5-8

I2:Use mathematics to describe the motion of objects (e.g., speed, distance, time, acceleration).

Curriculum Organizing Questions	How can you describe the motion of this object mathematiucally? How fast is the object traveling? How far did it travel? How long did it take to travel? is this object accelerating? If so, calculate its acceleration.
Elaboration	The motion of an object can be described by its position, direction of motion, and speed. That motion can be measured and represented on a graph or in a numerical sentence. NSES B2a.
Specific Idea	Acceleration is any change in motion and occurs when something speeds up, slows down, or changes direction. Acceleration = change in speed/time. Speed = distance/time.
Developmental & Instructional Implications	This is an introduction to the mathematical concepts involved in motion. It will be further developed in 9-12. Children's ideas and descriptions of motion tend to be less differentiated than a physisicist's. They tend to see objects objects as either at rest or moving. The period of change, when an object speeds up from rest to a steady speed or slows down and stops, is less frequently focused on by children. The term "acceleration" is not commonly used by school-age pupils prior to its introduction in science lessons. ... Some students leave time out of their thinking such that they were imagining an object getting to a certainv elocity rather than accelerating over a period of time. ... It is common for pupils to think that, if speed is increasing, then acceleration is also increasing. ... It is important to note here the need for proportional reasoning in developing scientific concepts of velocity and acceleration. Driver p. 155. The early introduction of the concept of momentum in qualtitative terms prior to considering forcesis an important porposal with considerable support. Although in traditional courses this has been seen as a mathematical motion to be faced by older pupils, many studies nsuggest that we need to offer the idea of momentum so that pupils can attach to it their own idea that a moving object has something which keeps it going. ... There is a general suggestion that Newtonian ideas about motion become harder to accept as pupils become firmer in their own dynamcis. Intorducing momentum before force then allows force to be seen as that which causes a change in momentum, and it prevents the label "force' being attached to the pupils' notion of "something in the object which keeps it moving." Driver p. 161.
Examples	Have students make tables and graphs from data collected.

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