YEAR 8 MATHS FOCUS
MEASUREMENT AND GEOMETRY
RIGHT ANGLED TRIANGLES (PYTHAGORAS)
OUTCOME
A student:
MA416MG:
 applies Pythagoras’ theorem to calculate side lengths in rightangled 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, threedimensional object (3D object), prism, cube, pyramid, base, uniform crosssection, face, edge, vertex (vertices), top view, front view, side view, net. 
EXPECTATIONS OF ATTAINMENT
Investigate pythagorastheorem and its application to solving simple problems involving rightangled triangles (ACMMG222)  identify the hypotenuse as the longest side in any rightangled triangle and also as the side opposite the right angle 
establish the relationship between the lengths of the sides of a rightangled triangle in practical ways, including with the use of digital technologiesInformation and communication technology capability Critical and creative thinking
 
use Pythagoras’ theorem to find the length of an unknown side in a rightangled triangle
 
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
 
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

solve a variety of practical problems involving Pythagoras’ theorem, giving exact answers (ie as surds where appropriate), eg √5 
to be added
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