• 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.

Available in
NT QLD SA TAS VIC WA

Overview

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.

Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 42 concepts.

  • Discovering Pythagoras' Theorem 7 concepts

    1. Identify a surd as an irrational number

    2. Identify a Pythagorean triad

    3. Discover and use Pythagoras' theorem to establish whether a triangle has a right angle

    4. Solve a variety of practical problems involving Pythagoras' theorem, giving exact answers (ie as surds where appropriate)

    5. Use Pythagoras' theorem to find the length of an unknown side in a right-angled triangle

    6. Solve a variety of practical problems involving Pythagoras' theorem

    7. Use Pythagoras' theorem to find the length of the hypotenuse side in a right-angled triangle

  • Area of Special Quadrilaterals and Circles 7 concepts

    1. Finding the area of a circle or sector using approximations of pi

    2. Develop and use the formulas to find the area of rhombus/ kites

    3. Develop and use the formula to find the area of trapeziums

    4. Identify a trapezium, rhombus or kite in different orientations

    5. Develop and use the formula to find the area of circles

    6. Calculate the areas of composite figures by dissection into triangles, special quadrilaterals, quadrants, semicircles and sectors

    7. Find the areas of quadrants, semicircles and sectors

  • Volume of Prisms and Cylinders 7 concepts

    1. Draw representations of prisms from different views

    2. Identify and draw the cross-sections of different prisms

    3. Find the volumes of composite solids involving prisms and cylinders

    4. Convert between metric units of volume

    5. Develop and use the formula for the volume of right prisms and find the capacity

    6. Develop and use the formula for the volume of cylinders and find the capacity

    7. Convert between metric units of volume and capacity

  • Time 8 concepts

    1. Add and subtract time mentally using bridging strategies

    2. Converting fractions or decimals to hours, minutes and seconds

    3. Solve a variety of problems involving duration

    4. Compare times using Australian time zones

    5. Add and subtract time with a calculator, including by using the 'degrees, minutes, seconds' button

    6. Round answers to time calculations to the nearest minute or hour

    7. Converting units of time

    8. Solve problems involving international time zones

  • Length 13 concepts

    1. Investigate pi as the ratio of the circumference to the diameter of a circle

    2. Develop and use the formulas to find the circumferences of circles in terms of the diameter or radius

    3. Use an approximation of pi to find the circumference of a circle

    4. Identify and name parts of a circle and related lines, including arc, tangent, chord, sector and segment

    5. Find the diameter and/or radius of a circle, given its circumference

    6. Find the perimeters of quadrants and semicircles

    7. Find the perimeters of composite figures including sectors

    8. Solve problems involving circles and parts of circles, giving answers in terms of pi, using the calculator or using approximations of pi

    9. Compare perimeters of rectangles with the same area

    10. Find the dimensions of a rectangle, given its perimeter and the length of one side

    11. Use formulae to find the arc length of a sector

    12. Find the perimeter of sectors including quadrants and semicircles

    13. Find the perimeters of a range of plane shapes, including composite figures

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Measurement & Pythagoras' Theorem

Reporting

  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

Fully flexible

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Access to practice questions

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