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Notes - Unit 5 Day 1 Match Me

By Grace Hamilton,2014-11-25 18:03
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Notes - Unit 5 Day 1 Match Me

    Unit 5: Day 1: Match Me! Grade 9 Applied

    Materials Math Learning Goals viewscreen Use Calculator Based Ranger (CBR?) and graphing calculators to analyse graphing calculators motion graphs in terms of starting position, direction of motion, and rate of BLM 5.1.1, 5.1.2 change (speed).

     75 min

     Assessment

     Opportunities Minds On ... Whole Class ; Demonstration

    Using the CBR? (motion detector), graphing calculator, and viewscreen, with a student volunteer demonstrate connections between the shape and

    position of the graph and the direction, speed (including stopped), and

    starting position of their walk. Before each walk, students predict what they

    think the graph will look like and draw the actual graph after the walk

    (BLM 5.1.1).

    Action! Pairs ; Peer Coaching

    Students investigate the connection between the shape and position of the graph and the direction, speed, and starting position by using the “DIST

    MATCH” application of the Ranger program (BLM 5.1.2). One student

    reads the graph and gives walking instructions to a partner who cannot see

    the graph. They reverse roles.

    Students match as many graphs as possible in the allotted time.

    Consolidate Whole Class ; Summarizing Debrief Discuss the key understandings involving the starting position relative to the CBR?, direction of walk, speed of the walk.

    Whole Class ; Exploration

    Learning Skill (Teamwork/Initiative)/Observation/Rating Scale: Assess

    students’ ability to work collaboratively and to take initiative.

    Check that students understand the difference between the path walked and

    shape of the graph by asking students to predict which alphabet letters can

    be walked, e.g., a student could make the letter “w” but the letter “b” is not

    possible. Ask students to explain why.

    Discuss which letters of the alphabet can be “walked” using the CBR?.

    Students use a CBR? to verify/disprove predictions about the shape of

    distance time graphs.

     Home Activity or Further Classroom Consolidation Draw a graph to match the following descriptions: Application Stand 4 metres from the CBR? and walk at a constant rate towards the Concept Practice CBR? for 5 seconds. Stand still for 3 seconds then run back to the

    starting position.

     Begin 0.5 metres from the CBR?, run away for 3 seconds at a constant

    rate, then gradually slow down until you come to a complete stop.

    5.1.1: Walk This Way

1. Student walks away from CBR? (slowly).

2. Student walks towards CBR? (slowly).

3. Student walks very quickly towards CBR?.

5.1.1: Walk This Way (continued)

4. Student increases speed while walking towards the CBR?.

5. Student decreases speed while walking away from the CBR?.

6. Student walks away from ranger, at 2 metres stops for 5 seconds, then returns at the same

    pace.

5.1.2: CBR?: DIST MATCH Setup Instructions

You will need:

     1 CBR? with linking cable 1 graphing calculator

Insert one end of linking cable FIRMLY into CBR? and the other end FIRMLY into graphing

    calculator.

    Setting up the DIST MATCH Application

    Press the APPS key

    Select 2: CBL/CBR

    Press ENTER

    Select 3: RANGER

    Press ENTER

    You are at the MAIN MENU

    Select 3: APPLICATIONS

    Select 1: METERS

    Select 1: DIST MATCH

    Follow the directions on the screen.

    If you are not happy with your graph,

    Press ENTER

    Select 1: SAME MATCH to try again

    If you would like to try a different graph to match,

    Press ENTER

    Select 2: NEW MATCH

    Select 5: Quit to quit

5.1.2: CBR?: DIST MATCH Setup Instructions (continued)

Part One: Walk the Line

Draw your graph.

    Copy the scale markings on the distance and time axes from your calculator. Mark your start and finish position on the graph using the coordinates Time and Distance. Connect the start and finish position with a line made with your ruler.

    ________________________’s Walk

    Calculate the rate of change of the graph (speed of your walk).

Draw a large right-angled triangle under the graph and label it with the height as the rise and the

    base as the run. Show the lengths of each.

    riserate of change ;Calculate the rate of change of your walk using the formula: run

Complete the following:

    a) The rate of change of my walk is ________________.

b) The speed of my walk is ________________ m/s away from the CBR?.

5.1.2: CBR?: DIST MATCH Setup Instructions (continued)

Describe your walk.

Use your starting position and rate of change to write a walking description statement:

    I started ____metres from the CBR? and walked away from it at a speed

    of ____metres per second.

    After 10 seconds, I was ____ __ from the motion detector. At this rate, estimate how far you would have walked after 30 seconds.

    Construct an equation to model your walk.

Read this walking statement:

    A student started 0.52 metres from the CBR? and walked away at a speed of

    0.19 metres/second.

    The equation D = 0.52 + 0.19t models the student’s distance, D, from the CBR?

    after t seconds.

    To graph it on the graphing calculator use: Y = 0.52 + 0.19x.

    Write a walking statement and equation for your walk: _____________ started _____ from the CBR? and walked away at a speed of

    _____ metres/sec.

    The equation __________________________ models my position from the CBR?.

    The graphing calculator equation is ____________________.

5.1.2: CBR?: DIST MATCH Setup Instructions (continued)

    Verify your equation of your walk using the graphing calculator.

Turn off the STATPLOT

Type your equation into the Y = editor Graph your equation

    (Press: GRAPH)

Turn on the STATPLOT. Press GRAPH again.

    Change the numbers in your Y = equation until you get the best possible match for the graph you walked.

The best equation that matches your walk is: ___________________.

5.1.2: CBR?: DIST MATCH Setup Instructions (continued)

Use the equation to solve problems.

    The equation D = 0.52 + 0.19t models the student’s position from the CBR?.

    We can calculate the student's distance from the CBR? after 30 seconds:

    D = .052 + 0.19t

    D = 0.52 + (0.19)(30)

    D = 0.52 + 5.7

    D = 6.22

    The student will be 6.22 metres from the CBR? after 30 seconds.

Calculate your position from the CBR? after 30 seconds:

    a) The equation ____________________ models your position from the CBR?

    (from previous page).

b) Calculate your distance from the CBR? after 30 seconds.

Check your answer with your graph.

    First, turn off the STATPLOT

    Next, press: GRAPH

    Then press: TRACE

    Arrow right until you reach 30 seconds.

    Record the distance the CBR? displays for 30 seconds _________. How does this compare with your answer using the equation? ________________________________________________________________

How does this answer compare with your estimate at the beginning of the activity?

    ________________________________________________________________

5.1.2: CBR?: DIST MATCH Setup Instructions (continued)

Part Two: Walk Another Line

Draw your graph.

    Copy the scale markings on the distance and time axes from your calculator. Mark your start and finish position on the graph using the coordinates Time and Distance. Connect the start and finish position with a line made with your ruler.

    ________________________’s Walk

    Calculate the rate of change of the graph (speed of your walk). Hint: The rise will be a negative number!

Draw a large right-angled triangle under the graph and label it with the rise and run values.

    riseCalculate the rate of change using the formula:. rate of change = run

Complete the following:

    The rate of change of my walk is ________________.

    The speed of my walk is ________________ m/s away from the CBR?.

5.1.2: CBR?: DIST MATCH Setup Instructions (continued)

Describe your walk.

Use your initial position and rate of change to write a walking description statement:

    I started ______metres from the CBR? and walked towards it at

    a speed of _____metres per second. After 10 seconds, I was

    ______from the motion detector.

    At this rate, how far would you have walked after 30 seconds?

Construct an equation to model your walk.

Read this walking statement:

    A student started 4 metres from the CBR? and walked towards it at a speed of

    0.32 metres/second.

    The equation D = 4 0.32t models the students position from the CBR?.

    To graph it on the graphing calculator use: Y = 4 0.32x.

    Write a walking statement and equation for your walk:

    _______________ started ____ metres from the CBR? and walked towards it at a speed of _____ metres per second.

The equation ___________________________ models my position from the CBR?. To graph

    it on the graphing calculator use: ________________________.

    Verify your equation with your walk using the graphing calculator.

    Remember that you can change the numbers in your Y = equation until you get the best possible match for the graph you walked.

    The best equation that matches your walk is: ___________________.

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