Mental SubtractionMental SubtractionIn your head, compute:In your head, compute:

65 - 2865 - 28

71 - 3971 - 39

80 - 4680 - 46

Explain what you did so that a Explain what you did so that a second grader will understand.second grader will understand.

Let’s subtract

CBD- ADC =

CBD is ADC 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

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 = CA is the minuendB is the subtrahendC 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

• 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)

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

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…

6 7 8- 3 9 2 2 8 6

51

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

9 8 4- 3 6 8

6 1 6

7

1

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 9 4 2 -7 0 1 0 0

• 100 - 70 + 2 = 132

A real problem• Place the digits 1, 2, 3, 6, 7, 8 in the

boxes to obtain:

• Greatest sumLeast sumGreatest differenceLeast difference