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Math problem set Grade 5 Math

Fallowgate Water Tower Levels: A Grade 5 Coordinate Graph Set

A grade 5 problem set plotting a fictional town's water tower depth every two hours in the first quadrant, then reading the points to explain the daily pattern.

Objectives

  1. Students will plot ordered pairs of time and depth in the first quadrant.
  2. Students will interpret the x-coordinate and y-coordinate of a point in context.
  3. Students will compare points on a graph to find the largest rise and fall.

Vocabulary

Water tower
A water tower is a big tank raised high above town that stores drinking water. Its height is what pushes water through the pipes, keeping the pressure steady even when the power goes out.

Also: ordered pair, coordinate, x-axis, y-axis

Teacher overview

Fallowgate is a fictional town whose water tower fills at night and drains during the busiest parts of the day. An operator writes down the depth of water in the tank every two hours, starting at 6 in the morning, and the pair of numbers goes on a graph so the pattern is easy to see. This set has students plot those pairs in the first quadrant and then read individual points to describe when the town used the most water. The misconception it targets is reversing the order in an ordered pair, so that a student plots the depth along the horizontal axis and reads a 24-foot depth as 24 hours.

Fallowgate Water Tower Levels: A Grade 5 Coordinate Graph Set — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

An operator in Fallowgate recorded the depth of water in the tower every two hours. The first number in each pair is the number of hours after 6 in the morning. The second number is the depth of water in feet.

  • (0, 28)
  • (2, 24)
  • (4, 22)
  • (6, 25)
  • (8, 27)
  • (10, 26)
  • (12, 30)

Draw a first-quadrant grid. Number the horizontal axis from 0 to 14 hours and the vertical axis from 0 to 32 feet. Plot the seven points, then answer the problems.

  1. Look at the point (6, 25). What does the first number, 6, tell you?
  2. What was the depth of water 4 hours after 6 in the morning?
  3. How many hours after 6 in the morning was the tank at its lowest depth?
  4. The tank read 28 feet at hour 0 and 22 feet at hour 4. How many feet did the depth drop over those 4 hours?
  5. The tank read 22 feet at hour 4 and 30 feet at hour 12. How many feet did the depth rise over those 8 hours?
  6. Between which two back-to-back plotted readings did the depth rise the most?
  7. How many feet was that largest rise?
  8. The operator plotted one more point at (14, 32). How many feet higher is that reading than the reading at hour 12?
  9. Explain why the point (2, 24) does not mean the same thing as the point (24, 2).

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: 6 hours after 6 in the morning. The first number of an ordered pair is the x-coordinate, which is measured along the horizontal axis, and here that axis counts hours after 6 in the morning.
  2. Answer: 22 feet. Find 4 on the horizontal axis, move up to the plotted point, and read 22 on the vertical axis, which matches the pair (4, 22).
  3. Answer: 4 hours. The lowest plotted point is (4, 22), and no other point has a depth below 22 feet.
  4. Answer: 6 feet. 28 - 22 = 6 feet.
  5. Answer: 8 feet. 30 - 22 = 8 feet.
  6. Answer: Between hour 10 and hour 12. The rises are 3 feet from hour 4 to hour 6, 2 feet from hour 6 to hour 8, and 4 feet from hour 10 to hour 12, so the last one is largest.
  7. Answer: 4 feet. The depth went from 26 feet at hour 10 to 30 feet at hour 12, and 30 - 26 = 4 feet.
  8. Answer: 2 feet. The hour-12 reading is 30 feet and the hour-14 reading is 32 feet, so 32 - 30 = 2 feet higher.
  9. Answer: The order of the numbers decides what each one means. In (2, 24) the tank is 24 feet deep 2 hours after 6 in the morning, while (24, 2) would mean a depth of 2 feet at 24 hours after 6 in the morning, which is a different point on the grid.

Differentiation

Support

Give students grid paper with the axes already labeled and the first two points already plotted. Have them say each pair aloud as "over, then up" before marking it, and provide a two-column table of the seven pairs so they can check off each point as it is plotted.

Extension

Ask students to write a short account of Fallowgate's day using only the graph: when the town used the most water, when the pumps refilled the tower, and what they would expect the reading to be at hour 16. They should support each statement with at least one ordered pair.

ELL supports

Label the two axes with both the unit and a picture, a clock for hours and a tank for feet of depth. Pre-teach "rise," "drop," "ordered pair," and "coordinate," and provide a sentence frame for problem 9: "The pair (2, 24) means ___, but the pair (24, 2) means ___."

Extensions

Have students collect a real time-and-amount data set at school, such as the number of water bottles filled at a filling station every hour of a school day, and plot it on a first-quadrant grid. Ask them to compare the shape of their graph with Fallowgate's and explain what causes the two patterns to differ.