Pi Project Deriving Pi from the Objects around Us Lesson Plan

Transcription

1 Pi Project Deriving Pi from the Objects around Us Lesson Plan Subject Area: Math Grade Levels: The lesson can be adapted for grades 4 10 (ages 9 6). Time: At least one 50-minute class period; time outside of class as necessary Lesson Objectives: Students will: Accurately use appropriate measurement tools. Develop an understanding of relationships between measures. Solve problems involving the diameter and circumference of circular objects. Make conclusions based on data presented in tables and axis (scatter) plots. Explain their findings in writing and visual slide shows. Standards: Common Core State Standards 1 : Common Core State Standards for Mathematics: Mathematical Practices Reason abstractly and quantitatively. Use appropriate tools strategically. Measurement and Data Represent and interpret data. Number and Operations in Base Ten Understand the place value system. Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. College and Career Readiness Anchor Standards for Writing: Standard 6. Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others. Standard 7. Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation. 1

2 Overview: Students are often familiar with the value of π (pi), but they may not understand its meaning or where the value comes from. This lesson divides students into teams to measure the circumference and diameter of circular objects in the classroom. Data is entered into InspireData s Table View, and then students investigate it through dynamic visualizations in Plot View. Students will strengthen their measurement skills and their understanding of the components of a circle (radius, diameter, and circumference) as they gain an understanding of the meaning and power of π. Students will explain their findings in annotated slide shows with InspireData s Slide Shows feature. Preparation: This lesson requires the InspireData software application published by Inspiration Software, Inc. You can download a 30-day trial at Have tape measures, rulers, or meter sticks available for student teams. Each team will also need string, preferably without a lot of elasticity. Utilize objects in the classroom or bring in a collection of objects with circular edges (plates, cans, CDs, lids, bicycle wheels, etc.), and set up stations where students can measure them. Lesson: 1. Ask students to suppose that they are ordering a perfectly round window custom built for their bedroom. What diameter would they choose? Have students estimate the circumference of the window. Are there many possibilities for circumference based on that diameter, or just one? 2

3 2. Open the Pi Project database (InspireData Starter>Databases>Science>Pi Project). 3. In Table View, explain to students the process of gathering data as documented in the table notes of the Database Template tab. Click the field headings to view the Notes area, and show students that tenths is the expected level of precision for diameter and circumference. Solicit ideas for measuring methods that will yield accurate measures of the diameter and circumference of a circle. 4. Hold up a circular object and ask for volunteers to come forward and demonstrate how the diameter and circumference can be accurately measured to a tenth of a centimeter. Ask one of the students to record the name of the object and its measurements in the table in the Database Template tab. Demonstrate how to show or modify the formula in the last column that automatically divides the circumference by the diameter. 3

4 Note: For more information about using the Formula feature, refer to InspireData Starter>Learn to Use>Documentation>Handouts>Learn to Use Formulas. 5. Tell students they will be recording data for at least six circular objects. They can enter data directly into the table, or you can demonstrate how they can use the Survey or e-survey tools. 1 Note: Students can select Table>Launch Survey to enter data via the Survey tool. They simply click Add Record each time they are finished adding a record to the form. Once they are finished entering the information about the objects, they can click Close, and the data will be automatically entered into the database. Alternatively, students can enter data directly into the table or record data on paper first and enter it into the database later. A third option for entering data is via the e-survey tool if Internet connectivity is available. 4

5 For more information about the Survey and e-survey tools, refer to InspireData Starter>Learn to Use>Documentation>Handouts>Learn to Use Surveys. 6. Divide the students into teams of two to four, and give each team a measuring device and string. Tell the groups they will have 10 to 15 minutes to record their data before you reconvene as a class to discuss how to analyze it. Circulate among the students, answering questions as they arise. 7. After 10 to 15 minutes, have the class come back together and briefly discuss the students preliminary observations about the relationship between the circumference and diameter of circular objects. Then click on the Sample Data tab to show students an example of a completed table. Point out the Investigation Questions listed in the table notes. Questions include: What is the relationship between the diameter and circumference of each circular object? What is the average value for circumference/diameter? (Suggestion: Show the mean on an axis plot.) 5

6 8. Demonstrate how to click the Plot View button on the Toolbar to switch to Plot View and analyze the data. Your demonstration should include how to select plot types via the buttons on the Toolbar. As you show students how to create plots, they should develop an understanding of how they can be used to answer the Investigation Questions. Tell students that they should create at least one plot that will address each question. Demonstrate how to define the x/y axes in the plots (e.g., for an axis plot, click X Axis and choose Diameter. Click Y Axis and choose Circumference.) Use the InspireData handouts to help with plotting and analysis (Help>Documentation>Handouts). You may want to print one or more sets of handouts to make them available for students. You should also remind students they can refer to the example plots in the table in the Sample Data tab. 9. Ask students how they could show the relationship between circumference/diameter and diameter. Encourage students to experiment with different plots until a plot similar to the one shown below is created. Note that the observation is strengthened by adding the mean value to the Circumference/Diameter axis in the axis plot. If they haven t already, the class should 6

7 notice that this ratio is always close to 3. Discuss possible sources of error for any data points that deviate from the pattern. 10. Introduce the Greek symbol π, and discuss the actual value of π when it is not arrived at through measurement ( ). How are the circumference and diameter of a circle related? Why were some of the ratios found in the activity not exactly the value of π? 11. Demonstrate for students how to record explanations of plots and answers to the questions in the Notes area at the bottom of the screen. Click on in the lower right to open the area. Be sure to show students how to capture a slide for each plot, including their notes, by clicking the Slide Sorter button and then the Capture Slide button. 12. Conclude the lesson by asking students to write an equation that documents the relationship between the value of π and the circumference and diameter of a circle. Ask students to use the formula to determine the circumference of their custom window based on the diameter they initially chose. How close was their estimate? Adaptations/Extensions: If students complete the basic Investigation Questions, they can attempt the Advanced Question listed in the table notes: Add another column to record the height of each object. How could you calculate the volume of the object with a formula in another column? 7

8 For younger students, consider gathering and analyzing the data as a whole class, at least until students understand the process. It may be instructive to have some students measure in metric units and others in US customary units. Does this alter the relationship between circumference and diameter? Rather than measuring objects in class, assign each student a specified number of objects to measure at home. For homework, they can enter their data using the e-survey tool or bring the data back for entry at school. Ask students to add other fields to the database in Step 5, such as Circumference + Diameter, Circumference - Diameter, and Circumference x Diameter. This will make the activity more open ended as students will have to discover which operator yields a unique relationship. Students can enhance their plots by adding other InspireData features and computations. Direct students to the InspireData handouts, and/or pass out the Learn to Use Plots handout for student reference (Help>Documentation>Handouts). 1 Copyright Common Core State Standards. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Learn more online at 8