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Classroom activity Grade 4 Math

Grindley Lift Station Cards: Area Models for Pump Totals

A grade 4 card activity where teams pair a pump card with a run-time card for four fictional sewer lift stations and build area models to find total gallons.

Objectives

  1. Students will build an area model for a two-digit by two-digit multiplication and record all four partial products.
  2. Students will multiply a four-digit pump rate by a one-digit number of minutes.
  3. Students will compare two stations' totals using subtraction and find one station's daily total in two steps.

Vocabulary

Lift station
A lift station is a pumping setup that raises wastewater from a low spot so it can keep flowing toward the treatment plant. Sewers mostly flow downhill, so low areas need a lift.
Pump
A pump is a machine that adds energy to water to move it or push it uphill, doing the job gravity cannot do on its own. Water systems use many different kinds of pumps to move water from wells, through treatment, and out to customers.
Wastewater
Wastewater is used water from sinks, showers, toilets, and businesses that goes down the drain. It travels through sewer pipes to a treatment plant to be cleaned before returning to nature.

Also: area model, partial product

Teacher overview

In the fictional town of Grindley, used water from homes flows downhill through sewer pipes until it reaches a low spot, where a lift station pumps it back up so it can keep flowing toward the treatment plant. This activity is a four-round card game for teams of three. Each round a team turns over a pump card, which gives the gallons a station moves each minute, and a run card, which gives the minutes the pump ran, then draws an area model on grid paper and finds the total gallons. The activity teaches the mathematics directly, because the rectangle the team draws is the run time along one side and the pump rate along the other, so the partial products they shade are the actual gallons pumped in each block of minutes. The card pairs are fixed and printed on the handout, so every team should reach the same totals. A common error to watch for is a team that shades only two of the four boxes, multiplying 30 by 10 and 2 by 5 for a rate of 32 gallons each minute over 15 minutes and reporting 310 gallons instead of the correct 480.

Activity Directions

  1. Before class, print one set of station cards per team: for each of the four stations, a pump card giving its gallons each minute and a run card giving the minutes it ran. Print the student handout, which lists the same four pairs so no team is stuck waiting for a card.

  2. Take 5 minutes to group students into teams of three and assign roles: a dealer who turns the cards, a drawer who builds the area model on grid paper, and a checker who adds the partial products and reads the total aloud. Roles rotate after each round.

  3. Spend 10 minutes modeling one practice round with the whole class on chart paper, using a demonstration station that is not on the handout: a pump that moves 32 gallons each minute and ran 15 minutes. Draw a rectangle, split one side into 30 and 2 and the other into 10 and 5, and label all four inside boxes: 300, 150, 20, and 10. Add them to get 480 gallons, and say out loud that every one of the four boxes is part of the answer.

  4. Run four rounds of 5 minutes each, one per station, in this order: Alder, Birch, Cedar, Dell. In each round the dealer reads the station's pump card and run card, the drawer builds the area model, and the checker adds the parts and writes the total on the handout.

  5. For the Cedar and Dell rounds, remind teams that a one-digit number of minutes still gets a rectangle, split by place value along the pump-rate side only.

  6. Call time after the fourth round. The activity ends when every team has recorded four totals, which takes 20 minutes of play.

  7. Give teams 5 minutes to finish handout questions 5 through 9, which compare the stations rather than adding new cards.

  8. Close with a 5-minute debrief. Ask one checker to read aloud the four boxes from their Alder model, then ask the class why shading only the two corner boxes gives a total that is far too small. Take three answers before summarizing that the area model has four parts because each side was split into two parts.

Grindley Lift Station Cards: Area Models for Pump Totals — Grade 4 Math
Name: ____________________________ Date: ______________

Student Handout

Grindley has four lift stations. Use the numbers in this table.

Station Gallons each minute Minutes it ran
Alder 48 25
Birch 36 45
Cedar 275 8
Dell 1,340 4

  1. Station Alder pumps 48 gallons each minute and ran for 25 minutes. How many gallons did it pump?

  2. Station Birch pumps 36 gallons each minute and ran for 45 minutes. How many gallons did it pump?

  3. Station Cedar pumps 275 gallons each minute and ran for 8 minutes. How many gallons did it pump?

  4. Station Dell pumps 1,340 gallons each minute and ran for 4 minutes. How many gallons did it pump?

  5. Look at your four totals. Which station pumped the most gallons?

  6. Station Dell pumped 5,360 gallons and Station Alder pumped 1,200 gallons. How many more gallons did Station Dell pump?

  7. Station Alder runs for 25 minutes, 3 times every day. How many minutes does it run in one day?

  8. Station Alder pumps 48 gallons each minute and runs 75 minutes in a day. How many gallons does it pump in one day?

  9. Explain in one or two sentences why the area model for 48 times 25 has four boxes inside it and not two.

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: 1,200 gallons.
    Split both factors by place value: 48 becomes 40 and 8, and 25 becomes 20 and 5. The four partial products are 40 times 20 equals 800, 40 times 5 equals 200, 8 times 20 equals 160, and 8 times 5 equals 40. Adding 800 plus 200 plus 160 plus 40 gives 1,200 gallons.

  2. Answer: 1,620 gallons.
    Split 36 into 30 and 6, and 45 into 40 and 5. The partial products are 30 times 40 equals 1,200, 30 times 5 equals 150, 6 times 40 equals 240, and 6 times 5 equals 30. Adding 1,200 plus 150 plus 240 plus 30 gives 1,620 gallons.

  3. Answer: 2,200 gallons.
    Split 275 into 200, 70, and 5. Then 200 times 8 equals 1,600, 70 times 8 equals 560, and 5 times 8 equals 40. Adding 1,600 plus 560 plus 40 gives 2,200 gallons.

  4. Answer: 5,360 gallons.
    Split 1,340 into 1,000, 300, and 40. Then 1,000 times 4 equals 4,000, 300 times 4 equals 1,200, and 40 times 4 equals 160. Adding 4,000 plus 1,200 plus 160 gives 5,360 gallons.

  5. Answer: Station Dell.
    Compare the four totals: 1,200 gallons, 1,620 gallons, 2,200 gallons, and 5,360 gallons. Station Dell's 5,360 gallons is the largest, even though Dell ran for the fewest minutes, because its pump moves far more gallons each minute.

  6. Answer: 4,160 gallons.
    Subtract 1,200 from 5,360. Take away 1,000 to reach 4,360, then take away 200 to reach 4,160 gallons.

  7. Answer: 75 minutes.
    Multiply the run time by the number of runs: 25 times 3 equals 75 minutes.

  8. Answer: 3,600 gallons.
    Split 48 into 40 and 8, and 75 into 70 and 5. The partial products are 40 times 70 equals 2,800, 40 times 5 equals 200, 8 times 70 equals 560, and 8 times 5 equals 40. Adding 2,800 plus 200 plus 560 plus 40 gives 3,600 gallons.

  9. Answer: Each side of the rectangle was split into two parts.
    Accept any explanation stating that splitting one side into two pieces and the other side into two pieces cuts the rectangle into two rows and two columns, which makes four boxes, and that leaving out any box leaves out part of the gallons.

Differentiation

Support (below grade level)

Give these teams grid paper with the rectangle already drawn and the two splits already marked for questions 1 and 2, so students fill in four labeled boxes rather than deciding where to cut. Provide a multiplication chart through 12 and let students use it for the basic facts inside each box. Reduce the required rounds to Alder and Cedar, and let the team copy the Birch and Dell totals from a partner team during the debrief.

Extension (above grade level)

Ask these teams to design a fifth lift station for the fictional town of Grindley with a two-digit pump rate and a two-digit run time whose total lands between 2,000 and 2,500 gallons. They must show the area model that proves their total, explain which pair of numbers they tried first and why they changed it, and state how many gallons their station would move in a full day of three runs.

ELL supports

Pre-teach "lift station," "pump," and "partial product" with a labeled side-view drawing of a pipe running downhill into a pit, a pump, and a pipe carrying the water back up. Post an area model on chart paper with the four boxes numbered and the word "part" written in each. Provide sentence frames for questions 5 and 9: "Station ___ pumped the most because ___," and "The model has four boxes because each side was split into ___ parts."

Extensions

Teams can extend the game by writing their own pump and run cards on index cards, trading decks with another team, and checking each other's area models. A teacher who wants a longer arc can have the class total all four stations for a full week of three runs a day and discuss why an operator in the town of Grindley keeps a written pumping log rather than trusting memory.