Mathematics / Year 9 / Measurement

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Curriculum content descriptions

solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles (AC9M9M03)

Elaborations
  • investigating the applications of Pythagoras’ theorem in authentic problems, including applying Pythagoras’ theorem and trigonometry to problems in surveying and design
  • 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
  • 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
  • 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
  • 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
  • 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
  • investigating how autonomous vehicles solve spatial problems using algorithms based on geometric properties relating to angles, distances and scale
General capabilities
  • Critical and creative thinking Critical and Creative Thinking
  • Numeracy Numeracy
ScOT terms

Similarity (Geometry),  Trigonometric ratios,  Distance,  Ratios,  Scale (Proportions),  Pythagoras theorem

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