Reading a Line Plot With Eighths
A class measures bean plant heights to the nearest eighth of an inch and records the data on a line plot: 1/8 inch (two plants), 2/8 inch (three plants), 3/8 inch (one plant), 5/8 inch (four plants), 6/8 inch (two plants), and 7/8 inch (one plant). Student T reads the line plot and says, “The tallest plant is 7/8 inch, and the difference between the tallest and shortest is 6/8 inch because 7 − 1 = 6.” Student S says, “The difference is 6/8 inch, but the shortest is 1/8, so the difference is 6/8; that is 3/4 inch.” The teacher notices several students label the scale with only the numerator and ignore the eighths. The class must answer: How many plants were measured? What is the difference between the tallest and shortest plant? The teacher wants students to justify using the scale and to express the difference in simplest form.
1. How many plants were measured? Show how to use the line plot counts.
Read the worked answer
Add the number of marks at each height: 2 + 3 + 1 + 4 + 2 + 1 = 13 plants. Each mark represents one plant measured to the nearest eighth of an inch. The counts at the heights are 2, 3, 1, 4, 2, and 1, so the total is 13. Students should not count the number of distinct heights, which is 6; they must count the marks.
2. What is the difference between the tallest and shortest plant? Express the answer in simplest form and explain the scale.
Read the worked answer
The tallest plant is 7/8 inch and the shortest is 1/8 inch. The difference is 7/8 − 1/8 = 6/8 inch. Since 6 and 8 have a common factor of 2, 6/8 = 3/4 inch. The scale is in eighths, so each tick mark is 1/8 inch, not 1 inch. The subtraction 7 − 1 = 6 is only the numerator difference; the denominator stays 8 because the units are eighths.
3. Student T and Student S both get 6/8 inch. What is the difference in the quality of their reasoning, and how would you help students who ignore the eighths?
Read the worked answer
Student S’s reasoning is stronger because it identifies the shortest height as 1/8 inch and keeps the denominator, then simplifies 6/8 to 3/4. Student T’s statement “7 − 1 = 6” works only if the 7 and 1 are understood as eighths. Student T does not explicitly show that the heights are 7/8 and 1/8, so the reasoning is incomplete. To help students who ignore the eighths, have them label each tick mark with the full fraction, not just the numerator, and write the subtraction with units: 7/8 − 1/8 = 6/8 = 3/4 inch. Ask them to explain what one tick mark represents before computing.