From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

CONTENTS OF CURRICULUM UNIT 17.05.10

  1. Unit Guide
  1. Introduction
  2. Demographics
  3. Objectives
  4. Unit Content
  5. Teaching Strategies
  6. Classroom Activities
  7. Sample Problem Sets
  8. Teacher and Student Resources
  9. Appendix
  10. Bibliography

Exploring Kinematic Proportional Relationships

Zachary J. Meyers

Published September 2017

Tools for this Unit:

Classroom Activities

Creating a Unit

At the start of the kinematic unit each student will be given a piece of blank card stock. Each student will take multiple measurements of known distances, using his/her card as unit length, and will use these measurements to determine the conversion rate of their unknown base unit to develop ratios. Students will subdivide their card stock to measure more precisely. They can mark their ruler in smaller intervals based upon a new unit interval, like the width of their thumb or the length of a locker key, to construct a more precise measuring instrument. Students will pair up, and using their new conversion factors, estimate the length of a specific object, like a table length. Units are essential to understanding multiplicative comparison problems and this will be especially important in the context of an object’s position and movement through time. The standardization of units allows data to be effectively communicated which leads to the refinement of understanding physical phenomena.

Move to the Movement

This lab is an adaptation of a PHeT simulation titled “The Moving Man”.V Students will record the time at every 5 meter interval as a walker travels at a constant velocity on a simulated football field. Students will plot the data on a distance vs. time graph for three walkers and interpret the meaning of the slope. Each walker will travel at a constant rate, but different rates for different walkers. The data gathered will be used to prompt a discussion about proportional relationships. Student will be asked to predict the distance that each walker will walk in a given time, based on their recorded speed. Students will work in groups of 2-3 to develop and analyze a variety of scenarios, including resting in place (speed = zero) and reversing directions. Each group will present their conclusions to the class and discuss the relationship(s) with respect to time, distance, and speed. To ensure engagement of all students, each will be expected to take notes and ask questions during whole group discussion.

Relay Race

A relay race will be performed in the lab to reinforce the relationships between position, time, and speed. Students will work in groups of three to develop a data table that records three trials of walking, skipping and hopping for distances of 50 and 100 meters. Each group member will rotate roles, participating in turns as a racer, timekeeper, and recorder. Each group will calculate the average speed for all three types of movements (i.e., walking, skipping, and hopping) at both distance intervals. Students will be asked to compare the speeds between 20 m and 40 m for walking skipping, or hopping. In addition students will create position-time graphs for each and compare the slope to determine which movement created the greatest speed? An automatic timer will be setup on the football field prior to the activity to minimize error.

Graphical Translation of Movement

Students will be asked to translate position-time and velocity time graphs into descriptive texts of an object’s movement. For example, students comparing object I and II in figure 2 might state that the position time graph illustrates the motion of two objects. The linear slope of objects I depicts constant motion whereas object II demonstrates motion at varying rates of velocity of movement. In addition, students will be given data and complementary text to generate corresponding position-time and velocity-time graphs. This will allow students to practice translating movement from text to visual representation (i.e., graphs) and vice versa.

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