Graphing Exponentials

Syllabus Indicators:

• Graph simple non-linear relations, with and without the use of digital technologies (ACMNA296)
  • Complete tables of values to graph simple non-linear relationships and compare these with graphs drawn using digital technologies

Learning goals:

• Quantify the rates of growth of linear and exponential relationships.
• Model real situations using graphs, tables, and words.
• Recognise the equation of an exponential curve as y =ae^x

Working Mathematically Skills:

• Make generalisations about the characteristics of non-linear relationships (Reasoning)
• Compare two remuneration rates to ascertain which is the most profitable (Reasoning)
• Make decisions about the means to solve the problem and transform a word problem into two algebraic relationships (Problem Solving)
• Make predictions about the path of relationships (Reasoning)

Resources:

• Last Man Standing activity: https://www.teacherspayteachers.com/Product/Last-Man-Standing-A-Hands-On-Activity-to-Introduce-Exponential-Functions-1195202
• 100 paper squares for every 3-4 students; one side blank, the other reading 'ALIVE'
• Pocket Money problem
• A range of pretend money
• What Comes Next?

Description of Lesson:

Introduction: (15 mins)

• Activity One: Pocket Money Problem [AFL]

• This problem is open ended and can be approached in different ways: students can plot, make a table, create an equation, role play with fake money, or play out both scenarios in words. Students can work in pairs to complete this task. Bring the class together to explore the different strategies students adopted, and plot the two scenarios on the board together to reach a consensus.

Body: (35 mins)

• Activity Two: Last Man Standing [TECH]
  • In groups of 3-4, students play out the 'last man standing' scenario, leading to point plotting of a decreasing exponential function
  • Discussion Questions:
  • Did every group get the same graph?
  • Do the graphs have anything in common?
  • This leads to the term 'intercept'.
  • Is the y-intercept always 1?

Conclusion: (5 mins)

Reiterate the key learning ideas for the lesson.

Lesson Evaluation Questions:

• Did all of your students understand and meet the learning goals?
• Were all students engaged and participating?
• Were the activities appropriate and relevant for the stage of my learners?
• What would you change about the activities next time?

Homework/Enrichment Activities:

Students complete the activity "What Comes Next?" [TECH]. This activity presents an interactive side of Desmos; and allows the teacher to review answers as an Assessment For Learning (AFL).