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Math problem set Grade 5 Math

Ptarmigan Dam Reservoir Levels: A Grade 5 Coordinate Graph Set

Grade 5 students plot a week of reservoir water levels as points in the first quadrant, read coordinates, and interpret changes at a fictional dam.

Objectives

  1. Students will plot ordered pairs of day and water level in the first quadrant.
  2. Students will read and interpret coordinate points to describe reservoir changes.

Vocabulary

Reservoir
A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.

Also: coordinate, ordered pair, axis

Teacher overview

Ptarmigan Dam holds back the fictional Amberlake Reservoir. Each day the operators write down how high the water sits, in feet above a low marker. This set has students plot those daily levels as points on a coordinate grid, read the points, and describe how the water changed. A common student error is switching the two numbers in an ordered pair, so remind students that the day goes first on the x-axis and the level goes second on the y-axis.

Ptarmigan Dam Reservoir Levels: A Grade 5 Coordinate Graph Set — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

The operators recorded the water level for six days. The day is the x-value and the level in feet is the y-value.

Day (x) Level in feet (y)
1 30
2 34
3 36
4 33
5 38
6 40
  1. On grid paper, plot the six points with the day on the x-axis and the level on the y-axis.
  2. What was the water level on Day 3?
  3. On which day did the level reach 40 feet?
  4. Between Day 3 and Day 4, did the level rise or fall, and by how many feet?
  5. How much did the level rise from Day 1 to Day 6?
  6. Which day had the highest water level?
  7. Write the ordered pair for Day 5.
  8. On Day 7 the level rises 5 feet above the Day 6 level. Write the ordered pair for Day 7.
  9. Explain in one or two sentences what the point (2, 34) tells you about the reservoir.

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: Six plotted points: (1, 30), (2, 34), (3, 36), (4, 33), (5, 38), and (6, 40), with day on the x-axis and level on the y-axis.
  2. Answer: 36 feet. Find x = 3 and read the y-value, which is 36.
  3. Answer: Day 6. The level of 40 feet lines up with x = 6.
  4. Answer: Fell 3 feet. The level went from 36 feet to 33 feet, so 36 - 33 = 3 feet lower.
  5. Answer: 10 feet. Day 6 is 40 feet and Day 1 is 30 feet, so 40 - 30 = 10 feet.
  6. Answer: Day 6. Its level of 40 feet is the highest of the six days.
  7. Answer: (5, 38). Day 5 is the x-value and its level of 38 feet is the y-value.
  8. Answer: (7, 45). Day 7 is the x-value, and 40 + 5 = 45 feet is the y-value.
  9. Answer: The point (2, 34) means that on Day 2 the reservoir level was 34 feet above the marker.

Differentiation

Support

Give students a grid with the axes already labeled "Day" and "Level in feet" and the first point (1, 30) already plotted as a model. Let them plot the rest by matching each row of the table.

Extension

Ask students to predict a level for Day 8 that continues the general upward trend, plot it, and write a sentence explaining why they chose that value using the earlier points.

ELL supports

Pair the words "x-axis," "y-axis," and "ordered pair" with a labeled picture of the grid. Provide a sentence frame for problem 9: "On Day 2 the level was ___ feet."