Unit 2: Number Relationships
Unit 2: Number Relationships
Embedded Files
Chapter definitions:
Chapter definitions:
Factor: a number or quantity that when multiplied with another, produces a given number or expression.
Factor: a number or quantity that when multiplied with another, produces a given number or expression.
If you're looking for the factors of 12.... 12 is the sum.
Ex. 1 x 12 = 12 .... 2 x 6 = 12 .... and 3 x 4 = 12 .... The factors of 12 are 1, 2, 3, 4, 6 and 12.
Multiple: a number that can be divided by another number without a remainder.
Multiple: a number that can be divided by another number without a remainder.
Multiples go on forever!!
If you're looking for the multiples of 12.... start with 0 and add 12 more each time.
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, ....
**Note:
**Note:
- If you are asked to list the multiples of a number, remember to keep adding that number. For example, the first 5 multiples of 10 are 10, 20, 30, 40 and 50!
- However, if you are asked to list the factors of 10, you will get a very different answer! There are only 4 factors of 10. The factors of 10 are 1, 2, 5 and 10!
Prime Number: a whole number that has only two different factors (1 and itself).
Prime Number: a whole number that has only two different factors (1 and itself).
For example: 2, 3, 5, 7 and 11 are prime numbers).
Composite Number: a whole number that has more than 2 different factors.
Composite Number: a whole number that has more than 2 different factors.
For example, 6 is a composite number because it has four factors: 1, 2, 3 and 6).
Prime Factorization: A composite number can be written as the product of prime numbers. This is called the prime factorization of the number. You can see the prime factorization by making a factor tree.
Prime Factorization: A composite number can be written as the product of prime numbers. This is called the prime factorization of the number. You can see the prime factorization by making a factor tree.
See the section on factor trees below for an example!
40 has a total of 8 factors. The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40!
40 has a total of 8 factors. The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40!
Factors Rainbows!
Factors Rainbows!
- We use factor rainbows to find all the factors of a given number (40 in this example)
- Always start with 1 x itself (40 here)
- Go in order, after 1x40, does 2 x ___ give you your sum (40)? how about 3 x ____ ? 4 x ___?
- Keep going until you factors start to repeat on the bottom, then you're done!
- Using manipulatives or drawings to create arrays is another strategy students can use to determine the factors of a number!
- In the following example, you can represent the factors of 12 in 6 different ways.
- 1 x 12 and 12 x 1
- 2 x 6 and 6 x 2
- 3 x 4 and 4 x 3
- They all create equal groups with no remainders.
Finding multiples
Finding multiples
There are many ways to find the multiples of a number. If you're looking for the multiples of 10, you start with 0 and add 10 each times. Multiples can go on forever! The first 5 multiples of 10 are:
There are many ways to find the multiples of a number. If you're looking for the multiples of 10, you start with 0 and add 10 each times. Multiples can go on forever! The first 5 multiples of 10 are:
0, 10, 20, 30, 40, ...
0, 10, 20, 30, 40, ...
You can find the multiples of a number by making a list!
Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...
Multiples of 9: 0, 9, 18, 27, 36, 45, 54, 63, 72, ...
You can find the multiples of a number by using a number line:
You can find the multiples of a number by using a counting chart! Here we see multiples of 4 shaded a darker blue:
Common Multiples
Common Multiples
In order to find common multiples, you need to know the multiples of 2 different numbers, compare them and highlight which ones they have in common!
In order to find common multiples, you need to know the multiples of 2 different numbers, compare them and highlight which ones they have in common!
For example: Find the first 4 common multiples of 3 and 4!
Multiples of 3: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, ...
Multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
The first 4 common multiples of 3 and 4 are: 0, 12, 24 and 36.
Factor Trees
Factor Trees
Factor trees help to find the prime factorization of a number. These are all prime factors that you can multiply to give you the product. Keep breaking the numbers down into smaller multiplications until you cannot do so any further. (Do not use 1x something in a factor tree). By doing this, you're only left with prime numbers - thus the prime factorization.
Factor trees help to find the prime factorization of a number. These are all prime factors that you can multiply to give you the product. Keep breaking the numbers down into smaller multiplications until you cannot do so any further. (Do not use 1x something in a factor tree). By doing this, you're only left with prime numbers - thus the prime factorization.
**Note: When completing a factor tree, there may be multiple ways to start it! No matter which factors you start with, your answer will be the same!
**Note: When completing a factor tree, there may be multiple ways to start it! No matter which factors you start with, your answer will be the same!
Extra math
practice for
Unit 2 topics!
Extra math
practice for
Unit 2 topics!
Lesson 1 (Factors - arrays)
p. 72 - #s 1-4
Lesson 1 (Factors - arrays)
p. 72 - #s 1-4
Lesson 2 (Factors - rainbows)
p. 72-73 - #s 7, 10
Lesson 2 (Factors - rainbows)
p. 72-73 - #s 7, 10
Lesson 3 (Multiples)
p. 76 - #s 2, 3, 4, 6, 7
Lesson 3 (Multiples)
p. 76 - #s 2, 3, 4, 6, 7
Lesson 4 (Common multiples)
p. 76 - # 7
Lesson 4 (Common multiples)
p. 76 - # 7
Lesson 5 (Prime and Composite Numbers)
p. 80 - #s 2, 4, 5, 6
Lesson 5 (Prime and Composite Numbers)
p. 80 - #s 2, 4, 5, 6
Lesson 6 (Prime factorization)
p. 84 - #s 2a, 4, 5, 7
Lesson 6 (Prime factorization)
p. 84 - #s 2a, 4, 5, 7
Integers: a whole number; a number that is not a fraction; a number that is not a decimal.
Integers: a whole number; a number that is not a fraction; a number that is not a decimal.
Integers can be negative or positive.
Positive integers are to the right of the number line.
Negative integers are to the left of the number line.
Watch this video to learn more about integers!
Learning more about Integers:
Learning more about Integers:
Here are some strategies students should be able to with Integers:
Here are some strategies students should be able to with Integers:
- Place integers on a number line
- List integers from both greatest to least and least to greatest
- Compare integers using the symbols greater than (>), less than (<) and equal to (=)
- Use an integer to represent a situation (see below)
**Please see the video on integers above if there is any confusion! This video covers many of these topics and explains integers well with examples and images.
Using Integers to Represent a Situation
Using Integers to Represent a Situation
Students should be able to read a sentence and use an integer to represent it.
Students should be able to read a sentence and use an integer to represent it.
For example:
Three days before Christmas -3
Three days after Christmas 3
Ten meters above sea level 10
Ten meters below sea level -10
Earned 15 dollars 15
Spent 15 dollars -15
Five degrees above freezing 5
Five degrees below freezing -5
Order of Operations
Order of Operations
When a math problem has more than one operation (+, -, x, ÷), you must solve the problem using the following order!:
When a math problem has more than one operation (+, -, x, ÷), you must solve the problem using the following order!:
- Brackets
- Multiplication or division
(left to right) - Addition or subtraction
(left to right)
For multiplication or division, left to right means whichever operation comes first.
For multiplication or division, left to right means whichever operation comes first.
For addition or subtraction, left to right also means whichever operation comes first.
For addition or subtraction, left to right also means whichever operation comes first.
Think of the acronym B.E.D.M.A.S.
Think of the acronym B.E.D.M.A.S.
Brackets
Exponents (don't need to know this)
Division
Multiplication
Addition
Subtraction
Brackets
Exponents (don't need to know this)
Division
Multiplication
Addition
Subtraction
Here are some online games to practice using the
Order of Operations:
Here are some online games to practice using the
Order of Operations:
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