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This map was created to be a resource for parents of elementary math students. It is intended to assist parents as they encourage and support their children during study time at home. This map includes videos, games, and other activities that parents and students can use together to build the student's number theory skills.
Here are some additional fun sites you can enjoy as a family.
The Lowest Common Multiple (LCM) is the smallest multiply that two or more numbers share. (Remember a multiple is found by mulitpling one number by another; 5x6 =30, 30 is a multiple of both 5 and 6)
Here's an example:
Find the LCM of 16 and 24
Some Multiples of 16 include: 16, 32, 48, 64,80, 96, 112 .....
Some Multiples of 24 include: 24, 48, 72, 96, 120, 144, 168, .....
Without multiplying any further I can see that 16 and 24 share common multiples. Two of those common multiples include the numbers 48 and 96. 48 is the smallest of all the multiples that 16 and 24 have in common, therefore 48 is the lowest common multiple of those two numbers.
There are various methods to use when finding LCMs. The videos and links below demonstrate a few of those methods.
Prime Factorization is an efficient method to use when searching for LCMs.
Making a chart or diagram may be helpful in finding multiples. This method can be time consuming, especially when working with large numbers. However, making lists or charts of multiples will be beneficial for students learning the reasoning and the concepts of finding LCMs.
When you click on the next link you will see examples of how charts are used to list multiples.
A multiple is the product of a number that is multiplied times itself or another number.
Example:
42 is a mulitple of 6. 42 is also a multiple of 7 because 6x7 = 42
42 is also a multiple of the numbers 1, 2, 3, 14, 21, and 42
The greatest common factor (GCF) may also be refered to as the greatest common divider (GCD).
The greatest common factor is the largest factor shared by two or more numbers.
Here's an Example:
Consider the numbers 28 and 56. What is the GCF of these two numbers?
All of the factors of 28 include: 1, 2, 4, 7, 14, 28
All of the factors of 56 include 1, 2, 4, 7, 8, 14, 28
The common factors of 28 and 56 include: 1, 2, 4, 7, 14, 28. Of these factors, 28 has the greatest value, therefore 28 is the greatest common factor of the numbers 28 and 56
There are various methods to use when searching for the GCF of two or more numbers. The blog links and the videos below demonstrate some of these methods.
It is important to know that the number 1 is neither a prime nor a composite number.
The fundamental theorem of arithmetic states that each composite number can be written as an unique product of prime numbers. This is shown in the process of factoring a composite number down to its make up of prime factors.
It is as if the prime numbers used to build a composite number represent the composite number's DNA. No two different composite numbers are contructed from the same group of prime numbers.
Example:
The composite number 12 is the product of the prime numbers 2x2x3. No other number will be "constructed" using this same equation.
A prime number is a number that has only two different factors. These factors included the number itself and the number 1.
The number 2 is the only even number that is prime.
Example:
The factors of 2 include: 1 and 2
The number 2 has only two factors so it is prime.
The factors of 4 include: 1, 2 , and 4.
The number 4 has more than two factors so it is not prime.
Factorization of Prime Numbers
To find the prime factors of a number you break the number down until it is expressed as a product of only it's prime numbers.
Example:
The prime factorization of the number 18 is written as:
2*3*3=18
When a prime number is repeated in prime factorization it may be written in exponents. Looking at the prime factorization of 18, the number 3 could be written 3 to the 2nd power using and exponent.
Prime Factorization Using Stacked Division
Prime Factorization Using a Factor Tree
A composite number is a natural number that has more than 2 factors.
Example:
The factors of 8 include: 1, 2, 4, 8.
The number 8 has more than two factors so it is composite.
The factors of 13 include: 1, 13.
The number 13 has only two factors so it is not a composite number
When trying to find the factors of a number, you divide by other numbers to see if they are factors of your first number. Consider the number 133, you can start with the number 1, is 133 divisible by 1, how about 2, how about 3, 4, 5.....
How high up in the number line should you go before you quit checking which numbers can divide evenly into 133? Move over on the map to the Factor Test Theorem explanation to get an answer to this question.
The factor test theorem states that to find the factors of a number, test only the natural numbers that are not greater than the square root of the number
Example:
The square root of 36 is 6 so when finding the factors of 36 you would only need to test numbers 1 through 6.
A factor is a number multiplied with another number to get a product.
Example:
3 is a factor of the number 18 because when 3 is multiplied with the number 6 the product 18 is formed
6x3 = 18
6 and 3 are not the only factors of 18
The numbers 1, 2, 3, 6, 9, and 18 are all factors of 18.
This is proven in the following facts:
1 x 18 =18
2 x 9 = 18
3 x 6 = 18
This video demonstrates how rectangular arrays can be used to discover factors of a number. This technique is beneficial in helping students understand the concept and reasoning of factoring.
The video also touches on prime and composite numbers which is covered in the next topic on this mind map.
Divisibility Theorems can be used to simplify the process of discovering if one number is divisible by another. Continue on with the map to see how the knowledge of rules for division are beneficial.
Considering the rules of divisibility, is the number 872,591,587 divisible by the number 4?
Hint: Check out the attached link to find the rule for dividing with the number 4.
872,591,587 is not divisible by 4. This is because the last two digits of 872,591,587 make the number 87, and 87 is not divisible by 4
A number is divisible when a divisor can divide into the number and have no remainder left over.
6/2 = 3
3 is a whole number with no remainder so 6 is divisible by 3
6/4 = 1 with a remainder of 2
4 does not divide into 6 without a remainder so 6 is not evenly divisible by 4
