Transcript Number theory powerpoint

Basic number theory concepts
Factor, Common factors, GCF
Divisors, Common divisors
Multiple, Common multiples, LCM
Prime vs composite
Odd vs even
Factor or divisor
Note: These names may be used interchangeably, except in a context like
A divided by B, we call B the divisor and not a factor
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A part
2 is a factor of 6
The numbers that you skip counted by to land on the number
Skip count by 2’s—land on 4,6,8,etc.. so 2 is a factor of 4, 6, 8, etc….
Common factor (divisor)
• A factor that 2 or more numbers share
• 2 is a common factor of 4 & 6
GCF (GCD)
• Look at the common factors of 2 numbers, the
largest is the GCF
• The GCF of 12 &18 is 6 because their common
factors are 1,2,3,6 and 6 is biggest
• Take 12 and look at the numbers underneath
it (and closest to it) that you can skip count by
and land on 12, the biggest one that lands on
12 and 18 is the GCF
Multiple
• To expand
• The multiples of 12 are 12,24,36, etc..
• The numbers you land on when you skip count
by a given number
Common multiple
• The common numbers landed on when skip
counting by two different numbers
LCM
• The first number landed on by both numbers
you are skip counting by
Prime vs composite
• Prime has only one rectangle associated to
it—the long one
• Composite has more than one rectangle
• 1 is neither prime nor composite
• Composite means part
Odd vs even
• Even—think pairs
• Odd—odd man out, a pair is incomplete
Your project
• Use the ideas that you generated with your
class work
• Start working on this in class
• You will finish this outside of class and should
expect to spend at least an extra 6 hours on it
• It should be typed, but diagrams can (and
most likely should be for times sake) be hand
written in nicely
• Neatness does count
Your project
• For each concept (i.e. multiple) make sure to
include how EACH model that applies (i.e. skip
counting, tile sequences, arrays, and/or rods)
does explain the concept and include
diagrams
• For each concept, don’t forget your metaphor
and explain how it does not work and does
work. See the next slide for an example
metaphor and explanation.
Metaphor for “multiplication”
Multiplication is letting a rabbit have a new litter of the same
size over and over…
Explanation: Multiplication is just repeated addition, where I
add the same quantity (hence the litter has to be the same
size) to itself a prescribed number of times. So 2x3 is 3
added to itself twice. The “3” would be the litter size and
the rabbit would produce 2 litters. This is where my
metaphor breaks down, I say over and over when really
each product restricts me to how many times I have the
rabbit produce a new litter. Now also, the number of
rabbits in a litter can vary and the poor rabbit might get
tired of having new little ones to take care of so the process
will end for the rabbit.