In Class Activity Plan

Week Three: Becoming Quantitative with Constant Acceleration

 

 

20 min������������ Becoming Quantitative (Page one) (Word, Pdf)

PURPOSE: The first page gets students to agree on one specific model which is then generalized in the second page������������

Video Examples: (Discussion1, Discussion2)

Logistic Notes:

o  This works best if you print this as two separate pages and hand out the pages one at a time and do a whiteboard discussion about each page

-          The first page should be the one without numbers, and the second page should be the one with numbers

o  Watch out for d = vt, they will try to use this (and it doesn�t apply in the constant acceleration model), enforce class norms of only using things we�ve established as rules

 

Page 1 Goals:

o   Create quantitatively accurate position versus time and acceleration versus time graphs

o   Focus on finding slope and area and writing them correctly on the relevant graphs

o   Note that they will have to make an assumption about the initial position of the object

 

10 min������������ Whiteboard � Becoming Quantitative (Page One)

PURPOSE: Share specific model

o   Put the complete model on your whiteboard

 

20 min������������ Board Meeting

PURPOSE: Students share solutions to problem, articulate process of modeling specific situation

o   Make sure the models are internally consistent

o   What can you find?

-          p-t graph, a-t graph, motion map

-          writing down assumptions you make

-          values for displacement (total and for each second), acceleration

o   Compare and contrast different people�s models (particularly those who make different initial position assumptions)

 

20 min����������� Becoming Quantitative (Page Two) (Word, Pdf)

PURPOSE: This problem is identical to the first side, but with the numbers replaced by variables, so students can model the situation but get equations for constant a.

Video Examples: (Why you get confused)

Page 2 Goals:

o   Again, create quantitatively accurate position versus time and acceleration versus time graphs, but this time they will be using variables

o   During the process they will find 2 equations:

-         

-         

 

-          Seed: In the displacement equation we can replace ∆v with a∆t and get

 

10 min������������ Whiteboard � Becoming Quantitative (Page Two)�����������������������

PURPOSE: Share model

o   Put the complete model on your whiteboard

 

30 min������������ Board Meeting

PURPOSE: To develop a set of equations for use with the constant acceleration model

Video Examples: (Group1, Group2)

o   The area under the curve give

o   The slope gives

 

o   Will probably have to explicitly show the algebraic steps between the first displacement equation and

 

 

o   Initial position assumption � the d in the equation represents displacement, not the position because we can�t tell anything about the initial position

o   Make these equations part of the rules for the constant acceleration model

 

30 min������������ Specific models using constant a (Word, Pdf)

PURPOSE: Practice using equations in modeling of variety of situations.

Video Examples: (Whiteboards, We like them, Discussion)

Presumably you have 10 groups, so you would have 2 groups complete each problem (no group does all 5).

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Goal:

o   To use the equations developed, graphs, and motion maps, to create quantitatively accurate specific models of the situation

o   To help guide towards the need for a basic model for constant acceleration instead of several specific models

 

10 min������������ Whiteboard � Specific models using constant a

PURPOSE: Share specific model

o   Give each group one of the 5 situations to model

o   This is an opportunity, and you should point it out, that groups are presenting problems that most students have not done, so it�s important that they pay attention, check for mistakes, and make sense of each problem.

 

45 min ����������� Board Meeting

PURPOSE: Build consensus about characteristics of basic constant acceleration model

Video Examples: (Group1, Group2, Group3)

Note: If you read about a general model in a paper, a basic model is the same concept

o   Let each group discuss their model for the specific case

o   Ask what is common about all of their specific models

-          Develop a basic constant acceleration model which consists of the following:

�         Curved p-t graphs, constant slope v-t graphs, horizontal line a-t graph

�         Relations between graphs

-          Slope of v-t graph is acceleration

-          Integral of v-t graph is change in position

-          Slope of p-t is instantaneous velocity

-          Integral of a-t is change in velocity

�         Motion maps: changing arrows, the way that they change indicates the acceleration

�         Equations: v = vo + at & d = vot + � at2

-          Point out that the specific models are only useful in a very particular case, but the basic model applies to all the constant acceleration cases, so we want to look for a basic model

o   What goes into a good model?

-          Representations

�         P-t graphs, v-t , a-t graphs,

�         Motion maps

�         Mathematical (equation) representation

-          Assumptions

-          Interpretations

�         Working out the math � for example, �What is the value of the acceleration for the car?�

 

30 min������������ Five Situations using constant v (Word, Pdf)

PURPOSE: Practice using equations in modeling of variety of situations.�

Give each problem to 2 groups

����������������������� Goal:

o   To see the constant v is a different basic model than constant a

o   Develop rules for a constant v basic model

 

10 min ����������� Whiteboard - Five Situations using constant v

PURPOSE: Practice using equations in modeling of variety of situations.�

o   Give each group a different situation to whiteboard

 

Seed:

o   Get a group to draw an a-t graph to see the acceleration is 0, but constant

 

20 min������������ Board Meeting

PURPOSE: Build consensus about characteristics of basic constant velocity model

Note: This discussion is pretty straight forward because they have just had a similar discussion regarding the constant acceleration basic model

 

o   What is common about the specific models?

-          Graphs: linear p-t graphs, horizontal v-t graphs

-          Relation between graphs:

�         Slope of p-t graph is velocity

�         Area under v-t graph gives change in position

�         Slope of v-t graph is always 0, which is the value of the acceleration

-          Motion Maps: constant spacing between points, length of arrow stays the same

-          Equation: v = ∆p/∆t

o   What about constant position? (boring)

o   Point out that basic constant v model is just a special case of the basic constant a model when a=0

 

60 min������������ Practice with One Dimensional Motion (Word, Pdf)

PURPOSE: Practice adapting basic constant a model to a variety of situations.

Logistic Notes:

o  The antelope problem is super complicated with equations, but easy with graphs.

o  If you don�t finish this worksheet in class, assign 1 or 2 problems for homework

 

Assign for homework as a bridge to next activity (not for collection, just for thought): �How do these models change with two dimensional motion?�