Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A line plot shows how often each value appears in a data set by stacking an X above a number line for every measurement. In fifth grade the measurements are in fractions of a unit, halves, quarters and eighths, so the number line must be marked with those intervals. A class might measure the lengths of pencil stubs to the nearest 1/8 inch, or the amount of water left in several beakers.
The real purpose is to use the data. Students answer questions with the fraction operations they learn this year: the total of all measurements, the difference between the longest and shortest, or how much each item would hold if the total were shared out equally. The standard's example asks how much liquid each beaker would contain if all the liquid were redistributed evenly, which is finding the mean using fraction addition and division. Reading a line plot accurately, including counting each X, is the first step.
Students sometimes space 1/8, 1/4 and 1/2 equally apart. Converting all values to eighths before drawing keeps spacing correct.
When totaling, a value with three Xs must be counted three times. Students who add each value once get too small a total.
The tallest stack shows the most frequent measurement, not the biggest one. Students should read the scale as well as the stacks.
To redistribute equally, the total must be divided by how many items there are, which is the number of Xs.
A line plot shows water in 6 identical beakers: 1/4 L (2 beakers), 1/2 L (3 beakers) and 3/4 L (1 beaker). If the water were shared equally, how much would each beaker hold?
Answer: Each beaker would hold 11/24 of a liter.
Have students collect real data, such as measuring hand spans to the nearest 1/4 inch, so the line plot means something to them. Then pose a range of questions from simple reading to multi-step fraction calculations.
Assessment items often show a completed line plot and ask for the total, the difference between two values, or the number of measurements above a certain value.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 3 (also accepted: 3 feet)
3 × 1/2 = 3/2 and 2 × 3/4 = 6/4 = 3/2. 3/2 + 3/2 = 6/2 = 3 feet.
Answer: D) 1 1/2
2 5/8 - 1 1/8 = 1 4/8 = 1 1/2 inches.
Answer: 1 1/2 (also accepted: 1 4/8, 3/2, 12/8)
In eighths: 2/8 + 6/8 + 4/8 = 12/8 = 1 4/8 = 1 1/2 inches.
Answer: B) At the 6th mark
3/4 = 6/8, so it sits at the 6th eighth-mark after 0.
Answer: 1/2 (also accepted: 2/4, 1/2 cup)
Total = 1/2 + 1/4 + 3/4 + 1/2 = 2 cups. 2 ÷ 4 = 1/2 cup each.
A full lesson with slides, activities and an exit ticket on line plots with fractional data, pitched to grade 5 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 5.MD.B.2 with an answer key, ready in about a minute.
Make a worksheet →Turn line plots with fractional data into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Measurements in halves, quarters and eighths of a unit.
Not by name, but redistributing a total equally, as in the standard's beaker example, is the same idea and prepares students for the mean in sixth grade statistics.