Line Plots with Fractional Measurements

Lesson 1 of 1: Measurement and Data

In this lesson:

• Build line plots with fractional intervals
• Read and interpret line plot data
• Use fraction operations to solve line plot problems

Goals for Line Plots and Fractions

In this lesson, you will:

1. Create a line plot with fractional intervals
2. Choose an appropriate fractional scale
3. Read and interpret line plot data
4. Add fractions from a line plot
5. Subtract fractions from a line plot
6. Multiply a fraction by a whole number from plots

Quick Review: Whole-Number Line Plots

You've made line plots before with whole numbers:

• Each X above a value means one data point
• The number line shows the values
• Stacked X marks show how many at each value

Today's challenge: What happens when the data uses fractions?

Butterfly Wingspans Measured in Fractions

Ten butterflies measured to the nearest inch:

How do we plot fractions on a number line?

Building the Butterfly Line Plot

Every interval is the same width — that's the key rule.

Placing X Marks Step by Step

To build a line plot with fractional data:

1. Find the range — smallest to largest
2. Choose the scale — largest denominator
3. Mark equal intervals on the number line
4. Place one X per data point
5. Count X marks — must equal data points

Choosing the Right Scale for Mixed Denominators

When data has mixed denominators, use the largest one:

• Data includes halves and fourths → use fourths
• Data includes fourths and eighths → use eighths

Rename all fractions to match the scale:

Quick Check: Choosing a Scale

A data set contains these measurements:

What scale should you use for the number line?

Think about it before the next slide...

Caterpillar Lengths: Reading a Line Plot

Fifteen caterpillars measured to the nearest inch.

Reading the Plot: Direct Questions

From the caterpillar line plot:

• How many at inch? Count: 3
• Most common length? inch with 4 caterpillars
• How many past inch? Count X marks to the right

Each X is one caterpillar — never lose sight of that.

Comparison Questions from the Plot

• Longer than inch or shorter? Count X marks on each side
• Range: longest minus shortest

• Pattern: Most caterpillars cluster between and inch

Error Analysis: Find the Missing Data Point

A student plotted 12 values, but only 11 X marks appear.

• Check each value against the data table
• Find the missing data point

Which measurement is missing an X mark?

Transition: From Reading to Computing with Fractions

You can now build and read line plots.

Next step: use fraction operations to answer deeper questions.

The two-phase approach:

• Phase 1: Read the plot — identify values and frequencies
• Phase 2: Compute — add, subtract, or multiply fractions

Plant Watering Data for Computation Practice

Ten plants measured to the nearest cup.

Problem One: Addition of Like Fractions

Three plants each received cup. What is their total?

Phase 1: Read the plot — 3 X marks at

Phase 2: Compute:

Or: cups

Problem Two: Subtracting to Find the Difference

How much more water did the most-watered plant get than the least?

Phase 1: Read the plot — most = , least =

Phase 2: Compute:

Problem Three: Total of All Values

What is the total water for all 10 plants?

Problem Four: Multi-Step Challenge for You

Combine the water for the two plants at cup and the one plant at cup. How much less than 2 cups is that total?

Part 1: Add the three amounts

Part 2: Subtract from 2

Try both parts, then advance for the answer...

Problem Four: Solution in Two Parts

Part 1: cups

Part 2: cup

Remember: Read the plot first, then compute.

Measure and Plot: Activity Setup

Your turn to collect real data!

• Measure 10 objects to the nearest inch
• Record each measurement in a data table
• Choose the right scale for your number line
• Build your line plot with equal intervals
• Count X marks to verify your total

Example: Pencil Lengths from a Class Activity

Scale: eighths, from to . Total: 10.

Practice: Compute from the Data

Use the pencil line plot to solve:

1. Combined length of the three pencils at in.?
2. How much longer is the longest than the shortest?
3. Total length of all pencils at in. or more?

Work through each, then check your answers.

Answers to the Practice Computation Problems

1. inches

2. inch

3. in.

Reflection: Why Use a Line Plot?

What does a line plot show us that a data table does not?

• Clusters — where most data points gather
• Gaps — values with no measurements
• Spread — how far apart the smallest and largest values are
• Shape — the overall pattern of the data

Key Takeaways for Line Plot Success

✓ Mark fractional intervals with equal spacing

✓ Use the largest denominator as your scale

✓ Two phases: read the plot, then compute

Watch out: Common denominator before adding

Watch out: X marks at means , not

What Comes Next in Data and Statistics

You can now:

• Build line plots with fractional measurements
• Read and interpret line plot data
• Solve problems using fraction operations

Coming up: In Grade 6, you'll explore new statistical displays — histograms, box plots, and measures of center like mean and median.