Section B Practice Problems

Problem 1

Mai and Tyler play a game. They each roll 6 dice. They must make each number they roll either a tenth or a hundredth. Then they find the sum of those 6 numbers

  1. Mai rolls 6 sixes. How close can she get to a sum of 1 (without going over)?
  2. Tyler rolls 6 fours. How close can he get to a sum of 1 (without going over)?
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Solution
  1. 0.9. Sample response: She can choose one 0.6 and the rest have to be 0.06 or else she goes over.
  2. 0.96. Sample response: He can choose two 0.4s and the rest have to be 0.04 or else he goes over.

Problem 2

  1. Which whole number is 3.62+1.493.62 + 1.49 closest to? Explain or show your reasoning.

  2. Find the value of 3.62+1.493.62 + 1.49.

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Solution
  1. 5. Sample response: The whole numbers add up to 4 and the two decimals are a little more than 1, but close to 1.
  2. 5.11. Sample responses:
    • addition algorithm with decimals
    • 3+1=43 + 1 = 4
      0.6+0.4=10.6 + 0.4 = 1
      0.02+0.09=0.110.02 + 0.09 = 0.11
      4+1+0.11=5.114 + 1 + 0.11 = 5.11

Problem 3

Find the value of the expression 215.7+64.94215.7 + 64.94.

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Solution
280.64. Sample response:
Addition algorithm.

Problem 4

  1. Which whole number is 9.36−6.529.36 - 6.52 closest to? Explain or show your reasoning.

  2. Find the value of 9.36−6.529.36 - 6.52.
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Solution
  1. Sample responses:
    • 3. 9−6=39 - 6 = 3 and the decimal parts of the two numbers are pretty close in value.
    • 2. 9.36 rounds to 9 and 6.52 rounds to 7. 9−7=29 - 7 = 2
  2. 2.84. Sample response: 9−6.5=2.59 - 6.5 = 2.5, 0.36−0.02=0.340.36 - 0.02 = 0.34, 2.5+0.34=2.842.5 + 0.34 = 2.84

Problem 5

  1. Here is how Elena found the value of 15.37−8.1915.37 - 8.19.

    Subtract. 15 and 37 hundredths, minus, 8 and 19 hundredths, equals, 7 and 18 hundredths.

    Explain her calculations and the meaning of the 15 written above the digit 5 and the 17 written above the digit 7 in 15.37.

  2. Use Elena's algorithm to calculate 52.63−17.5552.63 - 17.55.
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Solution
  1. Sample response: Elena could not subtract 9 hundredths from 7 hundredths so she broke up a tenth from 15.37 to make 10 hundredths and then subtracted. She also broke a 10 into 10 ones to subtract 8 from 15 instead of from 5.
  2. 35.08. Sample response:
    Subtraction algorithm.

Problem 6

Find the value of each expression.

  1. 37.06−22.5737.06 - 22.57
  2. 555−4.44555 - 4.44
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Solution
  1. 14.49. Sample response:
    subtraction algorithm
  2. 550.56. Sample response:
    4.44+0.56=54.44 + 0.56 = 5
    5+550=5555 + 550 = 555
    0.56 + 550 = 550.56

Problem 7

  1. Kiran finds the value of 35.16−18.7935.16 - 18.79 with these calculations.

    18.79+0.21=1918.79 + 0.21 = 19
    19+16.16=35.1619 + 16.16 = 35.16
    16.16+0.21=16.3716.16 + 0.21 = 16.37

    Explain why Kiran’s strategy works.
  2. Find the difference 22.86−9.9922.86 - 9.99 in a way that makes sense to you.
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Solution
  1. Sample response: Kiran finds what he needs to add to 18.79 to get 35.16. This strategy allows him to work with easier numbers. He first adds 0.21 to get 19 and then adds 16.16 to get the total, 35.16. He then finds the total amount he added, 16.16+0.21=16.3716.16 + 0.21 = 16.37.
  2. 12.87. Sample response: I can first add 0.01 to 9.99 to get 10 and then 12.86 more to get 22.86. That's 12.86+0.01=12.8712.86 + 0.01 = 12.87.

Problem 8

Lin tries to use the digits 1, 3, 4, 2, 5, and 6 to make 2 two-digit decimals whose sum is 1. Each digit can only be used once.

  1. Explain why this can’t be done.
  2. What is the closest Lin can get to 1? Explain how you know.
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Solution
  1. Sample response: The hundredths would have to be 4 and 6 because they are the only numbers that add up to 10 which means there are 0 hundredths in the sum. But it is not possible to make 9 more tenths with 1, 2, 3, and 5.
  2. 0.99. Sample response: 0.64+0.350.64 + 0.35