Measure halves and quarters of an inch and make a line plot

Learning goal: Use a ruler marked in halves and quarters of an inch to measure lengths, and display repeated measurements on a line plot. A ruler is a number line with physical unit lengths. The interval from zero to one inch is one inch long. The metal or plastic edge before zero is not part of that measured interval.

Place the object's starting endpoint at the zero mark and keep the ruler straight alongside its length. Read the scale at the other endpoint. Looking from an angle or placing the object diagonally can make the reading inaccurate. If the ruler has several scales, identify the inch scale rather than combining centimeter labels with inch intervals.

A one-inch interval can be divided into two equal halves or four equal quarters. Halfway between zero and one is one half inch. The first quarter mark is one fourth inch and the third is three fourths inch. There are three interior quarter marks but four quarter-length intervals. The half-inch mark is also two fourths of an inch.

Beyond one inch, keep the same spacing. An endpoint at the first quarter mark after two inches measures two and one fourth inches. In this lesson, mixed-number words and labels identify the measurement; no mixed-number computation rule is required. Explain it as two whole inch intervals followed by one more quarter-inch interval.

A line plot records how often each measurement occurs. For a fictional set of eight paper strips, the measured lengths are 2, 2 1/4, 2 1/4, 2 1/2, 2 1/2, 2 1/2, 2 3/4 and 3 inches. Draw a horizontal scale from two to three inches with equal quarter-inch spacing. Place one X above a value for each strip with that length, stacking repeated values vertically.

The tallest stack is at two and one half inches, with three X marks. That means three strips have that length, not that the strips are three inches long. The horizontal position gives a length; the number of marks gives a frequency. A title and a key such as “one X = one strip” distinguish those roles.

Count all X marks to check the total number of observations. Here 1 + 2 + 3 + 1 + 1 = 8, matching the eight listed strips. A line plot should preserve repeated values. Replacing the three equal measurements with a single X would lose information even though the possible lengths were still labeled correctly.

Worked measurement: A strip starts at zero and ends halfway between the two-inch and three-inch marks. Its length is two and one half inches. If it ends one quarter-inch farther along, it measures two and three fourths inches. Identify the whole inches first and then count the equal fractional interval beyond them.

Worked line-plot question: How many of the fictional strips measure less than two and one half inches? Include the one strip at two and the two at two and one fourth: three strips. Do not include the three strips exactly equal to two and one half, because the question says less than, not less than or equal to.

Guided performance: Use an actual inch ruler to measure several teacher-prepared strips that end at whole, half and quarter marks. A ruler or scale drawn on a screen, including this lesson's line-plot scale, is a diagram and must not be assumed to have physical inch dimensions on every device. Record the measured values before making the plot so the display can be checked against the raw data.

Independent evidence: Measure a new collection of objects or strips and construct a line plot with an appropriate whole, half or quarter-inch scale. Explain one repeated value and answer a question about the collected data. If marks are unevenly spaced, redraw the unit intervals; if counts disagree, match each original observation to exactly one plotted X.