and Cuboids
• Objective: Accurately calculate the surface area of cubes and cuboids using the appropriate formulas.
• Example: $\text{For a cube with side length } s, \text{ the surface area } SA = 6s^2.$ $\text{For a cuboid with length } l, \text{ width } w, \text{ and height } h, \text{ the surface area } SA = 2(lw + lh + wh).$

#### Key Concepts

1. Calculate the Perimeter of Rectangles, Triangles, Parallelograms, Trapezia, and Compound Shapes
• Concept: The perimeter is the total distance around the edge of a shape. It is calculated by summing the lengths of all sides.
• Example: $\text{For a rectangle with length } l \text{ and width } w, \text{ the perimeter } P = 2l + 2w.$ $\text{For a triangle with sides } a, b, \text{ and } c, \text{ the perimeter } P = a + b + c.$ $\text{For a parallelogram with sides } a \text{ and } b, \text{ the perimeter } P = 2a + 2b.$ $\text{For a trapezium with sides } a, b, c, \text{ and } d, \text{ the perimeter } P = a + b + c + d.$ $\text{For compound shapes, add the lengths of all the outer sides.}$
2. Calculate the Area of Rectangles, Triangles, Parallelograms, Trapezia, and Compound Shapes
• Concept: The area is the amount of space inside a shape. It is calculated using specific formulas for each type of shape.
• Example: $\text{For a rectangle with length } l \text{ and width } w, \text{ the area } A = l \times w.$ $\text{For a triangle with base } b \text{ and height } h, \text{ the area } A = \frac{1}{2} b \times h.$ $\text{For a parallelogram with base } b \text{ and height } h, \text{ the area } A = b \times h.$ $\text{For a trapezium with parallel sides } a \text{ and } b \text{ and height } h, \text{ the area } A = \frac{1}{2} (a + b) \times h.$ $\text{For compound shapes, divide the shape into simpler shapes, calculate their areas, and sum them up.}$
3. Calculate the Volumes of Cubes and Cuboids
• Concept: The volume is the amount of space inside a 3D shape. It is calculated using specific formulas for cubes and cuboids.
• Example: $\text{For a cube with side length } s, \text{ the volume } V = s^3.$ $\text{For a cuboid with length } l, \text{ width } w, \text{ and height } h, \text{ the volume } V = l \times w \times h.$
4. Calculate the Surface Areas of Cubes and Cuboids
• Concept: The surface area is the total area of all the faces of a 3D shape. It is calculated using specific formulas for cubes and cuboids.
• Example: $\text{For a cube with side length } s, \text{ the surface area } SA = 6s^2.$ $\text{For a cuboid with length } l, \text{ width } w, \text{ and height } h, \text{ the surface area } SA = 2(lw + lh + wh).$

#### Common Misconceptions

1. Calculate the Perimeter of Rectangles, Triangles, Parallelograms, Trapezia, and Compound Shapes
• Common Mistake: Forgetting to include all sides when calculating the perimeter, especially with compound shapes.
• Example: $\text{Incorrect: For a rectangle with } l = 5 \text{ and } w = 3, \text{ calculating the perimeter as } P = l + w = 5 + 3 = 8.$ $\text{Correct: For a rectangle with } l = 5 \text{ and } w = 3, \text{ the perimeter } P = 2l + 2w = 2(5) + 2(3) = 10 + 6 = 16.$
2. Calculate the Area of Rectangles, Triangles, Parallelograms, Trapezia, and Compound Shapes
• Common Mistake: Using incorrect formulas for the area of different shapes, such as confusing the formula for a triangle with that of a rectangle.
• Example: $\text{Incorrect: For a triangle with base } b = 6 \text{ and height } h = 4, \text{ calculating the area as } A = b \times h = 6 \times 4 = 24.$ $\text{Correct: For a triangle with base } b = 6 \text{ and height } h = 4, \text{ the area } A = \frac{1}{2} b \times h = \frac{1}{2} (6 \times 4) = 12.$
3. Calculate the Volumes of Cubes and Cuboids
• Common Mistake: Mixing up the dimensions or using incorrect units when calculating volume.
• Example: $\text{Incorrect: For a cuboid with } l = 4, w = 3, \text{ and } h = 2, \text{ calculating the volume as } V = l + w + h = 4 + 3 + 2 = 9.$ $\text{Correct: For a cuboid with } l = 4, w = 3, \text{ and } h = 2, \text{ the volume } V = l \times w \times h = 4 \times 3 \times 2 = 24.$
4. Calculate the Surface Areas of Cubes and Cuboids
• Common Mistake: Forgetting to account for all faces of the shape or incorrectly applying the formula.
• Example: $\text{Incorrect: For a cube with side length } s = 3, \text{ calculating the surface area as } SA = 3s^2 = 3(3^2) = 27.$ $\text{Correct: For a cube with side length } s = 3, \text{ the surface area } SA = 6s^2 = 6(3^2) = 54.$

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