For Educators
Graphing With RXTE Teacher Guide and Answer Key
Part One
1) If the data doesn't look "friendly" enough to the students, you may ask them to round the data. Rounding will have little to no effect on this task.
2) Students should see a difference in scales on one another's graph. They may also comment on the type of graphs, ie. scatterplot, bar, line. Be sure everyone is doing a scatterplot from this point on. The data represents discrete numbers. The teacher can choose a students graph to illustrate the best scale. If your class is using a calculator, a discussion of the window is appropriate at this point.
3) Quadrants 2 and 3 were not used. Most calculators will not draw quadrants that are not being used. Pre-Algebra and Algebra one may have their first introduction to graphs that do not show all four quadrants.
4) The first column represents independent values and the second represents dependent values. A discussion of how input/output, domain/range and independent dependent terms are related is appropriate. Students may not have made the connection in those terms.
5) Quadrant 3 is omitted. A discussion of translation is appropriate here. Advanced Algebra students should be able to answer this question without drawing or looking at their graphs. A whole class discussion of why and how this is true would be appropriate.
6) This may be the first time the groups actually work cooperatively. The student should present at completion three graphs. On page one and two will be one scatterplot each. On page three, the two graphs will be combined.
7) This answer may vary depending on whether you allowed the kids to round. Certainly the numbers are all real integers.
8) If your students have not had any experience in drawing the line of best fit, ask them to draw a straight line using a ruler that will "hit" or "go through" the most points.
9) Students should conclude that the line represents the average of the points above and below the line.
Part Two
1) Teachers will need to point out that Aitoff map is a flat projection of the curved sky. Therefore, it is much like the projection of a Globe with the coordinates being marked in longitude and latitude and measured in degrees. The center of the map, which in Astronomy would represent the Galactic Center, is 0 degrees; longitude ranges from 0 to 360 and latitude from 0 to 90 in the upper quadrants and 0 to -90 in the lower. Moreover, the points selected in the data set are location coordinates for pulsars in the galaxy. Notice on the graph, most points are near the x-axis or the center of the galaxy. An astronomer would expect this. (Example) This section is marginally more difficult.
2) The students should discuss the visual differences as well as the fact that one graph is two dimensional. The Aitoff projection map allows you to put the data into a real world context-earth! The Cartesian map is a model but not a very real one.
3) Again, the students are expected to make a connection between their maps/graphs and the data representation. The Cartesian plane models the data into any situation. It can be manipulated to fit any situation, therefore lending to more creativity. The Aitoff projection map clearly identifies the situation as planetary.
Assessment Question
See the rubric for grading instructions. The intent of the assessment question is to allow students time to process what they have learned. Encourage your students to look at the assignment as a whole and carefully choose the skills and information most needed to explain to a six year old. Discourage your students from reporting to you a step by step process. This answer can be as short as one paragraph if explained fully.
Back to the "Graphing with RXTE" activity.
