4. Exponents and Powers

Student Resource:1

1.  Exponential and Linear Growth

2. Exponential and Linear Decay

Student Resource: 2

Student Resource: 3

Student Resource: 4

Student Resource: 5

Student Resources: 6

Student Resources: 7

Teacher Notes: 

General Instructions for GeoGebra:

• Before starting with graphing, the teacher is advised to make learners draw meaning from the tables given below. An initial differentiation of the different “ways” (i.e. either iterative addition/subtraction or iterative multiplication/division) in which a value can “increase/decrease” should be done.

• To hide the Algebra interface on GeoGebra, Click on the left hand toggle switch > three dots > cross button

• To deselect a point(s) on GeoGebra, click on the respective coloured bullet(s) in the Algebra section

Activity: 

• Before starting with graphing, the teacher is advised to make learners draw meaning from the tables given below. An initial differentiation of the different “ways” (i.e. either iterative addition/subtraction or iterative multiplication/division) in which a value can “increase/decrease” should be done.
• To hide the Algebra interface on GeoGebra, Click on the left hand toggle switch > three dots > cross button
• To deselect a point(s) on GeoGebra, click on the respective coloured bullet(s) in the Algebra section

• Table (SR1) contains sample data for exponential and linear growth and decay. 
• Learners express on the IFP: On an empty graph with initial points (SR2, SR4), they use GeoGebra to plot the remaining points.
• Learners join these points using the annotation/free-hand function/pen tool on the IFP and the teacher helps them critically observe the different types of growth/decay.

Assessment:

• Each learner starts with a piece of paper with an assumed thickness of 1mm.
• The teacher asks them to fold the paper in half and pose the question: what is the thickness now?
• Learners are urged to do this process again and answer the same question.
• After 5 iterations, the thickness of the paper becomes 32mm. Are learners able to answer this? 
• Compare the above process to a linear model wherein the thickness is increased linearly (by adding subsequent layers of identical papers, for example, 6 pages of a notebook held together for 5 iterations). Are learners able to answer this?
• In the same activity, learners are asked to evaluate the rate of change/decrement factor of the decreasing area. 
• On an empty Geogebra sheet (SR6), learners create, graph, and analyse the above example. (Hint: Put the number of iterations on the x-axis and length/area on the y axis). Compare with the sample (SR7) provided. Assume initial thickness = 1 mm and Initial area = 64 square units.
• Based on the graph, learners may answer the following:
  • At which iteration is thickness numerically equal to the area?
  • Fill in the blanks: After at least ___ iterations, the area will be less than 0.5 square units.