Create and Interpret Fractional Line Plots - 4th Grade Math

1. A carpenter measured a set of wood screws: two screws measured $\frac{1}{4}$ inch, three screws measured $\frac{1}{2}$ inch, three screws measured $\frac{5}{8}$ inch, four screws measured $\frac{3}{4}$ inch, and two screws measured $\frac{7}{8}$ inch. If the screws measuring $\frac{1}{2}$ inch and $\frac{7}{8}$ inch are removed from the collection, what length appears most frequently among the remaining screws?
   Answer: $\frac{3}{4}$ inch After removing the 1/2-inch and 7/8-inch screws, the remaining lengths are 1/4 inch (2 screws), 5/8 inch (3 screws), and 3/4 inch (4 screws), so 3/4 inch appears most often. Choice A has the second-highest count, not the highest. Choice C has the fewest screws remaining. Choice D was removed from the collection and can't be the answer.
2. Based on the line plot of student jump distances, how many students jumped farther than $1\frac{1}{4}$ feet but not more than $1\frac{3}{4}$ feet?
   Answer: 5 students The correct answer is A, 5 students, based on counting the data points on the line plot that fall in the given range. Choice B overcounts by including students outside the range. Choice C undercounts by leaving out students who belong in the range. Choice D is close but still misses one student who should be included.
3. The line plot shows the weights of packages in pounds. What is the total weight of all packages that weigh less than $1$ pound?
   Answer: $3\frac{3}{4}$ pounds The correct answer is B, $3\frac{3}{4}$ pounds, based on adding the weights of every package on the line plot that weighs less than 1 pound. Choice A misses some of the data points shown. Choice C adds in a package that weighs 1 pound or more, which should not be included. Choice D only accounts for a few of the values instead of the full set below 1 pound.
4. A baker recorded cookie thicknesses: 7 cookies were thicker than $\frac{1}{2}$ inch, and 4 cookies were exactly $\frac{1}{2}$ inch thick. How many more cookies were thicker than $\frac{1}{2}$ inch than were exactly $\frac{1}{2}$ inch thick?
   Answer: 3 more cookies Subtracting the number of cookies exactly $\frac{1}{2}$ inch thick from the number thicker than $\frac{1}{2}$ inch gives $7 - 4 = 3$ more cookies. Choice B overstates the difference, as if there were more thick cookies than were actually recorded. Choice C understates the difference by one, missing part of the gap between the two groups. Choice D also understates the difference by one in the other direction. Choice A correctly matches the true difference between the two cookie counts.
5. Students measured their hand spans in inches. According to the line plot shown, what fraction of students had hand spans of $5\frac{3}{4}$ inches or greater?
   Answer: $\frac{2}{3}$ of the students because 8 out of 12 students qualify The correct answer is A, $\frac{2}{3}$ of the students, based on counting the 8 out of 12 students on the line plot whose hand spans meet the threshold. Choice B undercounts by leaving out some qualifying students. Choice C and Choice D are both close but come from miscounting one or two data points on the plot.

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