Systems of Equations Project

Project created and designed by English teacher Sharlene Moss, M.A. (sharlene.moss@lausd.net) and Kyle Ramstad

This project was designed to align with 8th grade Math and English Common Core State Standards. 

Click here to view the aligned math standards. Systems of Equations

Click here to view the aligned English standards. Persuasion: Ethos, Logos, Pathos

The files below were used in guiding the students through this project. 

Please download and make copies for your own students.

All assignments were given online. Google Classroom, Google Drive, and Google Sites were used to distribute and collect files.

Click here to view the project page my students used.

Linear Regression

Computer Supported Collaborative Learning (CSCL) is an effort by California State University, Northridge to support science teachers in the San Fernando Valley. The concepts being developed by CSUN can be applied to all subject matter at all grade levels.

Click here to visit the CSCS website

“Demand for Computer Systems Analysts with big data expertise increased 89.9% in the last twelve months , and 85.40% for Computer and Information Research Scientists.”
— Forbes.com 2014

Data collection and analysis is a growing industry. Being able to pull ideas out of big data is what drives many of the newest and most successful technology companies.

Go through the steps below to collect, view, and analyze data about height and shoe size. Linear regression is one way that data can be analyzed to find patterns/relationships between two sets of data.

  • Data Collection
  • View Data
    • Google Sheet
    • Make sure you copy this data to use in the next step
  • Calculator
  • Analysis
    • What can this line tell us about the relationship between the data?
    • In regression, the R2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data.
    • Use your linear equation to predict what height someone would be if they had a size 15 shoe.

Linear regression lines can be used to help predict future results. The linear equation models what is happening in the real world. The better your R2 value, the better your equation will model the real world situation.

Linear Function Transformations

Computer Supported Collaborative Learning (CSCL) is an effort by California State University, Northridge to support science teachers in the San Fernando Valley. The concepts being developed by CSUN can be applied to all subject matter at all grade levels.

Click here to visit the CSCS website

What is a Linear Function?

Linear functions are those whose graph is a straight line. A linear function can be written in the following form. 

y = f(x) = mx + b

This is called slope-intercept form. Where m represents the slope of the line and b represent the y-intercept.

What happens when m or b changes?

  1. What happens as the value of m changes?
  2. What happens as the value of b changes?

Distance Between Two Points

Computer Supported Collaborative Learning (CSCL) is an effort by California State University, Northridge to support science teachers in the San Fernando Valley. The concepts being developed by CSUN can be applied to all subject matter at all grade levels.

Click here to visit the CSCS website

How do you get from one point to another?

  • Open the map and the Google Form. Answer the questions on the form.
  •  The shortest distance between two points is a straight line. To find that distance, it may be easier to find the distance by "taking the streets" first. These distances for a right triangle. The shortest distance is the hypotenuse of the triangle. Open the example.
    • Example
    • This example shows that you can easily count the distance of the legs of the triangle, but it is impossible to count the distance of the hypotenuse. 
  • To find the distance between two points, we use the Pythagorean Theorem. Open the Desmos calculator to view the points and the distances between them. 
    • Desmos
    • Type the Pythagorean Theorem in for the hypotenuse. It solves for the length automatically!
    • Now create your own right triangle and find the length of the hypotenuse by solving the Pythagorean Theorem for c. 
    • This is the distance between the two points
    • Take a screenshot of your triangle and answers and add it to our class Google Slides

    Favorite Desmos Activities & Graphs

    “Desmos wants to help every student learn math and love learning math. But “every student” is a lot of students so we create digital math tools and let the Internet take them to anyone who wants them.”
    — Desmos.com

    Direct Variation

    Students practice creating direct variation equations of the form y=mx while playing a game.

    Click here to view my lesson

    This was my first attempt at creating a MarbleSlide activity using Desmos. In this activity students practice creating direct variation equations while trying to launch marbles into stars. I found that this activity really motivates my students to keep trying and to persist. Turning a difficult task into a game allows more of my students to access the material and provide them with instant feedback.

    Pythagorean Theorem

    This was my first attempt at using a Desmos activity in my classroom. It is also the first activity I created myself.

    Click Here to view my lesson

    In this activity, students use the Pythagorean Theorem. They will discover that the theorem only works for right triangles. Then use their knowledge to solve some real world problems.

    This lesson was created because I noticed that my students were trying to use the Pythagorean Theorem for all sorts of triangles. Acute, Right, and OBTUSE! It occurred to me that I had never told my students that it only worked for right triangles. Then I asked myself, "Why should I tell them when they can discover it for themselves?"