Applications of Measurement

measurement year11 standard

Applications of measurement | NSW Curriculum Website

• MST-11-05 solves problems involving measurement in practical contexts

📖 Prior Knowledge

Content	Prior knowledge	Used for
Length	- perimeter of plane shapes	- repeated content
Right-angled Triangles	- Pythagoras’ theorem	- repeated content - irregular shaped land
Area	- converting units of area - area of plane shapes	- repeated content - trapezoidal rule
Area and Surface Area A	- surface area of prisms, cylinders.	- repeated content
Area and Surface Area B	- surface area of spheres, composite solids	- repeated content
Volume A	- surface area of prisms and composite solids	- repeated content
Volume B	- volume of pyramids, cones, spheres, composite solids	- repeated content
Numbers of Any Magnitude	- converting metric units, significant figures	- repeated content

Practicalities of measurement

• Identify and convert between the metric units of length: millimetres (mm), centimetres (c), metres (m) and kilometres (km)
• Identify and convert between metric units of area using $1{\text{cm}}^2=100{\text{mm}}^2$, $1{\text{m}}^2=10000{\text{cm}}^2$, $1\text{ha}=10000{\text{m}}^2$, and $1{\text{km}}^2=1000000{\text{m}}^2$
• Identify and convert between metric units of volume, using $1{\text{ cm}}^3=1000{\text{ mm}}^3$, $1{\text{ m}}^3=1000000{\text{ cm}}^3$, and $1{\text{ km}}^3=1000000000{\text{ m}}^3$
• Identify and convert between the metric units of capacity: millilitres (mL), litres (L), kilolitres (kL) and megalitres (ML)
• Identify and between metric units of volume and capacity, using $1{\text{cm}}^3=1000{\text{mm}}^3$, $1{\text{cm}}^3=1\text{mL}$, $1{\text{m}}^3=1000\text{L}=1\text{kL}$, $1000\text{kL}=1\text{ML}$
• Identify and convert between the metric units of mass: milligrams (mg), grams (g), kilograms (kg) and tonnes (t)
• Apply scientific notation to represent numbers involving standard prefixes: nano- (n) for ${10}^{-9}$, micro- (µ) for $10^{-6}$, milli- (m) for $10^{-3}$, centi- (c) for ${10}^{-2}$, kilo- (k) for ${10}^3$, mega- (M) for ${10}^6$, giga- (G) for ${10}^9$ and tera- (T) for ${10}^{12}$, with and without a required number of significant figures

Perimeter, area, and volume

• Solve practical problems requiring the calculation of perimeters and areas of triangles, rectangles, parallelograms, trapeziums, circles, sectors of circles and composite shapes in a variety of contexts
• Apply Pythagoras’ theorem to solve problems involving right-angled triangles
• Calculate perimeters and areas of irregularly shaped blocks of land by dissection into triangles, rectangles and trapeziums
• Solve practical problems involving the surface area of prisms, cylinders, spheres and composite solids in a variety of contexts
• Solve practical problems involving volume and capacity of prisms, cylinders, spheres, cones, pyramids and composite solids in a variety of contexts
• Apply the Trapezoidal rule $A\approx \frac{h}{2}\left(d_f+d_l\right)$, where $A$ is the area, $d_f$ and $d_l$ are the lengths of the parallel sides of the trapezium, $d_f$ is the first length and $d_l$ is the last length, and $h$ is the perpendicular distance between them, to solve a variety of practical problems involving area, volume and capacity for up to four applications