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Mental Subtraction
In your head, compute:
65 - 28
71 - 39
80 - 46
Explain what you did so that a
second grader will understand.
Subtraction in Alphabitia
CBD
− ADC
Let’s subtract
CBD
- ADC
CBD is
=
CBD - ADC is
You Try…
D00
-B0B
B0A
- BD
You try: Use manipulatives
or drawings to explain
BBC
- A0C
A0A0D
BCA
Exploration 3.1 Part 2
• #1 Write two subtraction story
problems. One must require
regrouping. Share these in your group.
• #2
• What interpretations of subtraction can
you describe?
Estimation
•
•
•
•
•
•
•
•
382 - 147
Actual answer: 235
Ways to estimate:
380 - 150 = 230
400 - 150 - 20 = 230
375 - 150 = 225
385 - 145 = 240
390 - 140 = 250
Subtraction
• Vocabulary:
• A-B=C
A is the minuend
B is the subtrahend
C is the difference
Try this:
• Is A - B = B - A?
• 6 - 4 = 4 - 6?
• What is true of 6 - 4 and 4 - 6?
• One of the worst things we can say: “You
can’t take a bigger number away from a
smaller number.” Or “You have to put the
bigger number first (in the minuend).”
Pictorial Models
• Take away
• Comparison
Number Line Model
• 7 - 9 = -2
• Why is it important to start at 0?
-2 -1 0 1
2 3
4 5 6
7 8 9 10
Four related facts
• If 9 - 4 = 5, then
9 - 5 = 4, 4 + 5 = 9, and 5 + 4 = 9
• You try: If 74 - 61 = 13, then …
Mental Subtraction
Subtract mentally:
65 − 28
Mental Subtraction
Not as obvious as mental addition
65 – 28
•
•
•
•
Break apart the second number (65 - 20) - 8
Adding up 28 + 30 = 58, 58 + 7 = 65, 30 + 7
Compensation (65 + 2) - (28 + 2), 67-30
Compatible Numbers (65 – 25, 40-3)
You try… and be ready to explain how
you did it. Are there other ways?
• 73 - 82
• 97 - 39
• 301 - 293
Regrouping
Show a diagram for
302 - 84
302 - 84
• Start with…
Now, indicate what you
are subtracting
• 302 - 84: Let red be the part you take
away
You try: draw pictures
• 58 - 37
• 47 - 29
Subtraction the way you
learned it…
5
1
678
- 392
286
Why did you cross out
the 6? Why did you put
a little “1” next to the 7?
Can you show this with
pictures?
Here are three other ways
to think about subtraction
Explain why this works--use pictures or
manipulatives
1
87 4
-
9
3 6 8
6 1 6
Why does this work?
• This way worked because
• 984 - 368 is the same as adding 10 to
both numbers:
• 984 + 10 = 980 + 4 + 10 = 980 + 14
• 368 + 10 = 360 + 8 + 10 = 370 + 8
Use drawings or
manipulatives to explain…
• Here is yet another one.
•
-
•
3 2 6
2 94
2
-7 0
1 00
100 - 70 + 2 = 132
A real problem
• Place the digits 1, 2, 3, 6, 7, 8 in the
boxes to obtain:
• Greatest sum
Least sum
Greatest difference
Least difference