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.

Is your curriculum optimized for Common Core math?

How is the transition to Common Core working for your class? Does it seem like you have more to teach than before? If so, here are some critical questions to consider when adjusting a unit of instruction from a prior year or from older curriculum materials.

1) How close of a match are the content goals of the unit to the goals of Common Core for your grade?
For quick reference, see the goals list for your grade level at www.mathpaths.com. For more depth, read the actual wording of the standards using the CCSS links on that same page. Make a list and mark the unit goals as required, not required, or uncertain.

2) Which content goals in the unit should be considered as review or as preparation for the next year? 
The color coding and domain icons in the list at www.mathpaths.com will help you find related content in the prior or next grade. If the goal is review, you might be able to give it less emphasis. If the goal is not needed until the next year, considering skipping it! It is much more important for students to learn all goals for this year than to preview goals for the next year. Instead of uncertain, mark that goal as not required. When you skip content, remember to remove related questions from tests or assessment materials.

3) Does the unit include appropriate emphasis on the Standards for Mathematical Practices (MP)?
Mathematical practices are the important habits or processes needed to effectively solve problems including word problems and non-routine problems. These habits are often called problem-solving skills. For Common Core, it is important that problem-solving pages or activities relate to content standards of the prior year or current year. If a publisher's correlation mentions only an MP standard for a lesson, you may be able to skip the lesson. You can increase emphasis on MP standards during other lessons that develop required content.

4) Does Common Core require content that is missing or not sufficiently covered in the unit from a prior year or older materials?
If publishers simply updated the curriculum with "gap" lessons, there may be minimal content for some standards. And, the "gap" content might not be assessed. You may need to supplement the unit with free or low cost activities from TeacherPayTeachers.com, TeachersNotebook.com, or other sources.

In the past, most curriculum materials included 100 to 150 content goals/objectives per year. With CCSS, there are only 50-60 goals/objectives (based on the goals at www.mathpaths.com). Compared to prior years, the curriculum should include fewer topics in more depth! Good luck with Common Core!

Welcome back to school! The summer has been busy!

Can you believe that August is over? The summer has gone by too quickly. I've been busy updating checklists and making other resources for Common Core!
 
New Icons ~ Letter-shaped domain icons have been added to all checklists and posters to help students and teachers identify domains (strands) quickly, even if the signs are printed in black/white.

 

FREE Goals Leaflets using “I Can” Statements ~  There are now free leaflets of goals for each grade from K-8, numbered to match the goals on my poster checklists. These require just one sheet of paper, printed on both sides and folded to make a 4-page leaflet. You can download these from my website, www.mathpaths.com.

New Class Goal Signs ~ The 50-60 goals on each grade’s checklist are now available as individual goal signs illustrated with the domain icons, to be printed or displayed on a screen.

New and Expanded Products for the Standards for Mathematical Practice ~  In 2012, I developed “Be a Star” posters to emphasize practice standards in grades 3 to 8. Over the summer, I wrote a simpler K-2 version of "Be a Star" posters. Versions for 3-8 and K-2 include unique star-shaped icons for each practice standard. Both versions also include a mini book.

Have a great school year!

Angie

What's New with Problem Solving in Common Core?

In addition to content standards, Common Core includes 8 practice standards that are the same for all grade levels. These standards are designed to improve students' problem-solving abilities. The first five practice standards are very similar to the process standards that NCTM has advocated for years. However, there are a few notable differences in Mathematical Practices 6, 7, and 8. I feel that the wording of these is advanced for elementary grades, but the ideas are critical to helping students become proficient with solving problems.

MP6: Attend to precision.

Precision involves using appropriate vocabulary, measurement units, graph labels, and symbols. It also includes adjusting answers to be appropriate for the context of the problem. For example, if the answer to an area or volume question has more nonzero digits than the given information, digits that don't make sense should be rounded. In summary, students need to "pay attention to details" when writing or showing answers to problems. For my students, I extend this to include neatness in written work.

MP7: Look for and make use of structure.

Proficient students can discern patterns and structure in problems. In both geometric and numeric problems, students should be encouraged to break apart or combine parts as they look for patterns. It may also be helpful to sort or rearrange information. An easier summary statement for this standard is to "break apart problems."

MP8: Look for and express regularity in repeated reasoning.

With elementary students, I call this the "look for shortcuts" standard. Students should notice similarities between problems and look for general methods and shortcuts. In the past, some math teachers have expected students to show every step in calculations or solving equations. But to be proficient in math, it is important to recognize and apply shortcuts. For example, students in Grades 4-8 may be able to solve an equation such as 500 + x = 560 by mentally thinking of the missing addend. Because of the general relationship between subtraction and finding a missing addend, students should be encouraged to solve this mentally rather than writing a step of subtracting 500 from each side. The use of shortcuts should be rewarded, not penalized.

Overall, the goal of the Standards for Mathematical Practice is to help students learn habits and processes for solving problems. By encouraging students to pay attention to details, break apart problems, and look for shortcuts, you will help them become better problem solvers.

I have developed a set of 12 posters called "Be a Star" that have checklists and an icon for each practice standard written in language that is easier for elementary students to understand. You can find these on the following site:
http://www.mathpaths.com/practice.html