Tag Archives: Linear equations

Graph

Graph Example

Graph

This is an excellent free graphing software. I use this quite frequently in the office when I need to sketch a quick example for an item. In the classroom it can be used to create your own custom graphs for instruction and assessments. Students can also benefit from this resource. SHARE! It’s very intuitive and easy to navigate. Graphs can be snagged and/or saved to insert into just about any type of document, including websites. Click the “Graph” link above and get started. Have fun!

Working Systems in Groups

Once the three methods of solving systems of equations have been taught, graphing, substitution and elimination, a wonderful review activity is for students to work in groups of 4 solving systems together, discussing solutions and methods chosen. I did this activity over a two day period as a review for the cumulative chapter test in algebra honors.

Objectives

  • To have students become more proficient in solving systems of equations, both abstract and in context
  • To have students discuss their method of solution and analyze its efficiency
  • To have students utilize technology in solving systems of equations

Materials

  • Graph paper, ruler, graphing calculator, pencil, paper

Activity

     Divide students into groups of 4, if necessary a group of 3 will sufficient. Create small name plates to identify the job(s) of each student reading Graphing, Substitution, Elimination, and Calculator. Give each group a set of system of equations, with the first day focusing on the abstract and the second day focusing on the system problems in context. Each member of the group works out the problem, showing all necessary work for their method. The calculator person will have no work to show except the solving of each equation for y. After each person determines the solution, they compare results. As a team, if a member did not come to the correct answer, or if the group as a whole disagreed on the answer, discussion would occur. Each member would analyze other student’s work, ask for assistance from group members or lend support to group members if they can. The goal is to get students discussing the mathematical process for each of the methods of solution. After an answer has been agreed upon and work corrected as needed, students will then discuss which method, or methods, was/were the most efficient. It’s important that students do not get stuck utilizing the same method over and over again, simply because they don’t know how to do the other methods. There are instances where one method is more efficient than others. For each question, each member will write to why their method was the most efficient, or not efficient. For each question, the jobs rotate. This is to insure that each student gets the necessary practice on all methods.

Algebra Alien

As I’m cleaning up the last 5 years worth of files from two computers and two thumb drives, I want to share a really fun end-of-the-year activity that was a HUGE hit! I have included the directions/rubric and student sample work.

The premise of this activity is that students research their own notebook for the BEST sample problem that meets the criteria to showcase on their alien. The alien is of their own creation and depicts the scope and depth of the algebra learned throughout the year. Students are allowed to get as creative as they wish. When all students have competed their alien, have them post them all around the room and have the class do a walking gallery. With post-it notes and pencil, have students examine the difficulty level of the problems on their peer’s alien and make comments. Students can bring these comments back to their desk to share out with the whole class or they can post them beside the alien. This provides yet another type of review of the content for the students. You’ll be amazed at your student’s creativity, as well as how on-mark they will be with showcasing the BEST problems from the year.

 Directions and Rubric  algebra-alien

                                                                                                      

4-Corners Linear Equation Poster

PosterGraphic

This is a culminating activity that ties together students finding the slope from a graph, from two points and from an equation. This activity can be differentiated based on the level of students you teach. I used this for an honors algebra class, but varied the equation based on the level of the student. I gave slope intercept form of equations to struggling students and equations that were in no particular form to students who needed a challenge, so they must arrange into either standard form or slope intercept form. Once students have their equation, they must complete all four sections of this poster, of which can be done nicely on a 11 by 14 sheet of white paper. They can start in any section they wish, but they must find the necessary information to graph the equation of the line. This can be done first by creating a table of values for x and evaluating the equation to find the corresponding y-values and plotting these points. It can also be done by solving the equation for y, if not done so already, to create the slope intercept form. From this students can identify the slope and the y-intercept and graph the line. Finally, students can determine the x and y-intercepts from the equation and plot these two points to graph the line. Moreover, students can calculate the slope between these two intercepts to verify the value of the slope of the line.

What students should take away from this activity is that they have multiple ways to access the information they need to graph the equation of the line, regardless what they are given. As a teacher, you want to teach students flexibility in their solving methods and to be able to come at a problem from many different angles. To increase this flexibility you can have students do this activity again without giving them the equation, but rather one of the four corners of the poster. For instance, provide them with only the slope and the y-intercept and have them find the equation of the line, in multiple forms if you desire, the graph of the line, the x and y-intercepts and the table. Students will find it more difficult to go from just the slope and the y-intercept to a table, but if they understand what slope is they will quickly figure out what needs to be done. If the slope is 2/3 and the y-intercept is (-2, 4), then they have a starting point to work from, increasing the y-values by 2 and the x-values by 3. Additionally, students should also see they can decrease the y-values by 2 while also decreasing the x-values by 3 to create new order pairs for their table. This is the flexibility that is essential for students to fully understand working with linear equations.

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