Transcript b) Add Integers Hands On MODEL

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Emily’s mother is an accountant. One
day, Emily heard her Mom talking to a
client on the phone. During the
conversation, her Mom used the phrases
“in the red” and “in the black”.
That evening at dinner, Emily asked her
Mom what the terms meant. Here is what
her Mom said:
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“When people in business talk about
income and expenses, they often use
colors to describe the numbers they are
dealing with.
Black refers to profits or income.
A company that is making money is
“in the black.” POSITIVE INTEGERS.
Red refers to losses or expenses.
A company that is losing money or owes
money is “in the red.” NEGATIVE INTEGERS.
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One positive and one negative has
a value of zero because they
cancel each other out.
+ –
This is called a NEUTRAL FIELD
or a ZERO BANK.
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Emily was studying Integers in her Math
class & thought she could use these ideas
of “in the black” and “in the red” to model
the addition of positive & negative integers.
Her model uses a positive black and a
negative red. Each black represents +1 and
each red represents -1.
For example, this shows a value of +5:
+ + + + +
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We can show +5 using more than 5 tiles.
+
–
+
+
+
+
+
They also don’t need to be in a straight line.
–
+
+
+
+
+
–
+
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+
This shows a value of -6
– – – – – –
So does this!
– –– +–––+– –
It has 2 zeros!
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+ or –
+ or –
1) Put in the 1st number of
2) Add the 2nd number of
3) Balance out what you have
4) One + balances out one –
5) The leftovers are the final answer
When a + and – cancel each other out it is
called a NEUTRAL FIELD or ZERO BANK
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To represent 3 + 2
Put +3 in
Put +2 in
+++
++
Since all the signs are the same you
just figure out your answer.
3+2= 5
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To represent -4 + -3
Put – 4 in
Put – 3 in
– – – –
– – –
Since all the signs are the same you
just figure out your answer.
-4 + -3 = -7
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To represent 5 + -2
Put + 5 in
Put – 2 in
+
+
+
+
+
– –
Equalize, or balance out, what you have.
2 positives cancel out with 2 negatives.
5 + -2 = 3
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To represent -3 + 4
Put -3 in
Put +4 in
– – –
+++ +
Equalize, or balance out, what you have.
3 positives cancel out with 3 negatives.
-3 + 4 = 1
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Take Out Your Study Guide!!!
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#3
Integers are the set of numbers including positive
whole numbers, negative whole numbers and zero.
-5 -4 -3 -2 -1 0 1 2 3 4 5
Positive
Negative
* Negative integers are
less than zero
<
*Positive integers are
greater than zero
* The integer zero is neither
positive or negative
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>
#4
Steps To Add Integers
1) Put in the 1st number of + or –
2) Add the 2nd number of + or –
3) Balance out what you have
4) One + balances out one –
5) The leftovers are the final answer
When a + and – cancel each other out it is
called a NEUTRAL FIELD or ZERO BANK
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Hyperlinked Website
Below Goes With Lesson
Hands on Model on the INTERNET
http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html
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