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Math problem set Grade 5 Science

Corven Ridge Storm Test: Where the Rain Went on Two Slopes

A grade 5 problem set comparing runoff and soak-in on a burned slope and a forested slope of a fictional ridge, using fractions and decimals to hundredths.

Objectives

  1. Students will write a measured part of a storm as a fraction of the whole storm in simplest form.
  2. Students will add and subtract fractions with unlike denominators to compare two hillside plots.
  3. Students will add and subtract decimals to hundredths to compare runoff across four storms.
  4. Students will explain how ground cover changes where a storm's water goes.

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: runoff, leaf litter, slope, soil

Teacher overview

Corven Ridge is a fictional hillside where a watershed crew studies what happens to rain after it lands. Two study plots sit on the same slope and receive the same storms. One plot lies under standing forest with a thick layer of dead leaves, while the other burned two summers ago and is now bare soil. A trough at the low edge of each plot catches the water that runs across the top of the ground, and pans buried in each plot catch the water that soaks down, so one storm can be split into two measured parts on each plot. This set is written to correct the belief that bare ground takes in more rain because no plants are in the way to block it or to drink it up. Dead leaves and living roots slow the water and open paths into the soil, so the forested plot absorbs far more of the same storm than the burned one, and the extra water the burned plot sheds reaches the creek within minutes rather than over the following weeks. Watch for students who read 12 out of 96 as 8 rather than as one eighth, which is the most common slip in problems 1 through 5.

Corven Ridge Storm Test: Where the Rain Went on Two Slopes — Grade 5 Science
Name: ____________________________ Date: ______________

Problems

Corven Ridge is a fictional hillside. A crew studies two plots on the ridge. The plots are the same size, and both got the same storm.

  • Plot F is under forest. Dead leaves cover the ground.
  • Plot B burned two summers ago. The soil is bare.

The storm put 96 liters of water on each plot. A trough at the low edge of each plot caught the water that ran across the top of the ground. Pans buried in each plot caught the water that soaked into the soil. Here is what the crew measured.

  • Plot F: 12 liters ran off the top of the ground, and 72 liters soaked into the soil.
  • Plot B: 48 liters ran off the top of the ground, and 32 liters soaked into the soil.
  1. Write the water that ran off Plot F as a fraction of the 96 liters that fell on it. Put the fraction in simplest form.
  2. Write the water that ran off Plot B as a fraction of the 96 liters that fell on it. Put the fraction in simplest form.
  3. Water that runs off the top of the ground reaches the creek fast. Use your fractions from problems 1 and 2. How much more of the storm ran off Plot B than off Plot F?
  4. Write the water that soaked into Plot F as a fraction of the 96 liters. Put the fraction in simplest form.
  5. Write the water that soaked into Plot B as a fraction of the 96 liters. Put the fraction in simplest form.
  6. Use your fractions from problems 4 and 5. How much more of the storm soaked into Plot F than into Plot B?
  7. On Plot F, 1/8 of the storm ran off and 3/4 of the storm soaked in. What fraction of the storm is that in all?
  8. On Plot B, 48 liters ran off and 32 liters soaked in. The rest stayed on the ground and on dead roots. How many liters stayed?
  9. One storm is not enough to trust, so the crew measured four more storms on Plot B. The runoff was 48.60 liters, 51.25 liters, 44.80 liters, and 50.15 liters. What was the total runoff from Plot B in those four storms?
  10. In those same four storms, Plot F had 49.80 liters of runoff in all. Use your total from problem 9. How many more liters ran off Plot B than off Plot F?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 1/8 of the storm. Plot F shed 12 liters out of the 96 liters that fell, so the fraction is 12/96. Both numbers divide by 12, and 12 divided by 12 is 1 while 96 divided by 12 is 8, which gives 1/8.
  2. Answer: 1/2 of the storm. Plot B shed 48 liters out of 96, so the fraction is 48/96. Both numbers divide by 48, giving 1/2. Half of everything that fell on the burned plot left across the surface.
  3. Answer: 3/8 of the storm. Rewrite 1/2 as 4/8 so both fractions share a denominator, then subtract: 4/8 minus 1/8 is 3/8. Three eighths more of the same storm headed straight downhill from the burned plot.
  4. Answer: 3/4 of the storm. Plot F took in 72 liters out of 96, so the fraction is 72/96. Both numbers divide by 24, and 72 divided by 24 is 3 while 96 divided by 24 is 4, which gives 3/4.
  5. Answer: 1/3 of the storm. Plot B took in 32 liters out of 96, so the fraction is 32/96. Both numbers divide by 32, giving 1/3.
  6. Answer: 5/12 of the storm. The smallest common denominator for 4 and 3 is 12. Rewrite 3/4 as 9/12 and 1/3 as 4/12, then subtract: 9/12 minus 4/12 is 5/12.
  7. Answer: 7/8 of the storm. Rewrite 3/4 as 6/8, then add: 1/8 plus 6/8 is 7/8. The missing 1/8 reached neither the trough nor the pans, because it stayed on the leaves and in the litter and later returned to the air.
  8. Answer: 16 liters. Add the two measured amounts: 48 plus 32 is 80 liters. Then subtract from the storm total: 96 minus 80 is 16 liters left on the ground and on dead roots.
  9. Answer: 194.80 liters. Add in order, keeping the decimal points lined up: 48.60 plus 51.25 is 99.85; 99.85 plus 44.80 is 144.65; 144.65 plus 50.15 is 194.80 liters.
  10. Answer: 145.00 liters. Subtract the forest total from the burned total: 194.80 minus 49.80 is 145.00 liters. The gap held up across the four storms combined, so the first result was not a one-time accident of that one storm.

Differentiation

Support

Give these students the four fractions in problems 1, 2, 4, and 5 already set up as 12/96, 48/96, 72/96, and 32/96, so their work begins at simplifying rather than at building the fraction. A multiplication chart helps them find the largest common factor. For problems 9 and 10, hand out a place-value grid with the decimal points already aligned in a column.

Extension

Ask these students to find what fraction of the storm reached neither the trough nor the buried pans on Plot B, and to write a short explanation of where that water most likely went. Then have them suppose the crew adds a third plot covered in low grass, predict where its two numbers would fall relative to the forest plot and the burned plot, and defend the prediction with the fractions they have already computed.

ELL supports

Before the problems, work through a labeled side-view drawing of one plot with three arrows: rain landing on the plot, water running across the surface, and water soaking down into the soil. Label the arrows with the same words the problems use, which are "ran off" and "soaked in." Offer sentence frames such as "On Plot F, ___ of the storm ran off" and "More water soaked into Plot ___ because ___."

Extensions

Have students walk the schoolyard and mark the two places most like the plots on this fictional ridge, one with plant cover and one with bare or paved ground, then predict which one sends water off the property first. Students can also suppose the burned plot is replanted and describe, in fractions, how they expect its runoff share to change over the next five years, naming which measurement the crew would need to repeat to check the prediction.