Math problem set Grade 4 Math
Culvermere Marsh Mussel Beds: Multiplying Gallons Filtered
A grade 4 problem set about two fictional freshwater mussel beds, where students multiply, add, and divide to find how much marsh water the mussels filter.
Objectives
- Students will multiply a three-digit mussel count by a one-digit filtering rate to find gallons filtered in a day.
- Students will compare two beds' daily totals and combine them into one figure.
- Students will divide a mussel count by a tray capacity and decide what the remainder means.
Vocabulary
Key words: mussel, bed, filter, marsh, remainder
Teacher overview
Culvermere Marsh is a fictional wetland where a restoration crew is rebuilding two beds of freshwater mussels along the bottom. Mussels sit in the sediment and draw water through their bodies, trapping tiny bits of algae and silt, so a healthy bed helps clear the water above it. In this scenario each mussel filters 9 gallons of water a day, and the problems build from a single bed's count up to a week of filtering and a tray count for moving the animals. The misconception this set is designed to correct appears in problem 4, where students often multiply the mussel count by the number of days instead of multiplying the daily gallon total by the number of days, producing a number that counts mussels rather than gallons. Reading the unit out loud after each step is the fastest way to catch that error.
Problems
In this fictional marsh, each mussel filters 9 gallons of water a day.
Bed A holds 128 mussels. Each mussel filters 9 gallons a day. How many gallons does Bed A filter in one day?
Bed B holds 245 mussels. Each mussel filters 9 gallons a day. How many gallons does Bed B filter in one day?
Bed B filters 2,205 gallons a day. Bed A filters 1,152 gallons a day. How many more gallons does Bed B filter each day?
Bed A filters 1,152 gallons every day. How many gallons does Bed A filter in 7 days?
Bed A holds 128 mussels and Bed B holds 245 mussels. How many mussels are in the two beds together?
The two beds hold 373 mussels in all. Each mussel filters 9 gallons a day. How many gallons do the two beds filter together in one day?
The crew moves all 373 mussels into trays. Each tray holds 8 mussels. How many trays can the crew fill all the way?
The crew has 373 mussels, and each tray holds 8 mussels. Every mussel must ride in a tray. How many trays does the crew need in all?
Explain why counting the mussels in a bed helps the crew predict how clear the marsh water will be. Write one or two sentences.
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: 1,152 gallons.
Multiply 128 by 9 in parts: 100 times 9 equals 900, 20 times 9 equals 180, and 8 times 9 equals 72. Adding 900 plus 180 plus 72 gives 1,152 gallons a day.Answer: 2,205 gallons.
Multiply 245 by 9 in parts: 200 times 9 equals 1,800, 40 times 9 equals 360, and 5 times 9 equals 45. Adding 1,800 plus 360 plus 45 gives 2,205 gallons a day.Answer: 1,053 gallons.
Subtract the smaller daily total from the larger one: 2,205 minus 1,152. Take away 1,000 to reach 1,205, then take away 152 to reach 1,053 gallons.Answer: 8,064 gallons.
Multiply the daily gallon total by the days, not the mussel count by the days. In parts, 1,000 times 7 equals 7,000, 100 times 7 equals 700, 50 times 7 equals 350, and 2 times 7 equals 14. Adding 7,000 plus 700 plus 350 plus 14 gives 8,064 gallons.Answer: 373 mussels.
Add the two counts: 128 plus 245. Adding 128 plus 200 gives 328, then 328 plus 45 gives 373 mussels.Answer: 3,357 gallons.
Multiply 373 by 9 in parts: 300 times 9 equals 2,700, 70 times 9 equals 630, and 3 times 9 equals 27. Adding 2,700 plus 630 plus 27 gives 3,357 gallons. This matches the sum of the two daily totals, since 1,152 plus 2,205 also equals 3,357.Answer: 46 trays.
Divide 373 by 8. Eight goes into 37 tens 4 times with 5 tens left, and into 53 ones 6 times with 5 ones left. The quotient is 46 with a remainder of 5. Check: 46 times 8 equals 368 mussels.Answer: 47 trays.
The 46 full trays hold 368 mussels, which leaves 5 mussels with nowhere to ride. One more tray carries those 5, so the crew needs 46 plus 1, or 47 trays. The last tray will hold only 5 mussels.Answer: More mussels filter more water.
Accept any explanation stating that each mussel filters a set amount every day, so the total gallons filtered grows with the count, and that a crew who knows the count can estimate how much of the marsh will be cleared and how quickly.
Differentiation
Support (below grade level)
Provide an area model already drawn for problems 1 and 2, with the mussel count split into hundreds, tens, and ones along one side and the 9 written along the other. Supply a multiplication chart through 12 and a place-value chart through ten thousands. Let these students work problems 1, 2, 3, 5, and 7 only, and give them counters grouped in eights to build the tray problem physically before writing.
Extension (above grade level)
Ask students to design a third bed for the fictional Culvermere Marsh that would raise the daily total for all three beds above 5,000 gallons. They must state the mussel count they chose, show the multiplication that proves the new three-bed daily total, find how many gallons all three beds would filter in 7 days, and report how many 8-mussel trays the crew would need to move the entire marsh population.
ELL supports
Pre-teach "mussel," "bed," and "filter" with a labeled drawing showing a shell partly buried in sediment, an arrow for water going in, and a second arrow for cleaner water coming out. Post the drawing during the set. Provide sentence frames for problems 4 and 9: "I multiplied ___ gallons by ___ days, so the answer is ___ gallons," and "Counting the mussels helps because ___."
Extensions
Students can graph the two beds' daily totals on a bar chart and label each bar with the mussel count that produced it, then predict where a third bar would land for a bed of 300 mussels. A class studying local water can compare the fictional Culvermere numbers with a nearby restoration project's published mussel counts and discuss why a crew tracks the count year after year.