YEAR 8 MATHS FOCUS
MEASUREMENT AND GEOMETRY
RIGHT ANGLED TRIANGLES (PYTHAGORAS)
OUTCOME
A student:
MA4-16MG:
- applies Pythagoras’ theorem to calculate side lengths in right-angled triangles, and solves related problems
| TEACHING POINTS | In Stage 3, students are continuing to develop their skills of visual imagery, including the ability to perceive and hold an appropriate mental image of an object or arrangement, and to predict the orientation or shape of an object that has been moved or altered. Also see Year 5 |
| LANGUAGE | Students should be able to communicate using the following language: object, shape, three-dimensional object (3D object), prism, cube, pyramid, base, uniform cross-section, face, edge, vertex (vertices), top view, front view, side view, net. |
EXPECTATIONS OF ATTAINMENT
| Investigate pythagoras-theorem and its application to solving simple problems involving right-angled triangles (ACMMG222) | identify the hypotenuse as the longest side in any right-angled triangle and also as the side opposite the right angle |
establish the relationship between the lengths of the sides of a right-angled triangle in practical ways, including with the use of digital technologiesInformation and communication technology capability Critical and creative thinking
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use Pythagoras’ theorem to find the length of an unknown side in a right-angled triangle
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| write answers to a specified or sensible level of accuracy, using an ‘approximately equals’ sign, ie ≑ or ≈ | |
solve a variety of practical problems involving Pythagoras’ theorem, approximating the answer as a decimal
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| identify a Pythagorean triad as a set of three numbers such that the sum of the squares of the first two equals the square of the third | |
| use the converse of Pythagoras’ theorem to establish whether a triangle has a right angle |
| Investigate the concept of irrational numbers (ACMNA186) | use technology to explore decimal approximations of surds
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| solve a variety of practical problems involving Pythagoras’ theorem, giving exact answers (ie as surds where appropriate), eg √5 |
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