Create a line plot and interpret single-unit category graphs

Learning goal: Generate measurement data, display lengths on a whole-unit line plot and organize category data in picture and bar graphs with single-unit scales. These displays answer different kinds of questions. A measured length is numerical data; a preferred fruit category is a different variable.

Measure several safe classroom objects to the nearest whole unit with an appropriate tool, or repeat the measurement of one object and record each reading. Label the unit and what each entry represents. Repeated readings of one object are observations, not proof that several different objects were measured. If a reading is exactly halfway between whole marks, use the class's stated consistent recording convention.

The illustrated practice data are lengths of six fictional paper strips measured to the nearest centimeter: 4, 5, 5, 6, 6 and 6. A line plot places a mark above the measured value for each strip. There is one mark above 4, two above 5 and three above 6. Marks stack vertically when values repeat; their horizontal position still represents the measurement.

Each X stands for one strip in this example, not one centimeter added to the horizontal value. Three Xs above 6 mean three strips recorded as six centimeters each. They do not mean one strip is eighteen centimeters long. The horizontal scale uses equal spacing for whole-number units and includes labels so the measurements can be read.

For a separate category example, six learners each choose one activity: drawing gets three choices, reading two and puzzles one. A single-unit picture graph uses one symbol per learner. A bar graph with a single-unit vertical scale has bars of height three, two and one. The displays represent the same category counts when their titles, labels and keys match.

The measurement plot and activity graph must remain separate. A strip's length of six centimeters is not a sixth vote for drawing, and a vote is not a unit of length. Labeling the title, axis and key prevents two correct-looking graphs from answering the wrong question.

Use a category graph to put counts together, take them apart and compare. Drawing and reading together have five choices. Reading has one more than puzzles. If one drawing chooser were removed from this invented group, drawing would have two choices; state that as a changed scenario rather than silently altering the original data.

Create as well as read displays. Start with a list or tally record, choose consistent single-unit spacing and place each mark or bar correctly. A learner who answers from a completed graph has not yet demonstrated constructing one. Check the total represented observations against the original record to catch omissions or double counting.

Worked example 1: Read repeated measurements. Two Xs above 5 represent two strips recorded as five centimeters each. The number of marks and the measurement value answer different questions. Together the plot contains six observations.

Worked example 2: Build category bars. Drawing has three choices, reading two and puzzles one. Use a zero baseline and one equal vertical interval per learner. Different bar widths should not be used to encode additional values in this simple graph.

Worked example 3: Compare categories. Drawing has one more choice than reading because 3 − 2 = 1. Drawing and reading together have five because 3 + 2 = 5. State whether the question asks for difference or total.

Guided investigation: Generate a real measurement record, then construct its line plot. Separately survey a small group using no more than four categories and one response per person. Complete a single-unit picture graph and bar graph from the same category record.

Independent tasks: Measure and record several observations, create a correctly labeled line plot and explain a repeated value. Construct category displays from a new supplied record and solve a total, missing-part or comparison question. Keep the two datasets clearly identified.

Feedback: If Xs are added to the horizontal value, identify the mark's unit using the key. If a bar starts above zero without explanation, restore the intended single-unit scale. Compare represented totals with the source record before accepting a neat-looking graph.