Intro To Integers

Integers

-$1.24 -3.4 53 +$90 Integers -21 +4 + 1/2 -50%

Integers Integers are whole numbers that describe opposite ideas in mathematics. Integers can either be negative(-), positive(+) or zero. The integer zero is neutral. It is neither positive nor negative, but is an integer. Integers can be represented on a number line, which can help us understand the valve of the integer.

Positive Integers Are to the right of zero Are valued greater than zero. Express ideas of up, a gain or a profit. The sign for a positive integer is (+), however the sign is not always needed. Meaning +3 is the same value as 3.

Negative Integers Are to the left of zero Are valued less than zero. Express ideas of down or a lose. The sign for a negative integer is (-). This sign is always needed.

Zero is neither positive or negative Positive integers are valued more than zero, and are always to the right of zero. Negative integers are valued less than zero, and are always to the left of zero.

End of Part One

Representing Integers - 1

- 4

+ 3

- 3

+ 2

+ 2

+ 2

+ 2

Representing Integers - 4 using 6 counters + 2 using 6 counters 0 using 6 counters - 3 using 6 counters

Opposite Integers

The “net worth” of opposite integers is zero.

Opposite Integers Opposite integers always have a “net worth” of 0. This is called the ZERO PRINCIPAL. Opposite integer have the same “absolute value”, meaning the distance from the points on a number line to zero is the same. This can be referred to as the integers magnitude.

Movement on a Number Line Magnitude and Direction Every integer represents a magnitude and a direction. The integer +3 describes a movement of 3 units in a positive direction.(right) The sign (+) tells you the direction. The number (3) indicates how far to move or the MAGNIUDE( a move- ment of 3 units) + 3 Direction Magnitude

Which integer has a higher value? Comparing Integers Which integer has a higher value? -4 or -8

Comparing Integers Use your number line to help you compare each set of number. (i.e. for the numbers 3 ,and - 2 …. 3 > -2 -2 < 3) - 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15 e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14

Putting Things Together What is the greatest valued negative integer?

(3,5) (4,-2) (-1,-3) (-2,1)

(4,5) (-8,+3) (-5.-1) (-6,3) (0,-7)

Comparing Integers Use your number line to help you compare each set of numbers. Copy the question and write two sentences for each pair of numbers. (i.e. for the numbers 3 ,and - 2 …. 3 > -2 -2 < 3) - 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15 e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14 i) 8, 7 j) - 8, - 7 k) 5, -1 l) 0, -2 m) 0, 3 n) - 5, 0 o) – 14, -10 p) - 9, 0 q) -7, -6 r) -1, 0 s) 4, -4 t) 0, -15

Comparing Integers Again For each of the previous questions (a) to (t), write a new mathematical sentence showing how much bigger or smaller the first number is than the second. (i.e. 3, - 2 ….. 3 is 5 more than –2)

Review What We Know

- 4

+1

-2

Direction + 3 Magnitude

Comparing Integers -5 ___ -8 0 ___ -3 3 ___ +2

Quadrant l (4,-5) (-8,+3) (-5,-1)

Intro To Adding Integers

Outcomes A12 represent integers (including zero) concretely, pictorially, and symbolically, using a variety of models B11 add and subtract integers concretely, pictorially, and symbolically to solve problem B14 solve and pose problems which utilize addition of integers B2 use mental math strategies for calculations involving integers

Lab Performance Evaluation A – Student is performing beyond expected level. B – Student is performing at upper range of expected level. C – Student is performing at expected grade level D – Student is performing at lower range of expected level. E – Student is performing below expected level.

Areas of Evaluation Organization into activity Following directions Presenting work neatly Completion of work Representing Integer sentences in words Your ability to discover and represent Integer Rules Making use of the Integer mat Working quietly and cooperative

Net Result Positive 9 (+5) + (+4) = +9 Or (+4) + (+5) = +9

Finding The Sum of Positive Integers When finding the sum of positive integers you add the magnitudes and keep the positive sign.

Net Result Negative 10 (-3) + (-7) = -10 Or (-7) + (-3) = -10

Finding The Sum of Negative Integers When finding the sum of negative integers you add the magnitudes and keep the negative sign.

Net Result Positive 2 (+7) + (-5) = +2 Or (-5) + (+7) = +2

Finding The Sum of a Positive and a Negative Integer When finding the sum of a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.

Net Result Zero (+5) + (-5) = 0 Or (-5) + (+5) = 0

Integer Recap You Have or Positive symbol means You’ve Earned Negative symbol means You Owe

(+3) + (-7) (-5) + (-2) (-3) + (-6) + (+4) (+3) + (-2) + (+2)

(+50) + (-100) (-25) + (+10) -60 + -20 -20 + 15 30 + -5

Rules For Adding Integers Positive Integers To add two positive integers you add the magnitude and keep the positive sign. Negative Integers To add two negative integers you add the magnitude and keep the negative sign. A Negative and a Positive Integer To add a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.

Intro To Subtracting Integers

(+5) – (+3) = +2 (+5) – (+3) =

(-6) – (-2) = -4 (-6) – (-2) =

(+3) – (+5) = -2 (+3) – (+5) =

(-2) – (-6) = +4 (-2) – (-6) =

(+3) – (-2) = +5 (+3) – (-2) =

(+1) – (+4) = -3 (+1) – (+4) =

(-5) – (+3) = -8 (-5) – (+3) =

(-2) – (-5) = +3 (-2) – (-5) =

Try These (-8) – (-3) = (+4) – (-5) = (-4) – (-5) = (+1) – (-6) = (-5) – (+6) = (-2) – (-3) = (-20) – (-10) = (+30) – (-3) = (-20) – (-30) =

Try These (-3) – (-2) = (+6) – (-2) = (-1) – (-4) = (+3) – (-2) = (-5) – (+2) = (-2) – (-4) = (-30) – (-20) = (+50) – (-10) = (-20) – (-30) =

Try These (-5) + (+2) = (+6) + (-2) = (-2) – (-6) = (+7) + (-2) = (+8) + (-4) = (-3) – (+6) = (+50) – (-10) = (-20) + (-30) =

Try These (-5) + (+2) = -3 (+6) + (-2) = +4 (-2) – (-6) = +4 (+7) + (-2) = +5 (+8) + (-4) = +4 (-3) – (+6) = -9 (+50) – (-10) = +60 (-20) + (-30) = -50

Multiplying and Dividing Integers

Intro To Multiplying and Dividing Integers Site: www.aplusmath.com Go to Flashcards Go to Non-Java Flashcards Go to Adding, Subtracting, Multiplying and Dividing With Negative Numbers Click on Multiplying (One by One) Use the site to help you complete the chart Then, Go To Division (One by One)

(+2) x (+4) = +8 (+2) x (+4) = This means you have two sets of four positive tiles or you have earned two groups of four dollars.

(+2) x (-4) = -8 (+2) x (-4) = This means you have two sets of four negative tiles or you have two bills that you owe,each bill is for four dollars.

(-2) x (-4) = +8 (-2) x (-4) = This means you don’t have two sets of four negative tiles or you don’t owe two bills, each bill is for four dollars.

(-2) x (+4) = -8 (-2) x (+4) = This means you don’t have two sets of four positive tiles or you don’t have two groups of four dollars.

Try These (+3) x (-2) = (-2) x (-2) = (+5) x (-2) = (-3) x (+2) =

Try These (-91) x (-101) = (+152) x (-21) = (-19) x (+203) =

Try These (-91) x (-101) = (+152) x (-21) = (-19) x (+203) =

Multiplying Integers FACTOR PRODUCT + _

Dividing Integers DIVIDEND DIVISOR QUOTIENT + _

Try These (-1) x (+1) x (-1) = (+1) x (+1) x (-1) =

Short Cuts For Multiplying Several Integer Factors If there is an even number of negative signs, the product is positive (-1) x (+1) x (-1) = +1 (+1) x (+1) x (-1) = -1 c. (-1) x (-1) x (+1) = +1 d. (-1) x (-1) x (-1) = -1 If there is an odd number of negative signs, the product is negative

Short Cuts For Multiplying Several Integer Factors a. (-1) x (+1) x (-1) x (+1) = b. (+1) x (+1) x (-1) x(-1) = c. (-1) x (+1) x (-1) x (-1) x (+1) = d. (-1) x (-1) x (-1) x (-1) x (+1) x (-1) = e. (1) x (+1) x (-1) x (-1) x (+1) x (-1) = (-1) x (-1) x (-1) x (-1) x (-1) x (-1) = (-2) x (-3) x (-2) x (+1) = (-1) x (-3) x (-2) x (-2) x (-3) =

Try These (-2) x (+2) x (-1)(-3)= (+1) x (+4) x (-5) =

(+2) x (+4) = +2 (+2) x (+4) =

Positive and Negative Integers For each of the following numbers, write down an example of where it could be used and what it means in that situation. -3 -100m +15 +3050m -$45.83

Order of Operations With Integers

Order of Operations With Integers 3 x (–7) + 4 x (-5) 15 + (+5)2 x 2 (-18) -- 32 – 9 x 2

Practice for Problem Solving Fiona spends $5 per week on bus fare. How much does she spend in 2 weeks? Lucy spends 2 per week on snacks. How much does she spend in 4 weeks? Anton earns $8 each week for baby-sitting. How much does he earn in 3 weeks?

Practice for Problem Solving Lional pays $3 per day for bus transportation. How much does she pay in a school week? Jill has $100 in the bank. She owes 3 of her friends $10 dollars each. What is her net worth?