mental subtraction in your head, compute: 65 - 28 71 - 39 80 - 46 explain what you did so that a...
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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