VIEWS: 2 PAGES: 13 POSTED ON: 6/25/2011
Linda Schweikhofer Day 1 CI399 ATG Can You Walk the Walk? Activity 1 Summary Students will learn how to use a CBR to create graphs. Students will work with a partner to recreate graphs using the Distance Match program on a TI graphing calculator and a CBR. Students will work together to determine what changes need to be made in order to improve the accuracy of matching a graph. Goals Students will: Learn what a CBR is, how it works, and how to use it. Adjust rate of speed to recreate a graph using a graphing calculator and CBR. Understand the relationship between time, rate of speed and the direction of the walker in order to physically recreate a graph. . Prior Knowledge Students are able to: Read and comprehend graphs Use the basic features of a graphing calculator Materials Graphing Calculator – 1 per pair CBR – 1 per calculator Projection device for graphing calculator - optional Open space for students to work Activity (Time Frame- one 40 minute period) 1. Explain to the class what a CBR is and how it works. Demonstrate how to operate the CBR. Show the resulting graph to the class. 2. Discuss what the x and y-axis represent on the graph that was created. Ask the students to explain what the graph represents. 3. Pass out the graphing calculators and CBR’s. Explain the steps that need to be taken to locate the Distance Match program on the calculator. Assist students as needed. 4. After all students are able to successfully access the program, tell the students that they will try to create a graph that is close to the graph displayed. Partner one will go first. Both partners will look at the results. Then the CBR and graphing calculator passes to the 2nd partner. The partner tries to improve on the 1st partners graph. 5. Students repeat this task using different distance match graphs. Be sure to tell the student that they need to alternate who goes first explaining that the second partner has an advantage if they watch the first partner carefully make adjustments to their rate. 6. Exit Question- If you wanted to graph a horizontal line with your CBR and graphing calculator how would you do it? Explain what a horizontal line means in terms of distance and time. Linda Schweikhofer Day 2 and 3 CI399 ATG Can You Walk the Walk? Activity 2 Summary Students work with a partner to recreate numerous graphs using a graphing calculator and CBR. After successfully recreating each graph, the students will communicate in writing how each graph was created. Then students create their own graphs, which they then try to recreate. Goals Students will: Adjust rate of speed to recreate a graph using a graphing calculator and CBR. Understand the relationship between time, rate of speed and the direction of the walker in order to physically recreate a graph. Use written communication to explain the actions a walker would take to recreate a graph. Prior Knowledge Students are able to: Read and comprehend graphs Use a graphing calculator and CBR Materials Graphing Calculator – 1 per small group CBR – 1 per calculator Walk the Walk Activity Sheet 1 Activity (Time Frame- two 40 minute periods) Day Two 1. Discuss the Distance Match activity from yesterday. 2. Introduce today’s activity with a graph on the board. Ask students what they would need to do to create a similar graph with a calculator and CBR. Require students to be very specific in their explanation. Where would they be positioned at the start of the graph? How would they determine where to stand? What would they need to do next? Continue this discussion with the students as they progress through the graph you have on the board. 3. Pass out the Walk the Walk Activity Sheet #1. Explain the task to the students. Tell them that they need to write what they did to create each of the graphs on the sheet. Remind them to be specific. 4. Students begin activity. Check that students are clear on the instructions and that they are correctly answering the questions. Assist as needed. Day Three 1. Tell students to take out the activity sheet they started working on yesterday. Explain the exercises on the backside to the class. Once they finish part one of the assignment, they will create a graph that they will try to recreate. The graphs should be challenging and require a good understanding of rate of change. If a group creates one that they think is particularly challenging, they can put it on the board in the classroom for other groups to try when they finish today’s tasks. 2. After students create their own graphs, they then try the challenge problems. Encourage students to find multiple ways to recreate these graphs. 3. Bring class together prior to the end of class to discuss assignment and share solutions. 4. Explain and model the homework assignment for tonight. Assignment: Create a story about an imaginary walk you took to your friend’s house. Be sure to write about some obstacles you faced along the way that changed your walking rate. Then create a graph to match your story. Remember to label your axis’s. Note: These stories can be used as class openers or as closure questions for future lessons. Read a story, to the class. Students create a graph to represent the walk. Display the graph after you read the story so students can check their work. Walk the Walk – Activity 2 Name_________________________ The CBR is a distance sensor. It is a great tool for demonstrating Rate of Change. The graphs you create show the relationship between distance you traveled over a given time. In order to read the graph, you must understand what each axis represents. Distance Notes: Time You will be working with a partner to recreate the graphs below. After you create a close copy, explain what you did physically to create the graph. 1. 2. 3. __________________________ __________________________ ______________________ __________________________ __________________________ ______________________ 4. 5. 6. __________________________ __________________________ ______________________ __________________________ __________________________ ______________________ 7. 8. 9. __________________________ __________________________ ______________________ __________________________ __________________________ ______________________ Now it is your turn to challenge yourselves. Create a graph that you would like to recreate. The graph should be challenging yet possible. After you have drawn your graphs. Try to recreate it with the graphing calculator and CBR. Select your best one and put it on the board as a challenge for the rest of the class. Describe what you did physically to create these graphs. 10. ______________________ 11. ______________________ 12. __________________ __________________________ __________________________ ______________________ Now you should be ready for my challenge to you. Try to recreate the following graphs. Then describe how you did it. 13. _______________________ 14. ______________________ __________________________ __________________________ __________________________ __________________________ __________________________ __________________________ Linda Schweikhofer Day 4 and 5 CI399 ATG Can You Walk the Walk? Summary Students work in small groups to create graphs using a graphing calculator and a CBR. The goal is for students to create a graph of a line that has a slope that is as close to a given number as possible. After the group graphs a line, the students use the trace feature on the graphing calculator to locate two points and then calculate the slope of that line. Next, the group adjusts the walker’s rate of speed in order to create a graph that has a slope closer to the given number. Goals Students will: calculate the slope of a line given two points. adjust their walking rate (faster/slower) in order to obtain a graph of a line with an approximate slope. demonstrate the relationship between rate of change and slope of a line communicate the relationship between rate of change and slope Prior Knowledge Students are able to: calculate the slope of a line given two points. adequately use a graphing calculator including the trace feature to locate points on a line. use a CBR and graphing calculator to create graphs. Materials Classroom set of Graphing Calculators (1 calculator for every small group of students) Classroom set of CBR’s (1 per calculator) Open space for small groups of students to use CBR’s Overhead transparency of 4 graphs created using a CBR and a graphing calculator Overhead projector Group Record sheet Clipboards – one per group for recording data (optional) Pencils Student Response Sheet Activity Day 4 (Time Frame- Two 40 minute periods) 1. Put a transparency of a graph (created with a CBR and a graphing calculator) on the overhead. Discuss the relationship between distance and time displayed on the graph. Ask students to describe the possible scenario by which the graph was created. 2. Put a second transparency on the overhead. Have students discuss this graph with their small groups. Groups then share their thinking with the rest of the class. 3. Pass out record sheets and describe task. Tell students that they are to create a graph of a line using the CBR that has a slope as close to 2 as possible. In order to do this task correctly, it is important that the walker walks at a constant rate of speed. After the first trial, identify points, calculate slope and record findings on the record sheet. Next adjust the rate of speed so that the second trial results in a graph of a line that has a slope even closer to 2. Repeat as time permits. They will have 15-20 minutes to accomplish this task. Remind students to record data after each attempt. 4. Pass out a CBR and graphing calculator to each group. Review how this piece of equipment is used. 5. Groups of students go to assigned open space to work on this task. 6. After 15-20 minutes, students return to the classroom with their data. Ask students to share the strategies they used to accomplish this task. Have class identify the group that came the closest to a slope of 2. This group must support their findings with a list of points from the line they graphed. Class verifies their slope is correct. Activity- Day 5 1. Put transparency #3 (a graph created with a CBR and a graphing calculator) on the overhead. Discuss the relationship between distance and time displayed on the graph. Ask students to describe the possible scenario by which the graph was created. 2. Put a transparency #4 on the overhead. Have students discuss this graph with their small groups. Groups then share their thinking with the rest of the class. 3. Describe today’s task – create a line with the CBR and graphing calculator that has a slope as close to ½ as possible. Groups are allowed only 3 tries. Next they will try to create a line with a slope as close to 4 as possible. Again they will have only 3 tries. Remind students to think through and discuss this task thoroughly before they begin working with the CBR’s. Their final task will require each group to pick a slope and then in only one try with the CBR’s, they must try to create a line with a slope as close to the selected number as possible. If time permits, the group can repeat this task with different slopes. 4. Pass out materials 5. Groups of students go to their assigned open space to work on task. 6. Observe and listen to students as they work in groups in order to informally assess their discussion understanding of slope/ rate of change. 7. Bring students back to the class for a wrap-up and discussion of this activity. 8. Pass out Student Response Sheets. Students complete this independently for homework. Can You Walk The Walk? Name _________________________ Period _____________ 1) Which line was most difficult for your group to graph? Why? 2) Describe how your group determined how fast the walker should walk when the slope of the line changed? 3) If line m has a slope of 1, draw a second line that has a slope of approximately 4. m Explain how you determined where to draw the line. 4) If line n has a slope of 1, draw a second line that has a slope of approximately ¼. n Explain how you determined where to draw the line. 5) Describe what you have learned about the relationship between the slope of a line and rate of change. 6) How can this activity be improved? Give at least one suggestion. 7) On a scale of 1-10, how well do you feel you understand the relationship between the slope of a line and the rate of change? Can You Walk the Walk Record Sheet. Group Members ______________________________________________ _____________________________________________________________ Task 1: Line with a slope of 2 Trial # List 4 Points on the Line Slope of Line 1 ________________ ________________ ______ ________________ ________________ 2 ________________ ________________ ______ ________________ ________________ 3 ________________ ________________ ______ ________________ ________________ 4 ________________ ________________ ______ ________________ ________________ 5 ________________ ________________ ______ ________________ ________________ 6 ________________ ________________ ______ ________________ ________________ Task 2: Line with a slope of Trial # List 4 Points on the Line Slope of Line 1 ________________ ________________ ______ ________________ ________________ 2 ________________ ________________ ______ ________________ ________________ 3 ________________ ________________ ______ ________________ ________________ 4 ________________ ________________ ______ ________________ ________________ Task 3: Line with a slope of 4 Trial # List 4 Points on the Line Slope of Line 1 ________________ ________________ ______ ________________ ________________ 2 ________________ ________________ ______ ________________ ________________ 3 ________________ ________________ ______ ________________ ________________ Task 4: Group Choice Slope = _____ List 4 Points on the Line Slope of Line ________________ ________________ ______ ________________ ________________ Slope = _____ List 4 Points on the Line Slope of Line ________________ ________________ ______ ________________ ________________ Slope = _____ List 4 Points on the Line Slope of Line ________________ ________________ ______ ________________ ________________