Algebra (Quadratic Regression)
scatter plot example
Script for Presentation
My name is Vivian and the goal of my presentation was to create a sketch that explores an algebraic problem that dealt with plotting points. More specifically, I wanted to look at a linear trend given a table of coordinates and how to predict its direction of movement, or quadratic regression.
The sketch follows the problems chosen. After the whole problem is read and the students realize the points must be graphed, the first slider can be slid to the right to show the given points. Then looking at part a of the question, the students can come up with a method of finding the best-fitting quadratic model, which can then be shown with the second slider. Afterwards, they can predict the wind speed or fuel use which is asked by part b and onward, and then the answer can be shown on the geogebra sketch by checking the box.
In this way, this investigation is different from paper and pencil in that it enables me to illustrate these concepts in a clean and organized manner with several layers that I can control at my own pace.
Based on the 5th math practice, the tools I used in geogebra included:
- plotting and tracing a point that has the change in finish time as the independent variable and wind speed as the dependent variable.
- checkbox that controlled hiding and showing the point at (10, -1.9), the answer to part b of the question
- a slider that controls showing the coordinate points from the table plotted, and another slider for tracing the quadratic model
- 4) Model with mathematics-applying prior knowledge to new problems and reflect, and also using representations to solve real life problems. This example deals with using points and noticing the pattern that they're forming to predict another point. It would not be possible, or it would be much more difficult, if not for the chance to visualize it.
- 7) Look for and make use of structure-look for, develop and generalize relationships and patterns and also applying conjectures about patterns and properties to new situations. This applies to my example because the trend in the curve that follows the points being plotted are only going in one direction. Knowing that this is a unique line, we are able to look at the structure to make a prediction about an unknown variable.