Adding Whole Numbers
Adding Whole Numbers
©
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#5
Taking the Fear
out of Math
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© Math As A Second Language All Rights Reserved
Addition Through the Eyes of Place Value
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© Math As A Second Language All Rights Reserved
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Addition Through the Eyes of Place Value
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
Using the Properties of
Whole Number Addition
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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© Math As A Second Language All Rights Reserved
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Note
![MC900310816[1]](data/images/img3.png)
next
next
© Math As A Second Language All Rights Reserved
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2 3 4, 2 6 7, 5 8 0, 2 9 4
3 5 2, 3 1 2, 2 1 9, 6 0 2
+
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next
© Math As A Second Language All Rights Reserved
What Ever Happened to “Carrying”?
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© Math As A Second Language All Rights Reserved
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next
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next
© Math As A Second Language All Rights Reserved
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![MC900047886[1]](data/images/img4.png)
note
1 If we wanted to use grouping symbols, we could write 5(14) to indicate that thereare 14 ones and 5 tens but this would quickly become very cumbersome as thenumber of digits increases.
3
2
5
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9
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+
next
© Math As A Second Language All Rights Reserved
L
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next
$10 bills
$1 bills
Line 1
5
14
Line 2
6
4
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© Math As A Second Language All Rights Reserved
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.
next
next
next
© Math As A Second Language All Rights Reserved
T
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We never use more than one digit
per place value column.
next
Counting on Your FingersMyth
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!
![MC900211482[1]](data/images/img5.png)
![MC900211482[1]](data/images/img6.png)
© Math As A Second Language All Rights Reserved
next
next
C
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.
© Math As A Second Language All Rights Reserved
next
5 2 8 6
2 9 5 9
1 6 7 3
9 9 1 8
+
next
R
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.
© Math As A Second Language All Rights Reserved
next
note
3 Up to now we have talked about the sum of two numbers. However, no matter howmany numbers we are adding, we never add more than two numbers at a time.
For example, to form the sum 2 + 3 + 4, we can first add 2 and 3 to obtain 5 and thenadd 5 and 4 to obtain 9. We would obtain the same result if we had first added3 and 4 to obtain 7 and then add 2 to obtain 9.
next
5 2 8 6
2 9 5 9
1 6 7 3
+
next
T
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© Math As A Second Language All Rights Reserved
next
5 2 8 6
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1 6 7 3
+
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© Math As A Second Language All Rights Reserved
next
1 8
6 + 9 + 3 ones
5, 2 8 6
+
2, 9 5 9
1, 6 7 3
= 18 ones
2 0
8 + 5 + 7 tens
= 20 tens
1 7 0 0
2 + 9 + 6 hundreds
= 17 hundreds
8 0 0 0
5 + 2 + 1 thousands
= 8 thousands
9, 9 1 8
next
next
next
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next
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Even though there is a tendency to tellyoungsters that “grown ups don’t counton their fingers”, the fact remains thatwith a proper understanding of placevalue and knowing only how to count onour fingers, we can solve any wholenumber addition problem.
© Math As A Second Language All Rights Reserved
next
next
In particular at any stage of theaddition process, we are always
adding two numbers,
one of which is a single digit.
One goal of critical thinking is toreduce complicated problems to asequence of equivalent but simplerones. Here we have a perfectexample of the genius that goesinto making things simple!
© Math As A Second Language All Rights Reserved
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![MC900078625[1]](data/images/img7.png)
next
Same Sum Technique
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© Math As A Second Language All Rights Reserved
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![MC900232055[1]](data/images/img8.png)
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© Math As A Second Language All Rights Reserved
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4 You might want to postpone this method until after the students have studiedsubtraction.
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679 + 298 =
(679 – 2) + (298 + 2)
677 + 300
= 997
next
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© Math As A Second Language All Rights Reserved
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453 + 300
= 753
457 + 296
= 753
next
next
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© Math As A Second Language All Rights Reserved
![MC900059122[1]](data/images/img9.png)
385
261
594
addition
1240