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Math problem set Grade 5 Math

Pellamy Notch Snow Course: A Grade 5 Line Plot Problem Set

A grade 5 problem set building a line plot from ten snow-depth readings in eighths of a foot, then redistributing the snow and finding the melt water.

Objectives

  1. Students will make a line plot of measurements given in eighths of a foot.
  2. Students will use fraction operations to answer questions about a line plot.
  3. Students will multiply a mixed number by a unit fraction to find melt water depth.

Vocabulary

Watershed
A watershed is all the land where rain that falls will drain to the same stream, river, or lake. Everyone lives in a watershed, no matter how far from the water they live.

Also: line plot, snow course, eighth, mixed number

Teacher overview

Pellamy Notch is a fictional mountain pass where a water district measures the snow each March at ten marked stakes along a trail called a snow course. The readings tell the district how much water will run into the Linscombe River when the snow melts in spring, which is how it plans the summer supply. This set has students plot ten depths measured to the nearest eighth of a foot, read the plot, and then find how much melt water the snow would produce. The misconception it targets is treating a line plot as a bar graph, so that students count the height of a stack as a measurement rather than as the number of stakes that shared one measurement.

Pellamy Notch Snow Course: A Grade 5 Line Plot Problem Set — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

Here are the ten snow depths measured at Pellamy Notch, in feet.

  • Stake 1: 1 1/8
  • Stake 2: 1 1/4
  • Stake 3: 1 1/4
  • Stake 4: 1 3/8
  • Stake 5: 1 1/2
  • Stake 6: 1 1/2
  • Stake 7: 1 1/2
  • Stake 8: 1 3/4
  • Stake 9: 1 3/4
  • Stake 10: 2

Draw a number line from 1 to 2 marked in eighths. Place one dot above the correct mark for each stake. Use your line plot to answer the problems.

  1. How many stakes measured exactly 1 1/2 feet?
  2. Which depth was measured at the most stakes?
  3. The deepest stake read 2 feet and the shallowest read 1 1/8 feet. What is the difference between them?
  4. Add all ten depths. What is the total snow depth in feet?
  5. Suppose the snow from all ten stakes were spread out evenly so that every stake read the same. Using your total of 15 feet from problem 4, what would each stake read?
  6. How many stakes measured 1 3/4 feet or more?
  7. Suppose that at Pellamy Notch each foot of snow melts into 1/4 foot of water. A stake reads 2 feet of snow. How much melt water is that?
  8. Suppose that each foot of snow melts into 1/4 foot of water. A stake reads 1 1/2 feet of snow. How much melt water is that?
  9. Explain how the line plot makes it easier to see which depth was most common.

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: 3 stakes. Stakes 5, 6, and 7 each read 1 1/2 feet, so three dots sit above the 1 1/2 mark.
  2. Answer: 1 1/2 feet. That mark has 3 dots, while 1 1/4 and 1 3/4 have 2 dots each and the rest have 1 dot each.
  3. Answer: 7/8 foot. Rewrite both as eighths: 2 = 16/8 and 1 1/8 = 9/8. Then 16/8 - 9/8 = 7/8 foot.
  4. Answer: 15 feet. Rewrite each depth in eighths and add: 9/8 + 10/8 + 10/8 + 11/8 + 12/8 + 12/8 + 12/8 + 14/8 + 14/8 + 16/8 = 120/8, and 120/8 = 15 feet.
  5. Answer: 1 1/2 feet. Share the total equally among the ten stakes: 15 divided by 10 = 15/10 = 1 1/2 feet at each stake.
  6. Answer: 3 stakes. Stakes 8 and 9 read 1 3/4 feet and stake 10 reads 2 feet, so three stakes are at or above 1 3/4 feet.
  7. Answer: 1/2 foot. Multiply the depth by the melt fraction: 2 x 1/4 = 2/4, which simplifies to 1/2 foot of water.
  8. Answer: 3/8 foot. Rewrite the mixed number as a fraction: 1 1/2 = 3/2. Then 3/2 x 1/4 = 3/8 foot of water.
  9. Answer: The line plot stacks a dot for every stake that gave the same reading, so the tallest stack shows the most common depth at a glance without sorting the ten numbers again.

Differentiation

Support

Hand out a pre-drawn number line from 1 to 2 with every eighth already labeled, and give students ten small sticky dots so plotting is a physical placement rather than a drawing task. For problem 4, provide a table with the eighths column already filled in for the first three stakes.

Extension

Ask students to add two more stakes to the snow course so that the twelve-stake total comes to exactly 18 1/2 feet and the most common depth changes from 1 1/2 feet to 1 3/4 feet. Have them redraw the line plot and show the addition that proves both conditions are met.

ELL supports

Pre-teach "stake," "depth," "melt," and "evenly" with a labeled drawing of a measuring stake pushed into snow. Provide a partly completed sentence for problem 9: "The line plot helps because each dot stands for ___ and the tallest stack shows ___."

Extensions

Have students track snow or rainfall at school for two weeks, measuring to the nearest quarter inch, and build their own line plot from the readings. Ask them to answer the same six questions about their plot that they answered about Pellamy Notch, including the redistribution question.