Introduce the topic of inflation/deflation, and change in prices/quantities of commodities used commonly.
Show the learners the table (SR1) and intuitively expose them to different kinds of growth/decay.
Ensure learners express well on the IFP while maintaining an inclusive environment.
The sample graphs (TR1 and TR2), where points are already mapped out and the curve is already traced, can be used to compare student-made graphs and the actual graphs.
Learners think aloud on how "quickly" the graph climbs up or falls down for exponential vs linear.
Use mathematical terms such as slope and rate of change.
Ask them to find/guess the scales of growth/decay in A1. What happens when the scale is written as a negative exponent?
For example, ask them if the decay factor of 3-1 in the typewriter graph drop the percentage to 0 or lesser? Use the GGB files (SR3 and SR5) to explain the infinite/asymptotic nature.
Create a strong foundation for the positivity of exponential decay. Reiterate that negative exponents do not imply numerical negativity.
In both growth and decay, ask the learners to intuitively find the range of these datasets. Learners think aloud whether any entry can eventually become zero, less than zero, or as large as possible? Does the exponential model support the claim? What about linear?
For AS1:
Use a mathematical representation of decreasing area in negative exponent notation. This will enhance the argument of positivity and the asymptotic nature of exponential models.
Repeat the same activity, this time with a graph paper. Help the students on how this step will simplify the process of calculating area.
[Contributed by raju.sambari@tiss.edu on 6. Juli 2023 01:21:13]
For A1:
Introduce the topic of inflation/deflation, and change in prices/quantities of commodities used commonly.
Show the learners the table (SR1) and intuitively expose them to different kinds of growth/decay.
Ensure learners express well on the IFP while maintaining an inclusive environment.
The sample graphs (TR1 and TR2), where points are already mapped out and the curve is already traced, can be used to compare student-made graphs and the actual graphs.
Learners think aloud on how "quickly" the graph climbs up or falls down for exponential vs linear.
Use mathematical terms such as slope and rate of change.
Ask them to find/guess the scales of growth/decay in A1. What happens when the scale is written as a negative exponent?
For example, ask them if the decay factor of 3-1 in the typewriter graph drop the percentage to 0 or lesser? Use the GGB files (SR3 and SR5) to explain the infinite/asymptotic nature.
Create a strong foundation for the positivity of exponential decay. Reiterate that negative exponents do not imply numerical negativity.
In both growth and decay, ask the learners to intuitively find the range of these datasets. Learners think aloud whether any entry can eventually become zero, less than zero, or as large as possible? Does the exponential model support the claim? What about linear?
For AS1:
Use a mathematical representation of decreasing area in negative exponent notation. This will enhance the argument of positivity and the asymptotic nature of exponential models.
Repeat the same activity, this time with a graph paper. Help the students on how this step will simplify the process of calculating area.