Flexing the Left Hemisphere: What Burkies Learn in Math Classes

In our June 2018 News & Views issue, we asked Science teachers and Burkies to share examples of work their class work. Below are project samples.

TEACHER: Vivian Buckley
COURSES: Algebra 1, Algebra 2, Geometry, Statistics
GRADES: 9-12

Almost every job in today’s workplace involves using software of some type, from point of sales to analytics.  As a teacher of mathematics, I believe it is important to teach students to recognize technology as a tool beyond convenience and entertainment. Every time a student uses software to investigate concepts, create, and verify solutions, and organize and analyze data, they build connections in their brain that help them navigate programs with greater intuition and curiosity. The three most common software I use are Fathom, GeoGebra, and Google Sheets.  I use all three across Algebra 1, Algebra 2, Geometry, and Statistics. Fathom is used to analyze and model data, investigate transformations of functions, perform linear regressions and re-expressions, and for simulations. GeoGebra is used to verify solutions, particularly graphs and intersections of graphs; investigate phenomena such as extraneous solutions; and is used extensively in Geometry for constructions. Spreadsheets are a ubiquitous tool in today’s workplace and I insert experience with them whenever I can. I prefer Google Sheets because it is readily available and easy to share. I enjoy teaching students how to use formulas on Sheets for something as simple as making a table for a linear function, to calculating something complex such as standard deviation, and for applications such as financial investments and loans. We also use Sheets to perform simulations. As you can see there is overlap.  When time is available I like to have students perform and compare similar activities using pencil and paper and through various technologies including their graphing calculators.

Connor Marshke ’18

Fathom is a software that we commonly use in statistics class for everything from linear regression to simulation. Most recently we used it to discover the Central Limit Theorem. We examined five hundred-seventeen 2016 MLB salaries by making a histogram. The distribution of the original population of salaries is strongly skewed to the right. Fathom allowed us to take one hundred samples from each of three different sample sizes, n=5, n=10, and n=20. We then produced histograms for the means of each sample size. As the Central Limit Theorem says, the distribution of these sample means will become more unimodal and symmetric, while decreasing in spread as the sample size increases. The Central Limit Theorem is also known as the Fundamental Theorem of Statistics because we can apply methods that work for normal distributions to populations of other distributions. Fathom allowed us to perform this simulation in less than twenty minutes.

Katie Killian ’21
Algebra 2

Solve: x+1 = 7x+15
Graph 1
This graph produced on GeoGebra shows a line, f(x)=x+1 and a radical, g(x)=7x+15.
They intersect one time. The solution is (7,8).

The algebraic process would go like this:
x+1 = 7x+15
Square the both sides.
(x+1)(x+1) = 7x+15
x2+2x+1= 7x+15

Graph 2
After algebraic manipulation, the equation is completely changed. Now the graph shows a parabola, f(x) = x2+2x+1and a line, g(x) = 7x + 15. The solutions are (-2,1) and (7,64). In the new graph they intersect twice, but one of the solutions is extraneous. It is extraneous because by plugging the x value -2 back into the original equation, the equation becomes -2 + 1 = 7 (-2) +15 or -1 = 1 . 1-1

Lauren Cahill ’21
Algebra 1

In Algebra 1 we are studying quadratics. We have been working on factoring and solving. Solving means to set the equation equal to zero. By turning the equation into factors we can use the zero product property: if ab=0 either a or b is equal to zero. For example, 0=x2-2x-15 can be factored to 0=(x-5) (x+3). Therefore the zeros would be x=5and x= -3. These are the x-intercepts of the parabola, also known as solutions and roots. We can check our algebra by graphing them on our calculator (or using GeoGebra) and use the calc menu to search for zeros.