Download Lesson 1 - Factors (p. 70) x x x x x x x x x x x x

Lesson 1 - Factors (p. 70)
Factors are any numbers that are multiplied to form a product.
Example:
In the equation 3 x 4 = 12,
factor
factor
3 and 4 are the factors
product
There are different ways we can represent factors. (We can also use the representations to
help us figure out factors.)
Array - is an orderly arrangement of symbols in a rectangle form that models multiplication.
These are arrays that represent 12:
This is not an example of an array:
xxxxx
xxxxx
xx
The rows and columns must be complete.
Rectangles
We can also draw rectangles to represent factors. This is the same idea as drawing arrays, but
instead of dots, you are drawing blocks of a rectangle. The diagram below show the fators of 4
with rectangles.
Factor Rainbow
Shows pairs of factors by drawing a rainbow pattern (see example top of page 71)
The students will usually list all numbers so that they do not miss any factors, like the one
below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Multiples, p. 74
A multiple is a number that is the product of two whole numbers.
A list of multiples of a whole number begins with the whole number and ends with three dots to
show that the list goes on forever.
(it is like skip counting by a number)
Example: multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40...
(5 x1, 5x2, 5x3, 5x4, 5x5.....)
Prime Factorization (lesson 4, pg 82)
Any number can be broken down into nothing but prime factors. You can do this by dividing
repeatedly by prime numbers or by using a factor tree.
Repeated Division
Starting with the number given, think to yourself, "What prime number will divide evenly into
this?" So, if we started with the number 36, we could write:
36 divided by 3 = 12
12 divided by 3 = 4
4 divided by 2 = 2
We start with 36 and divide it by 3. The answer is 12, a composite number. So, we divide that by
3 and get 4. Again, a composite number. So, we divide this by 2 and finally get a prime number.
So basically, you just keep dividing by prime numbers until you get a prime number as the
answer. So the prime factors of 36 are 3, 3, 2 and 2.
The following site has a video demonstration of doing repeated division:
http://www.onlinemathlearning.com/prime-factors.html (just note that we do not write it with
exponents. In the example provided of 24, we would write 2x2x2x3 and that is as far as we go
for grade 6. About the first 3 minutes of the video is in depth enough for our purposes).
Factor Trees
An easy was to factor a number is by making a factor tree. To make a tree, simply start with
the number you want to factor. From there, make branches of factors - numbers that multiply
to give you the original number. Next, take each of those numbers and break those down into
more factors. Continue until all the remaining numbers are prime numbers and cannot be
factored anymore.
Prime factors:
2x2x3x3 = 36
Prime Factors:
2x2x3x3= 36
Here are two factor trees for 36. Even though they are different, the prime factors (the ends
of each branch) end up being the same.
Integers
Integers are the counting numbers, their opposites and zero.
Positive integers are greater than 0.
Negative integers are less than 0.
0 is neither positive nor negative.
Positive integers can be used to represent gaining, moving forward, moving up, climbing up,
elevation above sea level, earning money, earning interest, temperature above zero....
Negative numbers can be used to represent losing, moving backward, moving down, elevation
below sea level, losing money, spending money, temperature below zero.......
Opposite integers are numbers which are the same distance from zero in the opposite
direction. Every number has an opposite. 2 and -2 are opposite. 5 and -5 are opposites.
To order integers, or list from least to greatest (or greatest to least), a number line is
helpful. When you move to the left, numbers are getting smaller. When you move to the right
numbers are getting bigger.
For example, 3, -4, 6, 0, -5
getting smaller
getting larger
Place the numbers on the number line to help you visualize in what order they should be
placed. - 5 would the smallest because it is the farthest on the left on the number line. Next
would be -4, 0, 3, 6.
Order of Operations (Lesson 9)
The order of operations helps us avoid confusion
and ensures we all answer questions in the same
manner.
To help us remember the order we must follow, we use the acronym BEDMAS.
B - brackets, complete what is inside brackets first
E - exponents (we do not do exponents in grade 6, but students should be
aware that it is a step in the order of operations)
D & M - Division & multiplication, in the order they occur in the equation
A & S - Add & subtract, in the order they occur
Example:
12 + 3 x 6 =
12 + 18 =
30
25 - (8 + 2)=
25 - 10=
15
*This means 12 more than 3 groups of six.*
We must complete the multiplication first,
then can add the 12.
* This means (8 more than 2), less than 25
I must complete what is in the brackets first.
Then I can subtract it from 25.
This video is to the tune of Cupid Slide and is catchy. It is a great way to help remember the
Order of Operations.
http://www.youtube.com/watch?v=h7DLOYEvQ_4