|Lesson Plan ID:
Penny Drop That Thang!
This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College- and Career-Ready Standards showcase lesson plan.
|MA2013(8) ||12. Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2] |
|MA2013(8) ||14. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8-F4] |
|MA2013(9-12) Algebra||12. Create equations and inequalities in one variable, and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. [A-CED1] |
|MA2013(9-12) Algebra||17. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3] |
|MA2013(9-12) Algebra||20. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [A-REI6] |
|MA2013(9-12) Algebra||23. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11] |
Analyze change in various contexts
- approximate and interpret rates of change from graphical and numerical data
Mathematical Practice Standards
2. Reason abstractly and quantitatively.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
|Primary Learning Objective(s):
Students will be able to
- compute slope on a graph
- develop linear equations
- compare linear equations
|Additional Learning Objective(s):
|Approximate Duration of the Lesson:
|| 61 to 90 Minutes|
|Materials and Equipment:
Large Graph Paper, Markers/Colored Pencils, Pencils, Pennies or any coin, Rulers or Yardsticks
|Technology Resources Needed:
Students should already be aware of how to find the slope using the formula and on a graph. The linear forms of equations, Slope-intercept form y= mx + b; Point-slope form y - y1 = m(x - x1); Standard form Ax + By = C and writing linear equations should also be familiar. Divide students into groups of 3 or 4. Assign a role for each student: group recorder, group leader, group calculator, and group timekeeper. In addition, students should know how to input data into a graphing calculator. Make copies of the graphic organizer with the different forms of linear equations (See attachment).
BEFORE: Graphic Organizer- Students will fill in the appropriate spaces. The teacher will then teach/review explicit instruction ( I Do, You do, We do, Ya'll Do) how slope is related to linear equations.
DURING: Collaborative Groups/Graphic Organizer- Students are already in their assigned groups or stations. Students will be given needed materials. The teacher may demonstrate dropping the penny on the graph paper if needed. Students will then drop two pennies simultaneously. Wherever the pennies land, students will mark their graph paper labeling the coordinate points. Next, students will draw a line connecting the two points and proceed to find the slope of their graph. Ensure their lines cross the y-axis. Once students, have found the slope for the line, they then can write their linear equation in slope-intercept form. Students should be able to identify and explain the slope and y-intercept. Monitor students progress and ask leading questions (i.e., How does finding the slope of a line help you identify the direction of the line?). Students will repeat the same process for the second linear equation. While the 2 of the group members are working on the graph, the timekeeper and recorder should work on providing an explanation of the process of writing a linear equation and compare it to the graph on the graphing calculator(See scoring rubric).
AFTER: Think-Pair-Share-This is to be done within the group. Have groups to share what they found or noticed in the process of writing their linear equations. They may state any difficulties as well.
The following graphic organizers are from http://www.dgelman.com/graphicorganizers/#GRAPHING
|Attachments:**Some files will display in a new window. Others will prompt you to download.
The graphic organizer may be used as an ongoing assessment. Informal Oral Questioning as the teacher is monitoring students' progress may also be used as an assessment. Peer-to-Peer/Mathematical conversations may also be used as an assessment.
The teacher may want to review the terms slope, y-intercept, x-intercept, linear equations before beginning the activity.
Each area below is a direct link to general teaching strategies/classroom
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.
|Presentation of Material
||Using Groups and Peers
|Assisting the Reluctant Starter
||Dealing with Inappropriate
Be sure to check the student's IEP for specific accommodations.
|Variations Submitted by ALEX Users: