Integers The Positives and Negatives

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= B9= E2 = 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 IntegersWe dont subtract IntegersWe change the sign to positive and change the sign of the number behind the sign

+5 6 = +5 + - 6 = +5 + - 6 = -1WHITE 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) = 7960 + (-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 = $110You write a $20 check for food _$110-20 = $90Deposit $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 months 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 werent 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 = $110You write a $20 check for food _$110-20 = $90Deposit $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 months 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 werent responsible for writing the $400 check and the bank therefore deposited $400 back into your account. What would your balance be now?_______60_____ PRACTICEhttp://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

PracticeComplete pg 29 of workbookNumber Line2 + 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

PracticeComplete workbook pg 30Tiles 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 tilesIn order to take out negative tiles, you need to have enough zero pairs to balance the question. TilesTo 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)

TilesTo 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

PracticeComplete pg 31 in the booklet2.2Rules to Multiply IntegersDid you notice any patterns from yesterdays homework?Complete the multiplication chart and number 1 in workbook pg 32What is the sign of the product when you multiply 2 integers?If they are both positiveIf one integer is positive and the other integer is negativeIf both integers are negativeSign RuleThe product of two integers with the same sign is positive The product of two integers with different signs is negative

xPositive integerNegative IntegerPositive Integer+-Negative Integer-+PracticeComplete workbook pg 32 and pg 332.3 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 LinesPositive 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 LinesNegative 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 LinesNegative 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 LinesPositive 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 362.4 Rules to Divide IntegersIs there a pattern?Complete pg 37 - 38 of workbook #1 2

Yes The Sign Rule Applies to DivisionThe product of two integers with the same sign is positive The product of two integers with different signs is negativeFinish workbook

Play Integer BINGOFill in your boxes with the integers from -20 to +20. Each integer can only be used once2.5 Order of OperationsB racketsE xponentsD ivisionM ultiplicationA dditionS ubtractionWhich 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) 121. -4 32 + 6 2. 3 (-2)3 6 3. (6 + 2) 15 5 2 4. 4(13 6) 5. 8 4(2 + 52) 12White 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 24144 4 3 16 36 3 16 36 48 -12Key Words for Problem SolvingSymbolWords Used+Add, Addition, Sum, Plus, Increase, Total-Subtract, Subtraction, Minus, Less, Difference, Decrease, Take Away, DeductXMultiply, Multiplication, Product, By, Times, Lots OfDivide, Division, Quotient, Goes Into, How Many TimesTry Some More 6 8 - (42 + 2) + 72 862 + 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) -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 2PracticeWorkbook pg 39-41Integerthe 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 QuotientA result obtained by dividing one quantity by another.Zero PairThe result of adding any number to it's opposite ex: -2 + 2 = 0Commutative Propertycommutatively is the property that changing the order of something does not change the end result

Examples of Commutative Property2 + 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 PropertyThe 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 OperationsThe rules of which calculation comes first in an expression

They are:Do everything inside parentheses first: ()then do exponents: x2then do multiplication and division from left to rightlastly do the addition and subtraction from left to right

The Skinny of itAddingWhen the signs are the same add like normal and keep that signWhen the signs are different, find the difference between the two numbers and take the sign of the larger numberSubtractingWe dont subtract, We add the opposite Follow rules for addition

The Skinny of itMultiplying and Dividing have the same rules

When signs are the same (++ or --) the answer is positiveWhen the signs are different ( +- or -+) the answer is negative