Unit 6 More Decimal And Fraction Operations — Unit Plan

TitleTakeawaysVisual / Anchor ChartAssessment
Lesson 1
Place-Value Patterns
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Multiplication and Division Equations (1 problem)

Fill in the blank to make each equation true.

  1. 0.06×10=‾0.06 \times 10 = \underline{\hspace{1cm}}
  2. 60=‾ ×0.660 = \underline{\hspace{1cm}} \times 0.6
  3. ‾ =6÷100\underline{\hspace{1cm}} = 6 \div 100
Show Solution
  1. 0.6
  2. 100
  3. 0.06

Lesson 2
Powers of 10
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Exponential Notation (1 problem)

  1. Write 10,000 and 100,000, using exponential notation. Explain or show your reasoning.

  2. Write 10610^6 as a number. 

Show Solution
  1. 10410^4 and 10510^5. Sample response: 10,000 is 10×10×10×1010 \times 10 \times 10 \times 10, and 100,000 has one more factor of 10.
  2. 1,000,000
Lesson 3
Metric Conversion and Multiplication by Powers of 10
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Kilometers (1 problem)

Complete the table. Explain or show your reasoning.

meters centimeters millimeters
6.5

Show Solution
meters centimeters millimeters
6.5 650 6,500

Sample response:  100×6.5=650100 \times 6.5 =650, 10×650=6,50010 \times 650 = 6,500

Lesson 4
Metric Conversion and Division by Powers of 10
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Han’s Run (1 problem)

Han ran 12,500 meters last week. How many kilometers is that? Explain or show your reasoning.

Show Solution

12.5 km (or equivalent). Sample response: There are 1,000 meters in a kilometer, so I need to divide by 1,000. 12,000÷1,000=1212,000 \div 1,000=12 and 500÷1,000=0.500500 \div 1,000=0.500.

Lesson 5
Multi-step Conversion Problems: Metric Lengths
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Compare Lengths (1 problem)

Jada ran 15.25 kilometers. Han ran 8,500 meters. Who ran farther? How much farther? Explain or show your reasoning.

Show Solution
Jada ran 6.75 kilometers farther. Sample response: 8,500 meters is 8.5 kilometers. So Jada ran 15.25−8.515.25 - 8.5 kilometers farther and that’s 6.75 kilometers.
Lesson 6
Multi-step Conversion Problems: Metric Liquid Volumes
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Dance Team (1 problem)
A dance team used 60 bottles of water during their practices last week. Each bottle holds 750 mL. How many liters of water did the dance team drink during their practices?
Show Solution
45 liters. Sample response: First I found how many mL are in 60 bottles. That’s 60×75060 \times 750 or 45,000 mL. That’s the same as 45 liters.
Lesson 7
Multi-step Conversion Problems: Customary Lengths
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Whiteboard Width (1 problem)

The whiteboard is 4.5 feet in width.

  1. How many inches wide is the whiteboard? Explain or show your reasoning.
  2. How many yards wide is the whiteboard? Explain or show your reasoning.
Show Solution
  1. 54 inches. Sample response: 4.5×12=544.5\times12=54
  2. 1.5 yards (or equivalent). Sample response: 4.5÷3=1.54.5\div3=1.5
Section A Check
Section A Checkpoint
Problem 1

Complete the table, with equivalent measurements. 

kilometers meters centimeters
1.7

15,900

23
Show Solution
kilometers meters centimeters
1.7 1,700 170,000
0.159 159 15,900 
0.023 23 2,300
Problem 2

Choose all representations of the number 100,000,000.

Show Solution
A, E
Problem 3

It is 325 meters around a track. Jada ran around the track 12 times. How many kilometers did Jada run?

Show Solution

3.900 kilometers. Sample response: Jada ran 325×12325 \times 12 meters. That’s 3,250+6503,250 + 650 or 3,9003,900 meters. There are 1,000 meters in a kilometer so each digit moves three places to the right because 3 thousands divided by 1000 is 3 ones and 9 hundreds divided by 1000 is 9 tenths.

Lesson 8
Add and Subtract Fractions
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Sum of Fractions (1 problem)

Find the value of each expression. Explain or show your reasoning. 

  1. 56−13\frac{5}{6}-\frac{1}{3}
  2. 34+12\frac{3}{4}+\frac{1}{2}
Show Solution

  1. 36\frac{3}{6} or 12\frac{1}{2}. Sample response:

    Number line

  2. 114\frac{1}{4} or 54\frac{5}{4}. Sample response: I know that 34\frac{3}{4} = 12+14\frac{1}{2}+\frac{1}{4}, so I added the two halves to make 1 and then I added 14\frac{1}{4}.
Lesson 9
Use Expressions with the Same Value
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Write an Expression (1 problem)

Find the value of 912−14\frac{9}{12} - \frac{1}{4}.

Show Solution

24\frac{2}{4} (or equivalent)

Lesson 10
All Sorts of Denominators
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Sums of Fractions (1 problem)

Find the value of 45+27\frac{4}{5} + \frac{2}{7}.

Show Solution

3835\frac{38}{35} (or equivalent)

Lesson 11
Different Ways to Subtract
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Mixed Differences (1 problem)

Find the value of each expression. Explain or show your reasoning.

  1. 245−310\frac{4}{5}-\frac{3}{10}
  2. 123−34\frac{2}{3}-\frac{3}{4}
Show Solution
  1. 25102\frac{5}{10} (or equivalent). Sample response: I rewrote 2452\frac{4}{5} as 28102 \frac{8}{10} and then subtracted 310\frac{3}{10}.
  2. 1112\frac{11}{12} (or equivalent). Sample response: I added 14\frac{1}{4} to 34\frac{3}{4} to get 1, and then 23\frac{2}{3} more to get 1231\frac{2}{3}. Then 14=312\frac{1}{4} = \frac{3}{12} and 23=812\frac{2}{3} = \frac{8}{12}, so 312+812=1112\frac{3}{12}+\frac{8}{12} = \frac{11}{12}.
Lesson 12
Solve Problems
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Evaluate Expressions (1 problem)

  1. Priya hiked 1231\frac{2}{3} miles. Diego hiked 12\frac{1}{2} mile. How much farther did Priya hike than Diego? Explain or show your reasoning.
  2. On Monday, Andre hiked 34\frac{3}{4} mile in the morning and 1131\frac{1}{3} miles in the afternoon. How far did Andre hike on Monday? Explain or show your reasoning.
Show Solution
  1. 1161\frac{1}{6} miles (or equivalent). Sample response: 123−12=53−12=106−36=76=1161\frac{2}{3}-\frac{1}{2}=\frac{5}{3}-\frac{1}{2}=\frac{10}{6}-\frac{3}{6}=\frac{7}{6}=1\frac{1}{6}
  2. 21122\frac{1}{12} miles (or equivalent). Sample response: 34+113=912+1612=2512=2112\frac{3}{4}+1\frac{1}{3}=\frac{9}{12}+\frac{16}{12}=\frac{25}{12}=2\frac{1}{12}

Lesson 13
Put It All Together: Add and Subtract Fractions
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Fraction Addition and Subtraction (1 problem)

Find the value of each expression. Explain or show your reasoning.

  1.  87−23\frac{8}{7}-\frac{2}{3}
  2.  56+29\frac{5}{6}+\frac{2}{9}
Show Solution
  1.  1021\frac{10}{21} (or equivalent). Sample response: 87−23=2421−1421=1021\frac{8}{7}-\frac{2}{3}=\frac{24}{21}-\frac{14}{21}=\frac{10}{21}
  2. 1918\frac{19}{18} (or equivalent). Sample response: 56+29=1518+418=1918\frac{5}{6}+\frac{2}{9}=\frac{15}{18}+\frac{4}{18}=\frac{19}{18} 
Lesson 14
Representing Fractions on a Line Plot
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A Dozen Eggs (1 problem)

Here are the weights of a different collection of chicken eggs.

What is the combined weight of all the eggs that weigh more than 2122 \frac{1}{2} ounces? Explain or show your reasoning.

Dot plot titled Chicken Eggs from 1 to 3 by 1’s. 
Dot plot titled Chicken Eggs from 1 to 3 by 1’s. Hash marks by eighths. Horizontal axis, Weight, in ounces. Beginning at 1 and 2 eighths, the number of X’s above each eighth increment is 1, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1.

Show Solution
8 ounces (or equivalent). Sample response: There are 2 eggs that weigh 2582\frac{5}{8} ounces and 1 egg that weighs 2342\frac{3}{4} ounces, or 2682\frac{6}{8} ounces. If I add them up, I get 61686\frac{16}{8} ounces which is the same as 8 ounces.
Lesson 15
Problem Solving with Line Plots
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Reflect (1 problem)

In this section, you added and subtracted fractions and worked with data on line plots. What did you get better at during this section?

Show Solution
Sample response: I can add fractions that don’t have the same denominator.
Section B Check
Section B Checkpoint
Problem 1
Elena ran 27102\frac{7}{10} miles. Diego ran 2342\frac{3}{4} miles. How much farther did Diego run than Elena? Explain or show your reasoning.

Show Solution

120\frac{1}{20} mile or equivalent. Sample response: I used 20 as a common denominator and 34=1520\frac{3}{4} = \frac{15}{20} and 710=1420\frac{7}{10} = \frac{14}{20}, so Diego ran 120\frac{1}{20} mile farther.

Problem 2

Find the value of each expression:

  1.  21112−1382\frac{11}{12} - 1\frac{3}{8}
  2.  34+29\frac{3}{4} + \frac{2}{9}

Show Solution
  1. 113241\frac{13}{24} (or equivalent)
  2. 3536\frac{35}{36} (or equivalent)
Problem 3

The line plot shows the amount of blueberries Lin picked on different days during harvesting season. 

Dot plot titled Blueberries from 0 to 3 by 1’s.
Dot plot titled Blueberries from 0 to 3 by 1’s. Hash marks by eighths. Horizontal axis, cups picked. Beginning at 2 eighths, the number of X’s above each eighth increment is 1, 3, 1, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 1.

  1. What is the difference between the greatest number of cups and the least number of cups of blueberries?
  2. How many days did Lin pick more than 1121\frac{1}{2} cups of blueberries?
Show Solution
  1. 2282\frac{2}{8} cups (or equivalent)
  2. 6 days
Lesson 16
Compare Products
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Greater than or Less Than (1 problem)

  1. Is 18×20\frac{1}{8} \times 20 greater than or less than 20? Explain or show your reasoning.

  2. Is 108×20\frac{10}{8} \times 20 greater than or less than 20? Explain or show your reasoning.
Show Solution
  1. Less. Sample response: It takes eight 18\frac{1}{8}s to make 1 whole, so 18\frac{1}{8} of 20 is less than 20.
  2. Greater. Sample response: Since 108\frac{10}{8} is more than 1 whole, 108×20\frac{10}{8} \times 20 is more than 1 group of 20.
Lesson 17
Interpret Diagrams
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Read Books (1 problem)

Diego, Kiran, Elena, and Mai were reading a book.

  • Diego read 40 pages.
  • Elena read 78\frac{7}{8} times as many pages as Diego.
  • Mai read 2122\frac{1}{2} times as many pages as Diego.
  • Kiran read 45\frac{4}{5} times as many pages as Diego.

Write the 4 names in order of how many pages they read, from least to greatest.

Show Solution
Kiran, Elena, Diego, Mai
Lesson 18
Compare without Multiplying
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Comparison Statements (1 problem)
  1. The number N is shown on the number line.

    Number line. Tick mark, 0. Point, labeled N to the right.

    1. Locate and label 43×N\frac{4}{3} \times N on the number line.
    2. Is 43×N\frac{4}{3} \times N less than, equal to, or greater than N? Explain how you know.
Show Solution
    1. Number line
    2. Greater. Sample response: It is to the right on the number line. It is N and then an extra 13\frac{1}{3} of N. 
Lesson 19
Compare to 1
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Compare without Calculating (1 problem)
  1. Is (1−1633)×1114\left(1 - \frac{16}{33}\right) \times \frac{11}{14} greater than, equal to, or less than 1114\frac{11}{14}? Explain or show your reasoning.
  2. Is 4933 ×1114\frac{49}{33}\ \times \frac{11}{14} greater than, equal to, or less than 1114\frac{11}{14}? Explain or show your reasoning.
Show Solution
  1. Less than 1114\frac{11}{14}. Sample response: It’s 1114\frac{11}{14} minus some amount.
  2. Greater than 1114\frac{11}{14}. Sample response: It’s 1114\frac{11}{14} plus some amount as I can see by rewriting 4933\frac{49}{33} as 1+16331 + \frac{16}{33}.
Lesson 20
Will It Always Work?
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Compare (1 problem)
Write >>, <<, or == in each blank to make the statements true.

  1. 1318×113 ‾ 113\frac{13}{18} \times \frac{11}{3} \,\underline{\hspace{0.9cm}} \,\frac{11}{3}
  2. 1916×223 ‾ 223\frac{19}{16} \times \frac{22}{3}\, \underline{\hspace{0.9cm}} \,\frac{22}{3}
  3. 88×15 ‾ 15\frac{8}{8} \times \frac{1}{5}\, \underline{\hspace{0.9cm}} \,\frac{1}{5}
Show Solution
  1. <<
  2. >>
  3. ==
Lesson 21
Weekend Investigation
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No cool-down
Section C Check
Section C Checkpoint
Problem 1
Write >>, <<, or == in the blanks to make each statement true.

  1. 97×187 ‾ 187\frac{9}{7} \times 187 \, \underline{\hspace{1cm}} \, 187
  2. 1919×1113 ‾ 1113\frac{19}{19} \times \frac{11}{13} \, \underline{\hspace{1cm}} \, \frac{11}{13}
  3. 1919×1113 ‾ 1919\frac{19}{19} \times \frac{11}{13} \, \underline{\hspace{1cm}} \, \frac{19}{19}
Show Solution
  1. >>
  2. ==
  3. <<
Problem 2

Number line. Tick mark, labeled 0. 2 points. From left to right, labeled 19 seventeenths, Q.

What could be the value of the number labeled Q?

A. 23×1917\frac{2}{3} \times \frac{19}{17}
B. 1917×77\frac{19}{17} \times \frac{7}{7}
C. 1313×1917\frac{13}{13} \times \frac{19}{17}
D. 32×1917\frac{3}{2} \times \frac{19}{17}✓
Show Solution
D
Unit 6 Assessment
End-of-Unit Assessment