Math problem set Grade 4 Math

Opening the Gates at Nockford Dam: Whole-Number Problems

Nine grade 4 problems set at a fictional dam on the Varrow River, using gate release rates in gallons per minute to practice multiplication and division with remainders.

Grade: Grade 4
Subject: Math
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 3, 5, and 6 divide four-digit release totals by one-digit numbers of minutes or loads, and problem 6 leaves a remainder to interpret.

All materials for 4.NBT.B.6 →

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 7 interprets the remainder left by problem 6 as gallons still in the pond, and problem 8 chains two multiplications across the same dam scenario.

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 multiply a per-minute release rate by a number of minutes to find a total in gallons.
Students will divide four-digit gallon totals by one-digit numbers and interpret the remainder.
Students will solve two-step problems that combine a release total with a daily limit.

Vocabulary

Reservoir: A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
Fish ladder: A series of water steps built beside a dam so migrating fish, like salmon, can swim past it. Fish leap or swim from pool to pool to reach the river above.

Also: gate, release, remainder

Teacher overview

Nockford Dam is a fictional dam on the Varrow River, and the crew there opens gates to send water downstream, to keep the fish ladder running, and to drain a holding pond after repairs. Every problem in this set uses the same dam and the same crew, so a total computed early is reused later. The misconception this set targets is treating a per-minute rate as a finished total. Students frequently answer a two-gate, four-minute question with 1,200 gallons because that number appears in the problem, without multiplying by the minutes and then by the number of gates. Insist that students write the units beside each factor, since gallons per minute times minutes is the step that keeps the rate from being mistaken for an amount. The gallon amounts are kept small so the arithmetic fits grade 4. Tell students that one gate on a real river dam can pass tens of thousands of gallons a minute or more.

Opening the Gates at Nockford Dam: Whole-Number Problems — Grade 4 Math

Name: ____________________________ Date: ______________

Problems

At the fictional Nockford Dam, one open gate lets out 1,200 gallons of water every minute.

The crew opens one gate for 6 minutes. How many gallons go through that gate?
The crew opens 3 gates for 1 minute. How many gallons go through in that minute?
One gate stayed open for 7 minutes and let out 8,400 gallons in all. How many gallons went out each minute?
The fish ladder takes a slower flow of 500 gallons each minute. It runs for 9 minutes. How many gallons pass through the fish ladder?
A holding pond holds 6,300 gallons. The crew pumps it out in 9 equal loads. How many gallons are in each load?
A second holding pond holds 5,000 gallons. The crew pumps 7 equal loads and leaves the rest in the pond. How many whole gallons are in each load?
Use your answer from problem 6. After the crew pumps all 7 loads, how many gallons stay in the pond?
On Thursday the crew opens 2 gates for 4 minutes each. Each gate still lets out 1,200 gallons a minute. How many gallons go out in all?
The dam may release no more than 9,600 gallons on Friday. The crew already released 7,200 gallons in the morning. How many gallons may they still release?

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: 7,200 gallons.
Multiply the rate by the minutes: 1,200 gallons each minute x 6 minutes = 7,200 gallons.
Answer: 3,600 gallons.
Three gates each send 1,200 gallons in one minute, so 3 x 1,200 = 3,600 gallons.
Answer: 1,200 gallons.
Divide the total by the minutes: 8,400 divided by 7 equals 1,200 gallons each minute. This matches the gate rate given at the top of the set.
Answer: 4,500 gallons.
Multiply the slower rate by the minutes: 500 x 9 = 4,500 gallons.
Answer: 700 gallons.
Divide the pond total by the number of loads: 6,300 divided by 9 equals 700 gallons in each load.
Answer: 714 gallons.
Divide the pond total by the number of loads: 5,000 divided by 7 equals 714 with 2 left over, so each full load holds 714 gallons.
Answer: 2 gallons.
The seven loads carry 7 x 714 = 4,998 gallons, and 5,000 - 4,998 = 2 gallons stay behind. That is the remainder from problem 6.
Answer: 9,600 gallons.
First find one gate's total: 1,200 x 4 = 4,800 gallons. Then double it for the second gate: 4,800 x 2 = 9,600 gallons.
Answer: 2,400 gallons.
Subtract the morning release from the daily limit: 9,600 - 7,200 = 2,400 gallons.

Differentiation

Support

Give these students a partly filled rate table with the columns Minutes and Gallons, and the rows for 1 minute and 2 minutes already completed at 1,200 and 2,400 gallons. Let them extend the table by repeated addition for problems 1 and 8, and provide long-division graph paper with one digit per box for problems 5 and 6.

Extension

Ask students to find how many whole minutes one gate would need to release 9,600 gallons, then to write a tenth problem of their own for this dam that ends in a remainder, along with a sentence explaining what the leftover gallons represent in the scenario.

ELL supports

Pre-teach gate, release, and fish ladder with a labeled side-view sketch of the dam showing the gate opening, the river below, and the stepped fish ladder beside it. Provide a unit card reading "gallons each minute" that students place beside the rate before multiplying, and give the sentence frame "___ gallons each minute x ___ minutes = ___ gallons."

Extensions

Have students graph the gallon totals from problems 1, 3, and 4 (7,200, 8,400, and 4,500 gallons) on a bar chart with gallons on the vertical axis, then describe in one sentence why the fish ladder bar is shorter than the two single-gate bars even though the fish ladder ran longer.