Math - 2018-19
5.3 - Prime, Composite, Odd and Even Numbers
The student will
a) identify and describe the characteristics of prime and composite numbers; and
b) identify and describe the characteristics of even and odd numbers.
- So that I can break down any number into its prime number factors
- So that if I decide to get a job in digital security, I can create security codes using prime numbers
- So that I can identify patterns within even and odd numbers
- So that I can understand basic computation problems and how even and odd numbers affect the outcome
UNDERSTANDING THE STANDARD
- Natural numbers are the counting numbers starting at one.
- A prime number is a natural number, other than one, that has exactly two different factors, one and the number itself.
- A composite number is a natural number that has factors other than one and itself.
- The number 1 is neither prime nor composite because it has only one set of factors and both factors are one.
- The prime factorization of a number is a representation of the number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3.
- Prime factorization concepts can be developed by using factor trees.
- Prime or composite numbers can be represented by rectangular models or rectangular arrays on grid paper. A prime number can be represented by only one rectangular array (e.g., 7 can be represented by a 7 x 1 and a 1 x 7). A composite number can always be represented by more than two rectangular arrays (e.g., 9 can be represented by a 9 x 1, a 1 x 9, or a 3 x 3).
- Divisibility rules are useful tools in identifying prime and composite numbers.
- Odd and even numbers can be explored in different ways (e.g., dividing collections of objects into two equal groups or pairing objects). When pairing objects, the number of objects is even when each object has a pair or partner. When an object is left over, or does not have a pair, then the number is odd.
- Students should use manipulatives (e.g., Base-10 blocks, cubes, tiles, hundreds board, etc.) to explore and categorize numbers into groups of odd or even.
- Examples of ways to use manipulatives to show even and odd numbers may include (but are not limited to):
- for an even number, such as 12, six pairs of counters can be formed with no remainder, or two groups of six counters can be formed with no remainder; and
- for an odd number, such as 13: (a) six pairs of counters can be formed with one counter remaining, or (b) two groups of six counters can be formed with one counter remaining.
- Students should use rules to categorize numbers into groups of odd or even. Rules can include:
- An odd number does not have 2 as a factor or is not divisible by 2.
- The sum of two even numbers is even.
- The sum of two odd numbers is even.
- The sum of an even and an odd is odd.
- Even numbers have an even number or zero in the ones place.
- Odd numbers have an odd number in the ones place.
- An even number has 2 as a factor or is divisible by 2.
- The product of two even numbers is even.
- The product of two odd numbers is odd.
- The product of an even number and an odd number is even.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
- Identify prime numbers less than or equal to 100. (a)
- Identify composite numbers less than or equal to 100. (a)
- Demonstrate with concrete or pictorial representations and explain orally or in writing why a number is prime or composite. (a)
- Identify which numbers are even or odd. (b)
- Demonstrate with concrete or pictorial representations and explain orally or in writing why a number is even or odd. (b)
- Demonstrate with concrete or pictorial representations and
explain orally or in writing why the sum or difference of two
numbers is even or odd. (b)