Ice Drilling Program
School of Ice
Today’s Agenda…
Physical Models
Physical Models-Strengths and Weaknesses
Physical Models-Strengths and Weaknesses
Decoding Ice Cores
Developing Proxy Mathematical Models
Set-up Check
Your Classroom Ideas
Developing Mathematical Proxies. Bill G.
Proxy data are preserved physical characteristics of the environment that can stand in for direct measurements.
Proxy mathematical models are developed using relationships between data that can be measured directly.
After establishing a relationship, proxy mathematical models are then used to obtain estimates of data that cannot be directly measured.
Your Classroom Ideas
Page #
Developing Mathematical Proxies Bill G.
What are some ways that you could calculate the amount of thermal energy absorbed by this hot patch of ocean water?
Your Classroom Ideas
How does the mass of salt H2O change if different volumes of salt H2O are added to
a cup?
The goal of this mini-investigation is to use direct measurements of mass and volume to develop a mathematical proxy model that can predict the mass of large volume of salt water.
Developing Mathematical Proxies Bill G.
This will be done by finding the mass of different volumes of salt water that are poured into a measuring cup or graduated cylinder.
IV:
DV:
Different volumes of salt water
Mass of the salt water
Volume of
Salt Water (mL)
Mass of
Salt Water (g)
Investigable Question:
0 ml
0 g
230 ml
Your Classroom Ideas
0 50 100 150 200 250
Mass of Salt Water (g)
Volume of Salt Water (mL)
Mass vs. Volume of Salt Water
Developing Mathematical Proxies Bill G.
300
250
200
150
100
50
0
Relationship: The data suggest…
Y-Intercept: The Y-intercept on this graph shows…
Your Classroom Ideas
Your Classroom Ideas
0 50 100 150 200 250
Mass of Salt Water (g)
Volume of Salt Water (mL)
Mass vs. Volume of Salt Water
Developing Mathematical Proxies Bill G.
300
250
200
150
100
50
0
Relationship: The data suggest…
Y-Intercept: The Y-intercept on this graph shows…
Slope: The slope of this graph is…
Run = 250 mL
Rise = 300 g
Slope = 300g. = 1.2 grams
250mL. mL
Your Classroom Ideas
Your Classroom Ideas
0 50 100 150 200 250
Mass of Salt Water (g)
Volume of Salt Water (mL)
Mass vs. Volume of Salt Water
Developing Mathematical Proxies Bill G.
300
250
200
150
100
50
0
Relationship: The data suggest…
Y-Intercept: The Y-intercept on this graph shows…
Slope: The slope of this graph is… 1.2 grams/mL. This suggests that for every 1 mL of salt water added, the mass increased by 1.2 grams.
Run = 250 mL
Rise = 300 g
Slope = 300g. = 1.2 grams
250mL. mL
Mathematical Model: Y= mX + b
Mass of Ocean (g) = ( 1.2 g/mL ) * Volume of Salt Water (mL)
Volume = 500 mL Mass = ?
Volume of Pacific = 1.4 x 1022 mL Mass = ?
Your Classroom Ideas
Your Classroom Ideas
Page #
Developing Mathematical Proxies Bill G.
Example #1
Your Classroom Ideas
Developing Mathematical Proxies Bill G.
Example #2
Your Classroom Ideas
Developing Mathematical Proxies. Bill G.
Proxy data are preserved physical characteristics of the environment that can stand in for direct measurements.
Proxies mathematical models are developed using relationships between data that can be measured directly.
After establishing a relationship proxy mathematical models are then used to obtain estimates of data that cannot be directly measured.
Ice Drilling Program
School of Ice