Line Plots With Fractional Measurements

Grade 4 Measurement and Data: 4.MD.B.4

In this lesson:

• Build a line plot scaled in halves, fourths, or eighths
• Read a plot to find the mode, range, clusters, and gaps
• Add and subtract fractions using data from a plot

Learning Objectives for This Lesson

By the end of today, you can:

1. Build a line plot with a fractional scale
2. Find the mode, range, clusters, and gaps
3. Add fraction values read from a plot
4. Subtract fraction values read from a plot
5. Explain what a plot shows that a list can't

What If the Numbers Are Fractions?

You already know a line plot like "Number of Books Read" — whole numbers,
one X per student.

What changes when the measurements themselves are fractions, like 3/4 inch
or 1 1/4 inches?

Quick Check: Locate the Fraction

On a number line from 0 to 2, where does 3/4 sit? How do you know?

Twelve Caterpillars, Measured in Fourths

A class measures 12 caterpillars to the nearest quarter inch:

3/4, 1, 1, 1 1/4, 1 1/4, 1 1/4, 1 1/2, 1 1/2, 1 3/4, 1 3/4, 2, 2 1/4

Finding the Range and the Unit

Smallest value: 3/4 inch. Largest value: 2 1/4 inches.

Every measurement here is written in fourths — so the scale should mark
every fourth of an inch.

Equal Fractions Need Equal Spacing

Draw a number line from 3/4 to 2 1/4, with a tick at every fourth.

The gap from 3/4 to 1 must be the same length as the gap from 1 to 1 1/4:
check it with a ruler.

The Completed Caterpillar Line Plot

A Different Scale, Measured in Eighths

• Leaf widths (nearest eighth inch): 3/8, 3/8, 1/2, 5/8, 5/8, 5/8, 3/4, 3/4, 7/8, 1
• Which fractional unit does this scale need?

Predict: Where Does 1/2 Land?

The number line above is scaled in eighths.

Before the next slide, decide: which tick mark does the value 1/2 land on?

Reveal: 1/2 Is the Same as 4/8

The X for 1/2 goes at the 4/8 tick — four eighths counted from zero, not the
first tick mark.

The Number Line Is the Backbone

Equal fractions always get equal spaces on the number line.

If the spacing is accurate and every tick is labeled correctly, the plot
shows the shape of the data at a glance.

You Can Build It — Now Read It

You just constructed a line plot from raw data.

What can you learn from a completed plot, without ever seeing the original
list of numbers?

Reading the Completed Caterpillar Plot

How many caterpillars were measured? What length appears most often?

Reading the Extremes and the Gaps

What is the longest caterpillar? The shortest? Is there any length with no
caterpillars at all?

The rightmost X marks the longest, and the leftmost marks the shortest — a
tick with no X above it is a gap.

Where Most of the Data Clusters

Most of the Xs sit between 1 inch and 1 3/4 inches.

That's different from naming the longest or shortest — clustering describes
where the bulk of the data actually piles up.

How Many Are Longer Than 1 1/2 Inches?

• Above 1 3/4, 2, and 2 1/4 inches: 2 + 1 + 1 = 4 caterpillars

A New Context: Seashell Widths

Write two full sentences describing what this plot shows.

Which Tells You More at a Glance?

A raw list of 12 numbers versus the caterpillar line plot, side by side.

Which one shows you the most common length, the range, and the clusters
faster?

Moving From Reading to Computing

You can now read a plot for its most common value, range, clusters, and
gaps.

Next: the plot hands you the numbers, and your fraction skills tell you
what to do with them.

Ten Insects, a Fresh Data Set

What is the difference in length between the longest and the shortest?

Subtracting to Find the Range

This is the standard's own example: using a line plot to solve a fraction
subtraction problem.

Combining Two Equal Insect Lengths

Two insects on the plot measured 1/2 inch each.

What is their combined length if you laid them end to end?

The Total Under One Inch

What is the combined length of every insect shorter than 1 inch?

Converting to Fourths, Then Adding

Six data points, all converted to fourths first, then added numerator by
numerator.

Three Insects, One Length: What's the Total?

Three insects on the plot measured 3/4 inch each.

Is their combined length 3, or is it 3/4 + 3/4 + 3/4?

The Most Common Length Minus Shortest

The most common insect length is 3/4 inch. The shortest is 1/4 inch.

How much longer is the most common length than the shortest?

Read First, Then Compute Second

Before any arithmetic: mark exactly which Xs the question needs.

Then: convert to a shared denominator and compute.

Your Turn: Three Problems, No Help

Using the insect-lengths plot: find the range, find a combined length at one
value, and find the total of a small subset.

Mark the Xs each question needs before you compute anything.

Four Mistakes to Watch Out For

Equal fractions need equal spacing — check with a ruler
Count your Xs against your data list — a missing repeat won't match
Rewrite in the scale's denominator first — 1/2 is 4/8, not the 1st tick
"How many" counts Xs; "how much" adds the values

Key Takeaways From Today's Lesson

✓ A fractional line plot needs evenly spaced, correctly labeled ticks
✓ Total count, mode, range, clusters, and gaps all read from the shape
✓ The plot hands you values; your fraction skills compute with them
✓ "How many" and "how much" are two different questions

Coming Up Next: New Operations, Same Plot

You can now build, read, and add or subtract with fractional line plot data.

The next line plot lesson asks you to multiply and divide with that same
kind of data, using the exact same reading skills you practiced today.