Building+Functions+101

Park, Haserjian, Kim 7 Aug 2013

= Building Functions 101 =

CCSS.Math.Content.HSF-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context.

__Our understanding of the standard:__  Students will be presented with a context that includes quantitative data and will have to recognize patterns and determine an expression that best fits the context.

__Contexts:__ graph, table, scenario, sets of data, video

__Types of relationships:__ - Linear - Exponential (growth & decay) - Quadratic - Logarithmic - Logistic - Trigonometric - Cubing - Rational

__Sample idea:__

Skittles experiment.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">50 skittles are placed in a plastic ziploc bag. Each skittle represents a member of the population. Students will shake the bag, representing a catastrophe. Each skittle turned over with a S sign face up represents a member of the population that died. Students should record how many turns have taken place, how many skittle people died, and how many remain.

<span style="background-color: transparent; color: #000000; font-family: Arial; font-size: 15px; text-decoration: none; vertical-align: baseline;">After students collect data from this scenario, students will discuss which type of relationship best fits the pattern to explain the relationship and derive a function either recursively or explicitly. Once each group of students has proposed to the rest of the class their ideas, students will use a graphing calculator to plot the data and use the options of a best fit curve to finalize their guesses.