Length

measurementandspace core

Length | NSW Curriculum Website

• MA4-LEN-C-01 applies knowledge of the perimeter of plane shapes and the circumference of circles to solve problems

📖 Prior Knowledge

Content	Prerequisite relationships
Additive Relations A	- Add and subtract numbers with different numbers of digits → Calculate the perimeter of 2D shapes
Geometric Measure A	- Calculate the perimeter of 2D shapes (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
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
Area	- Find the interior angle of a sector → Find arc lengths and perimeters of sectors

Solve problems involving the perimeter of various quadrilaterals and simple composite figures.pdf

• 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.pdf

• 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 $l=\frac{\theta }{360}\times 2\pi r$ where $l$ is the arc length and $\theta$ 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 $\pi$ 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