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Math problem set Grade 4 Math

Quarrytown Well Field: A Line Plot of Eighths of a Foot

A grade 4 problem set where students build a line plot from twelve well readings in eighths of a foot, then add and subtract fractions and mixed numbers.

Objectives

  1. Students will make a line plot of measurements recorded in eighths of a foot.
  2. Students will add and subtract fractions and mixed numbers with like denominators.
  3. Students will explain why a well crew records drops in fractions rather than whole feet.

Vocabulary

Key words: well, line plot, eighth, mixed number, water level

Teacher overview

Quarrytown is a fictional town that draws its drinking water from a field of shallow wells. Each day of a twelve-day pumping test, a worker lowers a measuring tape into one well and records how far the water level dropped while the pump ran, rounded to the nearest eighth of a foot. This problem set has students plot those twelve readings and then combine them with fraction arithmetic. The error to watch for is in problem 9: when subtracting 5/8 from 2 1/8, students often take the smaller numerator from the larger and write 2 4/8 instead of regrouping one whole foot into 8/8.

Quarrytown Well Field: A Line Plot of Eighths of a Foot — Grade 4 Math
Name: ____________________________ Date: ______________

Problems

The twelve daily readings, in feet, are: 3/8, 5/8, 1/8, 5/8, 4/8, 3/8, 6/8, 5/8, 2/8, 4/8, 5/8, and 7/8.

  1. Make a line plot of the twelve readings. Mark the line in eighths from 1/8 foot to 7/8 foot and put one X above each reading.

  2. Which reading appears most often on your line plot?

  3. How many days had a reading of 5/8 foot?

  4. What is the difference between the largest reading and the smallest reading?

  5. Add the two readings of 3/8 foot. What is the sum?

  6. Add the four readings of 5/8 foot. What is the sum?

  7. How many days had a reading greater than 4/8 foot?

  8. On two days after the test, the level dropped 1 2/8 feet and then 2 3/8 feet. What is the total drop for those two days?

  9. One morning the level was 2 1/8 feet down. After a rain it was only 5/8 foot down. How far did the level come back up?

  10. Explain why the crew records each drop in eighths of a foot instead of rounding to the nearest whole foot.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: One X above 1/8, one above 2/8, two above 3/8, two above 4/8, four above 5/8, one above 6/8, and one above 7/8.
    The twelve X marks should total twelve. Check that students spaced the tick marks evenly and labeled every eighth, including 1/8 and 2/8, which each carry a single mark.

  2. Answer: 5/8 foot.
    Four days show a reading of 5/8 foot, which is more than any other value on the plot.

  3. Answer: 4 days.
    Counting the X marks stacked above 5/8 gives four, matching days 2, 4, 8, and 11 in the list.

  4. Answer: 6/8 foot.
    The largest reading is 7/8 and the smallest is 1/8. Subtracting gives 7/8 − 1/8 = 6/8 foot, since the eighths are the same size and only the numerators change.

  5. Answer: 6/8 foot.
    3/8 + 3/8 = 6/8 foot. Three eighths plus three more eighths is six eighths.

  6. Answer: 2 4/8 feet.
    5/8 + 5/8 + 5/8 + 5/8 = 20/8 feet. Eight eighths make one whole, so 20/8 is 2 wholes with 4/8 left, which is 2 4/8 feet.

  7. Answer: 6 days.
    The readings above 4/8 are the four days at 5/8, one day at 6/8, and one day at 7/8, which is 4 + 1 + 1 = 6 days.

  8. Answer: 3 5/8 feet.
    Add the whole feet first, 1 + 2 = 3. Then add the eighths, 2/8 + 3/8 = 5/8. The total is 3 5/8 feet.

  9. Answer: 1 4/8 feet.
    Rename 2 1/8 as 1 and 9/8 by trading one whole foot for 8/8. Then 9/8 − 5/8 = 4/8, and the whole foot stays, giving 1 4/8 feet.

  10. Answer: Whole feet would hide most of the change, because every reading in the test is less than one foot.
    Accept any answer noting that all twelve readings fall between 0 and 1 foot, so rounding to whole feet would record every day as either 0 or 1 foot and hide the differences between days.

Differentiation

Support

Give students a pre-drawn number line already labeled from 1/8 to 8/8 so plotting starts with placing X marks rather than building the scale. For problem 9, provide two paper strips divided into eighths so students can physically trade one whole for 8/8.

Extension

Ask students to add three more readings to the data set that would move the most common value from 5/8 foot to 4/8 foot, then redraw the line plot and explain why their choice works.

ELL supports

Pre-teach "reading," "drop," "line plot," and "most often" with a labeled sketch of a well, a measuring tape, and the water level marked before and after pumping. Provide the sentence frame: The water dropped ___ eighths of a foot on ___ days.

Extensions

Have students measure the height of classroom water bottles to the nearest quarter inch, build a line plot of the class results, and find the difference between the tallest and shortest bottle.