Lesson plan Grade 7 Math
Drumlin Fields Farm's Soil Moisture Ledger: A Grade 7 Lesson
A 50-minute grade 7 math lesson where students add and subtract signed decimals to track a fictional farm's stored soil water through a dry irrigation week.
Objectives
- Students will write daily gains and losses of soil water as signed decimals.
- Students will find the net change in stored soil water over a seven-day week.
- Students will predict when stored water will fall to an irrigation trigger level.
Vocabulary
Key words: stored soil water, crop water use, net change, irrigation, trigger level
Teacher overview
Growers who irrigate keep a running ledger of the water stored in the top few feet of soil, measured in inches of water depth. Rain and irrigation are gains, while the water a crop pulls out through its roots and leaves is a loss, and the ledger tells the grower when to turn the pumps on. This lesson follows one dry week at the fictional Drumlin Fields Farm, where students combine positive and negative decimals to find the net change and then predict the next irrigation date. The misconception to correct is treating every entry as an addition: a student who adds 1.25 inches of gains to 1.76 inches of crop use reports 3.01 inches, when the week actually lost 0.51 inch of stored water.
Procedure
Hook (5 min): Ask students how a farmer could tell whether a field needs watering without guessing. Introduce the idea of a soil water ledger measured in inches, and name the fictional Drumlin Fields Farm as the week's example.
Direct instruction (12 min): Build a two-day ledger on the board that is not on the handout. On the first day the crop uses 0.27 inch and no rain falls, so the entry is negative 0.27. On the second day the crop uses 0.24 inch and 0.55 inch of rain falls, so the entry is 0.55 minus 0.24, or positive 0.31. Show the running total moving down and then up, and write the rule that gains are positive and crop use is negative.
Guided practice (10 min): Distribute the handout and complete items 1 and 2 with the class, so students see how a day's added water and crop use combine into one signed net change. Ask a pair to explain aloud why day 4 comes out positive even though the crop still used water.
Independent practice (15 min): Students complete items 3 through 9 on their own. Watch for two errors: reporting the week's total crop use as the net change, and dropping the negative sign on the week's net change.
Closure and exit ticket (8 min): Poll the class on whether the week ended wetter or drier than it started and ask for the evidence. Then collect an exit ticket on an index card: "On day 9 the crop uses 0.24 inch and 0.30 inch of rain falls. What is the net change in stored water for day 9?" If more than a quarter of the class answers 0.54 inch, reteach the sign rule before the next class.
Student Handout
Drumlin Fields Farm is a fictional corn farm. Its soil held 3.20 inches of stored water at the start of the week. The table below lists what the crop used each day and what rain or irrigation added each day, both in inches.
| Day | Crop used (inches) | Added (inches) |
|---|---|---|
| 1 | 0.22 | 0.00 |
| 2 | 0.25 | 0.40 as rain |
| 3 | 0.28 | 0.00 |
| 4 | 0.30 | 0.75 as irrigation |
| 5 | 0.26 | 0.10 as rain |
| 6 | 0.24 | 0.00 |
| 7 | 0.21 | 0.00 |
- What is the net change in stored water on day 2, in inches?
- What is the net change in stored water on day 4, in inches?
- How many inches of water did rain and irrigation add over the whole week?
- How many inches of water did the crop use over the whole week?
- What is the net change in stored water for the whole week, in inches?
- How many inches of water were stored at the end of day 7?
- What was the mean daily crop water use for the week, in inches per day? Round to the nearest hundredth.
- Drumlin Fields irrigates again when stored water falls to 2.00 inches. If no rain falls and the crop keeps using 0.25 inch each day, after how many whole days will stored water first be at or below 2.00 inches?
- Suppose instead that on day 8 the crop uses 0.23 inch, no rain falls, and the farm wants to end day 8 back at 3.20 inches. How many inches of irrigation are needed?
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
- Answer: 0.15 inch.
Day 2 added 0.40 and lost 0.25, so the net change is 0.40 minus 0.25, which equals positive 0.15 inch. - Answer: 0.45 inch.
Day 4 added 0.75 of irrigation and lost 0.30, so the net change is 0.75 minus 0.30, which equals positive 0.45 inch. - Answer: 1.25 inches.
Only three days added water: 0.40 plus 0.75 plus 0.10 equals 1.25 inches. - Answer: 1.76 inches.
Add the seven daily crop use figures: 0.22 plus 0.25 plus 0.28 plus 0.30 plus 0.26 plus 0.24 plus 0.21 equals 1.76 inches. - Answer: -0.51 inch.
Subtract the losses from the gains: 1.25 minus 1.76 equals negative 0.51 inch, so the week ended drier than it began. - Answer: 2.69 inches.
Start with 3.20 and apply the net change: 3.20 minus 0.51 equals 2.69 inches. - Answer: 0.25 inch per day.
Divide the week's crop use by seven days: 1.76 divided by 7 equals 0.2514, which rounds to 0.25 inch per day. - Answer: 3 days.
The field starts at 2.69 inches. After one day it holds 2.44, after two days 2.19, and after three days 1.94, which is the first value at or below 2.00 inches. - Answer: 0.74 inch.
The farm must climb from 2.69 to 3.20, a gain of 0.51 inch, while also replacing the 0.23 inch the crop uses. Then 0.51 plus 0.23 equals 0.74 inch of irrigation.
Exit ticket answer: 0.06 inch. Day 9 adds 0.30 and loses 0.24, and 0.30 minus 0.24 equals positive 0.06 inch.
Differentiation
Support
Give these students a ledger template with a signed-number column already filled for days 1 and 2 and a running total column beside it, so each day requires one subtraction and one addition. Limit the assignment to items 1 through 6 and allow a calculator.
Extension
Ask these students to rewrite the week as an expression with seven signed terms, evaluate it in a different order than day by day, and explain why the order does not change the result. Then have them find the largest single day of crop use the farm could absorb on day 8 and still end the day above 2.50 inches.
ELL supports
Pre-teach "stored," "crop use," "gain," and "loss" with a vertical bar that fills and empties as entries are read aloud. Provide the frame "On day ___ the soil gained ___ and lost ___, so the net change is ___" for items 1 and 2.