Mathematics Grade Prototype Curriculum Guide

Objectives

The students should be able to

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  understand that friction is a force that acts to slow down a moving object;
  
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  explain that speed is a measure of motion;
  
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  collect and display in a table and line graph time and position data for a moving object.
  

Materials needed

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  Pictures or examples of inclined planes and wheel and axles
  
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  Attached data sheet for each student
  
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  Book whose main theme is motion

  Per group of 3 or 4 students:

  
  
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  Toy car (Lego™ cars are an excellent choice; Matchbox™ cars may be too light for this activity.)
  
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  Piece of stiff cardboard or thin wood about 50 cm long and 30 cm wide to use as a ramp
  
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  Stack of books
  
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  Roll of masking tape
  
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  Meter stick
  
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  Marker
  
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  1 or 2 pieces of poster board
  
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  Graph paper
  

Instructional activity

Content/Teacher Notes

Students in grade 4 should already be able to measure length in centimeters and meters. They should have had some experience with gathering, charting, and graphing data. Make sure to give simple directions for setting up the ramps (inclined planes).

Let students decide where to start and stop measuring. Let them determine the three different heights. Let them notice and comment on whether all groups need to be doing exactly the same thing.

Let them wrestle with the confounding event of the cars “nosing in” when the ramp is steep. When the tape is laid out by each group to measure the distance the car travels for the three heights, have the students explain their results to the class. There will be a great deal of discussion about why the data from the various groups differ. You may also wish to introduce the concept of potential and kinetic energy, although the results will not clearly illustrate this concept. You may choose to discuss independent and dependent variables. You may also discuss the variable introduced by the different vehicles.

Ask students to decide how they would test to find the “best” vehicle. What variables would they control? How does friction affect the results? Could the experiment be modified to test different surfaces?

Hang the tapes on the wall, side by side, so students can clearly see that the lengths of the three strands of tape convey a great deal of information, if you know how to read them.

Introduction

1. Introduce the lesson by having students read a book whose main theme is motion. Have the students answer questions pertaining to the book, and lead them in a discussion of motion.

2. Tell students that they will experiment with a car on three different heights of a ramp, which is a form of inclined plane.

Procedure

1. Demonstrate building the ramp by stacking books under one edge of the cardboard or wood, and show students that by adding books to the stack, the ramp (inclined plane) is made steeper. Show students how to measure the height of the ramp. Have students predict how the distance their car travels will be affected by the different heights of the ramp, and record their prediction on their Inclined Plane Data Sheet.

2. Demonstrate the experiment for the class before the students conduct their own. Without pushing, release the car from the top of the ramp, and allow the car to roll until it comes to a stop. Demonstrate how to mark off and label the distance the car travels, using masking tape and a marker, as described in step 6, below. These tape markers will be used later to construct a bar graph.

3. Divide the students into groups of three or four, provide materials for each group (toy car, ramp, books, tape, and marker), and have them spread out in the classroom. Ensure that each group has ample space, keeping in mind that they need room for the car to travel down and off the ramp.

4. Before allowing the students to release their cars, review the elements that must be kept constant in their trials: the same car must be used throughout the experiment; the distance should always be measured from the same starting point; the same meter stick should be used for all measurements.

5. Instruct the groups to build their ramp for the first trial, using books stacked to a height of approximately 10 cm. Have students measure and record the actual height on their Inclined Plane Data Chart.

6. Direct students to conduct the first trial. When the cars have come to a complete stop, instruct students to run a strip of masking tape from the bottom end of the ramp to the back of the car and label the strip “10 cm.”

7. Instruct students to repeat the procedure, with their books first stacked to a height of approximately 20 cm, and then to 30 cm.

8. When the three trials are complete, have students measure the three strips of tape and record the distances in centimeters. Then have them convert and record their measurements to meters.

9. When all the data has been recorded, ask each group to report their results. Then, have students remove their strips of tape from the floor and place them on the wall in order from lowest ramp to highest, forming a bar graph. These strips may be used in the graphing activity later.

Observations and Conclusions

1. Discuss with the students the effect that the change in ramp height had on the distance traveled by their cars.

2. Discuss with students the concepts of speed and friction.

3. Ask the students the following questions in order to stimulate conclusions:

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  What do the “bars” in the wall bar graph tell us? (The distance traveled from the bottom of the ramp)
  
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  When is the car traveling the fastest? (The car is traveling fastest, i.e., with the highest kinetic energy, when it is at the bottom of the ramp.) Why? (Because gravity increases the speed until the car reaches the floor, where friction begins to slow the car down)
  
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  What makes the distance traveled on the floor longer or shorter? (The different speeds of the cars at the bottom of the ramp and the differences in friction on the floor)
  
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  Why did the cars slow down? (Because of friction)