Bungie Barbie

Content Area: data collection & analysis; linear relationships; functions Text or Resource and Relevant Pages: Beginning Algebra with Graphing Calculators Summer Institute; Key Curriculum Press; July 1997; Berkeley, California Overview:

Students collect data for the distance a Barbie falls based on the number of rubber bands connected to her feet. The data collected is used to create a scatterplot and determine a line of best fit. Students are then given a specified height from which they will drop their Barbie and must use their model to determine how many rubber bands will be needed to perform the bungie jump successfully. Previous Lessons

Continuity:

Objectives:

Lessons on collecting, displaying and exploring data/trends in data. Some experience with graphing calculators and transformation graphing is needed. Basic understanding of linear relationships/functions.

This Lesson

This lesson takes uses data collection, modeling and linear relationships to create a model, predict an outcome, and test the model.

Next Lessons

Continue creation and analysis of data sets. Expand investigations to include: domain, range, dependent vs. independent variables, functions, linear relationships, linear equations, etc.

Students will collect, organize, and represent a set of data to identify the relationships between data. Students will write and graph linear functions. Students will use data to generate and test hypothesis. Students will work in groups/pairs to actively solve the problem situation. Students will communicate mathematically while engaging in problem solving and real world applications. This lesson addresses the following NCTM Standards: Algebra – understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; analyze change in various contexts Data Analysis – formulate questions that can be addressed with data; collect organize and display relevant data to answer questions; select and use appropriate statistical methods to analyze data; develop and evaluate predictions based on data Problem Solving – build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems Reasoning – make and investigate mathematical conjectures

Adapted from Teaching and Learning Middle Grades Mathematics ©2004 Key College Publishing

Communication – communicate their mathematical thinking coherently to peers, teachers, and others; use the language of mathematics to express mathematical ideas precisely This lesson addresses the following Arizona State Content Standards: Strand 3: Patterns, Algebra and Functions Concept 2: Describe and model functions and their relationships (PO7, PO8) Concept 3: Represent and analyze mathematical situations and structures using algebraic representations (PO4, PO5, PO6, PO10) Concept 4: Analyze change in a variable over time and in various contexts. (PO1, PO2) Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 1: Understand and apply data collection, organization, and representation to analyze and sort data (PO1, PO2, PO3, PO7, PO9, PO11, PO13, PO14) Materials:

Graphing calculator Barbies (one per pair/group) Rubber bands Meter stick Measuring tape Overhead sheets & pens

Use of Space:

Any surface within the classroom from which to drop Barbie Elevated area with access to top and bottom from which to test predictions

Launch Overview: As a whole class, students will watch a short video clip of a bungie jumper and discuss the various mathematical and physical components of a bungie jump. Learning Activities/Teacher’s Questions

Expected Students’ Reactions/Responses

1. Show a video clip of a bungee jumper.

Watch the video

2. Discuss what makes a “good” jump.

Getting as close to the ground as possible without actually touching the ground.

Teacher’s Support

3. Discuss mathematical and Length of bungie chord, physical aspects of a bungee jump. amount of give in the chord, weight of object attached to chord

Adapted from Teaching and Learning Middle Grades Mathematics ©2004 Key College Publishing

4. Explain the activity and give the purpose of the task: To determine how close without touching Barbie can bungee jump from an undisclosed height.

Think about additional element of # of rubber bands (as opposed to just length or give of chord)

Explore Overview: In pairs (or small groups) students will experiment with their given Barbie, trying to create a model that represents distance Barbie falls versus number of rubber bands attached to her feet. Learning Activities/Teacher’s Questions

Expected Students’ Reactions/Responses

Teacher’s Support

1. Give each pair/group a Barbie and collection of rubber bands. 2. Instruct students to test the distance Barbie falls for different numbers of rubber bands. 3. Monitor data gathering, clarify directions, and answer questions (as needed)

4. Instruct students to find the line of best fit using Transformation Graphing (or guess-and-check, or any other method they know for line fitting/finding equations of lines)

5. Tell students the height of the location from where Barbie will jump. Allow students time (about 5-10 minutes) to determine how many rubber bands they will need and to create their bungee chord.

6. In pairs, students will drop their Barbie using a bungee chord with

Drop the Barbie from different heights within the classroom. Gather data. Students may have trouble gathering correct heights.

Create scatterplot using graphing calculator. Students may need to be reminded how to find line of best fit using Transformation Graphing & what a line of best fit means. Use the equation for their line of best fit to predict the number of rubber bands needed. Students may have problems extended their model to the necessary distance.

Have students gather several data points for each tested height. Test the height fallen against a measurable object (e.g. wall) Help students interpret the data in their scatterplot. Discuss with students, as needed, what line of best fit means and which approximations are better than others.

Help students extend their window to fit in the new height. Show students how to use trace function or how to use their equation to make predictions.

Student drop their

Adapted from Teaching and Learning Middle Grades Mathematics ©2004 Key College Publishing

their predicted number of rubber bands from the predetermined high location. Teacher will be on ground to determine which Barbie(s) come closest to ground without touching.

Barbies. Be sure students do not push Barbie, but simply let her fall.

Share and Summarize Overview: In pairs (or small groups), students will reflect on and analyze their prediction. Students will make adjustments to their models as needed. Students will share differences in their models (e.g. type of Barbie, number of rubber bands, effectiveness of model, etc.) with the class in a short, informal share-out. Students will also write a brief summary of their experience, what they would do differently, and what they learned. Learning Activities/Teacher’s Questions

Expected Students’ Reactions/Responses

Teacher’s Support

1. Instruct students to return to classroom and prepare a summary of their experiences and reflections.

If needed, students can adjust their model by adding or removing rubber bands. Students can determine where their model may have gone wrong.

Discuss with students error during data collection procedure and different factors that may have influenced their model’s performance.

2. Give students overhead sheets to prepare a summary to share with classmates.

Create summaries to share with classmates. Include: original function, modified function (if needed), approach to creating model, performance of model.

3. Lead class discussion of different methods for data collection and performance of different model. Which factors influenced number of rubber bands and performance of model?

Compare own model with that of classmates. What made some models more successful than others?

4. Instruct students to prepare a brief write-up of their experience. Include: method of data collection, model developed, performance of model, what they would do differently next time, what they learned, etc.

Adapted from Teaching and Learning Middle Grades Mathematics ©2004 Key College Publishing

Application or Extension:

Change the focus of the lab to compare the stretch or length of the bungee chord and the mass of the weight when studying second degree equations. (Teacher may want to watch the Staff Development Video Bungee Jumping The Annenberg/CPB Math and Science Collection – WGBH Boston) The equation that best describes the length of chord and distance Barbie falls is linear. Try to determine why it is not second degree when falling is described by a quadratic equation. Adaptations:

Students with special needs may need to be given more direct instruction on how to effectively collect data points during experimentation phase of lesson. Teacher can demonstrate data collection method and give students ideas for places within classroom from which to drop Barbie. These students may also need extra guidance in coming up with the line of best fit and using their model to make predictions. Teacher can supply as much instruction as needed to clarify these areas for students. Hands-on, active nature of lesson should provide students with language barriers and/or learning disabilities a chance to actively engage in the mathematics.

Assessments:

Formative assessment of students will occur throughout the lesson by observing student data collection techniques and application of Transformation Graphing. Effectiveness of data collected and model developed will be demonstrated in the success of Barbie’s jump. Final summary and reflection will provide summative assessment of whole activity and learning objectives.

Attachments:

N/A

Adapted from Teaching and Learning Middle Grades Mathematics ©2004 Key College Publishing