Lesson plan Grade 7 Engineering & Design
Threshel Brook Culvert: Criteria for a Farm Road Crossing
A grade 7 lesson where students use a map scale to find a drainage area, size the design flow for a fictional culvert, and separate its criteria from its constraints.
Objectives
- Students will compute a drainage area in acres from a map drawn to a stated scale.
- Students will apply a runoff rule to convert drainage area into a design flow for a culvert.
- Students will distinguish the culvert's criteria from its constraints and justify a pipe size.
Vocabulary
Key words: drainage area, culvert, design flow, runoff coefficient, constraint
Teacher overview
Threshel Township is a fictional rural community whose gravel farm road crosses Threshel Brook through a rusted metal pipe set under the roadbed. That pipe, called a culvert, washed out in the last heavy storm and stranded three farms for two days. This lesson puts students on the replacement team: they find the brook's drainage area from a scaled map, run it through a standard runoff rule to get a design flow, and then choose a pipe from a capacity table while listing what else limits the choice. A common misconception in this work is that a bigger drainage area on the map means a bigger pipe by the same factor, when the runoff rule also depends on the ground cover and on the storm the design targets.
Procedure
Hook (5 min): Describe the washed-out crossing at fictional Threshel Brook and ask students what the replacement pipe must do. Record their answers on the board. Answers along the lines of "carry the water" rarely say how much water or from which storm, which sets up the day's point that a criterion has to be measurable.
Direct instruction (12 min): Define drainage area as all the land that sheds water toward one point in a stream. Introduce the township's runoff rule, which is written as design flow equals the runoff coefficient times the rainfall rate times the drainage area, with flow measured in cubic feet per second and area in acres. Explain that the runoff coefficient describes how much rain runs off instead of soaking in, and that pasture takes a coefficient of 0.2 while pavement runs much higher. Model the full chain on a parcel students will not be asked to key: a square that measures 2 inches on each side on a map drawn at 1 inch equals 500 feet is 1,000 feet on each side, which is 1,000,000 square feet, which is 1,000,000 divided by 43,560, or about 23.0 acres. With the 2-inch-per-hour design storm and the pasture coefficient, its design flow is 0.2 times 2 times 23.0, or about 9.2 cubic feet per second.
Guided practice (13 min): Distribute the student handout. Work questions 1 through 3 together at the board so every student has the drainage rectangle converted from map inches to real feet and then to square feet. Stop after question 3 and ask the class to predict, before computing, whether the answer in acres will be larger or smaller than the number of square feet, and why. This prediction catches students who divide in the wrong direction.
Independent practice (15 min): Students complete handout questions 4 through 8 in pairs. Circulate and check that pairs are carrying units through each step rather than stacking bare numbers. Pairs who finish early should write a second sentence on question 8 naming which of their constraints would be hardest to satisfy and why.
Closure and formative check (5 min): Collect the handouts and scan question 6 only. If fewer than three quarters of the class chose the 24-inch pipe, reteach the capacity table at the start of the next session by walking the class through why the 18-inch pipe fails and why the 30-inch pipe is oversized. Close by asking two students to read aloud one constraint they wrote for question 8.
Student Handout
Suppose you are on the design team for the Threshel Brook crossing. Use the figures below for every question.
The township's map is drawn at the scale 1 inch equals 500 feet. On that map, the land draining to the crossing is shaded as a rectangle 3 inches long and 2 inches wide. One acre equals 43,560 square feet. The land is pasture, which takes a runoff coefficient of 0.2. The township designs for a storm that drops 2 inches of rain per hour. The runoff rule is: design flow equals runoff coefficient times rainfall rate times drainage area, with flow in cubic feet per second and area in acres.
The pipe supplier offers three sizes:
| Pipe size | Capacity in cubic feet per second |
|---|---|
| 18 inches | 8 |
| 24 inches | 15 |
| 30 inches | 26 |
The shaded rectangle is 3 inches long on the map. How many feet long is it on the ground?
The same rectangle is 2 inches wide on the map. How many feet wide is it on the ground?
Using your answers to questions 1 and 2, how many square feet is the drainage area?
One acre equals 43,560 square feet. How many acres is the drainage area? Round to the nearest tenth of an acre.
Use the runoff rule with a coefficient of 0.2, a rainfall rate of 2 inches per hour, and your acreage from question 4. What is the design flow in cubic feet per second? Round to the nearest tenth.
Look at the pipe table. Which is the smallest pipe whose capacity is at least as large as your design flow from question 5?
What percent of that pipe's rated capacity does your design flow use? Round to the nearest whole percent.
Cost is one constraint on this project. Name two other constraints the design team must respect, and explain in one sentence why each one limits the choice of pipe.
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: 1,500 feet.
3 inches x 500 feet per inch = 1,500 feet.Answer: 1,000 feet.
2 inches x 500 feet per inch = 1,000 feet.Answer: 1,500,000 square feet.
1,500 feet x 1,000 feet = 1,500,000 square feet.Answer: 34.4 acres.
1,500,000 square feet divided by 43,560 square feet per acre = 34.435 acres, which rounds to 34.4 acres.Answer: 13.8 cubic feet per second.
0.2 x 2 x 34.4 = 13.76 cubic feet per second, which rounds to 13.8.Answer: The 24-inch pipe.
The 18-inch pipe carries only 8 cubic feet per second, which is less than the design flow. The 24-inch pipe carries 15, which is enough, so it is the smallest pipe that works.Answer: 92 percent.
13.8 divided by 15 = 0.92, which is 92 percent of the pipe's rated capacity. Accept 92 percent from the rounded flow or the unrounded 13.76, which also rounds to 92 percent.Answer: Two valid constraints with reasons.
Accept any two genuine limits with an explanation attached. Common correct answers include the height of the roadbed, since a taller pipe may not fit under the gravel without rebuilding the road; the length of time the road may be closed, since the farms need access; fish and other stream life needing to pass through, which favors a wide pipe set low with a natural bottom; the width of the township's right-of-way; and the weight of farm equipment the pipe must carry overhead. Do not accept restatements of the capacity criterion, which is a target rather than a limit.
Differentiation
Support
Give these students a handout copy with questions 1 and 2 already answered and the multiplication for question 3 set up. Provide a printed conversion strip showing one acre alongside a familiar reference such as a school football field, so the acreage answer in question 4 has a size students can picture. Let them choose from a word bank for question 8 rather than generating constraints from scratch.
Extension
Have students redo questions 5 through 7 for a version of the site where half the pasture has become a paved equipment yard with a runoff coefficient of 0.9, computing a blended coefficient first. Ask them to report whether any pipe in the table can carry the new flow, and what the township could do if none can, and to write a paragraph on why a township might restrict paving upstream of an old culvert.
ELL supports
Pre-teach drainage area, culvert, and design flow with a simple sketch of a hillside funneling water to a single pipe under a road. Provide the sentence frame "___ inches on the map equals ___ feet on the ground" for questions 1 and 2, and the frame "This is a constraint because it ___" for question 8. Allow students to point to the pipe table row rather than write the pipe size in a sentence.
Extensions
Have students write a one-page memo to the fictional township board recommending a pipe size, stating the design flow, naming the storm the design targets, and listing the constraints they identified. Ask them to include one sentence on what would have to change for the recommendation to change, which pushes students to state their assumptions rather than bury them.