Download Unit 2 - Fun and Games – Number Theory - CEISMC

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Further investigations:
Here are some activities you can do with
your student.
Items that are used together (like hot dogs
and buns or paper cups and paper plates)
are often sold in differently-sized packages. Look for examples of these in stores.
Discuss the smallest number of packages of each item you must buy so that
every hotdog has a bun or plates and cups
match exactly. The total number of each
type of item (hotdog, bun, plate, cup) will
be the LCM of their package sizes.
Look at the numbers on car license plates.
Discuss whether the number is a prime or
a composite and explain how you can tell.
If it is composite, find its prime factorization.
Consider the house numbers of houses
on your street. Are any of them square
numbers or do they have factors that are
square numbers?
Kathy Cox, State Superintendent of Schools
Fun and Games – Number Theory
Students will:
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Sixth Grade 2 of 10
Calculate multiples and factors of given numbers
Identify prime, composite, and square numbers
Decompose numbers into their prime factorizations
Determine the Least Common Multiple (LCM) and the Greatest Common Divisor (GCD)
for a set of numbers
Classroom Cases:
1. There are two traffic signals downtown. One signal light flashes north every four seconds.
The other signal light flashes north every five seconds. If they both flash north at 8PM, in
how many seconds will they again both flash north?
Case Closed - Evidence:
One signal flashes north in multiples of four seconds and the other signal flashes north in
multiples of five seconds. So I have to find the least common multiple of 4 and 5:
4: 4, 8, 12, 16, 20, 24, 28, 32
5: 5, 10, 15, 20, 25, 30
The least common multiple of 4 and 5 is 20. They will both flash north again in 20 seconds!
2. Use the clues below to determine my secret number.
Clue 1: My number is a factor of 72.
Terminology:
Case Closed - Evidence:
The secret number could be 1, 2, 3, 4, 6, 8, 9, 12, 24, 36, or 72.
Multiple: The product of a given number
and a whole number.
Clue 2: 48 is a multiple of my secret number.
Case Closed - Evidence: 48 is a multiple of 1, 2, 3, 4, 6, 8, 12, 24, and 48.
LCM: The smallest number that is a
multiple of two or more numbers.
Clue 3: My number is prime.
Factor: A whole number that divides
evenly into another whole number. Also the
process of identifying the divisors (factors)
of a given number or expression.
Case Closed - Evidence: There are only two prime numbers
in the list above: 2 and 3.
Clue 4: My number is even.
Case Closed - Evidence: The secret number iss 2.
GCF: The largest number that is a factor
of two or more numbers.
Decompose: To factor numbers or
expressions.
Prime: A number whose only factors are
itself and the number one. (The number
one is neither prime nor composite.)
Composite: A number which has more
than two factors.
Square Number: A number that is the
product of another number multiplied by
itself.
Book’em:
My Full Moon is Square
by Elinor J. Pinczes
The Doorbell Rang by Pat Hutchins
Spaghetti and Meatballs for All
by Marilyn Burns
Related Files:
www.ceismc.gatech.edu/csi
3. Brandon won the School Box Sweepstakes. He received 288 pencils and 120 notebooks.
He decided to share his winnings equally among his friends. Everyone will receive the same
number of pencils and everyone will get the same number of notebooks. What is the greatest number of friends Brandon could have and how many notebooks and pencils will each
friend get?
Case Closed - Evidence:
Since the friends who receive pencils are the same people as those who receive notebooks,
I need to find one value that will represent them. That value must divide evenly into 288 and
120. Here are the factors (divisors) of each number:
120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
288: 1, 2, 3, 4, 6, 8, 12, 24, 36, 48, 72, 96, 144, 288
The common factors represent the possible number of friends Brandon has. For these numbers of friends, here is a distribution of notebooks and pencils:
No. of friends
1
2
3
4
6
8
12
24
No. of notebooks
120
60
40
30
20
45
10
5
No. of pencils
288
144
96
72
48
36
24
12
The greatest number of friends Brandon could have is 24. Brandon could give each friend 5
notebooks and 12 pencils.
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