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Math problem set Grade 2 Math

Snow to Water at Frostpine Hollow: A Grade 2 Melting Depth Problem Set

Grade 2 students compare snow depth to melted water depth across three storms at Frostpine Hollow, adding and subtracting within 100 to measure this reversible change.

Objectives

  1. Students will subtract within 100 to compare snow depth to melted water depth.
  2. Students will add within 100 to find combined totals across multiple storms.
  3. Students will estimate a reasonable depth based on a pattern in given data.

Vocabulary

Key words: depth, melt, compare, estimate

Teacher overview

Frostpine Hollow (a fictional place used for this problem set) records both the snow depth and the melted water depth after every winter storm, giving students a concrete example of water changing from solid to liquid and back, a reversible change. A common misconception in this set is assuming that a foot of snow melts into about the same depth of water; every storm in this set shows the melted depth is much smaller than the snow depth, and problem 4 asks students to apply that pattern instead of guessing a number close to the snow depth.

Snow to Water at Frostpine Hollow: A Grade 2 Melting Depth Problem Set — Grade 2 Math
Name: ____________________________ Date: ______________

Problems

  1. Storm 1 left 8 inches of snow at Frostpine Hollow. After it melted, the water left behind was 1 inch deep. How many inches less is the melted water than the snow?
  2. Storm 2 left 12 inches of snow, which melted down to 2 inches of water. How many inches less is the melted water than the snow?
  3. Which storm left more snow, Storm 1 or Storm 2? How many more inches?
  4. Storm 3 left 6 inches of snow. Based on the pattern from Storms 1 and 2, about how many inches deep do you think the melted water will be? Explain your reasoning.
  5. What is the total snow depth from Storms 1, 2, and 3 combined? (Use 6 inches for Storm 3.)
  6. What is the total melted water depth from Storms 1 and 2 combined?
  7. How many more inches of snow fell in Storm 2 than in Storm 3?
  8. A fourth storm brought 5 inches of plain rain, with no snow at all. What is the total depth of water from the melted snow of Storms 1 and 2 plus the rain?

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: 7 inches less. 8 minus 1 equals 7.
  2. Answer: 10 inches less. 12 minus 2 equals 10.
  3. Answer: Storm 2, by 4 inches. 12 minus 8 equals 4.
  4. Answer: About 1 inch (accept about 1 inch or a little less; 2 inches does not fit, because Storm 1 had more snow than Storm 3 and made only 1 inch of water). Storms 1 and 2 both melted down to a much smaller depth than the snow, so a smaller snowfall like Storm 3's 6 inches should melt down to only about 1 inch of water.
  5. Answer: 26 inches. 8 + 12 + 6 = 26.
  6. Answer: 3 inches. 1 + 2 = 3.
  7. Answer: 6 more inches. 12 minus 6 equals 6.
  8. Answer: 8 inches. 1 + 2 + 5 = 8.

Differentiation

Support

Provide a two-column chart (Snow depth / Water depth) with Storms 1 and 2 already filled in, so students only need to compute the "how many less" subtraction rather than organize the data themselves.

Extension

Ask students to design a Storm 5 with a snow depth of their choosing between 10 and 20 inches, predict a reasonable melted depth using the same pattern, and check that their prediction is much smaller than the snow depth.

ELL supports

Pre-teach "melt," "depth," and "compare" using a simple picture sequence (a snow pile, an arrow, then a small puddle). Allow problem 4's explanation to be given orally to a partner before writing a sentence.