Section B Practice Problems

Problem 1

  1. Write the name of the number 8,500 in words.
  2. How many hundreds are there in 8,500? Explain how you know.
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Solution
  1. Eight thousand, five hundred
  2. 85, because each thousand is 10 hundreds. So, 8 thousands is 80 hundreds, and then there are 5 more.

Problem 2

  1. Count by 10,000 starting at 6,500 and stopping at 66,500. Record each number:
  2. Pick 2 numbers from your list and write their names in words.
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Solution

Sample responses:

  1. 6,500, 16,500, 26,500, 36,500, 46,500, 56,500, 66,500
  2. 6,500: Six thousand five hundred. 16,500: Sixteen thousand five hundred

Problem 3

 

Base ten diagram. 2 thousands, 1 hundred, 4 tens, 9 ones.

  1. If each small square represents 1, what number does the picture represent?
  2. If each small square represents 10, what number does the picture represent?
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Solution
  1. 2,149
  2. 21,490

Problem 4

  1. Write the names of the numbers 702,150, and 73,026 in words.

  2. How is the value of the 7 in 702,150 related to the value of the 7 in 73,026?
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Solution

Sample responses:

  1. 702,150: Seven hundred two thousand one hundred fifty. 73,026: Seventy-three thousand twenty-six
  2. The 7 in 702,150 represents 10 times as much as the 7 in 73,026.

Problem 5

  1. What is the value of the 6 in 65,247?
  2. What is the value of the 6 in 16,803?
  3. Write multiplication and division equations to represent the relationship between the value of the 6 in 65,247 and the value of the 6 in 16,803.
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Solution
  1. 60,000
  2. 6,000
  3. Sample responses: 60,000=10×6,00060,000 = 10 \times 6,000 and 60,000÷10=6,00060,000 \div 10 = 6,000

Problem 6

  1. Locate and label each number on the number line:

    • 100,000
    • 10,000

    • 1,000

    Number line. 0 to 200,000. 

  2. Which numbers were easiest to locate? Which were most difficult? Why?
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Solution

Sample responses:

  1.  
    Number line.
    The point really close to 0 is 1,000.
  2. The easiest point to plot was 100,000 because it is halfway between 0 and 200,000. To find 10,000, I needed to imagine dividing the half of the number line into ten equal pieces.

Problem 7

For each question, use only the digits 1, 0, 5, 9, and 3. You may not use a digit more than once and you do not need to use all the digits.

  1. Can you make 3 numbers greater than 3,000 but less than 3,500?
  2. Can you make 3 numbers greater than 9,000 but less than 10,000?
  3. Which numbers can you make that are greater than 39,500 but less than 40,000?
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Solution

Sample responses:

  1. 3,095, 3,051, and 3,150
  2. 9,310, 9,531, and 9,053
  3. 39,501 and 39,510

Problem 8

Number line. Scale, 0 to 1 million. Point A, more than halfway between 0 and 1 million. 

Estimate the value of the number labeled A on the number line. Explain your reasoning.

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Solution

Sample responses:

  • The number is more than halfway between 0 and 1, so it is more than 500,000. I tried to divide the line into 100,000s and point A is between the sixth and seventh tick marks, so it's more than 600,000 and less than 700,000. I would guess that it is about 650,000.
  • I cut out the number line and folded in half, then in half again, and then in half one more time. Point A is very close to the fifth fold. I'm not sure what that number is. It would be 58\frac{5}{8} if the number line went from 0 to 1.