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Lesson plan Grade 6 Math

Northgate Plant Shift Log: A Gallons-Per-Hour Rate Lesson

A 50-minute grade 6 lesson where students read a fictional treatment plant's shift log and use unit rate and percent to describe how much water it treats.

Objectives

  1. Students will find a treatment plant's rate in gallons per hour from a shift total and its hours.
  2. Students will find what percent of a plant's daily capacity a single shift treated.

Vocabulary

Key words: unit rate, percent, capacity, shift

Teacher overview

Operators keep a log of how much water a plant treats during each shift. Reading that log is a real use of unit rate: gallons treated divided by hours worked gives a gallons-per-hour rate. This lesson uses the Northgate plant, a fictional plant, so students can build a rate and compare a shift to the plant's daily capacity. A common misconception this lesson addresses is dividing the wrong way when finding a percent, such as dividing the daily capacity by the shift total, so students check that the part treated is divided by the whole capacity.

Procedure

Hook (5 min): Ask students how they would decide which of two workers was faster if one filled 600 buckets in 8 hours and another filled 900 buckets in 8 hours. Collect a few ideas, then say that plant operators answer this same question every day using rates.

Direct instruction (12 min): Model the idea with a teacher example that is not on the handout: a small plant treats 400,000 gallons in 5 hours. Show that the rate is 400,000 ÷ 5 = 80,000 gallons per hour. Then show percent of capacity with a different sample: if a plant's daily capacity is 1,000,000 gallons and a shift treats 250,000 gallons, that is 250,000 ÷ 1,000,000 = 25 percent of capacity. Keep this modeling separate from the handout numbers.

Guided practice (13 min): Hand out the shift log. Work item 1 together, finding the gallons-per-hour rate for the Northgate shift, and have students explain each step to a partner. Pause after item 3 for a formative check: ask for a thumbs-up from students who divided the shift total by the daily capacity to find percent, and re-teach to any table showing thumbs-down.

Independent practice (15 min): Students complete handout items 4 through 6 on their own, then compare answers with a partner and fix any differences they can explain.

Closure (5 min): Students write one sentence on the back of the handout explaining how they knew which of the two shifts in item 6 was faster. Collect the handouts as they leave.

Northgate Plant Shift Log: A Gallons-Per-Hour Rate Lesson — Grade 6 Math
Name: ____________________________ Date: ______________

Student Handout

The Northgate plant, a fictional plant, can treat up to 2,000,000 gallons of water each day. During Tuesday's 8-hour shift, the plant treated 600,000 gallons.

  1. What is the plant's treatment rate in gallons per hour during Tuesday's shift?

  2. At that same rate, how many gallons would the plant treat in 3 hours?

  3. The shift treated 600,000 gallons. What percent of the daily capacity of 2,000,000 gallons is that?

  4. Fill in this table for gallons treated at the Tuesday rate of 75,000 gallons per hour.

    Hours Gallons treated
    2
    4
    10

  5. A second shift treated 900,000 gallons in 8 hours. What is that shift's rate in gallons per hour?

  6. Which shift treated water faster, Tuesday's (600,000 gallons in 8 hours) or the second shift (900,000 gallons in 8 hours)? Explain.

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: 75,000 gallons per hour. 600,000 gallons ÷ 8 hours = 75,000 gallons per hour.
  2. Answer: 225,000 gallons. 75,000 gallons per hour × 3 hours = 225,000 gallons.
  3. Answer: 30 percent. 600,000 ÷ 2,000,000 = 0.3, which is 30 percent of capacity.
  4. Answer: 150,000; 300,000; 750,000. At 75,000 gallons per hour: 2 × 75,000 = 150,000, 4 × 75,000 = 300,000, 10 × 75,000 = 750,000 gallons.
  5. Answer: 112,500 gallons per hour. 900,000 gallons ÷ 8 hours = 112,500 gallons per hour.
  6. Answer: The second shift was faster. Its rate of 112,500 gallons per hour is greater than Tuesday's 75,000 gallons per hour, and both shifts ran 8 hours.

Differentiation

Support

Provide the Tuesday rate (75,000 gallons per hour) already found so students can begin at item 2. Give a reminder card with "rate = gallons ÷ hours" and "percent = part ÷ whole." Allow a calculator for the large-number division.

Extension

Ask students to find how many hours the Northgate plant would need to run at the Tuesday rate to reach its full daily capacity of 2,000,000 gallons, and to explain whether one 8-hour shift alone could ever reach capacity.

ELL supports

Pre-teach "capacity," "shift," "rate," and "per hour" with a labeled picture of a plant and a clock. Provide the sentence frame for closure: "The second shift was faster because its rate was ___." Allow students to show item 6 with the two rates circled rather than a full sentence.