bell work
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Bell Work. Explain why the location of point A(1, -2) is different than the location of point B(-2, 1). **Answer in complete thought sentences. Adding Integers. Using Counters to Add/Subtract Integers. Let represent our Positive Integers Let represent our Negative Integers - PowerPoint PPT PresentationTRANSCRIPT
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Explain why the location of point A(1, -2) is different than the location of point B(-2, 1).
**Answer in complete thought sentences.
Bell Work
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Adding Integers
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Let represent our Positive Integers Let represent our Negative Integers Pair up with to create “ZERO pairs”
since 1+(-1) = 0, the remaining counters will represent the left over amounts.
Example: -3 + 5
Thus we have 2 positive tokens left, so the answer would be -3+5 = 2.
Using Counters to Add/Subtract Integers
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1. 5+62. -4+33. -2+74. -5+(-2)5. -7+2
Check your answers with a number line
Use counters to find the following sums:
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If you are adding integers with the same sign (ex: 5+5), you simply add their absolute values and keep the sign.
5+5 = 10 -6+(-2) = -8
-2+-3 = -5
Tricks: Adding same-sign numbers
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1. Give an example of an addition sentence containing at least four integers whose sum is zero.
2. Explain how you know whether a sum is positive, negative, or zero without actually adding.
Practice
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Let represent our Positive Integers Let represent our Negative Integers
Example: -3 –21) Begin with the counters of the first integer given (-3)
2) Add the zero pairs determined by the number of the second integer.
3)Then, remove the positive or negative chips determined by the 2nd integer (+2). Create zero pairs and count the remaining!
Using Counters to Subtract Integers
-3 –2 = -5
Why can we add these zero pairs?
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Show -3 -2 on a number line. Can we rewrite the expression to make it addition?
How could we show -3 –(-2)? Hint think of assets and debts.
Using a number line
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1. 5-62. -4-(-3)3. -2-74. -5-(-2)5. -7-2
Use counters or a number line to solve the following expressions:
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Rewrite subtracting a positive as adding a negative: 5-7 = 5+(-7)
Taking away a debt is a good thing! 9-(-5) = 9+5
If the numbers have the same signs, add the absolute values and keep the sign.
-5-15 = -5+(-15) = -20 If the numbers have opposite signs, subtract the
two numbers and keep the sign of the number with the highest absolute value!◦ 9-12 = 9+(-12) think: 12-9 =3, but 12 is larger so -3!
Trick: Subtracting Integers
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Evaluate x-y if x=12 and y =7 Replace x and y with the numbers above and solve:
x-y 12-712+ (-7)5
Evaluate an Expression
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http://www.teachertube.com/video/integers-121930
Integer Video
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1-3B/C Multiply Integers
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How do I write5+5+5
as multiplication?
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How do I write6+6+6+6+6
as multiplication?
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How do I write(-6)+(-6)+(-6)+
(-6)+(-6)?
as multiplication?
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Explore Multiplying with Counters
The number of students who bring their lunch to Phoenix middle School has been decreasing at a rate of 4 students per month. What integer represents the total change after three months?
So what do we need to find? The integer -4 represents a decrease of 4
students each month. After 3 months, the total change will be 3(-4) Use counters to model 3 groups of 4 negative counters.
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Model 3 x (-4)
Place 3 sets of 4 negative counters on the mat.
How many negative counters do we have?
What does this represent?
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Use counters to find -2 x (-4)If the first factor is negative, you will need to
remove counters front the mat.
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Draw it!
With your partner, figure out how you could represent 4x2
on a number line.
Now try representing (-3)(2).
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Write it!! The RULES:
Ways to express multiplication:◦ x, parenthesis, ∙
For even numbers of factors:◦ Same (like) signs = POSITIVE◦ Different (unlike) signs = NEGATIVE◦ Or draw a triangle…
Example: 3(4) =12(-2)x(-7) = 14(3)(-4) = -122(-7) = -14
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Use the Triangle
+
−−
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But what about the EXPONENTS?
(8)2 = ? (-8)2 = ? Write the rule for powers of 2!
(2)3 = ? (-2)3 = ? Write the rule for powers of 3!
Try powers of 4 and 5. Is there a pattern?
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Explain Your Reasoning
1) Evaluate (-1)50. Explain your reasoning.
2) Explain when the product of three integers is positive.
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1-3D Divide Integers
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Integers- Part 2! Division
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The Rules: Same as Multiplication!
Division can be written in two ways: ÷ or by a
fraction (top divided by the bottom number)
We call the answer to a division problem a
Quotient
For 2 factors:
◦ Like signs = POSITIVE
◦ Unlike signs = NEGATIVE
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Multiplication/Division ONLY
Try this: (3)(-4)(4) ÷(-12) = # of negatives: 2 (24 ÷(-3))(7) ÷ 2 = # of negatives: 1 (-2)(-2)(4)(-2) ÷(-4)= # of negatives: 4 (7)(-2)(16 ÷(-8))(-3)= # of negatives: 3
If your problem has only multiplication or division (no addition or subtraction signs) what do you notice about even and odd number of negatives?
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Evaluating Expressions Rewrite the equation using given numbers.
Make sure to plug into variables using (), especially when the number is negative!
Ex: Let x = -8 and y = 5. xy ÷ (-10) =
(-8)(5) ÷ (-10) = (-40) ÷ (-10) = 4
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Evaluating Expressions
2)
= -9
Note: (10-x)/(-2) notice you simplify the top first in order of operations, then divide last!
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Review of all Rules!
Addition: Same sign: add and keep the sign Different sign: subtract and keep the sign of
the number with the largest absolute value
Subtraction: Change minus sign to a plus and flip the sign of the 2nd number: Ex: 5-2 become 5+(-2) or 6-(-2) becomes 6+2, then follow the addition rules.
____________________________________________________Multiplication/Division: Like sign: Positive
Unlinke sign: Negative
If it is all multiplication/Division, even negatives= positive odd negatives = negative
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Check Your Understanding
Page 63 #1-9 Rally Coach
* Remember: One sheet of paper for the pair. Take turns coaching and writing.