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	Prerequisite relationships
Represents Numbers A	- Approximate decimals to a given number of places → Round to significant figures
Multiplicative Relations B	- Multiply and divide decimals by powers of 10 → Convert between metric units of length - Multiply and divide decimals by powers of 10 → Convert between units of mass - Multiply and divide decimals by powers of 10 → Convert between units of area - Multiply and divide decimals by powers of 10 → Convert between units of volume and capacity - Multiply and divide decimals by powers of 10 → Express numbers in scientific notation
Geometric Measure A	- Use metres and kilometres → Convert between metric units of length - Calculate the perimeter of 2D shapes → Find the perimeter of composite figures - Calculate the perimeter of 2D shapes → Find a side length given the perimeter - Calculate the perimeter of 2D shapes → Solve problems with Pythagoras’ theorem
Geometric Measure B	- Convert between metric units of length (revisited content)
Two-dimensional Spatial Structure B	- Find the area of a triangle → Find an unknown side given the area - Find the area of a triangle → Find the surface area of a prism
Non-spatial Measure B	- Convert between units of mass (revisited content)
Fractions Decimals Percentages	- Solve problems with fractions and decimals of quantities → Find arc lengths and perimeters of sectors
Algebraic Techniques	- Substitute values into algebraic expressions → Find the circumference of a circle
Indices	- Evaluate numbers in index notation → Convert between units of volume and capacity
Equations	- Solve one-step linear equations → Find a side length given the perimeter - Solve one-step linear equations → Find the radius or diameter given the circumference - Solve 2-step linear equations → Find an unknown side given the area - Solve quadratic equations of the form $a{x}^2=c$ → Find an unknown given a circle or sector area
Length	- Find the perimeter of composite figures (revisited content) - Find missing sides of a rectilinear figure → Find the perimeter of composite figures - Find a side length given the perimeter (revisited content) - Define $\pi$ → Find the circumference of a circle - Find the circumference of a circle (revisited content) - Find arc lengths and perimeters of sectors (revisited content) - Find the radius or diameter given the circumference (revisited content) - Find perimeters of composites involving arcs (revisited content)
Right-angled Triangles	- Find a side using Pythagoras’ theorem → Solve problems with Pythagoras’ theorem - Find a side using Pythagoras’ theorem → Find the surface area of a prism - Solve problems with Pythagoras’ theorem (revisited content)
Area	- Find the area of a circle → Find the surface area of a cylinder - Find the area of a circle → Find the surface area of a sphere - Find the area of a circle → Find the volume of pyramids and cones - Find the area of sectors, quadrants and semicircles → Find an unknown given a circle or sector area - Find areas of composites involving circle parts → Solve composite area problems - Find the interior angle of a sector → Find arc lengths and perimeters of sectors - Find an unknown given a circle or sector area (revisited content) - Find the area of a trapezium → Apply the Trapezoidal rule - Choose appropriate units of area → Convert between units of area - Convert between units of area (revisited content) - Find an unknown side given the area (revisited content)
Volume	- Find the volume of a prism → Find the volume of pyramids and cones - Find the volume of a cylinder → Solve volume and capacity problems - Find the volume of a cylinder → Find volumes of composite solids - Find the volume of a cylinder → Find the volume of a sphere - Use units of volume and capacity → Convert between units of volume and capacity - Convert between units of volume and capacity (revisited content) - Solve volume and capacity problems (revisited content)
Indices A	- Apply negative-integer indices → Express numbers in scientific notation
Equations A	- Solve 3-step linear equations → Find the surface area of a prism
Numbers of Any Magnitude	- Identify measurement prefixes (revisited content) - Round to significant figures (revisited content) - Express numbers in scientific notation (revisited content)
Area and Surface Area A	- Solve composite area problems (revisited content) - Identify and create nets of prisms → Find the surface area of a prism - Find the surface area of a prism (revisited content) - Find the surface area of a cylinder (revisited content) - Find the surface area of a partial cylinder (revisited content) - Find surface areas of composite solids (revisited content)
Volume A	- Find volumes of composite prisms → Find volumes of composite solids - Find volumes of composite solids (revisited content)
Equations B	- Solve cubic equations of the form $a{x}^3=k$ → Find the volume of a sphere
Area and Surface Area B	- Identify slant and perpendicular heights (revisited content) - Find the surface area of a right pyramid → Solve surface area problems for composite solids - Find the surface area of a cone → Solve surface area problems for composite solids - Find the surface area of a sphere (revisited content) - Find the surface area of a hemisphere (revisited content) - Solve surface area problems for composite solids (revisited content)
Volume B	- Find the volume of pyramids and cones (revisited content) - Find the volume of a sphere (revisited content) - Find the volume of a hemisphere (revisited content) - Solve volume problems for composite solids (revisited 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