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Teacher guide reSolve: Gradient and Tangent

TLF ID M025321

This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign using the angle of elevation and create a sign for a ramp or slope around their school. In the second lesson students use photos and videos of 'the world's steepest street' to find the angle of elevation and tangent ratio of the street, then model the road system on a Cartesian plane. They analyse the elevation profile of the street and assess the accuracy of claims made about the street. The lessons are outlined in detail including curriculum links, vocabulary, materials needed, sample answers, discussion points and student resources. This sequence is part of the reSolve: Maths by Inquiry program.

Educational details

Educational value
  • This resource is very valuable for the year 9 mathematics content description about applying trigonometry to solve right-angled triangle problems. Students use the tangent trigonometric ratio to explore the grade or 'steepness' of streets and how this is related to the angle of elevation and 'rise over run'.
  • The resource is also valuable for the year 9 mathematics content description about finding the gradient of a line segment using a range of strategies, including graphing software. As students investigate the steepness of streets and signs, they use a range of representations and strategies to find the gradient of different streets and roads. This includes using a range of numerical data, photographs and graphs and employing software such as Geogebra to measure angles from photographs and represent the problems on the Cartesian plane.
  • The resource is of value for supporting the Numeracy general capability. The lesson provides multiple opportunities for students to solve and model problems involving complex data by estimating and calculating using a variety of efficient mental, written and digital strategies.
  • This resource is also of pedagogical value as it supports teachers in building an inquiry-focused learning environment with authentic application of mathematical skills and understandings. The unit aims to develop content knowledge as well as assisting students to understand the process of inquiry.
Year level


Other details

  • Contributor
  • Name: Education Services Australia
  • Organization: Education Services Australia
  • Description: Data manager
  • Address: VIC, AUSTRALIA
  • URL:
  • Copyright Holder
  • Name: Australian Government Department of Education and Training
  • Organization: Australian Government Department of Education and Training
  • Publisher
  • Name: Australian Academy of Science
  • Organization: Australian Academy of Science
  • Description: Publisher
  • URL:
  • Resource metadata contributed by
  • Name: Education Services Australia Ltd
  • Organisation: Education Services Australia Ltd
  • Address: AUSTRALIA
  • URL:
Access profile
  • Unknown
Learning Resource Type
  • Online
  • © Australian Government Department of Education and Training 2017. Unless otherwise indicated, this material may be used in accordance with the Creative Commons Attribution 4.0 International (CC BY 4.0) licence.