Stage 5 - graphs of physical phenomenon reading and interpreting a non-linear graph

  • Draw graphs to represent the relationship between cross-sectional area and the depth of water in containers of different shapes when they are filled with water at a constant rate.
  • Predict which cross-sections will result in a linear graph when containers are filled with water at a constant rate.
  • Match linear and non-linear graphs with a selection of containers that are used in everyday life that have uniform and non – uniform cross-sections.
  • Skill focus: Graph simple parabolas, exponentials and circles on the Cartesian plane using tables of values and digital technologies.

Strategy

The students can:

Graph simple parabolas, exponentials and circles on the Cartesian plane using tables of values and digital technologies.

Activities to support the strategy

Teachers provide students with the opportunity to work collaboratively in small groups using the following checklist of questions to think about when unpacking a graph in either Year 7 or 9. Use the thinking strategy questions for all three different types of graphs.

Thinking strategy when reading graphs

1. What is the title of the graph?

2. Look at the horizontal axis

  • What is the label on the axis?
  • What is the scale being used?
  • What is the unit of measurement?

3. Look at the vertical axis

  • What is the label on the axis?
  • What is the scale being used?
  • What is the unit of measurement?

4. Now are the numbers shown as fraction, decimals, percentage, hundreds, thousands etc.?

5. What do the numbers represent?

References

Australian curriculum reference: ACMNA296

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

NSW syllabus reference: MA5.1 – 7NA

Graphs simple non-linear relationships

NSW literacy continuum reference: VOCC15M2

Vocabulary knowledge, Cluster 15, Marker 2: Uses a range of vocabulary for precision, clarity, cohesion and effect.

Other literacy continuum markers: SPEC15M5

Aspects of speaking, Cluster 15, Marker 5: Listens to and interprets increasingly complex spoken texts on challenging issues and abstract concepts.

Teacher resources

Numeracy app

Quick Graph: Quick Graph plots high quality 2D and 3D mathematical expressions. Graphs can be shaded with custom colours and in 3D the lighting is enabled to demonstrate the depth of the surface.

You can zoom in and out by pinching the image and pan around with one finger (2D) or two (3D). In both 3D and 2D modes, the graph adapts the evaluation limits when the touch gesture ends, allowing you to focus on specific features of the graph.

The 3D view allows for interactive rotation, translation and zooming by simple touch gestures. In addition, you can change from wireframe to solid visualization, with a simple double tap.

Quick Graph includes a wide variety of mathematical features and coordinate systems: Cartesian, Cylindrical and Spherical systems are supported for 3D equations, 2D equations support both Cartesian and Polar.

All graphs are automatically saved/restored whenever the application is closed/open

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