Project Grade 9 Math
Ambervale Irrigation District: A Water Budget Project
A grade 9 project for the fictional Ambervale Irrigation District, where teams model a season of water use as a constraint system within an allocation and budget.
Objectives
- Students will model a season's irrigation as a system of a constraint equation and inequality.
- Students will find acre splits that stay within a water allocation and a budget.
- Students will present an irrigation plan to a fictional district board with a data table.
Vocabulary
- Acre-foot
- The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.
- 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.
- Flood irrigation
- Watering crops by letting water flow across the field or down furrows between the rows. It is one of the oldest irrigation methods, and it can lose a lot of water.
- Water budget
- A water budget is a way of tracking all the water coming into an area, like rain and snowmelt, against all the water leaving it, like evaporation and streamflow. Scientists use water budgets to see whether a watershed or aquifer is gaining or losing water over time.
Also: allocation, constraint
Teacher overview
The fictional Ambervale Irrigation District gives a community farm a fixed water allocation each season. This project asks teams to plan the season inside that allocation and a set budget, choosing how many acres to water by flood and how many by drip. Teams model the plan as a system of a constraint equation and an inequality, then present it to a fictional district board. The driving question is how to plant the whole farm without going over either limit.
Project Brief
Driving question: How can we water all 60 acres of the farm within a 120 acre-foot allocation and a fixed budget?
Scenario: The Ambervale Irrigation District board (a fictional board) has asked each team to plan one season for a 60-acre community farm. The team must choose how many acres to water by flood and how many by drip.
Constraints:
- Water allocation: 120 acre-feet for the whole season.
- Flood irrigation uses 3 acre-feet per acre. Drip irrigation uses 1.8 acre-feet per acre.
- The team must plant all 60 acres.
- Budget: a fictional budget of $18,000 for equipment and water, using the teacher's price sheet.
Final deliverable: A written irrigation plan with a data table and a short talk to the board. The plan must show the acre split, the water it uses, and the cost. Both totals must stay within the limits.
Milestones
- Session 1 (research and constraints): Teams find the water an all-flood plan would use. All 60 acres by flood needs 3 times 60, which is 180 acre-feet. Teams compare that with the 120 acre-foot allocation and see it is over. Output: a one-page constraints sheet.
- Session 2 (model the water budget): Let x be flood acres and y be drip acres. Teams write x plus y equals 60 and 3x plus 1.8y at most 120. They solve for the most flood acres allowed. Output: a solved system with a viable acre split.
- Session 3 (cost the plan): Teams use the teacher price sheet to cost equipment and water for their acre split. The total must stay at or under the budget. Output: an itemized cost table.
- Session 4 (compare footprints and draft): Teams compare water-footprint values, about 1,800 gallons per pound of beef and about 220 gallons per pound of wheat, and write two sentences on why a district might encourage lower-water farm products. Output: a draft written plan.
- Session 5 (present to the board): Teams present the plan, the table, and the budget to the class acting as the district board. Output: the final written plan and a short talk.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Rubric
| Criterion | Emerging | Developing | Proficient | Advanced |
|---|---|---|---|---|
| Water-budget model | The plan does not use the allocation or the system | The plan names the 120 acre-foot limit but the acre split is not shown to meet it | The system is written and solved, and the split stays within 120 acre-feet | The split meets the limit, is checked with the numbers, and the team explains the trade-off between flood and drip |
| Budget constraint | The cost is missing or over budget with no fix | The cost is near the budget but not itemized | The itemized cost is at or under the fictional budget | The itemized cost is under budget and the team explains one choice made to stay there |
| Plan and presentation | The plan is incomplete or hard to follow | The plan covers the split but the reasoning is thin | The plan clearly shows the split, water, and cost, and the talk explains them | The talk explains both limits clearly and answers a likely board question |
Differentiation
Support
Give teams the item from Milestone 1 already worked, so they start Session 2 knowing the all-flood plan is over the limit. Provide the system x plus y equals 60 and 3x plus 1.8y at most 120 already written, and a price sheet with fewer choices.
Extension
Ask teams to find the acre split that uses the fewest acre-feet while still planting all 60 acres, then to compute how much water and money that plan saves against a 10-flood, 50-drip split.
ELL supports
Pre-teach "allocation," "flood irrigation," "drip irrigation," and "constraint" with a labeled picture of a flooded field next to a drip line. Provide a sentence frame for the board talk: "We watered ___ acres by drip so we would stay under ___ acre-feet."