Math problem set Grade 4 Engineering & Design

Shepton Village's Pipe Order: Sections, Bundles, and Workdays

A grade 4 problem set where students divide a fictional village's pipe replacement into 6-foot sections, order bundles, and interpret a leftover remainder.

Grade: Grade 4
Subject: Engineering & Design
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: None

Standards

4.NBT.B.6 Common Core Math

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

How this material aligns: Problems 1, 3, and 6 find whole-number quotients with one-digit divisors: 3,600 divided by 6, then 576 divided by 8, then 600 divided by 9, which leaves a remainder.

All materials for 4.NBT.B.6 →

4.NBT.B.5 Common Core Math

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

How this material aligns: Problems 4, 5, 7, 8, and 9 multiply whole numbers, including the two-digit pairs 15 times 24 and 20 times 30 for crew output.

All materials for 4.NBT.B.5 →

4.OA.A.3 Common Core Math

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

How this material aligns: Problem 6 requires interpreting the remainder 6 as sections left for a later workday rather than as an extra day, the reasoning this standard names.

All materials for 4.OA.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will divide a total pipe length by a section length to find how many sections a job needs.
Students will multiply to find how many sections a truckload carries and how much pipe a crew installs.
Students will interpret a remainder as sections left over for the next workday.

Vocabulary

Water main: A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: section, bundle, workday

Teacher overview

The fictional village of Shepton is replacing 3,600 feet of old water main under Millrace Road, and the crew has to work out what to order before any digging starts. New pipe arrives in straight sections 6 feet long, packed in bundles, and the whole set of problems follows that one order from the total length down to the number of workdays. Problems 2 and 3 carry the section count found in problem 1 forward through the order, though each problem restates the figures it needs so a student who erred earlier can still work the rest. A common error in this math is reading the remainder in problem 6 as a number of days instead of a number of sections; the answer key names the unit at every step so students can see where a remainder belongs.

Shepton Village's Pipe Order: Sections, Bundles, and Workdays — Grade 4 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Shepton is replacing 3,600 feet of water main. Each new pipe section is 6 feet long. How many sections does the village need?
The village yard already holds 24 sections left from an older job. The job needs 600 sections in all. How many more sections must the village order?
Sections ship in bundles of 8. The village orders 576 sections. How many bundles is that?
One delivery truck carries 15 bundles. Each bundle holds 8 sections. How many sections does one truck carry?
Each section is 6 feet long. One truck carries 120 sections. How many feet of pipe does one truckload cover?
The crew puts in 9 sections on each workday. The job needs 600 sections. How many full workdays does that take, and how many sections are left over for the next day?
A second crew puts in 15 sections on each workday and works 24 workdays. How many sections does that crew put in?
Shepton plans 6 weeks of work. The crew works 5 days each week. How many workdays is that?
Suppose a crew puts in 20 sections on each of those 30 workdays. How many sections is that in all, and is it enough for the 600-section job?
The job needs 600 sections, but Shepton orders only 576 of them. Explain why the village does not order all 600.

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: 600 sections. Divide the total length by the length of one section: 3,600 / 6 = 600 sections.
Answer: 576 sections. Subtract the sections already in the yard from the sections the job needs: 600 - 24 = 576 sections.
Answer: 72 bundles. Divide the sections ordered by the number in each bundle: 576 / 8 = 72 bundles, with none left over.
Answer: 120 sections. Multiply the bundles on the truck by the sections in each bundle: 15 x 8 = 120 sections.
Answer: 720 feet. Multiply the sections on the truck by the length of one section: 120 x 6 = 720 feet.
Answer: 66 full workdays. Divide the sections by the daily pace: 600 / 9 = 66 with a remainder of 6, because 9 x 66 = 594 and 600 - 594 = 6. The remainder is 6 sections, not 6 days, so the crew finishes those 6 sections on a 67th day.
Answer: 360 sections. Multiply the daily pace by the number of workdays: 15 x 24 = 360 sections.
Answer: 30 workdays. Multiply the weeks by the workdays in each week: 6 x 5 = 30 workdays.
Answer: 600 sections. Multiply the daily pace by the workdays: 20 x 30 = 600 sections, which is exactly the number the job needs, so the plan works with none to spare.
Answer: The yard already holds 24 sections. Those 24 sections count toward the 600 the job needs, so the village orders only the 576 that are missing and saves the cost of pipe it already owns.

Differentiation

Support

Give these students a multiplication chart and a written reminder that 3,600 is 36 hundreds, so 3,600 / 6 can be found as 36 / 6 hundreds. Let them start with problems 4, 5, 7, and 8, which are single-step multiplications, before returning to the division items.

Extension

Ask these students to plan the delivery schedule: if the crew puts in 9 sections each workday and one truck brings 120 sections, how many workdays does one truckload last, and how many truckloads does the whole job take? Have them explain what the leftover sections from the last truck mean.

ELL supports

Provide a labeled drawing of one 6-foot pipe section, one bundle of 8 sections, and one truck holding 15 bundles, so the three units stay separate in students' minds. Give a sentence frame for the answers: "I ___ because the problem asks for the number of ___."