+$90 -$1.24 -3.4 -21 + 1/2 53 +4 -50% 0 integers integers are whole numbers that describe opposite...
TRANSCRIPT
+$90
-$1.24-3.4
-21
+ 1/2
53
+4
-50%0
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.
Negative integers are valued less than zero, and are always to the left
of zero.
Zero is neither positive or negative
Positive integers are valued more than
zero, and are always to the right of zero.
- 1- 1
- 4- 4
+ 3+ 3
- 3- 3
+ 2 + 2
+ 2 + 2
+ 2 + 2
+ 2 + 2
Representing Integers
• - 4 using 6 counters
• + 2 using 6 counters
• 0 using 6 counters
• - 3 using 6 counters
The “net worth” of opposite integers is
zero.
00
00
00
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?
-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)
a) - 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)(4,5)
(-8,+3)(-8,+3)
(-5.-1)(-5.-1)
(-6,3)(-6,3)
(0,-7)(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)
a) - 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)
- 4- 4
+1+1
00
-2-2
Magnitude
Direction
+ 3
Comparing Integers
• -5 ___ -8
• 0 ___ -3
• 3 ___ +2
Quadrant l
(4,-5)(4,-5)
(-8,+3)(-8,+3)
(-5,-1)(-5,-1)
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
Net Result
Positive 9
(+5) + (+4) = +9Or
(+4) + (+5) = +9
(+5) + (+4) = +9Or
(+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
Net Result
Negative 10(-3) + (-7) = -
10Or
(-7) + (-3) = -10
(-3) + (-7) = -10Or
(-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
Net Result
Positive 2
(+7) + (-5) = +2Or
(-5) + (+7) = +2
(+7) + (-5) = +2Or
(-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
Net Result
Zero
(+5) + (-5) = 0
Or (-5) + (+5) =
0
(+5) + (-5) = 0
Or (-5) + (+5) =
0
Integer Recap
• Positive symbol means
• Negative symbol means
You Haveor
You’ve Earned
You Haveor
You’ve Earned
You OweYou Owe
• (+3) + (-7)
• (-5) + (-2)
• (-3) + (-6) + (+4)
• (+3) + (-2) + (+2)
• (+50) + (-100)
• (-25) + (+10)
• -60 + -20
• -20 + 15
• 30 + -5
Rules For Adding IntegersPositive Integers
To add two positive integers you add the magnitude and keep the positive sign.
Negative IntegersTo add two negative integers you add the magnitude and keep the negative sign.
A Negative and a Positive IntegerTo add a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.
(+5) – (+3) =
(+5) – (+3) =
(+5) – (+3) = +2
(+5) – (+3) = +2
(-6) – (-2) =(-6) – (-2) = (-6) – (-2) = -4
(-6) – (-2) = -4
(+3) – (+5) =
(+3) – (+5) =
(+3) – (+5) = -2
(+3) – (+5) = -2
(-2) – (-6) =(-2) – (-6) = (-2) – (-6) = +4
(-2) – (-6) = +4
(+3) – (-2) =
(+3) – (-2) =
(+3) – (-2) = +5
(+3) – (-2) = +5
(+1) – (+4) =
(+1) – (+4) =
(+1) – (+4) = -3
(+1) – (+4) = -3
(-5) – (+3) =
(-5) – (+3) =
(-5) – (+3) = -8
(-5) – (+3) = -8
(-2) – (-5) =(-2) – (-5) = (-2) – (-5) = +3
(-2) – (-5) = +3
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
1. (-5) + (+2) = 2. (+6) + (-2) = 3. (-2) – (-6) = 4. (+7) + (-2) = 5. (-5) + (+2) = 6. (+8) + (-4) = 7. (-3) – (+6) = 8. (+50) – (-10) = 9. (-20) + (-30) =
Try These
1. (-5) + (+2) = -32. (+6) + (-2) = +43. (-2) – (-6) = +4 4. (+7) + (-2) = +55. (-5) + (+2) = -36. (+8) + (-4) = +47. (-3) – (+6) = -98. (+50) – (-10) = +609. (-20) + (-30) = -50
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) =
(+2) x (+4) =
(+2) x (+4) = +8
(+2) x (+4) = +8
This means you have two sets of four positive tiles or you have
earned two groups of four dollars.
This means you have two sets of four positive tiles or you have
earned two groups of four dollars.
(+2) x (-4) =
(+2) x (-4) =
(+2) x (-4) = -8
(+2) x (-4) = -8
This means you have two sets of four negative tiles or you have two bills
that you owe,each bill is for four dollars.
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) =(-2) x (-4) = (-2) x (-4) = +8
(-2) x (-4) = +8
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.
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) =
(-2) x (+4) =
(-2) x (+4) = -8
(-2) x (+4) = -8
This means you don’t have two sets of four positive tiles or you don’t have two groups of four
dollars.
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) =• (+3) x (+4) =• (+3) x (-2) =
Try These
• (-91) x (-101) =• (+152) x (-21) =• (-19) x (+203) = • (-69) x (-102) =• (-62) x (-11) =• (-128) x (+12) =
Try These
• (-91) x (-101) =• (+152) x (-21) =• (-19) x (+203) = • (-69) x (-102) =• (-62) x (-11) =• (-128) x (+12) =
Multiplying Integers
FACTOR FACTOR PRODUCT
+ + +
_ _ +
_ + _
+ _ _
Dividing Integers
DIVIDEND DIVISOR QUOTIENT
+ + +
_ _ +
_ + _
+ _ _
Try These
• (-1) x (+1) x (-1) =• (+1) x (+1) x (-1) =• (-1) x (-1) x (+1) =• (-1) x (-1) x (-1) =• (-1) x (-1) x (+1) x (-1) x (+1) =• (-1) x (+1) x (+1) x (-1) x (+1) =
Short Cuts For Multiplying Several Integer Factors
a. (-1) x (+1) x (-1) = +1
b. (+1) x (+1) x (-1) = -1
c. (-1) x (-1) x (+1) = +1
d. (-1) x (-1) x (-1) = -1
If there is an even number of
negative signs, the product is
positive
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) =
f. (-1) x (-1) x (-1) x (-1) x (-1) x (-1) =
g. (-2) x (-3) x (-2) x (+1) =
h. (-1) x (-3) x (-2) x (-2) x (-3) =
Try These
• (-2) x (+2) x (-1)(-3)=• (+1) x (+4) x (-5) =• (-17) x (-2) x (+2) =• (-2) x (-3) x (-6) x 4 =• (-2) x (-3) x (-3)
(+2) x (+4) =
(+2) x (+4) =
(+2) x (+4) = +2
(+2) x (+4) = +2
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
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?