By James Matte, Stephanie MyersChristopher PollardMED 600- Fall 2013

What is CSMP?The Project is for both primary and

intermediate gradesBasic program Harold Jacobs authored many books which

brought this project to life.

CSMP HistoryEstablished in 1966 under Burt Kaufman

Originally affiliated with Southern Illinois University

First programs for 7-12 called Elements of Mathematics

Focused on highly individualized instructionFrederque Papy

Mini-computer

Addition with JacobsAddition began by demonstrating oppositesDark circles represented negative numbers,

white circles represent positive numbersPositive Numbers: Negative

Numbers:

Addition used matching to solve problemsNegative 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 JacobsSimilar to additionPositive 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:

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

64

Example of Subtraction

Another Example of Subtraction

Eli the ElephantIntroduction story to Comprehensive School

Mathematics ProgramEli 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 usefulThe 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 ContinuedIf adding a positive integer move to the right

on the number line If adding a negative integer move to the left

on the number lineNegative integers are represented by: Addition can also be represented as ordered

pairs:

Addition-Examples

Addition-Examples

Addition- More Examples

Comprehensive School Mathematics Program- SubtractionThe number line is also extremely usefulThe 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 ContinuedIf subtraction a positive integer move to the

left on the number line If subtraction a negative integer move to the

right on the number lineNegative integers are still represented by: Subtraction is the exact opposite of addition

in the Comprehensive School Mathematics Program.

Subtraction-Examples

Jacobs MultiplicationMultiplication represented graphically

Earth and moon are moving apart at a rate of 4 feet each year

Time in Years

Distance in feet

Jacobs Multiplication

Time in Years

Distance in feet

Multiplication represented graphically

CSMP MultiplicationAlso represented multiplication graphically

^ was used to represent a negative numberGraphing ActivityExamples

4 x 2 = 8 4 x 3 = -12 4 x 2 = ?

^

^ ^

DivisionBoth 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…