Content:
MA4-LEN-C-01
Solve problems involving the perimeter of various quadrilaterals and simple composite figures
- Solve problems involving the perimeter of plane shapes, including parallelograms, trapeziums, rhombuses and kites
- Solve problems relating to the perimeter of simple composite figures
- Compare methods of solution for finding perimeter and evaluate the efficiency of those methods
Describe the relationships between the features of circles
- Identify and describe the relationship between circle features, including the radius, diameter, arc, chord, sector and segment of a circle, and a tangent to a circle
- Define \( \pi \) as the ratio of the circumference to the diameter of any circle
- Verify that the number \( \pi \) is a constant and develop the formula for the circumference of a circle
- Apply the formula for the circumference of a circle in terms of the diameter \( d \) or radius \( r \) (circumference of a circle = \( \pi d \) or \( 2\pi r \)) to solve related problems to solve related problems
- Establish the arc length formula \( l=\frac{\theta}{360^\circ}\times2\pi r \) where is the arc length and is the angle subtended at the centre by the arc
- Solve problems by finding arc lengths and the perimeter of sectors, giving an exact answer in terms of or an approximate answer
- Find the perimeter of quadrants, semicircles and simple composite figures consisting of 2 shapes in a variety of contexts, including using digital tools
MA4-ARE-C-01
Develop and use formulas to find the area of rectangles, triangles and parallelograms to solve problems
- Apply the formula to find the area of a rectangle or square: \( A=lb \) , where \( l \) is the length and \( b \) is the breadth (or width) of the rectangle or square
- Develop and apply the formula to find the area of a triangle: \( A=\frac{1}{2}bh \), where \( b \) is the base length and \( h \) is the perpendicular height
- Develop and apply the formula to find the area of a parallelogram: \( A=bh \) where \( b \) is the base length and \( h \) is the perpendicular height
- Calculate the area of composite figures that can be dissected into rectangles, squares, parallelograms or triangles to solve problems
Develop and use the formula to find the area of circles and sectors to solve problems
- Develop and apply the formula to find the area of a circle: \( A=\pi r^2 \) where \( r \) is the length of the radius
- Explain how the area of a sector can be developed from the area of a circle \( A=\frac{\theta}{360^\circ} \times \pi r^2 \)
- Find the area of quadrants, semicircles and sectors, and apply these formulas in the context of real-life problems
- Calculate the areas of composite shapes involving quadrants, semicircles and sectors to solve problems
Develop and use the formulas to find the area of trapeziums, rhombuses and kites to solve problems
- Develop and apply the formula to find the area of a kite or rhombus: \( A=\frac{1}{2}xy \) where \( x \) and \( y \) are the lengths of the diagonals
- Develop and apply the formula to find the area of a trapezium: \( A=\frac{h}{2}(a+b) \) where \( h \) is the perpendicular height and \( a \) and \( b \) are the lengths of parallel sides
- Calculate the area of composite shapes involving trapeziums, kites and rhombuses to solve problems
Choose appropriate units of measurement for area and convert between units
- Choose an appropriate unit to measure the area of different shapes and surfaces and justify the choice
- Convert between metric units of area using \( 1 cm^2=100 mm^2 \), \( 1 m^2=10 000 cm^2 \), \( 1 ha=10 000 m^2 \) and \( 1 km^2=1 000 000 m^2=100 ha \).
MA4-VOL-C-01
Describe the different views of prisms and solids that have been formed from prism combinations
- Represent prisms from different views in 2 dimensions, including top, side, front and back views
- Describe and illustrate solids formed from prism combinations from different views in 2 dimensions, including top, side, front and back views
- Identify and illustrate the cross-sections of different prisms
- Examine the idea that prisms have a uniform cross-section that is equal to the base area
- Determine if a particular solid has a uniform cross-section
Develop and apply the formula to find the volume of a prism to solve problems
- Develop the formula for the volume of a prism: \( V= base\ area \times height\), leading to \( V= Ah \)
- Apply the formula for the volume of a prism to prisms with uniform cross-sections to solve problems
Develop the formula for finding the volume of a cylinder and apply the formula to solve problems
- Develop and apply the formula to solve problems involving the volume of cylinders: \( V= \pi r^2h \)
where \( r \) is the length of the radius of the base and \( h \) is the perpendicular height
Choose appropriate units of measurement for volume and capacity and convert between units
- Recognise that 1000 L is equal to 1 kilolitre (kL) and use the abbreviation
- Recognise that 1000 kL is equal to 1 megalitre (ML) and use the abbreviation
- Choose an appropriate unit to measure the volume or capacity of different objects and justify the choice
- Convert between metric units of volume and capacity (\( 1 cm^3=1000 mm^3\), \( 1 cm^3=1 mL\), \( 1 m^3=1000 L= 1KL\), \( 1000 KL=1 ML\))
- Solve practical problems involving the volume and capacity of right prisms and cylinders
