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Lesson plan Grade 5 Math

Marlford Pump Station Wet Well: A Grade 5 Volume Lesson

A 50-minute grade 5 lesson in which students find a fictional pump station's wet well volume by adding two rectangular prisms, then convert it to gallons.

Objectives

  1. Students will find the volume of a rectangular prism using V = l x w x h.
  2. Students will find the volume of a figure made of two rectangular prisms by adding the volume of each part.
  3. Students will convert a volume in cubic feet to gallons using 7.48 gallons per cubic foot.

Vocabulary

Key words: wet well, sump, volume, cubic foot, rectangular prism

Teacher overview

Marlford is a fictional town whose water crew is rebuilding the underground chamber at its main pump station. That chamber is called a wet well, and it is where water collects before the pumps lift it uphill to the storage tank. Wet wells are rarely a single plain box, because a wide upper chamber gives the crew room to work while a narrower sump is dug beneath it so the pump intake always stays covered. The misconception this lesson targets is the habit of treating a two-part figure as one large box, using the greatest length, the greatest width, and the full depth, which in the lesson's first example overstates the capacity by more than four hundred cubic feet.

Procedure

Hook (5 min): Set a small box on the floor and place a larger box on top of it so the class can see a two-level shape. Ask students how they would find the amount of space inside the whole stack. Take two or three answers without correcting them, then tell the class that the crew in Marlford has to answer exactly this question before they can say how much water the new wet well will hold.

Direct instruction (12 min): Draw the Marlford wet well on the board as an upper chamber 14 feet long, 10 feet wide, and 6 feet deep, resting on a sump 5 feet long, 4 feet wide, and 4 feet deep. Model the calculation in two parts. The upper chamber gives 14 x 10 = 140, and 140 x 6 = 840 cubic feet. The sump gives 5 x 4 = 20, and 20 x 4 = 80 cubic feet. The whole wet well holds 840 + 80 = 920 cubic feet. Then show the wrong method beside it, treating the well as one box 14 by 10 by 10, which gives 1,400 cubic feet, and ask students to say in their own words why that answer is too large. Close the segment by introducing the conversion operators use, 7.48 gallons in every cubic foot.

Guided practice (10 min): Give pairs a second two-part wet well: an upper chamber 8 feet by 6 feet by 5 feet resting on a sump 4 feet by 3 feet by 2 feet. Pairs find 240 cubic feet for the chamber, 24 cubic feet for the sump, and 264 cubic feet in all. As a formative check, ask every pair to write their total on a small whiteboard and hold it up at the same time. If more than a quarter of the class shows a number other than 264, work a third example together before moving on.

Independent practice (15 min): Distribute the student handout and have students complete questions 1 through 5 alone. Circulate and watch for two errors in particular: multiplying all six dimensions together, and finding both part volumes correctly but then forgetting to add them.

Closure and exit ticket (8 min): Students answer handout question 6 on an index card and hand it in as they leave. Sort the cards into correct and incorrect piles before the next class so you know who needs the support scaffold.

Marlford Pump Station Wet Well: A Grade 5 Volume Lesson — Grade 5 Math
Name: ____________________________ Date: ______________

Student Handout

Marlford is rebuilding the wet well at its pump station. Each wet well in these questions is made of two boxes: a wide upper chamber sitting on a smaller sump. Show your work for each question.

  1. The upper chamber of a wet well is 12 feet long, 8 feet wide, and 5 feet deep. What is its volume in cubic feet?
  2. The sump under that same chamber is 6 feet long, 4 feet wide, and 3 feet deep. What is its volume in cubic feet?
  3. What is the total volume of the wet well in questions 1 and 2?
  4. A second wet well has an upper chamber 10 feet long, 6 feet wide, and 4 feet deep, and a sump 5 feet long, 4 feet wide, and 2 feet deep. What is its total volume in cubic feet?
  5. One cubic foot holds 7.48 gallons. The wet well in question 4 holds 280 cubic feet. How many gallons does it hold?
  6. A third wet well has an upper chamber 9 feet long, 6 feet wide, and 4 feet deep, and a sump 3 feet long, 3 feet wide, and 2 feet deep. What is its total volume in cubic feet?

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: 480 cubic feet.
    The floor covers 12 x 8 = 96 square feet, and 96 x 5 = 480 cubic feet.
  2. Answer: 72 cubic feet.
    The sump floor covers 6 x 4 = 24 square feet, and 24 x 3 = 72 cubic feet.
  3. Answer: 552 cubic feet.
    Add the two parts: 480 + 72 = 552 cubic feet. A student who answers 480 has found only the chamber, and a student who answers far more has most likely used one large box instead of two parts.
  4. Answer: 280 cubic feet.
    The chamber gives 10 x 6 = 60, and 60 x 4 = 240 cubic feet. The sump gives 5 x 4 = 20, and 20 x 2 = 40 cubic feet. Adding the parts gives 240 + 40 = 280 cubic feet.
  5. Answer: 2,094.4 gallons.
    Multiply 280 x 7.48. Because 280 x 7 = 1,960 and 280 x 0.48 = 134.4, the total is 1,960 + 134.4 = 2,094.4 gallons.
  6. Answer: 234 cubic feet.
    The chamber gives 9 x 6 = 54, and 54 x 4 = 216 cubic feet. The sump gives 3 x 3 = 9, and 9 x 2 = 18 cubic feet. Adding the parts gives 216 + 18 = 234 cubic feet.

Differentiation

Support

Give these students a two-row recording table with the headings length, width, depth, and volume, one row for the chamber and one row for the sump, plus a final box labeled total. The table turns each problem into a fill-in task and makes the missing addition visible. Let students build a small two-part model out of interlocking cubes, such as a 4 by 3 by 2 chamber on a 2 by 2 by 1 sump, and count the cubes before they write any multiplication.

Extension

Ask students to design a wet well that holds exactly 500 cubic feet using two rectangular parts with whole-foot dimensions, where the sump is no deeper than 4 feet. Have them record both sets of dimensions and explain why more than one correct design exists.

ELL supports

Label the two stacked boxes from the hook with cards reading "upper chamber" and "sump," and write "length," "width," and "depth" along the matching edges in English and, where possible, in students' home languages. Provide a sentence frame for the exit ticket: "The chamber holds ___ cubic feet and the sump holds ___ cubic feet, so the whole well holds ___ cubic feet."

Extensions

Have students measure a classroom recycling bin and a smaller storage tub in inches, convert each measurement to feet, and find the combined volume if the tub were set on top of the bin. Ask them to compare that combined volume with the volume of a single box tall enough to cover both, and to explain in writing which of the two numbers tells a crew how much water the space can really hold.