- Mathematics
- Year 8
Measurement & Pythagoras' Theorem
approx. 21 hrs
5 topics
42 concepts
Boost your knowledge of Measurement and Pythagoras' theorem and improve your results.
approx. 21 hrs
5 topics
42 concepts
Boost your knowledge of Measurement and Pythagoras' theorem and improve your results.
Measurement and Pythagoras' Theorem is aligned with requirements of the Measurement and Geometry strand of the Australian curriculum. In this learning program, we teach students the formulae to calculate the volume of rectangular prisms and cylinders, convert between units of length and area, and calculate the hypotenuse and/or shorter side of right angled triangles.
This learning program is made up of the following 5 topics, broken down into 42 concepts.
Finding the area of a circle or sector using approximations of pi
Develop and use the formula to find the area of circles
Develop and use the formulas to find the area of rhombus/ kites
Identify a trapezium, rhombus or kite in different orientations
Develop and use the formula to find the area of trapeziums
Calculate the areas of composite figures by dissection into triangles, special quadrilaterals, quadrants, semicircles and sectors
Find the areas of quadrants, semicircles and sectors
Draw representations of prisms from different views
Identify and draw the cross-sections of different prisms
Find the volumes of composite solids involving prisms and cylinders
Convert between metric units of volume
Develop and use the formula for the volume of cylinders and find the capacity
Develop and use the formula for the volume of right prisms and find the capacity
Convert between metric units of volume and capacity
Identify a Pythagorean triad
Solve a variety of practical problems involving Pythagoras' theorem, giving exact answers (ie as surds where appropriate)
Discover and use Pythagoras' theorem to establish whether a triangle has a right angle
Identify a surd as an irrational number
Solve a variety of practical problems involving Pythagoras' theorem
Use Pythagoras' theorem to find the length of an unknown side in a right-angled triangle
Use Pythagoras' theorem to find the length of the hypotenuse side in a right-angled triangle
Solve a variety of problems involving duration
Add and subtract time mentally using bridging strategies
Converting fractions or decimals to hours, minutes and seconds
Compare times using Australian time zones
Round answers to time calculations to the nearest minute or hour
Converting units of time
Add and subtract time with a calculator, including by using the 'degrees, minutes, seconds' button
Solve problems involving international time zones
Investigate pi as the ratio of the circumference to the diameter of a circle
Solve problems involving circles and parts of circles, giving answers in terms of pi, using the calculator or using approximations of pi
Identify and name parts of a circle and related lines, including arc, tangent, chord, sector and segment
Find the diameter and/or radius of a circle, given its circumference
Find the perimeters of quadrants and semicircles
Use an approximation of pi to find the circumference of a circle
Find the perimeters of composite figures including sectors
Develop and use the formulas to find the circumferences of circles in terms of the diameter or radius
Compare perimeters of rectangles with the same area
Find the dimensions of a rectangle, given its perimeter and the length of one side
Use formulae to find the arc length of a sector
Find the perimeter of sectors including quadrants and semicircles
Find the perimeters of a range of plane shapes, including composite figures
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