Integers – The Positives and Negatives http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/video_interactives/integers/integersSmall.html

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

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 19 + 3 = 22 -19 + - 3 = -22

Opposite Signs If the signs are opposite : OPPOSITE SIGNS - find the difference and take the sign of the larger number -15 + 3 = -12 15 + -3 = 12

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 = +5 + - 6 = +5 + - 6 = -1

WHITE BOARDS -10 + (-4) = 9 - 10 = -5 - (-2) = -7 - (-7) = -10 - 10 = 76 - (-3) = 60 + (-10) = -18 - (-7) = -6 + (-10) = 4 - (-4) = -7 - 4 = 22 + (-5) = 16 - (-8) = 76 + (-6) = -12 - (-8) =

WHITE BOARDS -10 + (-4) = -14 9 - 10 = -1 -5 - (-2) = -3 -7 - (-7) = 0 -10 - 10 = -20 76 - (-3) = 79 60 + (-10) = 50 -18 - (-7) = -11 -6 + (-10) = -16 4 - (-4) = 8 -7 - 4 = -11 22 + (-5) = 17 16 - (-8) = 24 76 + (-6) = 70 -12 - (-8) = -4

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 $100+10 = $110 You write a $20 check for food _$110-20 = $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?____________

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 $100+10 = $110 You write a $20 check for food _$110-20 = $90 Deposit $30 __90 + 30 = 120____ Write a $40 check for new shirts _120-40=80_______ Write a $220 check for two pairs of new shoes __80-220 = -140___________ Deposit $300 (payday at work!) __-140 + 300 = 160___ Write a $400 check for this month’s rent _160 – 400 = -240____________ Write a $50 check for groceries _-240 - 50 = -290____________ Deposit $150 (you won a raffle) __-290 + 150= -140___________ Deposit $200 (A birthday present) __-140 + 200 = 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_____

PRACTICE http://nlvm.usu.edu/en/nav/frames_asid_122_g_3_t_1.html?open=instructions&from=grade_g_3.html

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

Practice Complete pg 29 of workbook

Number Line 2 + 2 + 2 + 2 = 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.

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.

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

(-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

Practice Complete workbook pg 30

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.

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) = - 6 (put in 2 groups of -3)

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)

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

Practice Complete pg 31 in the booklet

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

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 + -

Practice Complete workbook pg 32 and pg 33

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)

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

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

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

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

Practice Try workbook pg 35 and 36

2.4 Rules to Divide Integers Is there a pattern? Complete pg 37 - 38 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

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

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

Which Operation Would You Do First 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

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

White Boards 42 ÷ 6 + 5 64 ÷ 4(2 - 6) 4(-12 + 6) ÷ 3 -122 ÷ 4 – 3 × 24

Answers 42 ÷ 6 + 5 7 + 5 12 64 ÷ 4(2 - 6) 64 ÷ 4 (-4) 64 ÷ (-16) -4 4(-12 + 6) ÷ 3 4(-6) ÷ 3 -24 ÷ 3 -8 -122 ÷ 4 – 3 × 24 144 ÷ 4 – 3 × 16 36 – 3 × 16 36 – 48 -12

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

Try Some More 6 × 8 - (42 + 2) + 72 ÷ 8 62 + 14 ÷ 2 – 8 9 ÷ 3 + 7 × 4 ÷ 2 12 ÷ 6 + 52 × 3 -4(1+ 5)2 ÷ 6 – (42+5) 7(5 + 3) ÷ 4(9 - 2)

6 × 8 - (42 + 2) + 72 ÷ 8 6 × 8 - (16 + 2) + 72 ÷ 8 6 × 8 - (18) + 72 ÷ 8 48 – (18) + 9 30 + 9 39 62 + 14 ÷ 2 – 8 36 + 14 ÷ 2 – 8 36 + 7 – 8 43 – 8 35 9 ÷ 3 + 7 × 4 ÷ 2 3 + 28 ÷ 2 3 + 14 17 12 ÷ 6 + 52 × 3 12 ÷ 6 + 25 × 3 2 + 25 × 3 2 + 75 77 -4(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) -24 + 47 -71 7(5 + 3) ÷ 4(9 - 2) 7(8) ÷ 4(9 - 2) 7(8) ÷ 4(7) 56 ÷ 4(7) 56 ÷ 28 2

Practice Workbook pg 39-41

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

Quotient A result obtained by dividing one quantity by another.

Zero Pair The result of adding any number to it's opposite ex: -2 + 2 = 0

Commutative Property commutatively is the property that changing the order of something does not change the end result Examples of Commutative Property 2 + 3 = 3 + 2. 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

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).

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

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

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