Watch Tools
You can use concrete objects, such as counters, to find the total yardage.
Use negative integers to represent the yards lost on each play.
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.....
..,
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Combine a set of 5 negative counters and
a set of 2 negative counters.
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There is a total ofi ..... :: negative counters.
The model shows that adding a negatÿe
number to another negative number results
in a negative sum.
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uÿ
So, -5 -I- (-2)= i,ÿ i.The team los..ÿt a total of! -/ iyards
on the first two plays.
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Nÿa{is-On Lab 1-a Use Models to Add Integers ÿ99
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The following two properties are important when modeling operations with
' ÿ ÿ_ d .with one negative coun,
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the res"'t's ca"edl z°r° ÿ°'ÿv°'"e °f° zer° ÿ°"'s °"
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- You can add or remove zero pairs from a mat because adding or"---.-ÿ removing zero does not change the value of the counters on the mat.
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Use counters to determine -4 -F 2.
Combine i ÿi.! negative counters with [ÿ'ÿi positive counters. "
The addends have different signs.
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Remove all zero pairs.
There are more negative counters
than positive counters,
4>2
Find the number of counters remaining.
The model shows that the sum
o
has the same sign as the greater
number of counters.
There areI
iÿ- ! inegative counters remaining.
So, -4 + 2 = iÿh- i.
1. ÿ Analyze Relationships How would the model and sum change if the
addition expression was 4 + (-2)?
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200 Chapter3 Operations with Integers
ii
Show your work using drawings.
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2. s+6="I\
's
4. - +(-4)=
ÿ ff
3. --3 + (--5) = -- ÿ7
5. 7+3=
1o
_
......
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ji
ÿli
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8. 8+(--3)=
_ ÿ ÿ,
9.
3+(--6)= _.'ÿ_ ._ÿ_.. ....
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Study
the exercises in which both addends are
10. Con.cot Models to
gules
6
E
m
negative. What do you notice about the sum?.
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5 uÿ.,vÿ ÿ ÿ---ÿ ÿ' bÿ ÿ"ÿ'
11, Connect Models to gules Study the exercises in which one addend
is negative and one is positive. What do you notice about the sum?
T
Lÿ
0
ttands-O. Lab 1-a Use Models to Add Integers 201
(ÿ)Orÿanize Ideas Work with a Partner to complete the table. The first one
is done for you.
' Addition ExpreSsiOn
:
" " :
: ÿSum
-
.%- :ÿ-: , ÿ.ÿ-ÿ,-.::ÿ ::/- 51gnOfSum
ÿ ÿreazerÿDsomÿevalue
......
/
+ (-Z)
ÿ
posit-ire
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rd
12.
13.
[
14.
15.
16.
Connect Models to Rules Write a rule you can use to find the sum of
two negative integers without using counters.
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18, Connect Models to 12ules Write a rule you can use to find the sum
of a positive integer and a negative integer without using counters.
19. (ÿOse Multiple Representations Write two addition sentences where the
sum iszero. Describe the numbers.
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ÿ ÿ ÿ .Sÿ,ÿIÿ,_ ÿ,ÿ,ÿoIucÿ_ V
20. ÿ HOW can I select tools and techniques to determine when the
sum of two integers is a negative number?
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202. .Chapter 3 Operations with Integers