Classroom activity Grade 11 Engineering & Design

Wynndale Main Replacement: A Quantity Take-Off Workshop

A grade 11 estimating workshop in which teams build a unit-price bid for a water main replacement, then reprice it when field crews hit unexpected rock.

Grade: Grade 11
Subject: Engineering & Design
Material: Classroom activity
Time: 55 min
Prep: Low prep
Materials: Printed unit-price sheets and plan description, one per team, Calculators, Two printed change-order cards for rounds two and three

Standards

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Teams carry linear feet, cubic yards, and square yards through the take-off and into dollar extensions, choosing consistent units at every step as this multi-step standard requires.

All materials for HSN-Q.A.1 →

HSG-MG.A.1 Common Core Math

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

How this material aligns: Items 1 and 2 model the rock trench and the pavement restoration strip as rectangular solids and surfaces, using their measures to describe the quantities being bid.

All materials for HSG-MG.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-03.

Objectives

Students will convert plan dimensions into bid quantities in cubic yards and square yards.
Students will extend bid quantities against unit prices to build a total construction estimate.
Students will reprice an estimate after a change in field conditions.

Vocabulary

Key words: quantity take-off, unit price, lump sum, change order, linear foot

Teacher overview

Teams of two or three act as estimators for competing contractors bidding a water main replacement in a fictional village, working from a written plan description and a unit-price sheet. The activity reproduces how construction bids are actually assembled, because the contractor is paid for measured quantities at agreed unit prices rather than for a single guessed number, and every team must therefore produce the same take-off before prices are applied. A second round introduces a change order when the field crew finds rock along a longer stretch than the plans showed, which is where the difference between a lump-sum item and a unit-price item becomes visible. The misconception this workshop is built to correct is the common student assumption that a construction estimate is one large guess adjusted by experience; in practice the judgment sits in the unit prices, while the quantities are measured off the drawings and can be checked line by line.

Activity Directions

Before class, print the plan description and the unit-price sheet from the Student Handout, and make the two change-order cards from the prompts in steps 5 and 6. Group students in twos or threes and give each team one packet and a calculator.
Explain the two kinds of bid items on the sheet. Unit-price items are paid for the quantity actually built, while lump-sum items are paid once regardless of quantity. Point out that this is why the rock excavation line matters later.
Round one, twenty minutes. Teams complete the take-off and the extensions for items 1 through 9 on the handout. Teams may check each other's cubic-yard conversion but must extend their own prices.
Post the engineer's estimate for the pipe item only after every team has an answer for it. Any team more than one percent away from that figure rechecks its arithmetic before continuing.
Round two, ten minutes. Read the first change-order card aloud: rock is found along an additional stretch of the alignment. Teams reprice items 11 and 12 and report a revised total.
Round three, ten minutes. Read the second change-order card aloud: the village asks whether the unit price per linear foot of finished main is competitive. Teams compute item 10 and write one sentence recommending whether the village should award the contract.
Round three closes when each team has posted its base bid, its revised bid, and its cost per linear foot on the board.
Debrief with two questions. First, why did the rock discovery change the price by a modest amount rather than a large one, given how alarming the words "rock excavation" sound? Second, if a contractor believed rock ran the entire length, how would that belief show up in the bid before any digging started?

Wynndale Main Replacement: A Quantity Take-Off Workshop — Grade 11 Engineering & Design

Name: ____________________________ Date: ______________

Student Handout

The fictional village of Wynndale is replacing an aging water main on the fictional Stallbrook Street. Use the plan description and the unit-price sheet below. All prices and quantities in this scenario are hypothetical figures written for this workshop.

Plan description:

Length of new eight-inch ductile iron main: 1,200 linear feet.
Open trench: 3 feet wide and 5 feet deep for the full length.
Rock is shown along 270 feet of the alignment, over a cross-section 3 feet wide and 3 feet deep.
Pavement restoration: a strip 6 feet wide over the full 1,200 feet of main.
Appurtenances: 4 gate valves, 3 fire hydrant assemblies, and 26 service reconnections.

Unit-price sheet for this fictional project:

Bid item	Unit	Unit price
Eight-inch ductile iron main, installed	linear foot	$185
Rock excavation	cubic yard	$95
Asphalt pavement restoration	square yard	$42
Gate valve, eight-inch	each	$2,400
Fire hydrant assembly	each	$6,800
Service reconnection	each	$1,900
Traffic control	lump sum	$12,000
Mobilization	lump sum	$28,000

Conversions: one cubic yard equals 27 cubic feet, and one square yard equals 9 square feet.

Find the rock excavation quantity, in cubic yards.
Find the pavement restoration quantity, in square yards.
Find the extended cost of the ductile iron main item.
Find the extended cost of the rock excavation item.
Find the extended cost of the pavement restoration item.
Find the extended cost of the four gate valves.
Find the extended cost of the three fire hydrant assemblies.
Find the extended cost of the twenty-six service reconnections.
Find the base bid total, including both lump-sum items.
Find the cost per linear foot of completed main, using the base bid total. Round to the nearest cent.
Change order: rock is found along an additional 180 feet of the alignment, at the same cross-section 3 feet wide and 3 feet deep. Find the added cost of that rock.
Find the revised bid total after the change order.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Every figure below belongs to the fictional Wynndale project and its hypothetical unit-price sheet.

Answer: 90 cubic yards.
The rock prism measures 270 feet by 3 feet by 3 feet, which is 2,430 cubic feet. Dividing 2,430 by 27 cubic feet per cubic yard gives 90 cubic yards.
Answer: 800 square yards.
The restoration strip is 1,200 feet by 6 feet, which is 7,200 square feet. Dividing 7,200 by 9 square feet per square yard gives 800 square yards.
Answer: $222,000.
Multiplying 1,200 linear feet by $185 per linear foot gives $222,000.
Answer: $8,550.
Multiplying 90 cubic yards by $95 per cubic yard gives $8,550.
Answer: $33,600.
Multiplying 800 square yards by $42 per square yard gives $33,600.
Answer: $9,600.
Multiplying 4 valves by $2,400 each gives $9,600.
Answer: $20,400.
Multiplying 3 hydrant assemblies by $6,800 each gives $20,400.
Answer: $49,400.
Multiplying 26 reconnections by $1,900 each gives $49,400.
Answer: $383,550.
The unit-price items total $222,000 plus $8,550 plus $33,600 plus $9,600 plus $20,400 plus $49,400, which is $343,550. Adding the two lump sums of $12,000 and $28,000 gives $383,550.
Answer: $319.63 per linear foot.
Dividing the base bid total of $383,550 by 1,200 linear feet gives $319.625, which rounds to $319.63 per linear foot.
Answer: $5,700.
The added rock prism measures 180 feet by 3 feet by 3 feet, which is 1,620 cubic feet, or 60 cubic yards after dividing by 27. Multiplying 60 cubic yards by $95 per cubic yard gives $5,700.
Answer: $389,250.
Adding the change-order amount of $5,700 to the base bid total of $383,550 gives $389,250.

Differentiation

Support

Give these teams a partially completed take-off sheet with the rock volume already converted to cubic yards and item 3 extended as a worked model. Provide a conversion strip showing 27 cubic feet per cubic yard and 9 square feet per square yard taped to the top of the calculator, so the unit step never has to be recalled from memory during the timed rounds.

Extension

Ask these teams to add a ten percent contingency to the base bid for the fictional project and to explain, in writing, why an owner carries a contingency on its own budget even when the contract prices are fixed. Then have them argue which two bid items on this fictional sheet carry the most quantity risk for the contractor and why.

ELL supports

Preteach four terms with a picture or a gesture: trench, linear foot, lump sum, and change order. Provide a bilingual glossary card for the bid items and allow teams to label their take-off rows in their first language before writing the English item name. Sentence frame for the debrief: "The rock change was small because ___."

Extensions

Have students find a published bid tabulation from a nearby city or county for a water or sewer project, which most public agencies post online, and compare its bid items against this fictional sheet. Students should identify one bid item that appears in the real tabulation but not in the workshop sheet and explain what work it pays for. A further step is to compare the spread between the low and high bidders on the real project and discuss what a wide spread suggests about how differently contractors judged the risk in the same set of drawings.