Section B Practice Problems

Problem 1

Find the value of 472−155472 - 155 in a way that makes sense to you.

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Solution

317. Sample response:

472−100=372472 - 100 = 372
372−50=322372 - 50 = 322
322−5=317322 - 5 = 317

Problem 2

Here is a subtraction calculation.

<p>Subtraction. Five-hundred plus forty plus five, minus three-hundred plus sixty plus three, equals one-hundred plus eighty plus two.</p>

  1. Explain what the 400 above the 500 means.
  2. Explain what the 140 above the 40 means.
  3. Explain how the calculation works to find 545−363545 - 363.

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Solution

Sample response:

  1. To take 6 tens from 4 tens, a hundred is broken into 10 tens. That means only 400 is left.
  2. A hundred is broken into 10 tens, which they are put together with the 4 tens to give 14 tens or 140.
  3. 400−300=100400 - 300 = 100
    140−60=80140 - 60 = 80
    5−3=25 - 3 = 2
    So the difference is 182.

Problem 3

  1. Write 617 and 173 in expanded form.
  2. Use the expanded form to find the difference of the two numbers.
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Solution

Sample responses:

  1. 500+10+8500+10+8
    300+40+6300+40+6
  2. 444. Sample response:

Subtraction.

Problem 4

Use an algorithm of your choice to find the value of each difference.

  1. 316−154316 - 154
  2. 647−285647 - 285
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Solution
  1. 162. Sample response:

    subtraction algorithm

  2. 362. Sample response:

    Subtraction.

Problem 5

Use an algorithm of your choice to find the value of each difference.

  1. 218−136218 - 136
  2. 473−258473 - 258
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Solution

  1. 273.. Sample response:

    Subtraction.

  2. 215. Sample response:

    Subtraction.

Problem 6

Use a strategy or an algorithm of your choice to find the value of each difference.

  1. 573−299573 - 299
  2. 653−341653 - 341
  3. 371−158371 - 158
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Solution
  1. 274. Sample response: I took away 300 and then added back 1.
  2. 312. Sample response: I took away hundreds from hundreds, tens from tens, ones from ones. I did not need to decompose.

  3. 527. Sample response:

    Subtraction.

Problem 7

Here is Noah's way to find the value of 523−371523 - 371.

371+100=471371 + 100 = 471
471+30=501471 + 30 = 501
501+20=521501 +20 = 521
521+2=523521 + 2 = 523

The answer is 100+30+20+2=152100+30+20+2=152.

  1. Explain why Noah’s method works.
  2. Use Noah’s method to calculate 618−266618−266.
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Solution
  1. Sample response: Noah adds on to 371 until he reaches 523, and then finds how much he added.
  2. 346. Sample response:

    266+300=566266 + 300 = 566
    566+40=606566 + 40 = 606
    606+10=616606 + 10 = 616
    616+2=618616+2 = 618

    300+40+10+2=352300 + 40 + 10 + 2 = 352.

Problem 8

  1. Find the value of 600−253600 - 253. Explain or show your reasoning.
  2. How is this problem different from other subtraction problems you have solved?
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Solution
  1. 347. Sample response: If I take away 2 hundreds, I have 400. That’s 300 and another 100. Then 100−53=47100−53=47, so the answer is 347.
  2. Sample response: There are only hundreds to break up, no tens or ones. Breaking up a hundred into 10 tens still leaves me with more to decompose since I have no ones. I have to decompose a ten into ones before subtracting the 3 ones in 253.