Math problem set Grade 4 Science

Erosion Rates from Sedgeholt School's Four Slope Trays

Nine grade 4 problems using a four-tray erosion test record, turning grams of washed-out soil into rates per minute and comparing trays that differ only in slope.

Grade: Grade 4
Subject: Science
Material: Math problem set
Time: 35 min
Prep: No prep
Materials: None

Standards

4-ESS2-1 NGSS

Make observations and/or measurements to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation.

How this material aligns: Problems 1, 2, and 8 turn measured sediment masses into erosion rates in grams per minute, and problems 3, 5, and 6 read the rate pattern across the three trays that differ only in slope height, which is the evidence about water's rate of erosion this standard asks students to work from.

All materials for 4-ESS2-1 →

4.MD.A.2 Common Core Math

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

How this material aligns: Every problem is a measurement word problem about masses in grams, and the record students draw from also carries the water poured in milliliters and the three-minute run time, so each problem requires choosing the right measurement.

All materials for 4.MD.A.2 →

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, 2, and 8 divide the two-digit and three-digit sediment masses 24, 120, and 144 by the one-digit divisor three to find a per-minute rate.

All materials for 4.NBT.B.6 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-04.

Objectives

Students will divide a measured sediment mass by the run time to find an erosion rate in grams per minute.
Students will compare trays that differ only in slope height to describe how steepness changed the amount of soil carried away.
Students will use the pattern in three measured trays to predict how much soil a fourth tray would lose.

Vocabulary

Erosion: Erosion is the wearing away and carrying off of soil and rock by moving water, wind, or ice. Fast-moving stormwater can strip soil from bare ground and stream banks.

Also: slope, rate, sediment, controlled test

Teacher overview

The fictional town of Sedgeholt has a bare slope beside its elementary school parking lot, and after every storm some of that soil ends up in the storm drain at the bottom of the hill. A fourth-grade class set up four trays of the same soil to measure how much soil running water carries away, raising the high end of three trays by different amounts and pouring twice as much water into a fourth. Every problem in this set works from that measured record: students divide the grams collected by the run time to get a rate in grams per minute, then compare trays to say what the numbers are evidence of. The error to watch for is comparing Tray C with Tray D and calling the difference a slope effect, because those two trays differ in both slope height and water amount, while only Trays A, B, and C hold everything except the slope steady. A smaller and more common arithmetic error is inverting the division and writing 3 divided by 24 when the question asks how many grams washed out in one minute.

Erosion Rates from Sedgeholt School's Four Slope Trays — Grade 4 Science

Name: ____________________________ Date: ______________

Problems

Suppose a fourth-grade class in the town of Sedgeholt fills four trays with the same soil. The trays are all the same size. The class raises the high end of each tray on wooden blocks, and each block lifts that end by 4 cm. Water goes into the high end through the same sprinkler cup, and every tray runs for 3 minutes. The water carries soil down the tray and into a catch cup at the low end. The class dries that soil and weighs it in grams. Water is measured in milliliters, written mL.

Tray	Blocks under the high end	Height of the high end (cm)	Water poured (mL)	Soil washed out (g)
A	1	4	900	24
B	2	8	900	72
C	3	12	900	120
D	2	8	1,800	144

Tray A sat on 1 block. Water washed 24 grams of soil out of Tray A in 3 minutes. How many grams of soil washed out each minute?
Tray C sat on 3 blocks. Water washed 120 grams of soil out of Tray C in 3 minutes. How many grams of soil washed out each minute?
Tray A lost 24 grams of soil, and Tray C lost 120 grams. Both trays got 900 mL of water and both ran for 3 minutes. How many more grams of soil did Tray C lose than Tray A?
Tray A lost 24 grams of soil, and Tray C lost 120 grams. How many times as much soil did Tray C lose as Tray A?
Tray A sat on 1 block and lost 24 grams. Tray B sat on 2 blocks and lost 72 grams. Tray C sat on 3 blocks and lost 120 grams. All three trays got 900 mL of water and ran for 3 minutes. How many more grams washed out each time the class added one block?
The class set up Tray E the same way, on 4 blocks, with 900 mL of water for 3 minutes. Trays A, B, and C lost 24 grams, 72 grams, and 120 grams. If the pattern keeps going, how many grams should Tray E lose?
Tray B and Tray D both sat on 2 blocks. Tray B got 900 mL of water and lost 72 grams. Tray D got 1,800 mL of water and lost 144 grams. Both trays ran for 3 minutes. How many more grams of soil did Tray D lose than Tray B?
Tray C lost 120 grams of soil in 3 minutes. Tray D lost 144 grams of soil in 3 minutes. How many more grams each minute did Tray D lose than Tray C?
Tray C lost soil at a rate of 40 grams each minute. Suppose the rain kept falling and Tray C kept losing soil at that same rate. How many grams would wash out of Tray C in 5 minutes?

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: 8 grams per minute.
The 24 grams washed out over 3 minutes, so divide the mass by the time: 24 divided by 3 = 8.
Check by multiplying back: 8 grams x 3 minutes = 24 grams. The unit is grams per minute because the answer tells how much soil moved in one minute.
Answer: 40 grams per minute.
Divide the mass by the time: 120 divided by 3. Twelve divided by 3 is 4, so the quotient of 120 and 3 is 40 grams per minute. Check by multiplying back: 40 grams x 3 minutes = 120 grams.
Answer: 96 grams.
Subtract the smaller mass from the larger one: 120 - 24. Take away 20 to reach 100, then take away 4 more to reach 96 grams. Because the two trays got the same water for the same time, the 96 grams is evidence that the steeper slope carried away more soil.
Answer: 5 times as much soil.
Ask what number times 24 gives 120. Counting up by 24 gives 24, 48, 72, 96, 120, which is five steps, so 24 x 5 = 120 and Tray C lost 5 times as much soil as Tray A.
Answer: 48 grams.
Find each step in the pattern. From Tray A to Tray B, 72 - 24 = 48 grams. From Tray B to Tray C, 120 - 72 = 48 grams. The two steps are equal, so each added block washed out 48 more grams.
Answer: 168 grams.
Suppose the pattern from problem 5 keeps going. Tray C is the 3-block tray at 120 grams, and one more block adds 48 grams, so 120 + 48 = 168 grams. Check the whole pattern: 24, 72, 120, 168, with a step of 48 grams each time.
Answer: 72 grams.
Subtract the smaller mass from the larger one: 144 - 72 = 72 grams. Tray B and Tray D sat on the same 2 blocks, so the slope was not what changed here. The only difference was the water, and Tray D got 1,800 mL instead of 900 mL.
Answer: 8 grams per minute.
Find each rate first. Tray D: 144 divided by 3 = 48 grams per minute. Tray C: 120 divided by 3 = 40 grams per minute. Then subtract: 48 - 40 = 8 grams per minute. Point out in the discussion that this comparison does not show a slope effect, because Tray C and Tray D differ in both slope height and water amount.
Answer: 200 grams.
Multiply the rate by the time: 40 grams x 5 minutes. Four times 5 is 20, so 40 x 5 = 200 grams.

Differentiation

Support

Give these students a copy of the table from the town of Sedgeholt with the 3-minute run time circled on every row, so the divisor in problems 1, 2, and 8 is easy to find. Model 24 divided by 3 = 8 on a strip of eight-gram groups before they start. Provide problems 3 and 7 with the two masses already stacked for subtraction, and give problem 6 as a number line marked in steps of 48 grams so the pattern can be counted rather than computed.

Extension

Suppose the class builds Tray F on more blocks and the same pattern holds. Ask these students how many blocks Tray F would need to wash out 264 grams, and have them show the pattern that got them there. A second task is to name which two trays they would compare to test the water amount by itself, and to explain in writing why Tray C and Tray D cannot answer that question.

ELL supports

Pre-teach slope, washed out, rate, and each minute with a side-view drawing of one tray from the town of Sedgeholt, labeled with the blocks, the sprinkler cup, and the catch cup. Provide a worked example of a division that ends in the words grams per minute. Give sentence frames for problems 3, 5, and 8: "Tray ___ lost ___ more grams than Tray ___." and "The trays were the same except for ___."

Extensions

Have students run one more tray to test a variable the class has not changed yet, such as a cover of grass clippings over the soil, keeping the blocks, the water, and the time the same as Tray B so that only the cover differs. Suppose their new tray loses less soil than Tray B did. Ask them to write what that result would suggest about planting the bare slope beside the parking lot, and to name one measurement they would want to repeat before recommending it to a public works crew.