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By James Matte, Stephanie Myers
Christopher Pollard
MED 600- Fall 2013
What is CSMP?
 The Project is for both primary and intermediate
grades
 Basic program
 Harold Jacobs authored many books which brought
this project to life.
CSMP History
 Established in 1966 under Burt Kaufman
 Originally affiliated with Southern Illinois University
 First programs for 7-12 called Elements of Mathematics
 Focused on highly individualized instruction
 Frederque Papy
 Mini-computer
Addition with Jacobs
 Addition began by demonstrating opposites
 Dark circles represented negative numbers, white
circles represent positive numbers
Positive Numbers:
Negative Numbers:
 Addition used matching to solve problems
 Negative match to positive and whatever is left over
would be your answer.
 Antiparticles and ordinary particles
Same Sign Addition
Different Sign Addition
Subtraction with Jacobs
Subtraction with Jacobs
 Similar to addition
 Positive numbers are represented by hollow circles and
negative numbers are represented by solid circles
 Adding pairs of particles and antiparticles because
they cancel each other out.
Let’s Consider the Problem from the
Cartoon:
4 6
Problem:
 Thinking in terms of particles:
We have 4 positive particles:
 This may seem impossible but if we add two pairs of
particles and antiparticles to the picture, we’ll have:
 Then we take away 6 positive particles and get:
 Therefore, the answer is -2
Example of Subtraction
Another Example of
Subtraction
Eli the Elephant
 Introduction story to Comprehensive School
Mathematics Program
 Eli had a problem, he liked to have peanuts for lunch. He
normally had his Old Favorite peanuts but the
supermarket introduced a New Style peanut.
 The problem was that when he put them on the same
plate they would disappear before he had time to eat
them.
 He went home and did some experiments to find out
what was happening.
 He discovered that when an Old Favorite peanut and a
New Style peanut were on the same plate they
disappeared two by two
Eli’s Conclusions
Experiment 1: 6 Old
Favorite and 6 New Style.
Result: Nothing Left!
Experiment 2: 5 Old
Favorite and 2 New Style.
Result: 3 Old Favorite.
Eli’s Conclusion
Experiment 3: 4 Old
Favorite and 6 New Style.
Result: 2 New Style.
 Eli also concluded that
peanuts only vanished when
they are together on the same
plate. So he did a few more
experiments.
Eli’s Conclusion
Experiment 4: 2 Old
Favorite and 6 Old Favorite.
Result: 8 Old Favorite.
Experiment 5: 3 New Style
and 4 New Style. Result: 7
New Style.
Comprehensive School Mathematics
Program- Addition
 The number line is extremely useful
 The first number is where you start on the number line
 The second number is how many spaces you move to
the left or the right on the number line
CSMP-Addition Continued
 If adding a positive integer move to the right on the
number line
 If adding a negative integer move to the left on the
number line
 Negative integers are represented by:
 Addition can also be represented as ordered pairs:
Addition-Examples
Addition-Examples
Addition- More Examples
Comprehensive School Mathematics
Program- Subtraction
 The number line is also extremely useful
 The first number is where you start on the number line
 The second number is how many spaces you move to
the left or the right on the number line
CSMP-Subtraction Continued
 If subtraction a positive integer move to the left on the
number line
 If subtraction a negative integer move to the right on
the number line
 Negative integers are still represented by:
 Subtraction is the exact opposite of addition in the
Comprehensive School Mathematics Program.
Subtraction-Examples
Jacobs Multiplication
 Multiplication represented graphically
 Earth and moon are moving apart at a rate of 4 feet each
year
Time in
Years
Distance in
feet
Jacobs Multiplication
 Multiplication represented graphically
Time in
Years
Distance in
feet
CSMP Multiplication
 Also represented multiplication graphically
 ^ was used to represent a negative number
 Graphing Activity
 Examples



4x2=8
^4 x 3 = -12
^4 x ^2 = ?
Division
 Both CSMP and Jacobs used inverse multiplication to
describe division.
Let’s try:
 -10/2 is the same as:
 What must be multiplied by 2 to get -10?
 -20/4 is the same as…