odometer teacher guide - Commission scolaire de Laval and tries to determine the advantages and disadvantages ... odometer_teacher_guide.doc 4/7 ... • Four giant size islands or

Center for pedagogical development Odometer odometer_teacher_guide.doc 4/7/09

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The odometer

TEACHER’S GUIDE

April 2009


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PREPARATION Activity 1 Objective: Context Material:

• Peg-Leg Max’s letter (2 versions) • Mathematical lexicon

Duration: 10 minutes Read or have the students read the messages from Peg-Leg Max. The first is addressed to the teacher who wishes to install several islands in the classroom or gym to allow several students to take measurements at the same time. The second offers the possibility of installing a single island that the students will measure in turn to then determine, from a listing, the island in question. In a large group, define the term « perimeter » so that the students have a common understanding of it. IMPORTANT Mention to the students that they will have to build an instrument of measurement.


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Activity 2 Objective: Recognise certain properties of the circle Material:

• Circular objects (record, plate, glass, toys, hoops, containers etc.)

• Activity #2 document « Study of the circle » • Annex 1 • Power Point on the study of the circle

Duration: 30 minutes (or more) A Power Point presentation is available to facilitate the students’ questioning regarding the circle. It also introduces an odometer to the students. The teacher places the concepts of circumference (perimeter), radius, diameter and angle to center. She or he can help the students to establish a relationship between the circumference (perimeter) and the diameter. This activity may be done by measuring different circular objects. Once the concepts are in place, the students complete Activity #2 in order to define the problem surrounding the design of the roller (wheel) of their odometer. It is also important to ensure that all the students are comfortable with the notion of scale.


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Solutions avenues: 1. The student cuts a 15 cm strip of cardboard and joins it with adhesive tape, which will provide him a cylinder. He measures its diameter with a ruler. Since the notion of the radius has already been established, the student can use his compass to trace a first circle. He cuts it out and tests it on the 15 cm scale that has been supplied to him. 2. The student may cut a 15 cm piece of string and place it on the table in order to obtain a circle. With a ruler, he measures the diameter approximately and proceeds as in #1. This technique is less precise and the student will make several circles before getting the correct measurement. 3. The student may proceed by trial and error by cutting out several circles and trying them on the 15cm scale supplied. This technique may necessitate several manipulations. 4. An advanced student may already know the formula P=2rπ and apply it directly.


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Activity 3 Objective: Discover the odometer and work on the techniques and language associated to the design and fabrication of instruments Material:

• Tin cans with various diameters • Circular objects • A land odometer, if available (see physical education specialist) • Pizza cutters • Pastry wheels • Paint rollers • Circular knives • Others

N.B. The purpose is to supply objects that have a link to the odometer to be designed. Duration: 30 minutes The teacher presents different circular objects in order to make the students to realise that the larger the diameter of the object, the greater the distance covered. The teacher proposes objects that may inspire the design of the odometer and tries to determine the advantages and disadvantages of each.


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REALISATION Activity 4 Objective: Design and fabrication of the odometer Material:

• Activity #4 document «Design of the odometer», pages 1 to 3.

• Scale of the map • Fairly rigid cardboard • Styrofoam (meat plates) • « Popsicle » sticks • Tongue depressors • Flexible PVC tubing • Plastic straws • Fine dowels, brochette sticks • Various wooden strips • Squared paper

Hardware:

• Thumbtacks • Two-pronged flat metal fasteners • 6-32 bolts with nuts (between 1 and 1½ inches) • Nails (between 1 and 1½ inches) • #6 screws (between 1 and 1½ inches) • Adhesive tape

Tools:

• Set of scrapbooking punches • Utility knife • Levelling saw and mitre box • Hammer • Screwdriver • Compass

Common steel nail Common aluminium nail Roofing nail (between 1 and 1½ inches)

Metal washers 6-32 nut #6 wood screw (Square head) (between 1 and 1½ inches)

3/16″ and ¼″ flexible PVC tubing


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Duration: 75 minutes or more The teacher explains what a specifications booklet is. She or he presents the materials and tools that will be supplied to make their odometer. The student becomes familiar with the specifications booklet and prepares to approach the problem. He indicates, in the Activity #4 booklet, the questions he has regarding the problem. N.B. The documents presented on the right are designed for teachers. Some of these images appear in the Power Point presentations. We leave it up to the teachers to evaluate if their group can interpret these drawings.


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Accompanied by his teacher, the student traces quick sketches and answers the questions on page 2 of activity document #4 « Design of the odometer » : o In relation to the scale of Peg-Leg Max’s map, what will the

most appropriate diameter be for your wheel? o How will you go about drawing a circle whose

circumference will allow you to measure the line on the map’s scale line?

o The wheel must turn easily. What could you use to reduce

friction? o The teacher presents appropriate and inappropriate

materials to make the students think. They manipulate certain materials and make a few quick tries.

o You must design a handle and attach it to the wheel. What

material will you use and how will you go about attaching them? o The teacher guides the students in their reflexion. It

may be useful to have glue if the student is painstaking and avoids smudges. Since the wheel can not rub on the handle, a space to separate them must be foreseen.

The students carry out the sketches (top view and side view) of the anticipated solution on page 3 of the #4 activity booklet. After having validated their sketches the students build their odometer.


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Activity 5 Objective: Allow the student to evaluate his process and to correct his instrument if needed. Material: An island where there is a beach, a palm tree and an anchor or another object allowing the students to verify the accuracy of their odometer. Duration: 30 minutes The students carry out two test runs while answering the two questions on page 4 of the activity #4 booklet. Next, they evaluate what works well, less well and not at all and correct their odometer if necessary.


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INTEGRATION Activity 6 Objective : Find Treasure Island Material:

• Four giant size islands or a single island to be made. • Students’ odometers

Duration: 30 minutes The teacher installs the island(s) in the class or in another area where the students can work in sub groups. They go searching for Treasure Island using their odometers. N.B. The islands may also be drawn on the ground in chalk in the school yard or on the board. They may also be drawn with coloured tape in a room (corridor, gym, class).

Example of an island

Examples of islands : Four assembled pieces of 57,5 cm by 72,5 cm cardboard Two assembled pieces of 57,5 cm by 72,5 cm cardboard

Documents

odometer teacher guide - Commission scolaire de Laval and tries to determine the advantages and disadvantages ... odometer_teacher_guide.doc 4/7 ... • Four giant size islands or