Creating Line Plots with Fractions of an Inch - Third Grade Mathematics

A line plot (sometimes called a dot plot) is a fast, visual way to display measurement data along a number line. Each data point is recorded as an "X" or a dot stacked neatly above its measurement value. In third grade, you connect measurement to data by measuring objects to the nearest half and fourth of an inch and plotting those fractions on a line plot. In this chapter, you will master constructing and interpreting line plots with fractional measurements.

What Is a Line Plot?

A line plot consists of a horizontal number line marked with measurement increments, with symbols (usually an "X") stacked vertically above the values.

The Anatomy of a Line Plot:
- Title: Describes what was measured.
- Number Line: Shows the scale of measurement (whole numbers and fractions).
- X Marks: Each X represents ONE single object or measurement observation.

Example Line Plot: Length of Classroom Crayons (in inches)

                X
                X       X
        X       X       X       X
    ----+-------+-------+-------+----
        2      2 1/4   2 1/2   2 3/4   Inches

Look at how much information this line plot reveals:
- 1 crayon measured 2 inches.

- 3 crayons measured 2 and 1/4 inches.

- 2 crayons measured 2 and 1/2 inches.

- 1 crayon measured 2 and 3/4 inches.

- Total crayons measured = 1 + 3 + 2 + 1 = 7 crayons in all!


Setting Up a Fractional Number Line for a Line Plot

To create a line plot with halves and fourths of an inch:
1. Find the smallest and largest measurements in your data set:
If your shortest pencil is 3 inches and your longest pencil is 5 inches, your number line needs to run from 3 to 5.
2. Partition each whole-inch space into equal fourths:
- Mark the whole numbers (e.g., 3, 4, 5). - Mark the half-inch point halfway between each whole number (3 1/2, 4 1/2). - Mark the fourth-inch points (3 1/4, 3 3/4, 4 1/4, 4 3/4).
3. Label the axis clearly with the measurement unit (e.g., "Length in Inches").


Fractional Number Line Scale from 4 to 5 Inches:
4              4 1/4           4 1/2           4 3/4           5
+---------------+---------------+---------------+---------------+

Step-by-Step Process for Plotting Data

Let us plot the lengths of 10 paper strips measured to the nearest fourth of an inch: Data: 3 1/2, 3 1/4, 4, 3 1/2, 3 3/4, 3 1/2, 4, 3 1/4, 3 1/2, 3 3/4.

Step 1: Organize the data using a tally or frequency count:
- 3 1/4 inches: 2 strips

- 3 1/2 inches: 4 strips

- 3 3/4 inches: 2 strips

- 4 inches: 2 strips
Total: 2 + 4 + 2 + 2 = 10 strips.

Step 2: Plot the Xs above each measurement:

Paper Strip Lengths:

                    X
                    X
            X       X       X       X
            X       X       X       X
        +-------+-------+-------+-------+
          3 1/4   3 1/2   3 3/4     4     Inches

Make sure all Xs are drawn at the exact same size and evenly spaced vertically so that the taller columns visually represent larger frequencies!

Analyzing Data on a Line Plot

Once your line plot is drawn, you can analyze the distribution:
- What was the most frequent (common) length?
Look for the tallest column of Xs: 3 and 1/2 inches (4 strips).
- What was the shortest length measured?
Look for the leftmost value with an X: 3 and 1/4 inches.
- What is the difference between the longest and shortest strips?
Longest (4 in) - Shortest (3 1/4 in) = 3/4 of an inch!

Chapter Practice Exercises

  1. Look at this line plot of ribbon lengths: 1 1/2 in: XX 1 3/4 in: XXXX 2 in: X 2 1/4 in: XXX a. How many ribbons were measured in all? b. What was the most common ribbon length? c. How many ribbons were longer than 1 3/4 inches?
  2. Create a frequency list from this data of worm lengths: Lengths: 2 in, 2 1/2 in, 2 1/4 in, 2 1/2 in, 3 in, 2 1/2 in, 2 1/4 in.
  3. Draw or describe the line plot you would construct for the worm lengths in exercise 2.
  4. A student measured 8 seashells: Four shells measured 1 1/2 inches, two measured 1 3/4 inches, and two measured 2 inches. What fraction of the shells measured 1 1/2 inches?
  5. What is the difference in length between the longest seashell (2 in) and the shortest seashell (1 1/2 in) from exercise 4?

Solutions and Step-by-Step Answers

  1. Ribbon line plot: a. Total ribbons: 2 + 4 + 1 + 3 = 10 ribbons. b. Most common length: 1 and 3/4 inches (4 Xs). c. Ribbons longer than 1 3/4 inches: 2 in (1) + 2 1/4 in (3) = 4 ribbons.
  2. Worm frequency list:
  3. 2 inches: 1
  4. 2 1/4 inches: 2
  5. 2 1/2 inches: 3
  6. 2 3/4 inches: 0
  7. 3 inches: 1 Total = 7 worms.
  8. Line plot description: Horizontal number line marked at 2, 2 1/4, 2 1/2, 2 3/4, 3 inches. Above 2: 1 X. Above 2 1/4: 2 Xs. Above 2 1/2: 3 Xs. Above 2 3/4: no Xs. Above 3: 1 X.
  9. 4 out of 8 shells measured 1 and 1/2 inches. Fraction = 4/8 (which equals 1/2 of the shells).
  10. Difference: 2 - 1 1/2 = 1/2 of an inch.