Relate that Rainfall Rate

 Author: Kristen Keish Unit Title: Relate that Rainfall Rate Grade: 12 Subject: AP Calculus Estimated Duration: 7 days of 100 minute classes Unit Activities: Activity 2: Dripping Cup Activity 4: Evaporation Activity 5: Rain Barrels Date: July 2015

HSS-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.

Since this is an AP course, most content is above Common Core.  Below is listed topics from the AP course description this unit addresses.

Applications of derivatives:

• Modeling rates of change, including related rates problems­
The Big Idea (including global relevance)

Water use and conservation of a valuable resource.

In the summers, nearly 40% of all water used is for gardening and lawns.  A Rain barrel collects water that comes down during a rainstorm either off of a roof or in a field from the storm itself.  Collecting the rainwater and using it helps save treated water from being used, which lowers costs and energy consumption.  It also helps in areas that may not have easy access to water.

The Essential Question

How can we design a rain barrel to maximize efficiency?

The Challenge
 Description of Challenge (Either Product or Process is clearly explained below): List the Constraints Applied Students will create a rain barrel and delivery system out of given supplies that will effectively supply water to plants. Supplies (see 2.2.02) Time – three days to completely build product
Anticipated Guiding Questions (that apply to the Challenge and may change with student input.)
• What are ways that that rainfall can be used?
• What are benefits of using rainwater?
• How can we collect rainfall?
• How can rainfall be distributed to plants?
• Is there an ideal rate for the rainwater to be distributed for plants to grow?
• Does the shape of a water collection devise have an impact on the rate or effectiveness of water distribution?

The Hook

Field trip to Wilmington weather service – have meteorologists talk to us about average rainfall during storms, average rate rain falls, average amount of rainfall per month.

How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.

• Students will design and build a rain barrel out of the provided supplies
• Students will test the rate of water flowing out and then calculate the rate of volume changing
• Students will be given time to tweak and refine their design
• Students will identify “next steps” to improve project at the end
How will students present or defend the solution?  Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.
• Students will have 90 seconds to explain their rain barrel and the reasons behind their designs
• Students will have a PowerPoint Poster of their barrel
• Students will demonstrate how their barrel works
• Students will be given a rubric of how they will be graded

What academic content is being taught through this Challenge?

Applications of derivatives:

• Modeling rates of change, including related rates problems­
Misconceptions

Students may have trouble seeing the connections between the rates of rainfall, evaporation, and water distribution to volume, surface area, etc.  The teacher needs to be aware of conceptual issues of related rates and help students see how all are related.

Unit Activities

Day 1:  Hook (2.1.01)

1.     Pre-test students on their prior knowledge of related rates (2.1.01.a)

2.     Field trip to Wilmington to weather station

3.     Have students take notes on weather collection, weather stats, how weather impacts our area (2.1.01b)

4.     Give students rainfall data to use throughout the unit (2.1.01c)

5.     Give students homework (2.1.01d)

Day 2:  Introduce Challenge and Cup Draining Water activity (2.1.02)

1.     Talk about and debrief the previous day’s fieldtrip

2.     Discuss the challenge of rainfall collection and distribution for gardens

3.     Students will develop the essential questions needed for the lesson and ultimately the challenge

4.     Students will be put into small teams of 2-3 to complete Cup Draining Water activity (2.1.02e)

5.     This activity will let students be engaged as they calculate the rate of a cup and a cone draining water and the rate of volume change

6.      Extensions for students who finish include looking at how rates change with multiple holes and sizes and truncated cones (2.1.02f)

7.     Give students homework  (2.1.02g)

Day 3:  Iced Tea Jars activity (2.1.03)

1.     Talk about and debrief the previous day’s activity and homework as needed

2.     Discuss how water that was collected could be dispersed to the plants

3.     In teams of 3-4, students will complete the Iced Tea Jar activity (2.1.03h)

4.     Students may use reference sheet (2.1.03i)

5.     This activity will let students be engaged as they test the effect of distribution holes in a tube in relation to the rate of the volume of the water changing

6.     Give students homework (2.1.03j)

Day 4: Evaporation activity (2.2.01)

1.     Discuss how evaporation effects the volume of a container of water

2.     With a partner, students will complete Evaporation Activity (2.2.01k)

3.     Students may use reference sheet (2.2.01l)

4.     This activity will let students be engaged as they test the effect of evaporation on rate of the volume of the water changing

5.     Give students homework (2.2.01m)

Days 5: Begin Creating Rain Barrels (2.2.02)

1.     Place students in teams of 3 if possible

2.     Review challenge and start the Engineering Design Process

3.     Provide students with copies of the challenge (2.2.02n), EDP worksheet (2.2.02o), and rubric (2.2.02p)

Day 6: Rain Barrels (2.2.02)

1.     Continue working on rain barrel

2.     Select a solution and start construction if not already done

3.     Evaluate and look at redesign process

4.     If time allows, start working on PowerPoint poster and brief elevator presentation

Day 7: Presentations of Rain Barrels and Posttest (2.2.02)

1.     Students will finish PowerPoint poster and presentation

2.     Teams will present their finalized rain barrel with PowerPoint poster during brief presentation where math is emphasized

3.     Rubric (2.2.02p)

4.     Students will complete the posttest for the unit (2.2.02q)

Pre-Unit and Post-Unit Assessment Instrument

The same test will be given as the pre and post assessments.  The only difference is the header for consistency and easy identification.

Results: Evidence of Growth in Student Learning

When the pretest was administered, the class average was .67/16.  Three students did not get any question correct, while six students scored a 1/16.  On the posttest, the class average rose to 7.33/16.  All but one student improved by at least 3 points, while two students improved by 14 points.

The homework problems consisting of past AP questions consistently showed students were learning the content, with students averaging half of the questions correct at first attempt.

Reflection

I selected this unit because historically, related rates is a topic that is hard for students to grasp during the first round of teaching.  Typically, it takes until the review before the AP exam for students to understand it.  This is a topic where real world applications are said to occur, but often hard to see.  The purpose of this unit was met because students were able to see how related rates was used in water flow and ultimately in the design of a rain barrel.  Students were able to successfully come up with solutions that met the challenge.  The Engineering Design Process was used as students identified and defined the problem of water conservation as a class, and then began working in groups to gather information, brainstorm solutions and identify alternatives, select and implement the solution, evaluate, and refine the solution.  Students then communicated their findings to the whole class through a presentation using google slides.  One thing I would change would be the actual product.  The material of Plexiglas was extremely hard to work with.  One option would be to let students research the materials they believe would be best used for the final product.  Also, there was not much room for evaluating the effectiveness and refining the actual barrel once made.  Some groups used cardboard models first, and this was extremely helpful.  I believe creating a computer model and simulation using google sketch up or a similar program would be a better alternative for final product.  I would teach this unit again with modifications because it was a way for students to see applications of related rates.  Also, the unit allowed students to apply the Engineering Design Process and work together as a team. Comparatively, I believe that the unit allowed for about the same level of understanding of related rates compared to traditional methods, but the Unit helped students see applications of Calculus more than would have occurred in the traditional method of teaching the content.