In this lesson, in addition to the third grade math standards, students are working with the following:
Science and Engineering Practice 4: Analyzing and interpreting data
Science and Engineering Practice 5: Using mathematics and computational thinking
I have read through the Next Generation Science Standards and am building background for the following disciplinary core ideas and cross-cutting concepts that they will encounter in later grades:
Disciplinary Core Idea ESS2 A: Earth’s Materials and Systems (understanding water use and basic measurements of consumption will enrich their deeper understanding of how the hydrosphere operates and how human actions interact with that cycle)
Disciplinary Core Idea ESS2 C: The Role of Water in Earth’s Surface Processes (Only a fraction of the Earth’s water is fresh water, and an even tinier percentage of that is available in streams, lakes, wetlands and the atmosphere).
Cross-cutting Concepts: Scale, Proportion and Quantity (Standard units are used to measure and describe physical quantities such as weight and volume).
I have integrated the ideas about water consumption into the study of measurement to build the background necessary for the concepts about water students will study in upper grades, specifically:
5-ESS2-2: Describe and graph the amounts and percentages of water and fresh water in various reservoirs to provide evidence about the distribution of water on Earth.
I show students a 1 and 2 liter bottle filled with water. I use soda or seltzer water bottles for each of these but any transparent container will work! I have students pour each of the bottles out into a separate basin so they can see what the amounts look like in a different container.
Then students work independently or with a partner on Water Use, Think About It (Practice with Estimation). Here is a Teacher Key so that you have the data at your fingertips! I circulate to listen to student conversations and give them prompting questions. I watch to make sure that students are not making absurd estimates (1 million liters) or rushing (guessing 10 liters for every item).
When the majority of students have completed their estimates, we reconvene at the carpet and I project the actual totals, one at a time. Using student estimates (randomly chosen) I model how to find the difference between the estimate and actual amount for the first two examples. I also monitor students carefully to make sure they are not erasing their estimates. Some children still think that an incorrect estimate is a wrong answer and this misses the point of estimation!
Then I project the rest of the actual totals and students work out the difference between their estimate and the actual total on their own on a separate piece of paper, using the algorithm of their choice.
When most students are done, we reconvene at the carpet and I randomly call on eleven students and write their guesses up on the board. 11 will make it easy to find the median. The goal is to expose students to this math, not to overwhelm them. All students copy the guesses. We then order these eleven guesses and calculate the range, the median, the mean and the mode. These numbers are compared to the actual data. We do this for as many items as time permits. This is a meaningful way to practice addition and division. They can use calculators to find the answer for the mean. Writing and understanding the equations is the important part.
This is how I define these terms for my students:
Median: This is the estimate in the middle. On a highway, the median is the strip of grass (or dirt) that separates the two directions of traffic. In mathematics, the median is in the middle of an ordered set of numbers.
Mode: The mode is the most common (frequently occurring) number in a data set. Sometimes there is no mode, or there can be more than one mode.
Range: The range is the difference between the estimate with the lowest value and the estimate with the highest value. For example, in a K-5 school, the ages range from 5-12 (usually). This is a range of 7 years.
Mean/Average: One way to think about an average is that it is a way of looking at a typical response from a group. The average estimate of a group, for example, our class, can be far away from an individual’s guess. Imagine a class of 3 students. One student received 100% on a test, a second student earned a 90% and a 3rd student had an 80%. The mean of these 3 scores would be 90%. I show them this simple example: 100 + 90 + 80 = 270 270 divided by 3 = 90
Then, in the context of this lesson, I have work with the class to calculate the mean student estimate for how many liters of water are used in an 8 minute shower. We write the equation and then they use calculators to solve it, though many of them do not need to and like the challenge of solving it longhand. I remind them that it is a two-step equation.
I ask students to reflect on the data we collected today and write a response to one or more of the following prompts:
I use their responses as an informal assessment. I focus on the following criteria:
An essential component in building students' ability to understand water use is to develop their awareness of how much water is available. 5th graders study how much water is available in various freshwater reservoirs. Not all surface water in a state is freshwater, but in order to start gaining a sense of scale, it is helpful for students to first examine the amount of surface water in a given state.
Here is one activity that can engage them in that. For 3rd grade, I would link students directly to this chart that shows the total square miles of each state, the total square miles of water in each state, and the percentage of each state that is water. (This is a surface area measure). Then students can graph or create a table of the states with the most water, the least water, or by region.
For 5th graders, I would provide students with a clipped version of a chart that shows the total area of a state in miles and the total amount of water, also in square miles. I clip that chart because it provides the percentage on the right. They then create a visual to show how much of each state's square miles are water covered. Here is how I would present that. I have found that students grasp the idea of percentages much more easily when there is visual assistance of the sometimes difficult to comprehend formulas.