Create and Analyze Fractional Line Plots - 5th Grade Math

1. The line plot shows the weight of each kitten at an animal shelter. What is the combined weight, in pounds, of the two heaviest kittens?
   Answer: $5\frac{3}{4}$ The two heaviest kittens weigh 3 pounds and $2\frac{3}{4}$ pounds: $3 + 2\frac{3}{4} = 5\frac{3}{4}$ pounds. Choice A adds two $2\frac{3}{4}$-pound kittens ($2\frac{3}{4} + 2\frac{3}{4} = 5\frac{1}{2}$), overlooking that the 3-pound kitten is the heaviest and belongs in the pair. Choice C adds 3 twice, but only one kitten weighs 3 pounds. Choice D combines the three heaviest kittens instead of the two heaviest: $3 + 2\frac{3}{4} + 2\frac{3}{4} = 8\frac{1}{2}$.
2. The line plot shows the weights of the rock samples a science class collected. How much heavier, in pounds, is the heaviest sample than the lightest sample?
   Answer: $\frac{5}{8}$ The heaviest sample is $\frac{3}{4}$ pound and the lightest is $\frac{1}{8}$ pound. Rewrite $\frac{3}{4}$ as $\frac{6}{8}$, then subtract: $\frac{6}{8} - \frac{1}{8} = \frac{5}{8}$ pound. Choice A subtracts from $\frac{1}{2}$, the most common weight, rather than from the heaviest. Choice B comes from subtracting the numerators and denominators separately. Choice D adds the two weights instead of subtracting.
3. The line plot shows the lengths of the jump ropes in a gym storage bin. What is the difference, in feet, between the longest jump rope and the shortest jump rope?
   Answer: $2\frac{1}{2}$ The longest rope is $7\frac{1}{2}$ feet and the shortest is 5 feet: $7\frac{1}{2} - 5 = 2\frac{1}{2}$ feet. Choice A subtracts the most common length, 6 feet, from the longest instead of from the shortest: $7\frac{1}{2} - 6 = 1\frac{1}{2}$. Choice B uses 7 as the longest length instead of $7\frac{1}{2}$: $7 - 5 = 2$. Choice D adds the two lengths instead of subtracting: $7\frac{1}{2} + 5 = 12\frac{1}{2}$.
4. The line plot shows the amount of water in each of the 8 beakers on a lab table. If the water were poured out and redistributed so that every beaker held the same amount, how many cups would be in each beaker?
   Answer: $\frac{3}{4}$ First find the total: $(1 \times \frac{1}{4}) + (2 \times \frac{1}{2}) + (2 \times \frac{3}{4}) + (2 \times 1) + (1 \times 1\frac{1}{4}) = 6$ cups. Then divide by the 8 beakers: $6 \div 8 = \frac{3}{4}$ cup each. Choice B divides by 6 instead of 8. Choice C is the greatest amount shown, not the equal share. Choice D is the total before dividing.
5. The line plot shows the number of hours each student in a book club read last week. What is the total number of hours read by the students who read more than 2 hours?
   Answer: $8$ Two students read $2\frac{1}{2}$ hours and one student read 3 hours: $(2 \times 2\frac{1}{2}) + 3 = 5 + 3 = 8$ hours. Choice A is the number of those students, not their hours. Choice B leaves out the student who read 3 hours. Choice C adds $2\frac{1}{2}$ and 3 only once each instead of once per X.
6. The line plot shows how far each member of a walking group went on Saturday. How many members walked at least 1 mile?
   Answer: $4$ "At least 1 mile" includes 1 mile itself, so count the X's above 1, $1\frac{1}{4}$, and $1\frac{1}{2}$: $2 + 1 + 1 = 4$ members. Choice A leaves out the members who walked exactly 1 mile. Choice C adds those members' distances instead of counting them. Choice D counts the members who walked less than 1 mile.
7. The line plot shows the lengths of the green bean pods Malik picked from his garden. What is the combined length, in inches, of all the pods Malik picked?
   Answer: $16\frac{3}{4}$ Multiply each length by the number of X's above it, then add: $(2 \times 2) + (1 \times 2\frac{1}{4}) + (3 \times 2\frac{1}{2}) + (1 \times 3) = 4 + 2\frac{1}{4} + 7\frac{1}{2} + 3 = 16\frac{3}{4}$ inches. Choice A is the number of pods, not their length. Choice B adds each labeled length only once instead of once per X. Choice C adds all five labels, including $2\frac{3}{4}$, which has no pods.
8. The line plot shows the weight of trail mix in each bag a hiking club packed. What is the total weight, in pounds, of all the trail mix the club packed?
   Answer: $2\frac{1}{4}$ Multiply each weight by its number of X's and add: $(3 \times \frac{1}{8}) + (2 \times \frac{1}{4}) + (1 \times \frac{3}{8}) + (2 \times \frac{1}{2}) = \frac{3}{8} + \frac{4}{8} + \frac{3}{8} + \frac{8}{8} = \frac{18}{8} = 2\frac{1}{4}$ pounds. Choice A adds each labeled weight only once. Choice B misses one bag at $\frac{1}{8}$ pound. Choice D is the number of bags.
9. The line plot shows the snowfall recorded on each of the 10 days it snowed in Jonesville last winter. What was the total snowfall, in inches, on the days when less than $\frac{3}{8}$ inch fell?
   Answer: $\frac{3}{4}$ Less than $\frac{3}{8}$ inch means the days at $\frac{1}{8}$ inch and $\frac{1}{4}$ inch: $(2 \times \frac{1}{8}) + (2 \times \frac{1}{4}) = \frac{2}{8} + \frac{4}{8} = \frac{6}{8} = \frac{3}{4}$ inch. Choice A adds $\frac{1}{8}$ and $\frac{1}{4}$ only once each. Choice C also includes the three days at $\frac{3}{8}$ inch, which are not less than $\frac{3}{8}$. Choice D is the number of those days, not the snowfall.
10. The line plot shows the lengths of earthworms found in a garden. What is the range of the earthworm lengths, and how many earthworms were measured in total?
    Answer: Range of $\frac{7}{8}$ inch with exactly 13 earthworms measured total From the line plot: 1 earthworm at $\frac{3}{8}$ inch, 3 earthworms at $\frac{1}{2}$ inch, 2 earthworms at $\frac{5}{8}$ inch, 4 earthworms at $\frac{3}{4}$ inch, 2 earthworms at $1$ inch, 1 earthworm at $1\frac{1}{4}$ inches. Total earthworms: 1+3+2+4+2+1=13. Range = maximum - minimum = $1\frac{1}{4} - \frac{3}{8} = \frac{5}{4} - \frac{3}{8} = \frac{10}{8} - \frac{3}{8} = \frac{7}{8}$ inch. Choice B has wrong range and wrong count. Choice C has wrong range. Choice D has wrong count.
11. A teacher recorded student jump distances on the line plot shown. What is the difference between the longest jump and the most common jump distance?
    Answer: $\frac{5}{8}$ foot difference, with $2\frac{1}{8}$ feet being most common From the line plot, the most frequent (mode) jump distance is $2\frac{1}{8}$ feet with 4 occurrences. The longest jump is $2\frac{3}{4}$ feet. The difference is $2\frac{3}{4} - 2\frac{1}{8} = 2\frac{6}{8} - 2\frac{1}{8} = \frac{5}{8}$ foot. Choice A identifies wrong mode. Choice B has wrong difference calculation. Choice D identifies wrong mode and has wrong difference.
12. A student measured the lengths of 10 pencils (in inches) to the nearest $\tfrac{1}{4}$ inch. The data can be represented and analyzed using line plots. Line plot (inches): Number line (inches): $5$ $5\tfrac{1}{4}$ $5\tfrac{1}{2}$ $5\tfrac{3}{4}$ $6$ Marks: - $5$: XX - $5\tfrac{1}{4}$: XXX - $5\tfrac{1}{2}$: XX - $5\tfrac{3}{4}$: X - $6$: XX Which claim about the measurements is incorrect?
    Answer: Exactly 5 pencils are longer than $5\tfrac{1}{2}$ inches. Line plots show measurement data by placing marks above a number line to represent the frequency of pencil lengths. Fractions are represented on the number line as quarters, such as 5 1/4 or 5 3/4, for lengths to the nearest quarter inch. To read the plot, count the X marks at each point; for lengths longer than 5 1/2, the total is three (one at 5 3/4 and two at 6). This pencil data connects to identifying incorrect claims, such as stating exactly five pencils longer than 5 1/2 when the plot shows only three. A common misconception is including the boundary value in 'longer than' counts, but 'longer than' excludes equals. Line plots help analyze data by allowing precise subgroup tallies and error detection. They support verifying statements through visual and numerical checks.
13. The line plot shows the amount of flour a bakery used in each of 6 batches of muffins. If the bakery had used the same amount of flour in every batch, how many cups would each batch have used?
    Answer: $1\frac{1}{2}$ First find the total flour used: $(1 \times \frac{1}{2}) + (2 \times 1) + (2 \times 2) + (1 \times 2\frac{1}{2}) = \frac{1}{2} + 2 + 4 + 2\frac{1}{2} = 9$ cups. Then divide by the 6 batches: $9 \div 6 = 1\frac{1}{2}$ cups per batch. Choice B is the most common amount, not the equal share. Choice C is the greatest amount shown. Choice D is the total before dividing.
14. Students measured the thickness of books and created the line plot shown. If you arranged the books from thinnest to thickest, what would be the thickness of the book in the middle position (median)?
    Answer: $1\frac{1}{8}$ inches, which is the 6th book out of 11 total books From the line plot: 1 book at $\frac{3}{4}$ inch, 2 books at $\frac{7}{8}$ inch, 3 books at $1\frac{1}{8}$ inches, 2 books at $1\frac{1}{4}$ inches, 2 books at $1\frac{1}{2}$ inches, 1 book at $1\frac{5}{8}$ inches. Total books: 1+2+3+2+2+1=11. For 11 books, the median is the 6th book when arranged in order. Counting from thinnest: positions 1 is $\frac{3}{4}$, positions 2-3 are $\frac{7}{8}$, positions 4-6 are $1\frac{1}{8}$. So the 6th book has thickness $1\frac{1}{8}$ inches. Choice B has wrong median value. Choice C has wrong book count. Choice D has wrong median value.

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