Download Celsius, Fahrenheit, Slopes, Lines

The South Mississippi Science
and Mathematics Partnership
Program (SMP)2
Supported by
The U.S. Department of Education
and Administered by
The Mississippi Department of Education (MDE)
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Our Team
Dr. Myron Henry (Co-Director), Mathematics
Dr. Sherry Herron (Co-Director), Science Education
Dr. Sharon Walker (Co-Director), Science Education
Dr. Shelia Brown, Science Education
Ms. Lida McDowell, Mathematics
Ms. Mary Peters, Mathematics
Dr. David Beckett, Science
The most important members of our team? Your teachers
who were participants and their students, which is you!
14. Celsius, Fahrenheit, slopes, lines
2
Mathematics Topics
•
Cartesian coordinate
system
•
Slope
•
function tables
•
line graphs
•
slope intercept form
of linear equation
•
Fahrenheit and Celsius temperature
•
graphing calculator charts and graphs
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Partial Objectives from the 2007 Mississippi
Mathematics Objectives (Revised)
•
6th grade 2b (Complete a function table based on a given rule), 2e
(Describe a rule for a function table using symbols), 5a (Construct,
interpret, and explain line graphs)
•
7th grade 2a (Recognize, describe, and state the rule of generalized
numerical and geometric patterns using tables, words, and symbols), 2b
(Solve equations that represent algebraic and real-world problems using
multiple methods), 2d (Complete a function table based on a given rule
and vice versa)
•
Pre-Algebra 2c (Solve and check equations using one variable), 2e
(Graph linear equations using multiple methods including t-tables and
slope-intercept), 2f (Given a linear graph, identify its slope as positive,
negative, undefined, or zero, and interpret slope as rate of change), 2g
(Determine slope, x-intercept, and y-intercept from a graph and/or
equation in slope-intercept or standard form)
•
Algebra 1 2a (Solve, check, and graph multi-step linear equations in one
variable), 2e (Graph and analyze linear functions), 2f (Use algebraic and
graphical methods to solve systems of linear equations in real-world
situations) 3a (Apply the concept of slope to determine if lines in a plane
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are parallel)
A mini lesson on slopes and lines
• “Stacking Cups” from Navigations through
•
•
•
•
•
•
•
Algebra in Grades 6-8, National Council of
Teachers of Mathematics
Two points determine a line and the slope
Slope intercept form y = mx + b
y=x (our favorite line?)
Fahrenheit and Celsius
Dr. Myron Henry, USM
(100, 212); (0, 32)
Ms. Lida McDowell, USM
F = (9/5)C+ 32
The Montana Equilibrium Ms. Mary Peters, USM
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“Stacking Cups” from Navigations through
Algebra in Grades 6-8, National Council of
Teachers of Mathematics
Goals
•
Connect the concept of linearity with real-world
contexts.
•
Use a table to organize information.
•
Make a graph to display data using correct labels and
scales.
•
Recognize that a constant rate of change exists
between the two variables.
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Activity
You have been hired by a
company that makes all kinds of
cups- foam hot cups, plastic cold
cups, paper cups, and more – of
different sizes. For each of the
kinds of cups it makes, the
company needs to know the
measurements of cartons that
can hold 50 cups.
Your task is to provide this
information.
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1. Make a table and record in it the measurement data
for different types of cups.
Cup type A
# of
cups
n
Stacked Ht.
of cups
(cm)
H
Cup type B
# of
cups
n
Stacked Ht.
of cups
(cm)
H
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-
2. Make a coordinate graph of each data set.
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3. Describe the variables being investigated and the
relationship between the variables.
4. Identify the units of measure for the dependent
variable H, the vertical intercept, the rate of change,
and the independent variable n.
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5. Predict how tall a stack of 50 cups would be and
explain how you made your prediction.
6. Compare the results for the different kinds of cups,
noting similarities and differences.
7. For each kind of cup, recommend the inside
dimensions of a carton that would hold a stack of 50
cups.
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A mini lesson on slopes and lines
•
•
•
•
•
•
•
•
Two points determine a line
Two points determine the slope
Slope intercept form y = mx + b
y=x (our favorite line?)
Dr. Myron Henry, USM
Fahrenheit and Celsius Ms. Lida McDowell, USM
(100, 212); (0, 32)
F = (9/5)C+ 32
The Montana Equilibrium
15
4
2
-5
5
-2
-4
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17
18
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Two points determine a line.
y
x
?
0
5
5
-3
-3
y2  y1
 slope  m
x2  x1
35
 slope  m
35
8
 slope  m
8
1  slope  m
form of a line
FSlope
 mCintercept
b
( y  mx  b)
y  1 x  b
y  xb
5  5b
0b
yx
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Fahrenheit and Celsius formulas
y2  y1
y
x
 slope
x2  x1
F
C
32
0
212
100
F2  F1
 slope
C2  C1
212  32
 slope
100  0
180
 slope
100
2 2  32  5 9
  slope
2
2
2 5
5
F  mC  b
( y  mx  b)
y  (9 / 5) x  b
21
F  mC  b
( y  mx  b)
y  (9 / 5) x  b
y  (9 / 5) x  b
32  (9 / 5)  0  b
32  b
y  (9 / 5) x  32
y
x
F
C
32
0
212
100
22
Fahrenheit and Celsius formulas
Two points determine a line.
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F   C  32
5
F
C
41
5
86
30
14
-10
-22
-30
F
C
32
0
212
100
23
Find the Montana Equilibrium
And Bozeman, MT
And West Yellowstone, MT
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25
26
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Down Right Cold!
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Temperature is in
Fahrenheit. What is
it in Celsius?
Low is -40.6 C
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F   C  32
5
9
 41   C  32
5
9
 41  32   C
5
5
 73    C
 9 29