AC9M9M03
See also: Learning Areas / Mathematics / Mathematics / Measurement / Year 9
solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles
Elaborations
- AC9M9M03_E1 - investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
- AC9M9M03_E2 - applying the formula for calculation of distances between points on the Cartesian plane from their coordinates, emphasising the connection to vertical and horizontal displacements between the points
- AC9M9M03_E3 - understanding the relationship between the corresponding sides of similar right-angled triangles and establishing the relationship between areas of similar figures and the ratio of corresponding sides, the scale factor
- AC9M9M03_E4 - using images of proportional relationships to estimate actual measurements; for example, taking a photograph of a person standing in front of a tree and using the image and scale to estimate the height of the tree, discussing the findings and ways to improve the estimates
- AC9M9M03_E5 - investigating theorems and conjectures involving triangles; for example, the triangle inequality, and generalising links between the Pythagorean rule for right-angled triangles, and related inequalities for acute and obtuse triangles; determining the minimal sets of information for a triangle from which other measures can all be determined
- AC9M9M03_E6 - using knowledge of similar triangles, Pythagoras’ theorem, rates and algebra to design and construct a Biltmore stick used to measure the diameter and height of a tree, and calculating the density and dry mass to predict how much paper could be manufactured from the tree
Achievement Standard Components
- ASMAT909 - Students solve problems involving ratio, similarity and scale in two-dimensional situations.
- ASMAT911 - Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles.
- ASMAT912 - They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings.