Mental Subtraction

1
Mental Subtraction

• In your head, compute
• 65 - 28
• 71 - 39
• 80 - 46
• Explain what you did so that a second grader will
  understand.

2
Subtraction

• Vocabulary
• A - B CA is the minuendB is the subtrahendC
  is the difference

3
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 cant
  take a bigger number away from a smaller number.
  Or You have to put the bigger number first (in
  the minuend).

4
Pictorial Models

• Take away
• Comparison

5
Number Line Model

• 7 - 9 -2
• Why is it important to start at 0?

6
Four related facts

• If 9 - 4 5, then9 - 5 4, 4 5 9, and 5
  4 9
• You try If 74 - 61 13, then

7
Mental Subtraction

• Not as obvious as mental addition
• 65 - 28Break 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)

8
The name of the strategy is not important

• You try and be ready to explain how you did it.
  Are there other ways?
• 73 - 82
• 97 - 39
• 301 - 293

9
Regrouping

• Show a diagram for
• 302 - 84

10
302 - 84

• Start with

11
Now, indicate what you are subtracting

• 302 - 84 Let red be the part you take away

12
You try draw pictures

• 58 - 37
• 47 - 29

13
Subtraction the way you learned it

• 6 7 8- 3 9 2 2 8 6

5
1
Why did you cross out the 6? Why did you put a
little 1 next to the 7? Can you show this with
pictures?
14
Here are three other ways to think about
subtraction

• Explain why this works--use pictures or
  manipulatives
• 9 8 4- 3 6 8
• 6 1 6

1
7
15
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

16
Use drawings or manipulatives to explain

• Here is yet another one.
• 3 2 6- 2 9 4 2 -7
  0 1 0 0
• 100 - 70 2 132

17
A real problem

• Place the digits 1, 2, 3, 6, 7, 8 in the boxes to
  obtain
• Greatest sumLeast sumGreatest differenceLeast
  difference