Model Bouncing Ball
Identify Mathematical Relationships
Use Models to make Predictions
Design an experiment
Collect & Analyze Data
Write a conclusion based on evidence and reasoning
How is the bounce height of a ball related to the release height of the ball?
To determine the type of relationship (linear, quadratic, inverse, or constant) that relates the bounce height to the release height.
to determine the effect of one quantity upon another quantity.
How does the mass of an object affect its acceleration? That is, to determine the effect of mass upon acceleration.
the variable that the scientist intentionally changes each trial.
the variable that changes in response to the changes that are made to the independent variable.
to determine the effect of mass upon the acceleration of an object.
mass (it is varied by the scientist from trial to trial)
acceleration (it varies in response to changes in the mass)
The dependent variable changes in response to the other variable; its values are plotted on the y-axis.
The independent variable is the one that is manipulated or changed by the scientist; values are plotted on the x-axis.
Any given change in the independent variable (x) will always produce the same change in the dependent variable (y).
When x changes by a certain amount (1 unit), the value of y always changes by the same amount (e.g., 2 units).
x | y |
---|---|
0 | 4 |
1 | 6 |
2 | 8 |
3 | 10 |
4 | 12 |
5 | 14 |
A special type of linear relationship - shows an x-y plot that is linear and has a y-intercept of zero.
Whatever change is made to one variable is made to the other variable.
Double x … double y
Triple x … triple y
Halve x … halve y
x | y |
---|---|
0 | 0 |
1 | 2 |
2 | 4 |
3 | 6 |
4 | 8 |
5 | 10 |
A special type of linear relationship - shows an x-y plot that is linear and has a y-intercept of zero.
Whatever change is made to one variable is made to the other variable.
Double x … double y
Triple x … triple y
Halve x … halve y
x | y |
---|---|
0 | 0 |
1 | 2 |
2 | 4 |
3 | 6 |
4 | 8 |
5 | 10 |
A special type of linear relationship - shows an x-y plot that is linear and has a y-intercept of zero.
Whatever change is made to one variable is made to the other variable.
Double x … double y
Triple x … triple y
Halve x … halve y
x | y |
---|---|
0 | 0 |
1 | 2 |
2 | 4 |
3 | 6 |
4 | 8 |
5 | 10 |
A special type of linear relationship - shows an x-y plot that is linear and has a y-intercept of zero.
Whatever change is made to one variable is made to the other variable.
Double x … double y
Triple x … triple y
Halve x … halve y
x | y |
---|---|
0 | 0 |
1 | 2 |
2 | 4 |
3 | 6 |
4 | 8 |
5 | 10 |
A change in one variable will have no effect upon the value of the other variable.
x | y |
---|---|
0 | 4 |
1 | 4 |
2 | 4 |
3 | 4 |
4 | 4 |
5 | 4 |
Most commonly, a quadratic will show an exponent of 2, indicating that the y value depends on the square of x.
Double x…Quadruple y
Triple x…Nine times y
Halve x…One-quarter y
x | y |
---|---|
0 | 0 |
1 | 2 |
2 | 8 |
3 | 18 |
4 | 32 |
5 | 50 |
Most commonly, a quadratic will show an exponent of 2, indicating that the y value depends on the square of x.
Double x…Quadruple y
Triple x…Nine times y
Halve x…One-quarter y
x | y |
---|---|
0 | 0 |
1 | 2 |
2 | 8 |
3 | 18 |
4 | 32 |
5 | 50 |
An increase in one variable causes a decrease in the other variable.
x | y |
---|---|
1 | 12 |
2 | 6 |
3 | 4 |
4 | 3 |
5 | 2.4 |
6 | 2 |
An increase in one variable causes a decrease in the other variable.
x | y |
---|---|
1 | 12 |
2 | 6 |
3 | 4 |
4 | 3 |
5 | 2.4 |
6 | 2 |
Block | Start | End |
---|---|---|
Block 1 | 9:40 | 10:33 |
Block 2 | 10:35 | 11:28 |
JR HS - Block 3A | 11:30 | 12:03 |
Lunch 7/8 | 12:04 | 12:34 |
Block 3B | 12:35 | 1:07 |
Block 4 | 1:09 | 2:00 |
Use Mathematical Models
Make a scientific argument
Claim:
Evidence:
Reasoning:
Which is an appropriate Claim for the Conclusion section of such a lab?
Which is an appropriate statement of the Evidence for the Conclusion section of such a lab?
Which is an appropriate statement of the Reasoning for the Conclusion section of such a lab?
Create a linear model to make predictions