Snow density: What percent of snow is water?

Snow can be an inspiration for a math activity. Have students calculate the percent of snow that is water. This will vary, as light and fluffy snow has much less water content than heavy and wet snow.

To do this, have students fill a measuring cup with snow. I used a one-liter container marked in milliliters and filled it to the top, 1000 mL. In metric, 1 mL takes up 1 cubic centimeter of volume. So this amount of snow is also 1000 cubic centimeters.

Let the snow melt. Then divide the measurement of water by the original measurement of snow. 

In this case, the snow melted down to 180 mL, and 180/1000 = 0.18. The snow was 18% water! Also, remind students that the density of water is very close to 1 gram per cubic centimeter. Thus, you can also say that the density of snow for this example was 0.18. Snow density can vary from 0.05 for very light snow to 0.5 for heavy packed snow.

As an extension of this activity, you might ask students to calculate the weight of a specific depth of the snow that was tested, over an area such as the roof of a house. This is easiest with metric measurements because 1 cubic centimeter of water weighs 1 gram.

Relating Decimals to Fractions (Grades 4-5)

Many students who come to me for math tutoring are very weak with fraction and decimal concepts. Here are a couple of sample responses from 5th grade students this week.

Q: How can you write 0.15 as a fraction?
A: Is it one-fifth?

Notice that the student tried to write the fraction using the same digits as the decimal.

Q: Write the number two and fifty-four hundredths.
A: 2.54
Follow-up Q: That's right. Can you also write it as a mixed number?
A: No, I don't know how.

Many students have trouble relating decimals to fractions because of inadequate emphasis on decimals as shortcuts for fractions. In Grade 4 of Common Core, there is a high emphasis on fractions in tenths and hundredths, and on meaning of decimals related to fractions. Here are examples of expectations from Common Core 4.NF.5 and 4.NF.6.

• Express fractions in tenths as hundredths.  (i.e. 2/10 is the same as 20/100)
• Add fractions in tenths and hundredths. (i.e. 3/10 + 4/100 = 34/100)
• Convert between decimals and fractions in tenths or hundredths (i.e. 4/10 = 0.4, 0.78 = 78/100)

It is very important that students have a strong understanding of fractions before tackling decimals or students will simply be manipulating digits. They may be getting the correct answers to decimal questions, yet have no idea what the decimals mean. In my tutoring, I emphasize that every number in decimal form is really just a shortcut for a fraction or mixed number.

With students in grades 4-8, I often show them how to change long decimals to fractions. For example, 0.123456789 is the fraction 123,456,789/1,000,000,000. Each digit to the right of the decimal point corresponds to a zero in the denominator of the fraction.