Grade Levels: 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade,
Topics: AlgebraCoordinate SystemsFractional exponentsFunctionsPatternsAstronomy
Common Core State Standard: F-IF.4, F-BF.1a, F-LE.2,
· Fractional exponents
· OrbitKnowledge and Skills:
· Can solve equations involving fractional exponents
· Can plot a point in a two-dimensional coordinate system, given the coordinates, or determine the coordinates of a given point
· Can identify and describe patterns in a collection of related numerical data
· Can describe the characteristics of the orbits of planets in the solar systemDownload the Teacher Guide PDFDownload the Student PDF
Procedure: The investigation is best done by students working individually or in teams of 2.
Distribute the handout and ensure that students understand the question. Graphing calculators may be used if available.
Step 1. Do research to fill out the chart below:
|Planet||Average distance from the sun, in millions of miles (d)||Time duration of orbit, in years (t)|
Step 2. Graph the data from the chart, with average distance from the sun as the independent variable and time as the dependent variable. Describe the pattern you see.
Step 3. Try to find a value of k for each of these functions which creates a curve that matches the graph of planet paths. To do this:
a) Put in the data for one planet to get a value of k.
b) Use that value of k to plot the function.
c) See how closely your function matches the function of planet paths.
Function #1: t = kd
Function #2: t = kd²
Function #3: t = kd³
Function #4: t = kd½
Function #5 t = kd3/2
Which is the correct function? __________
What is the value of k? _______________