CH08-04 lesson

Solving Problems Using Line Plots Learning Activity

A focused Grade 5 learning session for Solving Problems Using Line Plots using visual models, worked examples, strategy guidance, and a short mastery check.

Start the lesson Print practice sample
15
minutes
6
lesson parts
11
practice items
Learning goal

Students will solve problems using operations and information from line plots.

Student goal: I can use line plots to solve problems.

Helpful first: Line Plots with Fractional Data Word Problems with Fraction Addition and Subtraction
concept

Learn the Idea

Solving Problems Using Line Plots is the Grade 5 skill of students use operations on fractions to solve problems involving information presented in line plots. They find total amounts, differences, and averages from the fractional data displayed.

What do the numbers represent, and what strategy shows the idea clearly?

Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.

The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.

  • Identify what each number, unit, or symbol means before solving.
  • Choose a model or strategy that makes the relationship visible.
  • Explain why the answer fits the situation instead of stopping at computation.
  • Use the topic language from class discussions: Students use operations on fractions to solve problems involving information presented in line plots. They find total amounts, differences, and averages from the fractional data displayed.
visual model

See the Math

Visual Model 1

Question: The line plot below shows lengths of ribbon pieces, in inches, collected by an art club: The club uses only the pieces longer than \(1\frac{1}{2}\) inches. What is the total length of those pieces?

Grade 5 Solving Problems Using Line Plots figure 1

  • A. \(3\frac{3}{4}\) inches
  • B. \(4\frac{1}{2}\) inches
  • C. \(5\frac{3}{4}\) inches
  • D. \(6\frac{1}{2}\) inches

How the model helps: The pieces longer than \(1\frac{1}{2}\) inches are one piece of \(1\frac{3}{4}\) inches and one piece of \(2\) inches. Their total length is \(1\frac{3}{4}+2=3\frac{3}{4}\) inches.

worked example

Follow a Worked Example

Example 1

Question: The line plot shows lengths of ribbon pieces, in yards: What is the total length of all the ribbon pieces?

Grade 5 Solving Problems Using Line Plots figure 3

  • A. \(5\frac{1}{4}\) yards
  • B. \(5\frac{3}{4}\) yards
  • C. \(6\frac{1}{4}\) yards
  • D. \(6\frac{3}{4}\) yards
  1. Add the ribbon lengths shown: \(2(\frac{1}{4})+3(\frac{1}{2})+2(\frac{3}{4})+1+1\frac{1}{4}=5\frac{3}{4}\) yards.

Answer: \(5\frac{3}{4}\) yards

Example 2

Question: The line plot shows the heights (in half-inches) of plant seedlings in a garden: What is the total height of all seedlings in inches?

Grade 5 Solving Problems Using Line Plots figure 4

  • A. 21 inches
  • B. 22 inches
  • C. 23 inches
  • D. 24 inches
  1. The labels are in half-inches.
  2. The total is \((2 \times 4) + (4 \times 2) + (6 \times 2) + (8 \times 1) + (10 \times 1) = 46\) half-inches.
  3. Since 2 half-inches make 1 inch, \(46 \div 2 = 23\) inches.

Answer: 23 inches

real world

Connect It to a Real Situation

Problem 1

Question: The line plot shows distances (in meters) students jumped: What is the range of the data?

Grade 5 Solving Problems Using Line Plots figure 6

  • A. 2 meters
  • B. 3 meters
  • C. 4 meters
  • D. 5 meters

Answer: 3 meters

Why it works: Lowest: 2 m (2 marks), Highest: 5 m (1 mark). Range = \(5 - 2 = 3\) meters.

strategy

Avoid Mistakes and Choose a Strategy

  • Starting the computation before identifying what the numbers, units, or parts represent.
  • Skipping the model or visual and relying only on a memorized rule.
  • Forgetting to estimate, which makes it easier to miss an unreasonable answer.
  • Stopping at a number without explaining what the answer means in context.
  • Read the situation slowly and name what each number or label represents.
  • Use a model, table, chart, number line, or sketch before finishing the computation.
  • Estimate first so you already know the answer's approximate size.
  • Check the answer with an inverse operation, another representation, or a sentence explanation.
  • Say the math idea out loud in simple words before writing the final answer.
summary

Remember the Key Idea

Solving Problems Using Line Plots gets easier when students read the model, track what each number means, and explain why the answer fits the situation.

GOLDEN RULE

Understand the structure first, then solve, check, and explain why the answer makes sense.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G5-C06-T05-Q001 About 1 min

The line plot below shows lengths of ribbon pieces, in inches, collected by an art club: The club uses only the pieces longer than \(1\frac{1}{2}\) inches. What is the total length of those pieces?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q001
  1. A \(3\frac{3}{4}\) inches
  2. B \(4\frac{1}{2}\) inches
  3. C \(5\frac{3}{4}\) inches
  4. D \(6\frac{1}{2}\) inches
Check answer and explanation

Answer A: \(3\frac{3}{4}\) inches

The pieces longer than \(1\frac{1}{2}\) inches are one piece of \(1\frac{3}{4}\) inches and one piece of \(2\) inches. Their total length is \(1\frac{3}{4}+2=3\frac{3}{4}\) inches.

G5-C06-T05-Q002 About 1 min

The line plot shows the lengths (in inches) of ribbons collected by the art club: If the total ribbon length is shared equally among 4 posters, how much ribbon goes on each poster?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q002
  1. A \(7\frac{1}{4}\) inches
  2. B \(7\frac{1}{2}\) inches
  3. C \(7\frac{3}{4}\) inches
  4. D \(8\) inches
Check answer and explanation

Answer C: \(7\frac{3}{4}\) inches

Add the ribbon lengths shown by the marks: \((1 \times 3) + (3 \times 2) + (5 \times 3) + (7 \times 1) = 31\) inches. Sharing 31 inches equally among 4 posters gives \(31 \div 4 = 7\frac{3}{4}\) inches per poster.

guided

1 question
G5-C06-T05-Q003 About 1 min

The line plot shows lengths of ribbon pieces, in yards: What is the total length of all the ribbon pieces?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q003
  1. A \(5\frac{1}{4}\) yards
  2. B \(5\frac{3}{4}\) yards
  3. C \(6\frac{1}{4}\) yards
  4. D \(6\frac{3}{4}\) yards
Check answer and explanation

Answer B: \(5\frac{3}{4}\) yards

Add the ribbon lengths shown: \(2(\frac{1}{4})+3(\frac{1}{2})+2(\frac{3}{4})+1+1\frac{1}{4}=5\frac{3}{4}\) yards.

practice

5 questions
G5-C06-T05-Q004 About 1 min

The line plot shows the heights (in half-inches) of plant seedlings in a garden: What is the total height of all seedlings in inches?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q004
  1. A 21 inches
  2. B 22 inches
  3. C 23 inches
  4. D 24 inches
Check answer and explanation

Answer C: 23 inches

The labels are in half-inches. The total is \((2 \times 4) + (4 \times 2) + (6 \times 2) + (8 \times 1) + (10 \times 1) = 46\) half-inches. Since 2 half-inches make 1 inch, \(46 \div 2 = 23\) inches.

G5-C06-T05-Q005 About 1 min

The line plot shows lengths of ribbon pieces, in inches: What is the total length of the pieces longer than \(1\) inch?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q005
  1. A \(2\frac{3}{4}\) inches
  2. B \(6\frac{1}{2}\) inches
  3. C \(5\) inches
  4. D \(4\) inches
Check answer and explanation

Answer D: \(4\) inches

The pieces longer than \(1\) inch are two pieces of \(1\frac{1}{4}\) inches and one piece of \(1\frac{1}{2}\) inches. Their total is \(1\frac{1}{4}+1\frac{1}{4}+1\frac{1}{2}=4\) inches.

G5-C06-T05-Q006 About 1 min

The line plot shows the lengths, in feet, of boards used for a project: What is the total length of all the boards?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q006
  1. A \(8\) feet
  2. B \(11\frac{1}{2}\) feet
  3. C \(10\) feet
  4. D \(9\frac{1}{4}\) feet
Check answer and explanation

Answer D: \(9\frac{1}{4}\) feet

Add the board lengths: \(1 + 2(1\frac{1}{4}) + 2(1\frac{1}{2}) + 1\frac{3}{4} + 2 = 9\frac{1}{4}\) feet.

G5-C06-T05-Q007 About 1 min

The line plot shows distances (in meters) students jumped: What is the range of the data?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q007
  1. A 2 meters
  2. B 3 meters
  3. C 4 meters
  4. D 5 meters
Check answer and explanation

Answer B: 3 meters

Lowest: 2 m (2 marks), Highest: 5 m (1 mark). Range = \(5 - 2 = 3\) meters.

G5-C06-T05-Q008 About 1 min

The line plot shows the weight (in pounds) of puppies at the shelter: Each puppy gets \(\frac{1}{2}\) cup of food. How many cups of food are needed for all the puppies?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q008
  1. A \(4\) cups
  2. B \(5\frac{1}{2}\) cups
  3. C \(5\) cups
  4. D \(4\frac{1}{2}\) cups
Check answer and explanation

Answer D: \(4\frac{1}{2}\) cups

Count the puppies first: \(1 + 2 + 2 + 3 + 1 = 9\) puppies. Each puppy gets \(\frac{1}{2}\) cup, so \(9 \times \frac{1}{2} = 4\frac{1}{2}\) cups.

exit

3 questions
G5-C06-T05-Q009 About 1 min

Two line plots show ribbon lengths, in yards, used by two teams: How much more ribbon did Team 2 use than Team 1?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q009
  1. A \(\frac{1}{4}\) yard
  2. B \(\frac{1}{2}\) yard
  3. C \(\frac{3}{4}\) yard
  4. D \(1\) yard
Check answer and explanation

Answer A: \(\frac{1}{4}\) yard

Team 1 used \(\frac{1}{2}+\frac{1}{2}+\frac{3}{4}+1+1\frac{1}{4}=4\) yards. Team 2 used \(\frac{1}{2}+\frac{3}{4}+\frac{3}{4}+1+1\frac{1}{4}=4\frac{1}{4}\) yards. The difference is \(\frac{1}{4}\) yard.

G5-C06-T05-Q010 About 1 min

The line plot shows times (in minutes) students spent on homework: How many more students spent 30 minutes than 60 minutes on homework?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q010
  1. A 2 more students
  2. B 3 more students
  3. C 4 more students
  4. D 5 more students
Check answer and explanation

Answer A: 2 more students

At 30 minutes: 3 marks. At 60 minutes: 1 mark. Difference: \(3 - 1 = 2\) more students.

G5-C06-T05-Q011 About 1 min

The line plot shows the number of hours students exercise per week: What is the total number of hours shown in the line plot?

Using Fraction Operations with Line Plots visual for G5-C06-T05-Q011
  1. A \(12\frac{1}{2}\) hours
  2. B \(10\) hours
  3. C \(25\) hours
  4. D \(6\frac{1}{4}\) hours
Check answer and explanation

Answer A: \(12\frac{1}{2}\) hours

Add the fractional measurements shown: \(3(\frac{1}{2})+2(1)+3(1\frac{1}{2})+2+2\frac{1}{2}=12\frac{1}{2}\) hours.

Keep the learning path connected
Previous skillLine Plots with Fractional Data Recommended nextStem-and-Leaf Plots Same strandConverting Measurement Units Same strandSolving Multi-Step Problems with Conversions
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