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Solving Problems with Line Plots

A 50-minute Grade 5 lesson on line plots of fraction measurements, where the central problem is redistributing: total every measurement, then share the total equally.

Solving Problems with Line Plots is a free 50-minute Grade 5 math lesson plan for Common Core standard 5.MD.B.2 — make line plots of fraction measurements and use fraction operations to answer questions about them. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 5
Length:
50 minutes
Standard:
5.MD.B.2

Grade 5 · Measurement & Data

5.MD.B.2

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.

Objective

Students will be able to make a line plot of measurements in halves, quarters and eighths and use fraction operations to answer questions about it, including finding the amount each would have if the total were shared equally.

Students are successful when they can

  • Makes a line plot on an eighths scale, placing halves and quarters by their eighths names.
  • Finds the total of all the measurements, counting each X, not each scale value.
  • Shares the total equally among the number of measurements and checks the answer is within the range of the data.

What you need

  • Eight clear cups or beakers and a measuring cup marked in eighths
  • Water and food coloring
  • Blank line plot scales from 0 to 1 marked in eighths
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — level them out

6 min
  1. Show eight cups filled to different levels. Ask what would happen if the water were poured back and forth until every cup held the same amount.
  2. Ask whether each cup would end up with more or less than the fullest cup now. Less — and more than the emptiest. Keep that in mind for checking.

Teach — total it, then share it

15 min
  1. Give the amounts in cups: 1/8, 1/4, 1/4, 3/8, 1/2, 5/8, 7/8 and 1. Plot them on an eighths scale from 0 to 1, writing 1/4 as 2/8 and 1/2 as 4/8.
  2. Find the total by going through the X's, not the labels: 1 + 2 + 2 + 3 + 4 + 5 + 7 + 8 eighths = 32 eighths. 32/8 = 4 cups.
  3. Share the total equally among the 8 beakers: 4 ÷ 8 = 4/8 = 1/2 cup each.
  4. Check against the warm-up: 1/2 cup is less than the fullest, 1, and more than the emptiest, 1/8. The answer is sensible.
  5. Ask a second question: what is the difference between the fullest and emptiest beaker? 1 − 1/8 = 7/8 cup.
  6. Ask a third: what fraction of the beakers hold more than 1/2 cup? 3 of the 8 beakers, so 3/8 of them. That fraction is of the beakers, not of a cup.
“To share it out equally, put it all together first, then divide by how many there are. Count every X — the plot shows how many beakers are at each amount.”

Guided practice — pour and prove

14 min
  1. Pairs make a line plot from a new data set of eight measurements in eighths.
  2. They find the total, share it equally, and check the share lies between the smallest and largest value.
  3. One pair at each table checks a share by pouring: the equal amounts are measured into the cups and compared with the answer.

Independent practice

12 min
  1. Students complete a line plot problems page.
  2. A share larger than the biggest measurement or smaller than the smallest is an impossible answer; it is a quick check that catches most of the errors below.

Close

3 min
  1. Ask what the equal share would be if a ninth beaker, holding 1/2 cup, were added.
  2. The total becomes 4 1/2 cups and 4 1/2 ÷ 9 = 1/2 cup each. Adding a value equal to the share leaves the share unchanged, and seeing why is a good place to stop.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Adds each value on the scale once, ignoring stacks of X's.

Why: The scale labels are the visible numbers, so the total has been taken over the labels rather than over the measurements, and repeats have been missed.

Fix: Cross out each X as its value is written into the sum. The number of terms in the sum must equal the number of X's.

Divides the total by the number of different values on the scale, not by the number of measurements.

Why: The columns of the plot are being treated as the things being shared, because a line plot looks like a set of categories.

Fix: Ask what is being shared out and among what: the water, among the beakers. Count the beakers — the X's — and divide by that.

Adds 1/4 + 3/8 to get 4/12.

Why: Numerators and denominators are being added separately, because the eighths scale has not been used to rename the quarters first.

Fix: Rename every value in eighths from the scale before adding: 1/4 = 2/8, so 2/8 + 3/8 = 5/8. Once the pieces are the same size, adding is counting.

If they are not there yet

  • Work with four measurements in quarters only, so the total and the share are easy to model with fraction strips.
  • Write every measurement in eighths in a list before totaling.

If they finish early

  • Find a data set of six measurements whose equal share is 3/8 cup.
  • Find how much a ninth beaker would have to hold to make the equal share of all nine 5/8 cup, and explain it.
  • Compare the equal share with the most common value on the plot and explain why they differ.

Exit ticket

A line plot shows 4 jars holding 1/4, 1/2, 1/2 and 3/4 cup of rice. If the rice were shared equally among the 4 jars, how much would each jar hold?

What to look for: The total is 2 cups and 2 ÷ 4 = 1/2 cup. An answer of 2 cups means the total was not shared; 2/3 cup means it was divided by the three values on the scale rather than the four jars; 3/8 cup means the repeated 1/2 was added only once, giving a total of 1 1/2.

Printable practice for 5.MD.B.2

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Solving Problems with Line Plots

How long does the Solving Problems with Line Plots lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Solving Problems with Line Plots teach?

CCSS.MATH.CONTENT.5.MD.B.2 — 5.MD.B.2, Measurement & Data for Grade 5: “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.” In plain terms, make line plots of fraction measurements and use fraction operations to answer questions about them.

What do I need to teach this lesson?

Eight clear cups or beakers and a measuring cup marked in eighths, water and food coloring, blank line plot scales from 0 to 1 marked in eighths and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: adds each value on the scale once, ignoring stacks of X's; divides the total by the number of different values on the scale, not by the number of measurements and adds 1/4 + 3/8 to get 4/12. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “A line plot shows 4 jars holding 1/4, 1/2, 1/2 and 3/4 cup of rice. If the rice were shared equally among the 4 jars, how much would each jar hold?.” The total is 2 cups and 2 ÷ 4 = 1/2 cup. An answer of 2 cups means the total was not shared; 2/3 cup means it was divided by the three values on the scale rather than the four jars; 3/8 cup means the repeated 1/2 was added only once, giving a total of 1 1/2. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Solving Problems with Line Plots?

Yes — 1 printable 5.MD.B.2 worksheet, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Solving Problems with Line Plots free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on October 22, 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-10-22. Aligned to 5.MD.B.2 of the Common Core State Standards for Mathematics.