Case 2
- 1. Slope Baylee Hibshman, Shawn McMahon, Jennifer Dean Overview of Lesson Students will learn how to calculate slope and yintercept given a graph and an equation at the most basic level. Given worksheets the students will work on finding slope (m) and finding the yintercept (b) by using equations and graphs. Given their knowledge,they perform the last problem of each sheet without help from their personal mentors as an assessment. With the problems that the students complete they will be earning points, each problem is worth 1 point, the assessment problem is worth 5 points, and the challenge problem is worth 1 point alone. At the end of their time together students will receive rewards based on the number of points they have acquired. Description of Learners The intended audience of this lesson is a class of fifteen to twenty at risk students in the seventh grade.The students may be coming from a negative home environment and may not have the support of family members. Each student will be finding their own mode of transportation to campus and will meet in a classroom(TBA). The classroom will have a couple round tables, some white boards, and internet access, bare minimum things so as not to create a distraction for the students. Each student will also have a “buddy”, a college mentor who will be able to provide additional insight for the student. One goal of this lesson plan is for the students to fully be able to demonstrate a knowledge of slope and yintercepts given either a graph or an equation. Another goal is to give students a positive view of learning math. Learning Objectives ● The students will be able to calculate slope and y intercept given a graph. ● The students will be able to calculate slope and y intercept given an equation. Standards 7.AF.4: Define slope as vertical change for each unit of horizontal change and recognize that a constant rate of change or constant slope describes a linear function. Identify and describe situations with constant or varying rates of change. 7.AF.5: Graph a line given its slope and a point on the line. Find the slope of a line given its graph. Required Material
- 2. ● Whiteboard ● A computer (Hicks Undergraduate Library) ● The worksheet (provided) ● Writing utensil Procedures 1. The teacher writes the word “Slope” on the chalk/whiteboard. 2. The teacher asks the students if they had heard of slope or rate of change before. 3. Write the definition of the word slope below the word slope; a surface of which one end or side is at a higher level than another; a rising or falling surface. 4. Write on the board “Y=mx+b” and note that “m=slope” and “b=yintercept.” 5. Note that yintercept is the point that raises the graph by the value of the yintercept. Example: Y=x+3, this means that the graph of y=x is moved up three units. 6. Note that “m=slope” and that is “rise over run” on the graph. Example: If the equation is y=3x+1 that means that the “m” in this case is 3. 3/1=3 so the “rise” on the graph is up 3 units then over to the right 1 unit. 7. With the general knowledge given from the past procedures, introduce the activity. 8. Students and their mentors go to a computer located in the Hicks Undergraduate Library. 9. First the mentor logs onto a slopegraphing site, such as; http://www.mathportal.org/calculators/analyticgeometry/ graphinglinescalculator. php https://www.desmos.com/calculator and follow along the equations given to the students in the worksheet to give them a visual as to what the graph looks like acording to equation. 10. Note: Mentors should revert back to y=x before doing every equation to show the change in slope from the basic line. 11. Each mentor should be told to be of most use, without actually doing the worksheet for the students. Remind them that m=slope so in the equation y=mx+b the number in place of m is the slope. Remind them that the number in place of “b” is yintercept. 12. After the equation worksheet, the teacher teaches how to read a graph. By first finding the slope in a graph. (by use of rise over run on the graph from one point on a whole number unit and move up and over till you get to another integer.) 13. Then, teach yintercept and how to read on the graph. The original “y=x” crosses the yaxis at (0,0). By counting how many units it moves up or down, you can figure out the yintercept. (yintercept = b)
- 3. 14. Alternative: Ask the students to try to get the graph into an equation after they find “m” and “yintercept”. The equation should look like: Y=mx+b. 15. Each problem labeled 14 in the first worksheet is worth one “point” each. Every problem 5 is worth 5 “points” due to the students doing it by themselves. (Must get this problem right to achieve 5 points. They can retry the problem until they get it right.) The challenge problem is worth 1 “point” alone. Maximum for first worksheet: 19 16. The second worksheet’s first problem is worth 1 point. The last problem (the one they work on by themselves) is worth five points. Maximum on second worksheet: 6. Maximum overall: 25. 17. The students are then given the option to spend their “points” rewards: Points Prize 9 King Size Candy Bar of Choice 14 Deck of Cards 19 Headphones 24 Itunes gift card $5 25 Purdue TShirt and choice of one below. Assessment 1. After going through the first four problems of each section on the slope worksheet with their mentor, the students will answer the fifth problem themselves. They should be able to find the slope and yintercept of the equation. 2. On the second problem on the second page of the worksheet, students should be able to find the slope and yintercept given the graph. References and Reference Materials 1. Knezek, G., Christensen, R., TylerWood, T., & Periathiruvadi, S. (2013). Impact of Environmental Power Monitoring Activities on Middle School Student Perceptions of STEM. Science Education International, 24(1), 98123. This article discusses the importance of STEM education in middle at the middle school level. Middle school students need to have a foundation and a motivation for learning STEM before they reach higher levels. The journal discussed using activities and projects. We used this by having the
- 4. mentors do a slope activity with the students on the computer. 2. Martin, N. (2012) Teaching STEM to millennial students.Tech Directions, 71(7).Retrieved from http://web.b.ebscohost.com.ezproxy.lib.purdue.edu/ehost/pdfviewer/pdfvie wer?sid=173da8e18252499f85ea3cd2543f46fe% 40sessionmgr113&vid =18&hid=109 This article addresses different ways to teach STEM topics to “millennial students”, students who have grown up connected 247 to technology. The article provides ten different teaching strategies used by twenty first century teachers to teach technologically advanced students. One of the strategies discussed in the article is “integrating technology into teaching”, we decided that each student mentor pair would go to the Hicks Undergraduate Library and use an interactive slope calculator to have a good visual of what different slopes actually look like.
- 5. Slope 1. Y=x+1 points: 1 m= y-intercept= 2. Y=(1/2)x-3 points: 1 m= y-intercept= 3. Y=(-4)x+7 points: 1 m= y-intercept= 4. Y=(5/3)x-1 points: 1 m= y-intercept= 5. Y=(3/2)x+4 *Students must do this alone* points: 5 m= y-intercept= Get the equation into the form of y=mx+b. 1. Y-3=(-4)x points: 1 m= y-intercept= 2. Y+1=(-3/2)x points: 1 m= y-intercept= 3. Y-1=(22/11)x+1 points: 1 m= y-intercept= 4. Y+3=(4/5)x+3 points: 1 m= y-intercept= 5. Y+3x=4 *Students must do this alone* points: 5 m= y-intercept= Challenge Problem! 2y+4=x Hint: x = (1x/1) points: 1