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Lesson plan Grade 6 Math

Vennock Dam's Two Outlets: Unit Rates and Flow Units

A 45-minute grade 6 math lesson comparing two dam outlets by gallons per minute, then converting between gallons per minute and cubic feet per second.

Objectives

  1. Students will find a unit rate in gallons per minute from a total volume and a time.
  2. Students will convert between gallons per minute and cubic feet per second.
  3. Students will find what percent of a combined release comes from one outlet.

Vocabulary

Key words: unit rate, outlet, release, cubic feet per second

Teacher overview

A dam holds water back, and the crew running it decides how much to release downstream through outlets of different sizes. This lesson uses the fictional Vennock Dam, whose two outlets release different volumes over different lengths of time, so the only fair comparison is a per-minute rate. Students then meet a second flow unit, cubic feet per second, and convert between the two using the standard figure of 448.8 gallons per minute in one cubic foot per second. The misconception this lesson corrects is judging flow by total gallons alone; students frequently name the outlet that released more gallons as the faster one without checking how long each outlet was open.

Procedure

Hook (5 min): Write two records on the board: one outlet released 12,000 gallons in 8 minutes, the other released 9,000 gallons in 5 minutes. Ask for a show of hands on which outlet was running faster, record the vote without comment, and tell students they will settle it with a calculation.

Direct instruction (10 min): Model finding a unit rate by dividing gallons by minutes, and write both results with the label "gallons per minute" attached. Return to the hook vote and name the outlet that actually ran faster. Then introduce the second unit, cubic feet per second, and write the conversion that one cubic foot per second equals 448.8 gallons per minute.

Guided practice (12 min): Distribute the Student Handout and complete items 1 through 3 as a class, with one student at the board recording each division. Ask what would change if an outlet ran twice as long at the same rate, and confirm that the rate stays the same while the total grows.

Independent practice (13 min): Students finish handout items 4 through 9 in pairs. Watch for students who multiply by 448.8 when they should divide; have them check whether the answer should be a bigger or smaller number before computing.

Closure and exit ticket (5 min): On an index card, students answer one question: an outlet releases 6,000 gallons in 4 minutes, so what is its rate in gallons per minute? Collect the cards at the door and sort them into correct and incorrect piles. If more than a quarter of the class misses it, open the next class with a second guided division.

Vennock Dam's Two Outlets: Unit Rates and Flow Units — Grade 6 Math
Name: ____________________________ Date: ______________

Student Handout

The town of Vennock, a fictional town, owns a small dam with two outlets. Outlet A released 12,000 gallons in 8 minutes. Outlet B released 9,000 gallons in 5 minutes. Use those figures for every item below.

  1. Find the rate of Outlet A in gallons per minute.
  2. Find the rate of Outlet B in gallons per minute.
  3. Which outlet has the greater rate in gallons per minute?
  4. If both outlets are open at once, what is the combined rate in gallons per minute?
  5. At that combined rate, how many gallons leave the dam in 30 minutes?
  6. One cubic foot per second equals 448.8 gallons per minute. A release of 5 cubic feet per second equals how many gallons per minute?
  7. Outlet A runs at the rate you found in item 1. About how many cubic feet per second is that? Round to the nearest tenth.
  8. The dam must release at least 2,000 gallons per minute to keep fish safe downstream. Does Outlet A alone meet that requirement?
  9. What percent of the combined rate you found in item 4 comes from Outlet B? Round to the nearest whole percent.

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: 1,500 gallons per minute.
    12,000 gallons divided by 8 minutes equals 1,500 gallons per minute.
  2. Answer: 1,800 gallons per minute.
    9,000 gallons divided by 5 minutes equals 1,800 gallons per minute.
  3. Answer: Outlet B.
    Outlet B runs at 1,800 gallons per minute, which is greater than Outlet A at 1,500, even though Outlet A released more gallons in total.
  4. Answer: 3,300 gallons per minute.
    1,500 plus 1,800 equals 3,300 gallons per minute.
  5. Answer: 99,000 gallons.
    3,300 gallons per minute times 30 minutes equals 99,000 gallons.
  6. Answer: 2,244 gallons per minute.
    5 times 448.8 equals 2,244 gallons per minute.
  7. Answer: 3.3 cubic feet per second.
    1,500 divided by 448.8 equals 3.342, which rounds to 3.3 cubic feet per second.
  8. Answer: No.
    Outlet A runs at 1,500 gallons per minute, which falls 500 short of the 2,000 required. Both outlets together would clear the requirement.
  9. Answer: 55 percent.
    1,800 divided by 3,300 equals 0.5454, which rounds to 55 percent.

Differentiation

Support

Provide a two-column recording sheet labeled "gallons" and "minutes" so the order of the division is set before students compute, and give the first division worked out. Post the conversion sentence for cubic feet per second on the board for the whole period, and allow calculators.

Extension

Ask students to find how many minutes the two outlets must run together to release one acre-foot of water, using the figure that one acre-foot equals 325,851 gallons, and to explain why the answer is shorter than running either outlet alone.

ELL supports

Pair each new term with a simple drawing: a dam wall with two pipes labeled A and B, a clock, and a one-foot cube. Provide the sentence frame "Outlet ___ released ___ gallons in ___ minutes, so its rate is ___ gallons per minute" for items 1 and 2.

Extensions

Students can build a table showing the gallons released by each outlet at 5, 10, 15, and 20 minutes, then plot both outlets on the same grid. The steeper line belongs to the greater unit rate, which previews the slope work of grade 8.