1. Integers – The Positives and Negatives

2. Match the letters on the number line with the integers below:
5 = C
-6 = D
-2 = B
9 = E
2 = F
-8 = A

3. Adding Integers – Review
When adding integers, there is few simple rules to follow.
If the signs are the same
SAME SIGNS – add them and keep the sign
= 22
= -22

4. Opposite Signs If the signs are opposite :
OPPOSITE SIGNS - find the difference and take the sign of the larger number
= -12
= 12

5. Subtracting Integers We don’t subtract Integers
We change the sign to positive and change the sign of the number behind the sign
+5 – 6 = =
= -1

6. WHITE BOARDS
-10 + (-4) = = -5 - (-2) = -7 - (-7) = = 76 - (-3) = 60 + (-10) = (-7) = -6 + (-10) = 4 - (-4) = = 22 + (-5) = 16 - (-8) = 76 + (-6) = (-8) =

7. WHITE BOARDS
-10 + (-4) = = (-2) = (-7) = = (-3) = (-10) = (-7) = (-10) = (-4) = = (-5) = (-8) = (-6) = (-8) = -4

8. Activity
Directions: In a group of two complete this worksheet.
Your Bank Account
Directions: Below is listed your starting balance at your bank as well as a series of withdrawals and deposits. Complete the table below by adding or subtracting the given amount and see how much money you have at the end. Starting balance (how much money you have at first) = $100
Transaction Current Amount
You deposit $10 $ = $110
You write a $20 check for food _$ = $90
Deposit $30 _____________
Write a $40 check for new shirts _____________
Write a $220 check for two pairs of new shoes _____________
Deposit $300 (payday at work!) _____________
Write a $400 check for this month’s rent _____________
Write a $50 check for groceries _____________
Deposit $150 (you won a raffle) _____________
Deposit $200 (A birthday present) _____________
What is the current amount in your checking account?______________
What would your account balance be if your identity was stolen and a $400 check was written (by the identity thief)?______________
Afterwards, you were able to convince your bank that you weren’t responsible for writing the $400 check and the bank therefore deposited $400 back into your account. What would your balance be now?____________

9. Activity
Directions: In a group of two complete this worksheet.
Your Bank Account
Directions: Below is listed your starting balance at your bank as well as a series of withdrawals and deposits. Complete the table below by adding or subtracting the given amount and see how much money you have at the end. Starting balance (how much money you have at first) = $100
Transaction Current Amount
You deposit $10 $ = $110
You write a $20 check for food _$ = $90
Deposit $30 __ = 120____
Write a $40 check for new shirts _120-40=80_______
Write a $220 check for two pairs of new shoes __ = -140___________
Deposit $300 (payday at work!) __ = 160___
Write a $400 check for this month’s rent _160 – 400 = -240____________
Write a $50 check for groceries _ = -290____________
Deposit $150 (you won a raffle) __ = -140___________
Deposit $200 (A birthday present) __ = 60___________
What is the current amount in your checking account?_____60_________
What would your account balance be if your identity was stolen and a $400 check was written (by the identity thief)?___-340___________
Afterwards, you were able to convince your bank that you weren’t responsible for writing the $400 check and the bank therefore deposited $400 back into your account. What would your balance be now?_______60_____

10. PRACTICE

11. 2.1 Models to Multiply Integers
Multiplication is repeated addition
Recall that = 3 × 6 Instead of adding 6 three times, you can multiply 3 by 6 and get 18, the same answer. Similarly, = 7 × -6 = -42

12. Practice
Complete pg 29 of workbook

13. Number Line
= 4 × 2 In algebra, 4 × 2 can be written as (4)(2) You can think of this as 4 groups of 2 or 4 jumps of 2
The first number tells you how many jumps and the second number tells you how big each jump should be This situation is shown in the number line below. You basically start at 0 and count by 2's until you have put four 2's on the number line. You end up at 8 and 8 is positive.

14. The reasoning is the same; Instead of adding -3 two times, you can just multiply -3 by 2. To model this on the number line, just start at 0 and put 2 groups of -3 (2 x -3) of the number line or make 2 backwards jumps. You end up at -6.

15. The first number tells you what direction to look and the second number tells you to walk forwards or backwards
(4) x (-2) = face the positive direction and make 4 jumps of 2 backwards
(-4) x (2) = face the negative direction and make 4 jumps of 2 forwards

16. (-4) x (-2) = face the negative direction and make 4 jumps of 2 backwards
(4) x (2) = face the positive direction and make 4 jumps of 2 forwards

17. Practice
Complete workbook pg 30

18. Tiles can be used to model as well
The first number is how many groups and the second number is the quantity.
If the first number is positive, you will be ‘PUTTING IN’ the tiles
If the first number is negative, you will be ‘TAKING OUT’ the tiles
In order to take out negative tiles, you need to have enough zero pairs to balance the question.

19. Tiles (+2)(-3) = - 6 (put in 2 groups of -3)
To model the multiplication of an integer by a positive integer, you can insert integer chips of the appropriate colour. (Black is Positive, Red is Negative – Hence Black Friday, or in the Red)
(+2)(-3) = (put in 2 groups of -3)

20. Tiles
To model the multiplication of an integer by a negative integer, you can remove integer chips of the appropriate colour from zero pairs.
(-2)(-3) = 6 (Remove 2 groups of -3 – ensure to have zero pairs to remove negatives)

21. Another Example
(-2)(5)
Take 2 groups of +5 out

22. Practice
Complete pg 31 in the booklet

23. 2.2Rules to Multiply Integers
Did you notice any patterns from yesterdays homework?
Complete the multiplication chart and number 1 in workbook pg 32
What is the sign of the product when you multiply 2 integers?
If they are both positive
If one integer is positive and the other integer is negative
If both integers are negative

24. Sign Rule The product of two integers with the same sign is positive
The product of two integers with different signs is negative x
Positive integer
Negative Integer
Positive Integer + -

25. Practice
Complete workbook pg 32 and pg 33

26. 2.3 Dividing Integers with Number Lines
Remember that division is the inverse of multiplication
10 ÷ 2 = ? Is the same as __ x 2 = 10 (you are looking for how many jumps it takes)

27. Division with Number Lines
Positive ÷ Positive
(8) ÷ (2) We need to find how many jumps of 2 make +8. The jump size is +2, is positive, so we walk forward. Start at 0 and take jumps forward until you end at +8.
We took 4 jumps. We are facing the positive end of the line so (8) ÷ (2) = +4

28. Division with Number Lines
Negative ÷ Negative
(-8) ÷ (-2) We need to find out how many jumps of 2 make -8. The jump size, -2, is negative, so we jump backward. Start at 0. Take jumps backward to end at -8.
We took 4 jumps. We are facing the positive end of the number line so (-8) ÷ (-2) = +4

29. Division with Number Lines
Negative ÷ Positive
(-8) ÷ (2) We need to find out how many jumps of 2 make -8. The jump size, 2, is positive, so we jump forward. Start at 0. Take jumps forward to end at -8.
We took 4 jumps. We are facing the negative end of the number line so (-8) ÷ (2) = -4

30. Dividing with Number Lines
Positive ÷ Negative
(8) ÷ (-2) We need to find out how many jumps of 2 make 8. The jump size, -2, is negative, so we jump backward. Start at 0. Take jumps backward to end at 8.
We took 4 jumps. We are facing the negative end of the number line so (8) ÷ (-2) = -4

31. Practice
Try workbook pg 35 and 36

32. 2.4 Rules to Divide Integers
Is there a pattern?
Complete pg of workbook #1 – 2
Yes – The Sign Rule Applies to Division
The product of two integers with the same sign is positive
The product of two integers with different signs is negative
Finish workbook

33. Play Integer BINGO
Fill in your boxes with the integers from -20 to Each integer can only be used once

34. 2.5 Order of Operations B rackets E xponents D ivision M ultiplication
A ddition
S ubtraction

35. Which Operation Would You Do First
1. -4 × × (-2)3 ÷ 6 3. (6 + 2) – 15 ÷ 5 × (13 – 6) 5. 8 – 4(2 + 52) ÷ 12

36. 1. -4 × 32 + 6 2. 3 × (-2)3 ÷ 6 3. (6 + 2) – 15 ÷ 5 × 2 4. 4(13 – 6) 5. 8 – 4(2 + 52) ÷ 12

37. White Boards
42 ÷ 6 + 5
64 ÷ 4(2 - 6)
4( ) ÷ 3
-122 ÷ 4 – 3 × 24

38. Answers
42 ÷ ÷ 4(2 - 6) 64 ÷ 4 (-4) 64 ÷ (-16) -4 4( ) ÷ 3 4(-6) ÷ ÷ ÷ 4 – 3 × ÷ 4 – 3 × – 3 × –

39. Key Words for Problem Solving
Symbol
Words Used +
Add, Addition, Sum, Plus, Increase, Total -
Subtract, Subtraction, Minus, Less, Difference, Decrease, Take Away, Deduct X
Multiply, Multiplication, Product, By, Times, Lots Of ÷
Divide, Division, Quotient, Goes Into, How Many Times

40. Try Some More 6 × 8 - (42 + 2) + 72 ÷ 8 62 + 14 ÷ 2 – 8
9 ÷ × 4 ÷ 2
12 ÷ × 3
-4(1+ 5)2 ÷ 6 – (42+5)
7(5 + 3) ÷ 4(9 - 2)

41. 6 × 8 - (42 + 2) + 72 ÷ 8 6 × 8 - (16 + 2) + 72 ÷ 8 6 × 8 - (18) + 72 ÷ 8 48 – (18) ÷ 2 – ÷ 2 – – 8 43 – ÷ × 4 ÷ ÷ ÷ × 3 12 ÷ × × (1+ 5)2 ÷ 6 – (42+5) -4(6)2 ÷ 6 – (42+5) -4(6)2 ÷ 6 – (47) -4(36) ÷ 6 – (47) -144 ÷ 6 – (47) -24 – (47) (5 + 3) ÷ 4(9 - 2) 7(8) ÷ 4(9 - 2) 7(8) ÷ 4(7) 56 ÷ 4(7) 56 ÷ 28 2

42. Practice
Workbook pg 39-41

43. Integer
the numbers …-3, -2, -1, 0, 1, 2, 3 … 1, 2, 3, etc are positive integers -1, -2, -3, etc are negative integers 0 is neither positive nor negative

44. Quotient
A result obtained by dividing one quantity by another.

45. Zero Pair The result of adding any number to it's opposite
ex: = 0

46. Commutative Property
commutatively is the property that changing the order of something does not change the end result
Examples of Commutative Property
2 + 3 = Whether you add 3 to 2 or you add 2 to 3, you get 5 both ways.
4 × 7 = 7 × 4, Whether you multiply 4 by 7 or you multiply 7 by 4, the product is the same, 28.
Solved Example on Commutative

47. Zero Property
The sum of any number and zero is that number (2 + 0 = 2). The product of any number and zero equals zero (3 * 0 = 0).

48. Order of Operations
The rules of which calculation comes first in an expression They are: Do everything inside parentheses first: () then do exponents: x2 then do multiplication and division from left to right lastly do the addition and subtraction from left to right

49. The Skinny of it Adding Subtracting
When the signs are the same add like normal and keep that sign
When the signs are different, find the difference between the two numbers and take the sign of the larger number
Subtracting
We don’t subtract, We add the opposite
Follow rules for addition

50. The Skinny of it Multiplying and Dividing have the same rules
When signs are the same (++ or --) the answer is positive
When the signs are different ( +- or -+) the answer is negative