comprehensive school of mathematics project (csmp)
DESCRIPTION
Comprehensive School of Mathematics Project (CSMP). 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. - PowerPoint PPT PresentationTRANSCRIPT
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By James Matte, Stephanie MyersChristopher PollardMED 600- Fall 2013
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What is CSMP?The Project is for both primary and
intermediate gradesBasic program Harold Jacobs authored many books which
brought this project to life.
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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
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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
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Same Sign Addition
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Different Sign Addition
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Subtraction with Jacobs
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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.
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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
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Example of Subtraction
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Another Example of Subtraction
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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
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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.
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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.
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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.
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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
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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:
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Addition-Examples
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Addition-Examples
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Addition- More Examples
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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
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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.
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Subtraction-Examples
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Jacobs MultiplicationMultiplication represented graphically
Earth and moon are moving apart at a rate of 4 feet each year
Time in Years
Distance in feet
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Jacobs Multiplication
Time in Years
Distance in feet
Multiplication represented graphically
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CSMP MultiplicationAlso represented multiplication graphically
^ was used to represent a negative numberGraphing ActivityExamples
4 x 2 = 8 4 x 3 = -12 4 x 2 = ?
^
^ ^
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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…