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Course Profile Foundations of Mathematics, Grade 9 applied, Public

Unit 2

Course Profiles are professional development materials designed to help teachers implement the new Grade 9 secondary school curriculum. These materials were created by writing partnerships of school boards and subject associations. The development of these resources was funded by the Ontario Ministry of Education. This document reflects the views of the developers and not necessarily those of the Ministry. Permission is given to reproduce these materials for any purpose except profit. Teachers are encouraged to amend, revise, edit, cut, paste, and otherwise adapt this material for educational purposes.

Any references in this document to particular commercial resources, learning materials, equipment, or technology reflect only the opinions of the writers of this sample Course Profile, and do not reflect any official endorsement by the Ministry of Education or by the Partnership of school Boards that supported the production of the document.

Acknowledgments

Public District School Board Writing Teams – Foundations of Mathematics

Course Profile Writing Team

Myrna Ingalls, Lead Writer, York Region District School Board

Shirley Dalrymple, York Region District School Board

Carolyn Gallagher, Kawartha Pine Ridge District School Board

Mary Howe, Ontario Association for Mathematics Education

Irene McEvoy, Peel District School Board

Lionel LaCroix, Peel District School Board

Christine Surtamm, Peel District School Board

Reviewers

Bill Clarke, Ottawa Carleton DSB: Angela Con, Kawartha Pine Ridge DSB; Donna Del Re, Peel DSB; Sandra Emms Jones, Waterloo Region DSB; Ron Lewis, Rainbow DSB; Bob McRoberts, York Region DSB

Lead Board

Peel District School Board

Allan Smith, Project Manager

Partner Boards

Kawartha Pine Ridge District School Board, Ottawa Carleton District School Board, Rainbow District School Board, Waterloo Region District School Board, York Region District School Board

Associations

Ontario Association for Mathematics Education (OAME)

Ontario Mathematics Co-ordinators Association (OMCA)

Unit 2: Algebraic Models and Rates of Change

Activity 6 | Activity 7 | Activity 8 | Activity 9 | Activity 10

Time: 30 hours

Unit Description

Students use linear equations with variables x and y to algebraically summarize patterns derived from real-life contexts and to communicate using graphing technology. Working from real-life contexts, students develop a “common sense” understanding of slope as unit rate of change prior to the algebraic definitions. They also explore connections between initial conditions and the y-intercepts of lines. The intent is for students to understand slope, equation, and line concepts in a manner which lends itself to application when problem solving. Properties and equations of lines are investigated and algebraic manipulations are taught and practised as needed.

Strand(s) and Expectations

Some specific expectations from the Number Sense and Algebra, and Relationships Strands have been combined with overall expectations from the Analytic Geometry Strand. Weaving together the expectations of the strands in this way helps students make connections.

Analytic Geometry Strand Specific Expectations: AG1.01, .02, .03; AG2.01, .02, .03, .04; AG3.01, .02, .03, .04, .05.

Number Sense and Algebra Specific Expectations: NA1.01, .02, .03, .04, .05, .06; NA2.006; NA 3.01, .02, .03, .04, .05; NA 4.01, .02, .03.

Relationships: RE1.01, .04, .05, .06, .07; RE2.01, .03; RE3.01, .02, .04.

Activity Titles

What follows is a suggested sequence for teaching Unit 2. The timing for activities and skill development are included. This Profile develops the mathematics in a sequence that may be different from the sequence used in previous courses of study, and weaves expectations from all strands together. There are a few differences in use of time between this Applied version and the Academic version.

Since there are specific times when it would be best to introduce certain vocabulary and notation, and to develop certain skills, the outline for Unit 2 details when specific algebraic skills are required. Some of the activities include a large amount of skill development as indicated in the [square brackets]; other activities may require additional time for skills identified as Follow-Up Skills. Time has been allotted, in the table below, for the skill development within or following each activity. There is an additional 225 minutes of asterisked * time in this Unit for skill building needs, as identified by the teacher.

Activity 2.1 and Follow-Up	Match Me Up! [y = mx in contexts, where m is unit rate. No x’s and y’s until algebraic models are summarized. Then, use x and y notation so that graphing calculators can be instructed to create graphical models using “y =” form.] Follow-Up Skills: plot points in all 4 quadrants; use an equation in “y =” form to create a table of values to plot on the Cartesian plane	150 minutes
Activity 2.2 and Follow-Up	Ramps 'R Us [slope = ] Follow-Up Skills: reviewing Pythagorean theorem; solving equations from knowing 2 of the variables in slope =	150 minutes
Activity 2.3 and Follow-Up	Slippery Slope [slope through motion of students; finding slopes of lines and line segments; numeracy skills] Follow-up Skills, as homework: graphing lines, given slope and a point	150 minutes
Activity 2.4 and Follow-Up	Programs for Sale! [Use y = mx + b form when you know a point on the y-axis which represents initial conditions in a partial variation context; solve simple linear equations by inspection; use list features of graphing calculators to enter formulas, as with spreadsheets] Follow-Up Skills: combining like terms; using distributive property; exponent laws; linear equations involving some algebraic manipulation	300 minutes
Activity 2.5	What’s My Spring? Stretching a Penny [Apply y = mx + b form in a context that yields somewhat messy data]	75 minutes
Activity 2.6 and Follow-Up	Sunshine, Whiskers, and Windmill [Investigate slopes of parallel and perpendicular lines and lines that are reflections in either the x-axis or y-axis] Follow-Up Skills: graphing lines, given slope and a special point, the y-intercept; forming the equation of a line, given slope and y-intercept; forming the equations of families of lines that share a slope, or a y-intercept	150 minutes
Activity 2.7 and Follow-Up	How Many Donuts in a Dozen? [Recognize different forms of equations of lines; graph Ax + By + C=0 using the x- and y-intercepts; substitution and solving the resulting linear equation] Follow-Up Skills: practise substitution and solution of linear equations; graph lines, given: the intercepts, the equation in any form]	150 minutes
Activity 2.8 and Follow-Up	Fireworks and Twinkle, Twinkle [Use given slope and a point conditions to form the equation of a line; numeracy skills; substitute and solve the resulting linear equation] Follow-up Skills: graphing lines, given slope and a point, or given two points	150 minutes
Activity 2.9 and Follow-Up	All in the Family [Graph lines and curves from equations] Follow-Up Skills: recognize linear vs non-linear relations from tables of values and equations; numeracy skills; graph y = b and x = a	75 minutes
* Time to practise skills		225 minutes
Activity 2.10	Planning for a Trip: a Summative Assessment Activity Sample questions for a Pencil and Paper Test	225 minutes

Prior Knowledge Required

Unit 1 of the Profile

Unit Planning Notes

· The first activity is intended to introduce the use of x and y notation, with x’s representing independent variables, and y’s representing the dependent variables. Until now, letters having meaning in specific contexts have been used. To compare or summarize relations, or to instruct graphing technology to draw a graph, x’s and y’s are used.

· The word ‘slope’ is introduced as a measure of inclination of a line through the context of wheelchair ramps. At this time, rates of change are connected to the abstraction of slopes of lines.

· The summative assessment activity in Unit 2 is intended to help prepare students for the type of activities in Unit 4.

Teaching/Learning Strategies

Small group organization of students works well as the comparisons of equation and graphical models for relationships are explored. Issue each student a graphing calculator, but arrange students in pairs as they learn new techniques so that they can help each other. Independent work is important in developing skills with algebraic manipulation and graphing calculators.

Using graphing calculators to reproduce Kitty’s Whiskers, Rays of Sunshine, and other designs using sets of lines creates an interesting context for practise with equations of lines in y = mx + b form. Games like ‘Battleship’ make the learning of coordinate graphing fun.

Direct teaching of algebraic manipulation skills can be moved from concrete to pictorial to abstract symbolic stages through the use of algebra tiles. Time has been allotted for this in the Follow-up skills part of many Activities.

Assessment/Evaluation Techniques

As in Unit 1, a variety of assessment tools and strategies is recommended. Performance assessments may be used to effectively assess Thinking/Inquiry/Problem Solving, Communication, and Application Categories of the Achievement Chart when students do open-ended tasks. Learning Skills can be assessed using teacher and peer observation, and self-reflection. Rubrics and rating scales are useful when a wide range of performance is expected and when many complex criteria are to be judged. Checklists and marking schemes can still be used for more traditional tasks with predictable solutions.

Resources

Classroom Activities & Teacher Resources from Texas Instruments

www.ti.com/calc/docs/activities.htm

Ramp criteria

http://calder.med.miami.edu/pointis/ramp.html

Visualized Geometry: A van Hiele Level Approach. Portland, Maine: J. Weston Walch, 1990.

www.kings.k12.ca.us/math/lessons/ti83tutorial.html

(for instructions and sample data for using the LIST features of the TI-83+)

Activity 2.1: Match Me Up!

Time: 150 minutes

Description

Students construct tables of values for direct variation from a variety of scenarios. Lines of best fit are drawn by hand and an equation for each line developed. Students recognize that the multiplier or co-efficient in the equation relates to steepness, that several scenarios could produce lines with the same steepness, and that algebraic model can represent a variety of situations. The students then replaces the independent and dependent variables in their equations with x and y to enable them to graph their relations with a graphing calculator. The follow-up graphing skills include introducing the four quadrants of the Cartesian plane and graphing equations of the form ”y =” without technology by creating tables of values.

Strand(s) and Expectations

Strand(s): Number Sense and Algebra, Relationships, Analytic Geometry

Specific Expectations: NA1.01, .03, .04; RE1.04, .05, .06; RE2.01, .03, AG2.02, .03, .04, AG3.01, .02, .03.

Planning Notes

· The teacher must have identical, quadrant I grids photocopied onto acetate sheets for each of the groups. See the Appendix for a template. A washable overhead marker is required for each group of three students.

· A photocopy or overhead of the Class Example is needed so that students see the questions that need to be answered in their groups.

· A photocopy of the scenarios should be made and cut into strips so that each group receives one scenario on a strip of paper.

· The teacher leads a full class summary of the results from groups, drawing out the comparisons between the graphs, and introducing the usefulness of x and y notation.

· Provide a class set of graphing calculators, an overhead graphing calculator and LCD panel, and grid paper.

Prior Learning Required

From Unit 1: working with integers and rationals; discrete vs connected points; dependent vs independent variables; first differences; determining trends and patterns by making inferences from graphs; identifying and discussing patterns in algebraic terms; substituting into and simplifying an expression; entering lists and graphing scatter plots using the graphing calculator

Teaching/Learning Strategies

This activity is broken into two parts. The first part begins with the teacher working through the scenario below with the full class. The students then work in groups, examining different scenarios that are similar to the worked scenario. Graphs are then compared and generalized which leads into the introduction of graphing calculators to graph equations using x’s and y’s. The second part of the activity begins with a full class exploration of using the graphing calculators to graph lines in the form of “y =”. This includes moving from data and lines in the first quadrant to relationships in all four quadrants.

Part I

Teacher Facilitation: Introduce a scenario like the one below, and outline the questions to be considered in later scenarios. This example serves to review the concepts from Unit 1 that are needed for the Activity that follows. It is important to review with students how to determine dependent and independent variables using clues like unit rates. In expressing relations as equations, students should be using meaningful variables. DO NOT use x’s and y’s yet.

Class Example

A crystal growing kit contains enough material to perform two experiments. Complete the following steps to explore the relationship between kits and number of experiments.

i) The number of experiments performed depends on the number of kits purchased. Construct a table of values that shows the number of experiments that can be performed if up to five separate kits are purchased.

ii) Add a column in your table for first differences for the number of experiments that can be performed

iii) What is the independent variable? The dependent variable? How did you decide?

iv) Should the points be connected or not? Why?

v) Construct a scatter plot by hand.

vi) Write an equation that would describe this relation using letters appropriate for your scenario.

vii) What units are associated with the number in your equation? What does this number represent?

Teacher Facilitation: Place the students in groups of three and provide each group with a scenario and an acetate for constructing the graph of their scenario. The acetate should have a set of horizontal and vertical axes with appropriate scales photocopied onto it in order to facilitate the comparison of graphs later on. Students carry out the eight steps outlined in the previous example for the scenario that they are given.

The teacher should observe groups as they work to make sure that dependent and independent variables are being identified correctly, and that correct decisions are being made regarding graphing of discrete and continuous data.

Student Activity

Scenario 1: A radio-controlled model car travels at a speed of 2 m/s. Graph the relationship between time (in seconds) and distance (in metres).

Scenario 2: Luke is purchasing packages of peanut butter cups to sell at a school dance. Complete the table of values for the numbers of packages given. Graph the relationship between the number of peanut butter cups and the number of packages between 0 and 50.

Number of packages	10	20	30	40	50
Number of peanut butter cups	30

Scenario 3: In the tricycle department of a toy store, the number of wheels depends on the number of tricycles. Graph the relationship between the number of wheels and the number of tricycles.

Scenario 4: Bob’s sock drawer is a mess. All of his socks are in it, but none of them have been put together in matched pairs. The number of pairs of socks depends on how many socks are in the drawer. Graph the relationship between the number of pairs and the number of socks.

Scenario 5: Photocopying on both sides of a piece of paper saves money and space. The number of pieces of paper required for a copy of a document depends on the number of pages to be photocopied. Graph the relationship between the number pieces of paper required and the number of pages being copied.

Scenario 6: Chocolate bars are often sold in packages of two. The number of bars you have depends on the number of packages you buy. Graph the relationship between the number of chocolate bars and the number of packages purchased.

Scenario 7: The number of participants in a chess tournament depends on the number of chessboards available. Graph the relationship between the number of chessboards and number of participants.

Scenario 8: Legal documents are often produced in triplicate. The number of copies depends on the number of documents prepared. Graph the relationship between the total number of copies and the number of documents prepared if the documents are produced in triplicate.

Teacher Facilitation: Once the groups have followed the eight steps and have their graphs on the acetates, the teacher should bring closure to the activity by summarizing findings and connections with the full class. For example:

i) Ask a member of the group with Scenario 3 to bring their acetate up to the overhead projector and explain the graph.

ii) Ask which other group has a graph that matches Scenario 3 in some way. (Scenarios 2 and 8 should match in steepness; Scenario 4 matches for disconnectedness)

iii) Focus on the steepness comparison. Ask students from group 2 and 8 to come up to the overhead and explain their graphs.

iv) Pile the three acetates on top of each other to show that they match identically for steepness.

v) Ask the following questions and draw out all of the mathematics:

1. Why did the graphs match? (identical tables of values, same first differences, always tripling, same type of equation)

2. What is different about the three graphs? (discreteness, title on graph, labels on axes, units on axes, units on the number in the equation (the unit rate))

3. What is the real life meaning of the numerical multiplier in each equation?

vi) ***Introduce the idea that all three relationships could be summarized as y = 3x where x represents the independent variable and y represents the dependent variable ***

vii) Repeat using Scenarios 1, 6, and 7, then Scenarios 4 and 5, introducing direct variation vocabulary, and xy notation.

Follow-up: Before starting, discuss the need to use the variables x and y when using a calculator, and then replace the independent variable with x and the dependent variable with y in the specific scenario that you are using.

Using a full class presentation, the teacher chooses one of the above scenarios and coach the students through the steps for constructing a scatter plot and graphing the equation of the line using the graphing calculators.

Students:

· clear all lists and previous graphs;

· enter the data into two lists;

· create a scatter plot using those two lists and view it using the ZOOM, ZoomStat feature.

After examining the scatter plot, check the correctness of the equation that was determined for the relationship.

Does the line pass through the points of the scatter plot? Does the equation produce a fitting model?

The teacher discusses the fact that we are representing discrete data with a continuous line. However, this is similar to talking about lines of best fit for discrete data.

Student Activity or Homework:

Give students further scenarios of direct variation to graph and develop equations. These scenarios include decreasing relations (e.g., the distance below sea level as a submarine descends at 5 m/s), relations that have fractional slopes (e.g., currency exchange rates) and relations that require different scales (e.g., distance driven vs gas consumed).

This would also be a good place to take some time to review skills regarding ratios and rates.

Part II

Teacher Facilitation: When students have completed the above activity or homework, the teacher should use three sets of data from their work to “take up” and extend the activity in a whole class setting using the overhead graphing calculator. Students can be working either in pairs or individually with graphing calculators. The class enters their table of values in the lists, create a scatter plot and enters the “y =” equation for each of the three sets chosen by the teacher. The teacher should choose sets of data that include positive, negative, and fractional slopes and discuss: What is the same about these graphs? Different? What happens to the line when the multiplier or co-efficient is negative or positive?

Follow-up Graphing Skills: After the discussion of the previous work concludes, the teacher should introduce students to graphs in four quadrants by showing students how to move from Zoom-stat to Zoom-standard. This leads into a formal discussion and labelling of the axes for the four quadrants including:

· locating ordered pairs in each quadrant;

· playing a short game of Battleship to familiarize students with plotting points in all quadrants;

· graphing linear equations of the form “y =” by hand by creating a table of values. This helps students understand the process of creating a graph and reduces the “magic” of a calculator and understand different ways of modelling a relation. Use integer and fractional values in the equations and independent variables.

· Students may check the hand-drawn graphs by inputting the equations in the graphing calculator.

Assessment/Evaluation Techniques

While students work in pairs or groups, teacher can gather data on Learning Skills such as teamwork, working independently, and work habits, using Appendix 1- Phase 1. This activity also provides opportunities for formative assessment to determine areas where students need more assistance. This includes recognizing: gaps in knowledge or understanding about relationships from Unit 1; difficulties communicating with appropriate terminology; or weak technology skills. This informal formative assessment guides the teacher in terms of the degree of review or prompting that is required.

Activity 2.2: Ramps ’R Us

Time: 150 minutes

Description

In this activity, students use the specifications for designing wheelchair ramps to investigate slope in the “rise over run” form.

Strand(s) and Expectations

Strand(s): Number Sense and Algebra, Analytic Geometry

Specific Expectations: NA1.03, .05, NA3.04, AG2.01, .04.

Planning Notes

· The teacher may wish to show a brief movie clip that shows a person using a wheelchair. (e.g., Coming Home - the scene where John Voight is learning how to navigate a ramp; Forrest Gump - the scene where Lt. Dan uses the ramp to his boat; or use slides of ramps from local surroundings.)

· Provide students with rulers and graph paper.

Prior Learning Required

Pythagorean theorem; ratios; converting between fractions, decimals and ratios; drawing to scale

Teaching/Learning Strategies

Teacher Facilitation: Review the Pythagorean theorem, working with ratios, converting between fraction, decimals, and ratios, and the use of scale drawings before the activity or as the need arises. Students work in pairs for this activity.

Student Activity: Ramps 'R Us

If a family member becomes confined to a wheelchair, the home must be outfitted with ramps to provide access for that person.

Here are a few criteria adapted from suggestions by rehabilitation specialists (from http://calder.med.miami.edu/pointis/ramp.html):

· The maximum incline recommended for wheelchair users is 1:12, (i.e., for each centimetre in height, the ramp must extend 12 centimetres).

· For exterior ramps in climates where ice and snow are common, the incline should be more gradual, at 1:20.

· For unusually strong wheelchair users, for extra-powerful motorized chairs, and if the person is lightweight but the pusher is strong, the ramp can have an incline of 1:7. The steepest ramp should not have an incline exceeding 1:5.

· There should be at least 150 cm of straight clearance at the bottom of the ramp.

PART A

Refer to the descriptions of the following three clients as you design wheelchair ramps.

1. Client A lives in a split-level house. He owns a very powerful motorized chair. He wishes to build a ramp that leads from his sunken living room to his kitchen on the next level. The height of the ramp must be 60 cm.

2. Client B requires a ramp that leads from her back deck to a patio. She is of average strength and operates a manual wheel chair. The deck is 25 cm above the patio.

3. Client C lives in Sudbury where ice and snow are a factor. She is healthy, but not particularly strong. Her house is a single level bungalow but the front door is 0.45 m above ground level. The path that leads directly to the front door from the street is 60 m long. Keep in mind that the ramp does not need to be 60 m long.

On a piece of graph paper design a ramp that would meet the criteria listed above and that would conserve ground space.

Construct a scale drawing for each design. Justify your reasoning for each design. Watch the units!

PART B

Mathematicians call the steepness of an incline slope. The slope can be calculated by dividing the height of a ramp (called rise) by the horizontal length (called run). This is often written as m = where m is the variable used to identify slope.

· Determine the rise and run for each ramp from part A by forming a right angle triangle under each ramp. If your design includes resting points, use only one of the inclined sections for the chart.

· Sketch and label each ramp in the space provided.

· Complete the following table.

Wheelchair Ramps
Ramp #	Diagram	Rise, Vertical Distance (cm)	Run, Horizontal Distance (cm)	Slope, m =

Questions

1. Compare the slopes of your ramps. If all of the ramps were of equal lengths, which incline would be the easiest one to push a wheelchair up? The most difficult?

2. The following is a scale drawing of a ramp. Measure the sides and determine the slope. Does this design fall within the acceptable range for wheelchair ramps?

3. How long is each of the ramps in your chart?

4. A building code requires a slope of 1:12 for a wheel chair ramp. If the length of a wheel chair ramp is 13 m and its horizontal distance is 12 m, is it safe?

5. What would be a good slope for a ski jump or skate board ramp? Explain your reasoning.

6. What is the slope of a rest platform? Explain.

7. What is the slope of a vertical wall? Explain.

Extension Question

Locate a wheel chair ramp in your community. Measure the rise and the run and calculate the slope. Does it fall within the suggested range?

Challenge Questions

1. A safe wheel chair ramp has a slope in the range from 1:5 to 1:20. If a ramp has a length of 20 m, what are the ranges of values for the rise and run of the ramp?

2. On a long ramp of any steepness or on a steep ramp, level rest platforms are needed every 3 m of horizontal distance and should be 2 m long. Assume that such a ramp is a 2 m square. Given this information, how would you change your design for client C in Part A?

Teacher Facilitation: Bring closure to the Ramps inquiry by connecting steepness, developed in Unit 1- Activities 6 and 10, to slope. It might be advisable to re-visit some of the scenarios in Unit 1 and discuss them using slope vocabulary. Some of the questions in this activity provide beginning points for discussion surrounding such concepts as zero and undefined slopes.

Homework:

Students can be assigned other “rise over run” and Pythagorean theorem practice from their textbooks. Equations resulting from knowing 2 of the variables in the formula m = should also be practiced.

Assessment/Evaluation Techniques

The teacher may use this activity as an opportunity for informal, formative assessment of numeracy skills and facility with the Pythagorean theorem. This could be as simple as making observations to identify students who require remediation.

As this activity is inquiry-based, the teacher could assess students’ problem-solving skills, such as risk-taking or testing out a variety of solutions, as they design ramps to satisfy the given criteria in ramp design.

A journal entry with students reflecting on other situations where differences in slope make a significant difference (roofs, highway ramps, skateboard ramps) may also be appropriate. This journal entry would help the teacher assess the students’ application of knowledge and communication skills.

Activity 2.3: Slippery Slope

Time: 150 minutes

Description

Using the Slippery Slope Activity worksheet provided, students investigate slope as rise over run. They observe and explain when and why the slope is positive or negative and compare the value of the slope of a line to its steepness and its direction. A follow-up exercise focusses on the calculation of slope using a formula which sets the stage for determining the equation of a line given two points.

Strand(s) and Expectations

Strand(s): Analytic Geometry, Number Sense and Algebra, Relationships

Specific Expectations: AG2.01, .02, .04; AG3.01, .02; NA1.01, .02, .03; RE1.01, .02, .03, .04, .05, .06, .07; RE3.02.

Planning Notes

· Collect equipment needed: masking tape, metre sticks, graphing calculators, CBR™’s (Computer-Based Ranger), graphing calculator overhead display, class set of Slippery Slope Activity Worksheet.

· Students work in groups of three to collect the data for the Slippery Slope Activity. One student walks, one is responsible for the CBR™, and one is responsible for the calculator. They may change roles for different trials.

· Students need floor space for setting up this activity.

Prior Learning Required

Activities 1.8 and 1.9 (distance/time relationships, analysing and interpreting relationships), Activities 2.1 and 2.2 (using x and y notation, using m = , plotting points, substituting into formulas)

Teaching/Learning Strategies

Teacher Facilitation: For the first activity, Slippery Slope, group work should be interspersed with whole class discussion as needed. The teacher may want to refer to an overhead of the chart for this activity. Once the instructions to the students have been given, circulate and help groups as necessary. The teacher should make sure that the students are familiar with the procedure for setting up the CBR™. Students collect data and record their observations using the chart provided.

Student Activity: Slippery Slope

(Modified from “Slippery Slope”, Math and Science in Motion, TI Inc.)

In this activity, you create Distance-Time plots by moving in front of a CBR™, find slopes on the plots, and determine the formula for the slope of a line.

You will need the following materials: CBR™ unit, TI-83+ and calculator-to-CBR™ cable, metre stick, and masking tape

Collecting the Data:

1. Three students work together to collect the data. One is the walker, one controls the CBR™, and one controls the calculator. They change roles for subsequent trials.

2. Place the CBR™ on a table or desk so that the sensor is aimed at or above the walker's waist, the height can be adjusted using textbooks, if necessary.

3. Put a masking tape marker on the floor at a distance of 0.5 m from the CBR™ and at a distance of 3.0 m.

4. The walker stands at the 0.5 m mark and prepare to move away from the CBR™ at a slow and steady rate. When the walker is ready the calculator person presses [ENTER] to begin the walk. The partner presses the Trigger button on the CBR™ to stop the recording when the walker passes the 3 m mark. The walker must try to keep a steady pace for the whole walk.

The plot should look like a straight line that rises gently to the right.

5. If your line is reasonably straight, sketch it in your notebook and label the graph, A Trial 1", and go to question 6. If not, press [ENTER] select 3: REPEAT SAMPLE from the PLOT MENU, and try again.

6. Using the [u] and [t] keys, find and record the co-ordinates of two points on the line in the chart below. Choose points near the beginning and end, so that the line between them is the straight line that best models the plot.

7. Repeat steps 3-5 for the following motions, sketching your results for each in your notebook.

Trial 2 - moderate, steady walking away from the CBR™;

Trial 3 - slow, steady walking towards the CBR™;

Trial 4 - moderate, steady walking towards the CBR™.

Observations:

Answer the following questions, recording your results in the chart.

1. Refer to the graphs in your notebook and compare the four plots in terms of steepness of the line (slope), and the direction of the line (Is it going up or down, from left to right?). Enter this information into the chart.

2. Calculate the vertical change (rise) by calculating the change in y from starting point to ending point. Enter this amount into the table.

3. Calculate the horizontal change (run) by calculating the difference in x from the starting point to ending point. Enter this amount into the table.

4. Calculate the slope by finding rise ¸ run.

Collecting Data

Calculations

Trial

Starting Distance

Type of Motion

Steepness and Direction of Line

Starting Point

Ending Point

Vertical Change rise

Horizontal Change run

Slope (m/s)

rise

run