Technology Lesson Plan Contest
Slope as a Rate of Change
By
Shannon Hernandez
Slope as a Rate of Change
SUBJECT AREA: Math, Algebra I (Grade 9 - all learning abilities)
TIME LINE: 2 block schedule days
MATERIALS: TI-83 Plus calculator
TI CBR (Calculator-based Ranger)
Yardstick
Some means of displaying CBR data (TI Presenter with TV, computer, or projector or overhead TI-83 Plus Calculator)
Handouts #1, #2, #3, examples of graphs
CONTENT OBJECTIVE: The student understands that slope is defined as a rate of change.
TEKS CORRELATION: Algebra I: Ab(2)C, Ac(1)C, Ac(2)A, Ac(2)B, Ac(2)D, Ac(2)F, 8.14, 8.15, 8.16
ESSENTIAL QUESTIONS: Essential questions will be noted in bold throughout the activity.
ACTIVITY 1: 1. The teacher will use handout #1 to model usage of CBR.
2. Have volunteers come model usage of the CBR. What causes the graph to go up or increase? What causes the graph to go down or increase? What causes the graph to be a flat line? What do you think causes the graph to be steeper of flatter?
3. Break students up into groups of 3 to 4 students. The students must assign duties in their group. The roles in the groups would be the walker, the technician and the coach. The walker is the one who does all of the walking. The technician is the one who runs the CBR and calculator. The coach is the one who helps the walker model the given graph. Give each group a time and distance graph to model (examples given).
4. Move to a large area (cafeteria) so the students can spread out. The CBRs are very sensitive to any kind of movement in its path. Each group must practice walking the graph until they can walk it several times in a row perfectly.
5. The students will then go back to the classroom to walk their graphs for the teacher and class. Was the walker going fast or slow? How far away from the CBR was the walker at the start? At the end? Did they walk at a constant rate? Did the walker go towards or away form the CBR or did the walker do both? The group will be graded on starting point, direction, rate, overall fit and teamwork (Handout #2). Each category will be rated 1 - 5, 5 being the best.
ACTIVITY 2: 1. Now that the students have gotten familiar with the CBRs, they can use it to walk a description of a graph instead of modeling the graph itself. The students are broken up into the same groups of 3 to 5. They must assign duties before materials are passed out. The students do not have to have the same duty as last class. The students are given a verbal description of a graph to walk.
2. Move the class to a larger area again for them to spread out. They are to practice walking their verbal descriptions of the graph.
3. When practice is over, take students back to the classroom to do the walks. The students will assess the walk according to starting point, direction, rate, overall fit and teamwork (Handout #2). Was the walker going fast or slow? How far away from the CBR was the walker at the start? At the end? Did they walk at a constant rate? Did the walker go towards or away form the CBR? Why or why not?
4. When the assessment is done, the students are to sketch the graph on the paper given (Handout #3).
5. Then, we will collect actual data from the students’ graphs onto a given table.
6. Each individual student will write down the information for each group on the handout provided. When all data has been collected, the students may or may not stay with their groups depending on teacher’s choice. They will use finite differences to find the slope of each walk. The students will use the slope of the walk and starting point to write equations in slope-intercept form, y = mx + b.
ENRICHMENT ACTIVITY: Give descriptions of graphs that are not constant and have the students find the equation of the line for each part of the graph.
ASSESSMENT: Assessment occurs throughout the lesson process. See Handout #3. The students can be given tables of data to write equations from as well as verbal descriptions and graphs.
LESSON COVERAGE: This lesson covers many parts of the curriculum. It covers estimation, slope, y-intercept, and writing equations from, tables, graphs and verbal descriptions. It helps the student to understand the meaning of slope in a real world setting instead of just how to find slope from just the algebraic method.
STEPS FOR USING THE CBR
STEP 1: Link the CBR and calculator with the patch cord.
STEP 2: Press APPS and press the number for CBL/CBR (should be #2)
STEP 3: Press ENTER and then #3 for RANGER
STEP 4: Press ENTER then #1 for SETUP/SAMPLE
STEP 5: Move the arrow to REALTIME and press ENTER until it reads YES, move the arrow to UNITS: and press ENTER until it reads feet
STEP 6: Move the arrow up to START NOW and press ENTER
STEP 7: Follow calculator’s directions from there
STEP 8: To redo the graph, press ENTER and then #5 for REPEAT SAMPLE, press ENTER again when you are ready to start collecting data
Handout #1
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Direction |
Rate |
Overall Fit |
Team Work |
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Handout #2
Walking data
1. Start 3 feet away from the CBR and walk away quickly at a constant rate.
Time |
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2. Start 3 feet away from the CBR and walk away slowly at a constant rate.
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3. Start 12 feet away from the CBR and walk toward it quickly at a constant rate.
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4. Start 12 feet away from the CBR and walk toward it slowly at a constant rate.
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5. Walk slowly towards the CBR
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6. Walk quickly towards the CBR
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7. Walk slowly away from the CBR
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8. Walk quickly away from the CBR
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9. Stand still 4 feet in front of the CBR
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Handout #3
Graph Examples