Linear Progression

Course(s)/Subject(s): Mathematics / Algebra 1

Grade Level(s): 7, 8 (Pre-Algebra), & Algebra

Key Words: Linear Progression using the Graphing Calculator

Developer(s) Name: Suyi Chuang

School: Lake Braddock Middle School

Attached Files: worksheets

Approximate Time Frame: 2.5 hours

Materials/Equipment Needed:
Slinky (cut into 4 equal parts), wire cutter, M&M’s (or other candy that is about the same size and weight), another type of weight (heavier candy or dimes), two meter sticks or yardsticks per group, small cup (I used the containers that holds a roll of film), wire, masking tape, graph paper, looseleaf paper (for notes and to record information), straight edge, pencils, graphing calculators, ClarisWorks or Microsoft Word.

Description of Lesson (includes context):
Before conducting this activity, students should have experience creating tables of values and plotting points on a coordinate plane.This lesson is a concrete example of linear progression. The abstract ideas of slope and intercepts are represented in this activity as the constant weights (slope) and the length of the spring with no weights (y-intercept). Students will have the opportunity to create tables of values and graph lines using paper and pencil and the graphing calculator.Students will use either ClarisWorks or Microsoft Word to answer questions focusing on the effects of slope and intercepts on the graph of a line.

1. What is the objective of this lesson? Upon completion of this lesson, students will learn about slope, y-intercepts, linear progressions and the slope-intercept form of an equation of a line.

? VA FCPS POS Standards: 1, 2, 3, 6, 7

? VA FCPS POS Benchmarks: 1.1, 1.2, 1.3, 2.2, 3.1, 6.1, 7.1

? VA FCPS POS Indicators: 1.1.3, 1.2.1, 1.2.2, 1.3.1, 2.2.1, 3.1.2, 6.1.2, 7.1.2

VA SOL(s) (including Computer/Technology): 7.20, 7.22, 7.24, 7.26, 8.15, 8.17, 8.18, A.1, A.5, A.6, A.7, A.8, A.17, A.19, C/T8.1


Other: Students will learn to use the graphing calculators to graph lines and create tables of values.

2. What will we examine as evidence of students’ knowledge and/or skill?

Product(s): Students will have answered a series of questions on two worksheets and will write a thorough explanation of the effects of slope and intercepts on the graph of a line.

Performance(s):

Other:

3. What exactly will the students and teacher do during the lesson?

Directions to students for proceeding with the lesson:

1. Start by recording the number on your spring and bucket onto your worksheet.
   
2. Set up your activity as demonstrated by your teacher.
   
3. Measure the spring with the bucket and record this data onto your table of values.
   
4. Choose the number of M&M’s you would like to use for each interval.
   
5. Place one interval of M&M’s into your bucket and record the new length of the spring and the bucket onto your table of values.
   
6. Place a second interval of M&M’s into your bucket and record the new length.
   
7. Repeat this process until you have at least 7 entries for your table of values.
   
8. You have just completed your first trial. Repeat this trial again so that you have an accurate set of data.
   
9. Create a scatter plot by graphing the points from your table of value.
   
10. Create a best fit line for your data.
    
11. Answer the questions on worksheet A.
    
12. Repeat this entire activity using dimes or a heavier candy (i.e. jellybeans).
    
13. Answer the questions on worksheet B. Use ClarisWorks or Microsoft Word to write the answers for the “Extensions”.
    
14. Upon completing this activity, your teacher will show you how to create a table of values on the graphing calculator. Graph your tables of values and best fit lines on the graphing calculator.
    
15. On your graphing calculator, graph several lines with different values for slope (use the same y-intercept for each of the lines). Observe the effects of slope on the graphs of these lines.
    
16. On your graphing calculator, graph several lines with different values for the y-intercept (use the same slope for each of the lines). Observe the effects of the y-intercept on the graphs of these lines.
    
    

Directions to teacher/administrator using the lesson?
**This activity should be done in groups of 2-4 students depending on the class size.

1. Take a slinky and cut it into 4 or 5 equal pieces. These pieces will be your spring. Put a small piece of tape at each end of the spring to cover all sharp edges. Using masking tape, put a tag on each spring and number them so each group of students can identify the spring they used for the project.
   
   
2. Take the wire and create handles for the small cups. Be sure to use tape to cover all sharp edges. Use masking tape to label and number each cup.
   
3. Before handing out the materials to the students, demonstrate the activity set up.
   
4. Tape the spring to one end of a meter stick or yardstick. Tape the ruler to a desk so that the spring is hanging off the desk. Tape the bucket to the end of the spring.
   
5. Demonstrate how to measure the length of the spring and the bucket.
   
6. You may want to have the students choose whether to use the centimeters or inches to measure the lengths.
   
7. Once students have understood how to set up their activities, distribute the materials to each group. Be sure to have the students record the number on their spring and bucket.
   
8. Upon completion of the entire activity, demonstrate to the students how to create a table of values on the graphing calculator and how to graph lines on the graphing calculator.
   

4. What options in presentation(s) and/or response(s) are suggested in order to provide the opportunity for all students to demonstrate achievement of the benchmark(s) and indicator(s)?

Have the LD teacher present when dealing with students who may need the extra help. I would also pair weaker students with the stronger students who have the ability to explain several concepts.