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Lesson plan Grade 7 Math

Larkfen Farms Drip Irrigation: A Proportional-Reasoning Lesson

A 45-minute grade 7 lesson where students find the constant of proportionality and write an equation for water used per acre on a fictional drip-irrigated farm.

Objectives

  1. Students will identify the constant of proportionality in gallons per acre.
  2. Students will write and use an equation for a proportional relationship.

Vocabulary

Drip irrigation
Watering plants through tubes that release water slowly, drop by drop, right at the roots. Very little water is wasted along the way.

Also: proportional, constant of proportionality, acre

Teacher overview

Farms use most of the fresh water people withdraw, so how efficiently a field is watered matters a great deal. Drip irrigation delivers a steady amount of water to each acre, which makes the water used directly proportional to the number of acres watered. This lesson uses the fictional Larkfen Farms to give students a clean proportional relationship: a table of acres and gallons to test, a constant of proportionality to name, and an equation to write and use. The misconception this lesson addresses is thinking any table where both numbers grow is proportional; students learn to check that gallons divided by acres gives the same rate in every row.

Procedure

Hook (5 min): Ask students to estimate how much water it takes to grow the food on their lunch tray. After a few guesses, tell them that farms use about 70 percent of the fresh water people use worldwide, and that today they will study how a careful farm, the fictional Larkfen Farms, measures the water it puts on each acre.

Direct instruction (12 min): Show the acres-to-gallons table for Larkfen's drip system: 2 acres uses 24,000 gallons, 5 acres uses 60,000 gallons, 8 acres uses 96,000 gallons. Model dividing gallons by acres for the first row to get 12,000 gallons per acre, and have students confirm the other rows give the same rate. Name that shared rate the constant of proportionality.

Worked example (8 min): With the class, write the equation G = 12,000a, where G is gallons and a is acres. Use it to predict the water for 10 acres (120,000 gallons), and then work backward to find how many acres a 36,000-gallon tank can cover (3 acres).

Guided and independent practice (15 min): Distribute the handout. Complete problem 1 together, then have students finish problems 2 through 5 in pairs, checking that each keeps the rate at 12,000 gallons per acre.

Closure and exit ticket (5 min): Students answer one question on an index card: "A different field uses 90,000 gallons on 6 acres. What is its gallons-per-acre rate, and is it more or less efficient than Larkfen's 12,000?" Scan for the correct rate (15,000, which is less efficient) before dismissal.

Larkfen Farms Drip Irrigation: A Proportional-Reasoning Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Larkfen Farms is a fictional farm. Its drip system puts the same number of gallons on every acre. Here is the farm's watering log:

Acres watered Gallons used
2 24,000
5 60,000
8 96,000
  1. Divide gallons by acres for each row. What is the gallons-per-acre rate, and is it the same in every row?
  2. Write an equation for the gallons G used to water a acres.
  3. Use your equation to find the gallons needed to water 15 acres.
  4. Larkfen has a pond holding 84,000 gallons. How many acres can one watering cover?
  5. Explain how the equal ratios in your table show that the relationship is proportional.

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: 12,000 gallons per acre.
    24,000 ÷ 2 = 12,000, 60,000 ÷ 5 = 12,000, and 96,000 ÷ 8 = 12,000, the same rate in every row.
  2. Answer: G = 12,000a.
    Gallons equal the constant rate 12,000 times the number of acres a.
  3. Answer: 180,000 gallons.
    G = 12,000 × 15 = 180,000 gallons.
  4. Answer: 7 acres.
    84,000 ÷ 12,000 = 7 acres per watering.
  5. Answer: The ratio is constant.
    Because gallons divided by acres gives the same 12,000 in every row, the two quantities are proportional.

Differentiation

Support

Add a third column labeled "gallons ÷ acres" to the table and have students fill it in before problem 1. Seeing 12,000 repeat in every row gives them the constant of proportionality directly, before they are asked to write the equation. Allow a calculator for the division.

Extension

Ask students to compare Larkfen's drip system with an older sprinkler field that uses 18,000 gallons per acre. Have them write both equations, then find how many more gallons the sprinkler field uses to water 20 acres, and state the answer as a percent more than the drip system.

ELL supports

Pre-teach "acre," "per acre," and "proportional" with a labeled square standing for one acre and a water drop marked "12,000 gallons." Provide the sentence frame "each acre uses ___ gallons, so ___ acres use ___ gallons" for problems 3 and 4.

Extensions

Have students explore how much water different foods take to produce, using Water Footprint Network global averages that a pound of wheat takes roughly 220 gallons while a pound of beef takes roughly 1,800 gallons, most of it rainwater used by the pasture and feed crops cattle eat. Connecting a field's per-acre water rate to the water used to produce everyday foods applies the same proportional reasoning to the food students eat.