3: November
Your school as one among many CoCoRaHS stations
Purpose
Building on last month’s sense-making of students’ own rain gauge data, this month’s activities introduce students to the concepts of sampling and averages as they recognize that their school represents one of several stations contributing data for their county and exploring how the data can be summarized.
Using the Active Stations map (within the Interactive Maps options) on the CoCoRaHS website, locate and display the class station and surrounding stations within your county. Allow students time to talk with a partner about what they notice about this map, and invite students to share observations with the class, focusing on variation among stations (e.g., latitude, longitude, elevation, proximity to mountains or water).
Switch to the Precipitation Map (on the CoCoRaHS homepage), and locate the class station. Then Zoom out to display the county. Display a date on the county map, and prompt students to notice whether the amount of precipitation is the same or different among stations. Repeat this process, displaying different dates, to provide opportunities for students to recognize the variation among stations in a county.
Engage students in discussion about the importance of having multiple stations within a county due to variation in precipitation across stations. If there are too many stations to readily count, share with students how many stations are in the county using the “List Stations” report on the CoCoRaHS website.
Introduce students to the concept of an average, sharing that an average is used so that data from all stations are accounted for. (The narrative below includes one approach for introducing students to the concept of an average.)
Have students calculate their station-specific monthly totals for September and October. The Rainy Day Reports (i.e., county-level daily precipitation data) available through CoCoRaHS provide students with average totals for the county. Have students compare the totals they calculate to the average monthly totals for their county and consider why the two may be different.
Accessing the “Active Stations” Map
- Go to: https://maps.cocorahs.org/.
- Select Map Options in top-right corner.
- In the What dropdown menu, select Active Stations.
- Click Update Map.
- What do you notice about the different stations?
- What similarities do you notice between the stations?
- What differences do you notice?
Standards + Practices
Science Standards:
ESS.5.1.1 Analyze and interpret data to compare daily and seasonal changes in weather conditions and patterns
ESS.5.1.2 Analyze and interpret weather data to explain current and upcoming weather conditions in a given location.
Science Practices
SP4: Analyze and interpret data
SP5: Using mathematics and computational thinking
SP8: Obtaining, evaluating, and communicating information
Math Standards:
NC.5.MD.2 Represent and interpret data: Collect data by asking a question that yields data that changes over time.
NC.5.NBT.3 Read, write, and compare decimals to thousandths.
Math Practices
MP1: Make sense of problems and persevere in solving them
Resources + Supports
Ms. Clark Helps Students Visualize County Average
With the “rain doesn’t fall the same on all” saying in mind, Ms. Clark wants her students to work with data that represents an area broader than their single station. The Rainy Day Report (i.e., daily county-level data) available through CoCoRaHS serve this purpose. However, Ms. Clark realizes that these data are presented as averages, a concept typically not introduced until sixth grade. Students won’t need to calculate averages, but rather understand what they represent, so Ms. Clark decides to engage students in an activity to help them visualize the concept of a “county average.”
Without students present, Ms. Clark uses the rain gauge to measure 1 inch of water and pours this water into an unmarked cup. She then labels five other cups to represent five different “stations.” Once students enter class, she divides them into 5 teams and gives each team one of the labeled cups. She explains that each cup represents a station in their county. Ms. Clark circulates and pours a small amount of water into each team’s cup. To help students understand that it is possible to have no precipitation in a location, even when it is raining nearby, Ms. Clark bypasses one of the cups. Before asking students to combine the rain from each of their cups, she asks students to look around at the “rain” that has fallen in each part of the county. Is it the same? She then asks the teams to combine their precipitation into the rain gauge and then hands the rain gauge to the team with no precipitation requesting that they read the total amount in the gauge. The team reports “1 inch.” Ms. Clark writes 1 inch on the board and directs students to work in pairs to determine how much each station would have measured if it had rained the same amount at each location/station. Students use different methods (e.g., hundredths grids, algorithms, skip counting) and determine that each station would have had 0.20 inches.
Ms. Clark states that 0.20 would be the average precipitation for their county and explains that averages provide a general idea of the amount of precipitation for a county for a set time period. She continues to explain that it is likely that no one spot in the county would have recorded the exact average precipitation amount, in this case 0.20 inches.
Accessing County-Level Precipitation Data
- Select View Data on the CoCoRaHS homepage.
In the “Summary Reports” section of the list, select Rainy Days Report.
- Use the menus to select the County and Date(s) of interest.
There is not currently an option to export these data. However, data in the table can be copied and pasted into a spreadsheet in a different program. More information on how to access and copy these data can be found starting on page 2 of this pdf: https://media.cocorahs.org/docs/CoCoRaHS_Rain_Reigns.pdf
Average
Although the concept of a mathematical average, or mean, is not explicitly addressed by math standards until sixth grade, supporting students as they develop an understanding of this concept will help them make sense of the data collected throughout the CoCoRaHS project.
The average is calculated by adding all values in a data set and dividing the sum by the number of values in a set. For this engagement, that would mean having students add the precipitation at all county stations (e.g., on one day) and dividing by the number of stations to help students make sense of the amount of precipitation in their county. While computing the average may seem simple to students, a lack of conceptual understanding may limit students’ abilities to interpret the average itself.
If time allows, one extension possibility is to have students think about when using an average is useful and when it is not as useful to help build students’ conceptual understanding of how averages are used. What types of questions can be addressed using an average? What types of questions need information in addition to the average? What types of questions are not answered by the average and need different information?
Vocabulary: Many students have some experience with the term “average.” Elicit student prior knowledge with examples such as average weight, height, points per game, age for a particular achievement, cost of something, miles per gallon, etc.
Preconceptions: Help students see that “average” is an idea that exists for many things and question all students around what they think average really means. Student ideas may include a notion that something is in the middle, the goal of what something should be at, not really good or really bad, or even just normal. Make connections with discussion points that students bring up when intervening.
Connecting with County Level Data: Use what students know and understand about averages to help them make sense of what a precipitation average would mean in the context of county-level data. Averages provide a general idea of the amount of precipitation for a county for a set time period, but it is likely that no one spot in the county will have recorded the exact average precipitation amount. This may challenge student conceptions that an average is “what most are.”
Using Grid Paper With Decimals
Students may find it helpful to use grid paper to simulate a place value chart when working with decimal values. Encourage students to record the decimal point in a box, rather than along the grid line between the “ones” and “tenths” boxes. This approach allows students to draw on their understanding of place value when making comparisons.
Using Weather Data
Meteorologists are Mathematicians! They use weather data to make calculations and predictions on a daily basis. The following brief video explains how math is used by meteorologists each day: Weather Wise Kids.
More information about how researchers and engineers use data from the CoCoRaHS website can be found under the tab “Who Uses CoCoRaHS observations?.”
Additionally, every 10 years, US Climate Normals are released. Normals are standards for comparing today’s weather with what has occurred over the past 30 years. Meteorologists, climatologists, and others use the 30 year Normals to make comparisons with temperature, precipitation, and other variables. Climate Normals on the CoCoRaHS website posts the most recent 30 year normals and provides more information about them. Students can use the 30 year normals as Meteorological Mathematicians and make additional comparisons to their station’s averages.
Exit Ticket Prompt:
How does having multiple stations in a county help us understand CoCoRaHS data?
| Likely Response(s) | Next Steps |
|
Response suggests misinterpretation of what an average represents. A student explains that more stations are better because it will increase the county average. Having more stations is better because then it will make the average for the county bigger and more correct. |
Questions to develop student understanding:
|
|
Response suggests an emerging understanding of the importance of having multiple stations in a county, without mention of averages. A student explains that more is better as a generalization (i.e., more of anything is better). Having more stations is better for CoCoRaHS because then there are more people collecting CoCoRaHS data. Another student focuses on the benefits of multiple stations based on the voluntary nature of CoCoRaHS. Having multiple stations is helpful because sometimes people make mistakes when they read their measurements or they forget to collect data. If there are multiple stations, then even if one person forgets to collect data we can still see the precipitation for that day using another station. |
Questions to help extend students’ thinking and situate in the context of averages:
|
|
Response indicates student understanding of the importance of having multiple stations and the benefit of using an average. A student explains the benefits of having more of the county represented when there are multiple stations. Having multiple stations is helpful because then someone can see the precipitation amounts in different parts of the county. The county average makes more sense with multiple stations because I can see about how much rain fell in the county instead of only having one or two stations and then I really only know what fell there and not anywhere else in the county. Another student makes connections between the variable nature of precipitation and having stations placed throughout the county in addition to the quantity of stations. Having multiple stations is beneficial because the same amount of rain doesn’t fall everywhere. When there are multiple stations we can see how much rain falls in each spot. Like if there are three thunderstorms in the summer, you can look at CoCoRaHS for each one and see if the same parts of the county got more rain than others to see if it always happens in the same pattern. It’s really good if the stations are in different sections of the county for the average because then all of the parts of the county are part of it and we aren’t leaving a section out. It would be bad if we did the average but were missing the whole northern part of the county because what if that section got a whole lot more or less rain than the other sections? Then our average wouldn’t be as good. |
Questions to help students attend to the importance of both quantity and location of stations and further extend their thinking:
|
In next month’s engagement, you will be accessing another station’s data (from within your same region) from the CoCoRaHS website. Identify their station number and access their station in the Active Stations map or the “List Stations” report on the website.