Section D Practice Problems

Problem 1

Clare walks 11,243 steps on Saturday and 12,485 steps on Sunday.

  1. How many steps does Clare take altogether on Saturday and Sunday?
  2. How many more steps does Clare take on Sunday than on Saturday?
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Solution

  1. 23,728. Sample response:

    addition algorithm

  2. 1,242. Sample response: I subtracted each place value.

Problem 2

  1. Find the value of the sum. Explain your calculations.

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  2. Find the value of the difference. Explain your calculations.

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Solution
Sample responses:

  1. addition algorithm

    I added 5 and 8 ones and that gave me 13 ones. So, I recorded the 10 above and the 3 ones below. Then I added all the tens and there were 5. When I added 8 hundreds and 5 hundreds that gave me 1,300 so I put 3 hundreds below and 1 thousand above. Then I added the thousands.

  2. subtraction algorithm

    I took the 4 ones from the 7 ones. I could not take the 3 tens from 2 tens so I broke up a hundred. Then I took 1 hundred from the remaining hundreds and 2 thousands from the thousands.

Problem 3

Find the value of each sum and difference using the standard algorithm.

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Solution

addition algorithm

subtraction algorithm

Problem 4

Han finds the value of 300,526−4,472300,526 - 4,472.

Subtract. Three hundred thousand, five hundred, twenty six, minus, four thousand, four hundred, seventy two, equals two hundred six thousand, fifty four.<strong> </strong>

  1. How can you tell by estimating that Han has made an error?
  2. What error did Han make?
  3. Find the value of 300,526−4,472300,526 - 4,472.
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Solution
Sample responses:
  1. The value should be close to 300,000 but it is closer to 200,000.
  2. Han broke up one of the hundred-thousands but made it 10 thousands instead of 10 ten-thousands.

  3. subtraction algorithm

Problem 5

In 2018, the population of Boston is estimated as 694,583 and the population of Seattle is estimated as 744,995.

  1. Is the population difference between Boston and Seattle more or less than 100,000? Explain how you know.
  2. Is the population difference more or less than 50,000? Explain how you know.
  3. Find the difference in the populations of the 2 cities.
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Solution
Sample responses:
  1. Less, because the population of Seattle is less than 750,000. If I add 100,000 to the population of Boston, I get almost 800,000.
  2. More, because the difference between the thousands is 50,000. There are more hundreds in the Seattle population than in the Boston population.

  3. 50,412

    Subtract.
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Problem 6

Han says he uses a method to find the value of 1,000,000−267,9231,000,000 - 267,923 without decomposing a unit: “I write 1,000,000 as 999,999+1999,999 + 1.”

  1. How might rewriting 1,000,000, as Han suggested, help with finding the difference of 1,000,000−267,9231,000,000 - 267,923?

  2. Try Han’s method to find 1,000,000−267,9231,000,000 - 267,923.

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Solution
Sample responses:
  1. Because 1,000,000 is 1 more than 999,999, 1,000,000−267,9231,000,000 - 267,923 is 1 more than 999,999−267,923999,999 - 267,923 which can be found by subtracting each place without decomposing.
  2. 999,999−267,923=732,076999,999 - 267,923 = 732,076 so 1,000,000−267,923=732,0771,000,000 - 267,923 = 732,077.

Problem 7

Use the information to determine when the telephone, printing press, and automobile were first invented.

  • The airplane was invented in 1903.
  • The printing press was invented 453 years before the most recent invention.
  • The automobile was invented 15 years before 1900.
  • It was 426 years after the invention of the printing press that the telephone was invented.
  • The automobile and telephone were invented the closest together in time with only 9 years between them.
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Solution
  • Telephone: 1876
  • Printing press: 1450
  • Automobile: 1885