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Math problem set Grade 5 Math

Riverbend Farm's New Drip Line: A Grade 5 Conversion Problem Set

An 8-problem grade 5 set where students compute roof runoff at a fictional farm, convert gallons to quarts, and use a fill rate to plan a new drip irrigation line.

Objectives

  1. Students will multiply decimal quantities to calculate roof runoff using a real conversion rule.
  2. Students will convert a quantity of gallons into quarts as part of a multi-step problem.
  3. Students will divide decimal quantities to calculate run time and rate of use.

Vocabulary

Cistern
A large tank that stores rainwater collected from a roof so it can be used later, usually for watering plants.

Also: runoff, conversion, drip line

Teacher overview

Riverbend Farm, a fictional farm used for this problem set, collects rainwater from its barn roof to supply a new drip-irrigation line. The farm's barn roof measures 1,200 square feet, and roof runoff can be estimated using the rule roof area (sq ft) x rainfall (in) x 0.623 = gallons of runoff, the same conversion rule used to plan real rainwater-harvesting systems. This set follows one storm's runoff through the farm's cisterns and drip line, using multiplication, subtraction, division, and a unit conversion from gallons to quarts along the way. A common misconception in this math is multiplying only two of the three runoff factors (area and rainfall, or rainfall and the conversion constant) instead of all three; problem 1 is built to surface that error if it occurs.

Riverbend Farm's New Drip Line: A Grade 5 Conversion Problem Set — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

  1. A storm drops 1.5 inches of rain on Riverbend's 1,200-square-foot barn roof. Using the rule roof area x rainfall x 0.623 = gallons of runoff, how many gallons of rain fall on the roof? A real system collects somewhat less than this, but use the full amount for the rest of the problems.

  2. The farm's main cistern holds up to 900 gallons. Does the roof's runoff from problem 1 overflow the cistern? If so, by how many gallons?

  3. To catch the overflow, the farm adds a second, smaller cistern that holds 250 gallons, connected so it fills after the main cistern is full. What is the combined capacity of both cisterns, and is it enough to hold all the runoff from problem 1?

  4. The farm's new drip line uses water at a rate of 3 gallons per minute. Using the total runoff from problem 1, about how many minutes could the drip line run on that water? Round to the nearest whole minute.

  5. Convert your answer from problem 4 into hours and minutes.

  6. Convert the total runoff from problem 1 into quarts, using the fact that each gallon equals 4 quarts.

  7. The farm also plans a second, smaller drip line for its vegetable beds. This line has 40 emitters, and each emitter uses water at a rate of 0.5 gallons per hour. How many total gallons per hour does this smaller line use when all 40 emitters run at once?

  8. Using the rate from problem 7, about how many hours would it take the 40 emitters to use all of the runoff from problem 1? Round to the nearest tenth of an hour.

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: 1121.4 gal.
    1,200 x 1.5 = 1,800; 1,800 x 0.623 = 1,121.4 gallons of runoff.
  2. Answer: yes, by 221.4 gal.
    1,121.4 gallons of runoff is more than the cistern's 900-gallon capacity. 1,121.4 - 900 = 221.4 gallons of overflow.
  3. Answer: 1150 gal; yes.
    900 + 250 = 1,150 gallons of combined capacity. Since 1,150 is greater than the 1,121.4 gallons of runoff, the combined cisterns hold all of it, with 28.6 gallons of spare room.
  4. Answer: 374 min.
    1,121.4 divided by 3 gallons per minute equals 373.8, which rounds up to 374 minutes.
  5. Answer: 6 hr; with 14 min left over, so 6 hr 14 min.
    374 minutes divided by 60 equals 6 hours with a remainder. 6 x 60 = 360 minutes, and 374 - 360 = 14 minutes, so 6 hours 14 minutes.
  6. Answer: 4485.6 qt.
    1,121.4 gallons x 4 quarts per gallon = 4,485.6 quarts.
  7. Answer: 20 gal/hr.
    0.5 gallons per hour x 40 emitters = 20 gallons per hour.
  8. Answer: 56.1 hr.
    1,121.4 divided by 20 gallons per hour equals 56.07, which rounds to 56.1 hours.

Differentiation

Support (below grade level)

Provide the runoff formula already set up as 1,200 x 1.5 x 0.623 with only the final multiplication left to complete for problem 1, and give a printed conversion card listing "1 gallon = 4 quarts" for problem 6.

Extension (above grade level)

Ask students to find how many square feet of roof would be needed to collect exactly 1,500 gallons from the same 1.5-inch storm, working backward from the runoff formula and assuming all the rain that falls on the roof is collected. A real system collects somewhat less, so a real roof would need to be a little larger.

ELL supports

Pre-teach "runoff," "cistern," and "emitter" using a simple diagram of a roof, a rain gutter, and two connected barrels. Provide a sentence frame for problem 2: "The roof's runoff of ___ gallons is (more than / less than) the cistern's capacity of 900 gallons."