Math problem set Grade 4 Math

Winding Creek Water Testing Team: Sampling and Shipping Problems

A grade 4 math problem set where a fictional student water-testing team multiplies sites by bottles and visits, then divides samples among shipping cases with remainders.

Grade: Grade 4
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

Standards

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: Problems 6 and 7 require dividing 93 total sample bottles by a shipping case capacity of 8 and deciding that the leftover 5 bottles still need a twelfth case, the remainder-interpretation reasoning this standard requires in a multistep context.

All materials for 4.OA.A.3 →

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 1, 2, 4, and 8 multiply the number of sites by bottles collected per site and by the number of visits, using two-digit or smaller factors throughout, the multiplication this standard specifies.

All materials for 4.NBT.B.5 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will multiply site counts, bottles per site, and visit counts to find total water samples collected.
Students will divide a total number of samples by a shipping case capacity and interpret the remainder to determine how many cases are needed.

Vocabulary

Watershed: A watershed is all the land where rain that falls will drain to the same stream, river, or lake. Everyone lives in a watershed, no matter how far from the water they live.

Also: sample, site, remainder

Teacher overview

A fictional student water-testing team at Winding Creek collects small sample bottles at several sites along the creek throughout a season, modeled on the way real watershed-monitoring volunteers work. This problem set follows the team through a season of visits, multiplying to find how many samples they collect, then dividing that total among shipping cases and interpreting the remainder. A common misconception in this kind of problem is assuming that leftover samples that do not fill a whole case can simply be left behind, when in reality every sample still needs to be shipped, which means a partial case still counts as a full case for planning and cost purposes.

Winding Creek Water Testing Team: Sampling and Shipping Problems — Grade 4 Math

Name: ____________________________ Date: ______________

Problems

The team visits 6 sites. At each site, they collect 3 sample bottles. How many bottles are collected in one visit?
The team makes 4 visits. Each visit collects bottles the same way as problem 1. What is the total number of bottles for all 4 visits?
Each shipping case holds 8 bottles. Use your answer to problem 2. How many full cases can the team fill? How many bottles are left over?
For the last visit of the season, the team adds a 7th site. They still collect 3 bottles at each site. How many bottles are collected on this last visit?
Add the season total from problem 2 to the last-visit total from problem 4. What is the new season total?
Pack all the bottles from problem 5 into shipping cases that hold 8 bottles each. How many full cases can the team fill? How many bottles are left over for a partly filled case?
A partly filled case still costs a full shipping fee, the same as a full case. Use your answer to problem 6. How many cases in total will the team pay for?
Next season, the team plans a new schedule: 5 sites per visit, 5 visits total, still 3 bottles at each site. Would this new plan collect more, fewer, or the same number of bottles as problem 2's plan (72 bottles)? Show the work that proves your answer.

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: 18 bottles.
6 sites × 3 bottles per site = 18 bottles.
Answer: 72 bottles.
18 bottles per visit × 4 visits = 72 bottles.
Answer: 9 full cases, no bottles left over.
72 ÷ 8 = 9, since 8 × 9 = 72 exactly, with no remainder.
Answer: 21 bottles.
7 sites × 3 bottles per site = 21 bottles.
Answer: 93 bottles.
72 bottles (problem 2) + 21 bottles (problem 4) = 93 bottles.
Answer: 11 full cases, 5 bottles left over.
93 ÷ 8: 8 × 11 = 88, and 93 − 88 = 5. So there are 11 full cases and 5 leftover bottles that do not fill a case on their own.
Answer: 12 cases.
The 11 full cases from problem 6 plus 1 more case for the 5 leftover bottles equals 12 cases the team will be charged for, since a partly filled case still counts as a full case.
Answer: More bottles, by 3.
New plan: 5 sites × 3 bottles per site = 15 bottles per visit; 15 bottles × 5 visits = 75 bottles. Comparing 75 to the original 72 bottles: 75 − 72 = 3, so the new plan collects 3 more bottles than the original plan.

Differentiation

Support (below grade level)

Provide a printed table with columns for "sites," "bottles per site," "visits," and "total bottles" so students can fill in each number before multiplying, reducing the number of steps they must track in their head at once.

Extension (above grade level)

Ask students to find a combination of sites, bottles per site, and visits (different from any used in this problem set) that produces a season total between 90 and 100 bottles, and to show the multiplication that proves their combination works.

ELL supports

Pre-teach "site," "sample," and "remainder" using a simple map showing numbered dots along a creek, with small bottle icons at each dot to represent samples collected. Provide a sentence frame: "The team collects ___ bottles because there are ___ sites and ___ bottles at each site."