Line Plots

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Line Plots · Grade 5 · Worksheet 3

1. Aroha is measuring the lengths of different sticks she collected for a school art project. She measured each stick to the nearest eighth of an inch and recorded these lengths: 9 3/8 in, 9 5/8 in, 9 1/2 in, 9 7/8 in, 9 3/8 in, 9 5/8 in, 9 1/2 in, 9 3/8 in, 9 7/8 in, 9 5/8 in, 9 1/2 in, and 9 7/8 in. If Aroha makes a line plot of all these measurements, how many sticks are longer than 9 1/2 inches? Answer: 6 Solution: List all the measurements: 9 3/8, 9 5/8, 9 1/2, 9 7/8, 9 3/8, 9 5/8, 9 1/2, 9 3/8, 9 7/8, 9 5/8, 9 1/2, 9 7/8 Identify which measurements are longer than 9 1/2 inches.
   Full step-by-step solution

   Step 1: List all the measurements: 9 3/8, 9 5/8, 9 1/2, 9 7/8, 9 3/8, 9 5/8, 9 1/2, 9 3/8, 9 7/8, 9 5/8, 9 1/2, 9 7/8 Step 2: Identify which measurements are longer than 9 1/2 inches. Compare each to 9 1/2 (which is 9 4/8): - 9 3/8 is less than 9 4/8, so NOT longer - 9 5/8 is greater than 9 4/8, so YES - 9 1/2 is equal to 9 4/8, so NOT longer - 9 7/8 is greater than 9 4/8, so YES Step 3: Count how many sticks are longer than 9 1/2: - 9 5/8 appears 3 times - 9 7/8 appears 3 times - Total = 3 + 3 = 6 The answer is 6 sticks.

2. A rectangular prism is built from centimeter cubes. It has a length of 12 cubes, a width of 8 cubes, and a height of 5 cubes. What is the total volume of the prism in cubic centimeters? Answer: 480 Solution: We have a rectangular prism made of centimeter cubes. The length is 12 cubes, the width is 8 cubes, and the height is 5 cubes. Each cube has a volume of 1 cubic centimeter.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular prism made of centimeter cubes. The length is 12 cubes, the width is 8 cubes, and the height is 5 cubes. Each cube has a volume of 1 cubic centimeter. Step 2: Recall the formula for the volume of a rectangular prism. Volume = length × width × height. Step 3: Substitute the given values into the formula. Length = 12 cm Width = 8 cm Height = 5 cm Volume = 12 × 8 × 5. Step 4: Perform the multiplication step by step. First, multiply 12 and 8: 12 × 8 = 96. Step 5: Multiply the result by the height: 96 × 5 = 480. Step 6: State the final answer with units. The total volume is 480 cubic centimeters. Final answer: 480

3. Kaia is measuring the lengths of different leaves she collected for a nature project. She measured each leaf to the nearest eighth of an inch and recorded the lengths: 1 3/8 in, 1 5/8 in, 1 1/2 in, 1 3/8 in, 1 7/8 in, 1 5/8 in, 1 1/2 in, 1 3/8 in, 1 7/8 in, and 1 1/2 in. If she makes a line plot of all these measurements, what is the total combined length of all the leaves? Answer: 15 5/8 Solution: - 1 3/8 in: 3 leaves - 1 1/2 in: 3 leaves - 1 5/8 in: 2 leaves - 1 7/8 in: 2 leaves Convert each mixed number to an improper fraction with denominator 8: - 1 3/8 = 11/8 - 1 1/2 = 1 4/8 = 12/8 - 1 5/8 = 13/8 - 1 7/8 = 15/8 - 3 × 11/8 = 33/8 - 3 × 12/8 = 36/8 - 2 × 13/8 = 26/8 - 2 × 15/8 = 30/8…
   Full step-by-step solution

   Step 1: Count how many of each measurement there are: - 1 3/8 in: 3 leaves - 1 1/2 in: 3 leaves - 1 5/8 in: 2 leaves - 1 7/8 in: 2 leaves Step 2: Convert each mixed number to an improper fraction with denominator 8: - 1 3/8 = 11/8 - 1 1/2 = 1 4/8 = 12/8 - 1 5/8 = 13/8 - 1 7/8 = 15/8 Step 3: Multiply each measurement by the count: - 3 × 11/8 = 33/8 - 3 × 12/8 = 36/8 - 2 × 13/8 = 26/8 - 2 × 15/8 = 30/8 Step 4: Add all the totals: 33/8 + 36/8 + 26/8 + 30/8 = 125/8 Step 5: Convert to a mixed number: 125 ÷ 8 = 15 remainder 5, so 125/8 = 15 5/8 The total combined length of all the leaves is 15 5/8 inches.

4. A line plot shows the lengths of 5 ribbons in inches: 7 3/8, 7 5/16, 7 11/16, 7 1/2, 7 7/8. What is the difference between the longest and shortest ribbon? Answer: 9/16 Solution: Convert all measurements to sixteenths of an inch: 7 3/8 = 7 + 6/16 = 7 6/16 7 5/16 = 7 + 5/16 = 7 5/16 7 11/16 = 7 + 11/16 = 7 11/16 7 1/2 = 7 + 8/16 = 7 8/16 7 7/8 = 7 + 14/16 = 7 14/16 Longest: 7 14/16 (7 7/8) Shortest: 7 5/16 7 14/16 - 7 5/16 = (14/16 - 5/16) = 9/16 Check if 9/16 can be…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 7 3/8 = 7 + 6/16 = 7 6/16 7 5/16 = 7 + 5/16 = 7 5/16 7 11/16 = 7 + 11/16 = 7 11/16 7 1/2 = 7 + 8/16 = 7 8/16 7 7/8 = 7 + 14/16 = 7 14/16 Step 2: Identify the longest and shortest ribbons: Longest: 7 14/16 (7 7/8) Shortest: 7 5/16 Step 3: Find the difference: 7 14/16 - 7 5/16 = (14/16 - 5/16) = 9/16 Step 4: Check if 9/16 can be simplified. Since 9 and 16 share no common factors other than 1, the fraction is already in simplest form. The answer is 9/16 inch.

5. Mason is measuring the lengths of different screws in his toolbox. He measures each screw to the nearest eighth of an inch and records these lengths: 3 1/8 in, 3 3/8 in, 3 5/8 in, 3 1/2 in, 3 7/8 in, 3 3/8 in, 3 5/8 in, 3 1/8 in, 3 7/8 in, 3 1/2 in, 3 3/8 in, and 3 5/8 in. If Mason creates a line plot of the data, how many screws measure exactly 3 3/8 inches? Answer: 3 Solution: List all the measurements: 3 1/8, 3 3/8, 3 5/8, 3 1/2, 3 7/8, 3 3/8, 3 5/8, 3 1/8, 3 7/8, 3 1/2, 3 3/8, 3 5/8. Count how many times 3 3/8 appears: positions 2, 6, and 11. That is 3 times.
   Full step-by-step solution

   Step 1: List all the measurements: 3 1/8, 3 3/8, 3 5/8, 3 1/2, 3 7/8, 3 3/8, 3 5/8, 3 1/8, 3 7/8, 3 1/2, 3 3/8, 3 5/8. Step 2: Count how many times 3 3/8 appears: positions 2, 6, and 11. That is 3 times. Step 3: So, there are 3 screws that measure exactly 3 3/8 inches. The answer is 3.

6. A line plot shows the lengths of 5 pencils in inches: 5 1/8, 5 3/16, 5 5/8, 5 11/16, 5 7/8. What is the difference between the longest and shortest pencil? Answer: 3/4 Solution: Convert all measurements to sixteenths of an inch: 5 1/8 = 5 + 2/16 = 5 2/16 5 3/16 = 5 + 3/16 = 5 3/16 5 5/8 = 5 + 10/16 = 5 10/16 5 11/16 = 5 + 11/16 = 5 11/16 5 7/8 = 5 + 14/16 = 5 14/16 Longest: 5 14/16 (5 7/8) Shortest: 5 2/16 (5 1/8) 5 14/16 - 5 2/16 = (14/16 - 2/16) = 12/16 12/16 = 3/4…
   Full step-by-step solution

   Step 1: Convert all measurements to sixteenths of an inch: 5 1/8 = 5 + 2/16 = 5 2/16 5 3/16 = 5 + 3/16 = 5 3/16 5 5/8 = 5 + 10/16 = 5 10/16 5 11/16 = 5 + 11/16 = 5 11/16 5 7/8 = 5 + 14/16 = 5 14/16 Step 2: Identify the longest and shortest pencils: Longest: 5 14/16 (5 7/8) Shortest: 5 2/16 (5 1/8) Step 3: Find the difference: 5 14/16 - 5 2/16 = (14/16 - 2/16) = 12/16 Step 4: Simplify the fraction: 12/16 = 3/4 The answer is 3/4 inch.

7. Noah is measuring the lengths of different colored pipe cleaners in his art kit. He measures each pipe cleaner to the nearest eighth of an inch and records these lengths: 6 1/8 in, 6 3/8 in, 6 1/2 in, 6 5/8 in, 6 7/8 in, 6 1/8 in, 6 3/8 in, 6 5/8 in, 6 1/2 in, 6 7/8 in, 6 3/8 in, and 6 5/8 in. If Noah makes a line plot of all these measurements, how many pipe cleaners are shorter than 6 5/8 inches? Answer: 7 Solution: List all the measurements: 6 1/8, 6 3/8, 6 1/2, 6 5/8, 6 7/8, 6 1/8, 6 3/8, 6 5/8, 6 1/2, 6 7/8, 6 3/8, 6 5/8. Identify which measurements are shorter than 6 5/8 inches.
   Full step-by-step solution

   Step 1: List all the measurements: 6 1/8, 6 3/8, 6 1/2, 6 5/8, 6 7/8, 6 1/8, 6 3/8, 6 5/8, 6 1/2, 6 7/8, 6 3/8, 6 5/8. Step 2: Identify which measurements are shorter than 6 5/8 inches. Compare each to 6 5/8 (which is 6 5/8): - 6 1/8 is less than 6 5/8, so YES - 6 3/8 is less than 6 5/8, so YES - 6 1/2 (which is 6 4/8) is less than 6 5/8, so YES - 6 5/8 is equal to 6 5/8, so NOT shorter - 6 7/8 is greater than 6 5/8, so NOT shorter Step 3: Count how many pipe cleaners are shorter than 6 5/8: - 6 1/8 appears 2 times - 6 3/8 appears 3 times - 6 1/2 appears 2 times - Total = 2 + 3 + 2 = 7 The answer is 7 pipe cleaners.