Section C Practice Problems

Problem 1

Jada writes the same digit in the 2 blanks to make the statement true. Which digits could she write?

6 8 , 4 3 2<6 5 ,8 9 8\large \boxed{6} \ \boxed{\phantom{8}} \ , \ \boxed{4} \ \boxed{3} \ \boxed{2} < \boxed{6} \ \boxed{5} \ ,\boxed{\phantom{8}} \ \boxed{9} \ \boxed{8}

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Solution
0, 1, 2, 3, 4, 5

Problem 2

  1. Order these numbers from least to greatest:

    • 98,107

    • 102,356

    • 752,031

    • 88,207

    • 99,653

  2. How did you pick the smallest number? Explain your reasoning.
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Solution
  1. 88,207, 98,107, 99,653, 102,356, 752,031
  2. Sample response: Two of the numbers have hundred-thousands, so they are greater than the ones with just ten-thousands. 88,207 is the smallest of these because the others each have more ten-thousands.

Problem 3

  1. Which multiple of 10,000 is closest to 132,256?

  2. Which multiple of 100,000 is closest to 132,256?

  3. Which multiple of 100,000 is closest to the number labeled A?

    Number line. Scale 0 to 5 hundred thousand, by 100 thousand's. Point A, less than halfway between 300 thousand and 400 thousand.

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Solution
Sample responses:
  1. 130,000
  2. 100,000
  3. 300,000

Problem 4

For the number 583,642:

  1. What is the nearest multiple of 100,000?

  2. What is the nearest multiple of 10,000?

  3. What is the nearest multiple of 1,000?

  4. What is the nearest multiple of 100?

  5. What is the nearest multiple of 10?

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Solution
  1. 600,000
  2. 580,000
  3. 584,000
  4. 583,600
  5. 583,640

Problem 5

  1. Describe the numbers that are 460,000 when rounded to the nearest ten thousand.

    Number line. Scale, four hundred thirty thousand to four hundred eighty thousand, by ten thousands.  

  2. Where are these numbers located on the number line?
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Solution

Sample response:

  1. They are the numbers starting with 455,000 and ending with 464,999.
  2. On the number line, they are the points closer to 460,000 than to 450,000 or 470,000 and the point 455,000 which is the same distance from 450,000 and 460,000.

Problem 6

When rounded to the nearest thousand, Airplane X is flying at 30,000 feet, Airplane Y at 31,000 feet, and Airplane Z at 32,000 feet.

  1. Could Airplanes X and Y be within 1,000 feet of each other? If you think so, give some examples. If you don’t think so, explain why not.
  2. Explain why Airplanes X and Z could not be within 1,000 feet of each other. Use a number line if you find it helpful.
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Solution

Sample responses:

  1. Yes, Airplane X could be flying at 30,400 feet and Airplane Y could be at 30,600 feet. Or Airplane X could be flying at 30,000 feet and Airplane Y could be flying at 30,750 feet.
  2. The highest possible altitude for Airplane X is 30,499 feet and the lowest possible altitude for Airplane Z is 31,500 feet and that's more than 1,000 feet difference.

Problem 7

Rounded to the nearest 10 pounds, 1 bag of sand weighs 50 pounds.

Jada wants at least 1,000 pounds of sand for a sandbox. How many bags of sand does Jada need to buy to be sure that she has enough sand?

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Solution
Sample response: There is at least 45 pounds of sand in each bag. So, 10 bags will give at least 450 pounds and 20 bags at least 900 pounds. She will need 3 more bags to make sure she has at least 1,000 pounds. So, that's 23 bags in all, even though 20 bags will have 1,000 pounds if they each have 50 pounds of sand in them.

Problem 8

You will need a set of digit cards 0–9 for this exploration.

Place the cards facedown in a stack. Turn over 6 digit cards.

Can you put the 6 digits in the blanks so that all three statements are true?

  1. 4 ,8 2 3>8 ,9 7 8\large \boxed{4} \ , \boxed{\phantom{8}} \ \boxed{2} \ \boxed{3} > \boxed{\phantom{8}} \ , \boxed{9} \ \boxed{7} \ \boxed{8}
  2. 8 2 ,4 0 3>4 2 ,8 0 1\large \boxed{\phantom{8}} \ \boxed{2} \ , \boxed{4} \ \boxed{0} \ \boxed{3} > \boxed{4} \ \boxed{2} \ , \boxed{\phantom{8}} \ \boxed{0} \ \boxed{1}
  3. 4 3 8 ,2 5 7>4 8 5 ,9 3 7\large \boxed{4} \ \boxed 3 \ \boxed{\phantom{8}} \ , \boxed{2} \ \boxed{5} \ \boxed{7} > \boxed{4} \ \boxed{\phantom{8}} \ \boxed{5} \ , \boxed{{9}} \ \boxed{3} \ \boxed{7}
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Solution

Sample responses: I picked 0, 2, 3, 4, 6, 7, and was able to make all three statements true.

  1. 4,723>3,9784,723 > 3,978
  2. 22,403<42,40122,403 < 42,401
  3. 436,257>405,937436,257 > 405,937

Problem 9

Round to the nearest ten, hundred, thousand, and ten thousand to answer these riddles. Use a number line if it is helpful.

  1. I can be rounded to 100 or to 140. What number could I be?
  2. I can be rounded to 7,500 or to 8,000. What number could I be?
  3. I can be rounded to 60,000 or to 57,000. What number could I be?
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Solution

Sample responses:

  1. 136. A number greater than 134 and less than 145 can be rounded to 100 if it is rounded to the nearest 100. It is 140 if rounded to the nearest ten.
  2. 7,540. Any number greater than 7,499 and less than 7,550 can be rounded to 7,500 if it is rounded to the nearest 100. It is 8,000 if rounded to the nearest thousand.
  3. 57,018. Any number greater than 56,499 and less than 57,500 can be rounded to 57,000 if rounded to the nearest 1,000. It is 60,000 if rounded to the nearest 10,000.