TheAmazingBalloonRace.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science 1

Partnership Grant Program NCLB Title II Part B Revised 8/14/12 Mathematics Senior Level Capstone Course

Unit Overview

Title of Unit: The Amazing Balloon Race Unit Designers:

Adam Letizia Gliziel Gonzales

Northumberland County Public Schools

Editor: Vickie Inge, UVA-SCPS Office of Mathematics Outreach Context:

Summary of the issue, challenge,

investigation, or problem.

The relationships of speed, time, and distance have peeked curiosities of many people who travel. You will collect and graph data to analyze the relationships between these three variables.

Number of Class Hours:

5 – 6 hours Unit

Design: _x_Task Based

___Project Based

Other Subject Areas/Disciplines Addressed:

Science-Physics; English/Writing

Driving Question: What gets shorter as time drags on? P.S--It’s not your patience.

Mathematics Content Addressed:

Transfer between and analyze multiple representations of a function. Select and use appropriate representations for analysis, interpretation, and prediction. Recognize the general shape of a function. Convert between graphic and symbolic forms of a function. Inverse and Direct Variations.

MPE Addressed:

Understanding and Applying

Functions

Assumption of Prior Knowledge:

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 College and Career

Readiness/21st Century Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A):

Collaboration- students will work in groups of 3-5 (4 is preferred).

T and A Research – Use internet to find

instructions on building balloon rockets E

Communication (Oral and/or Written) - Writing a story, creating a table

and graphical representation of data

T and A Technology –calculator and internet A

Critical Thinking/Decision Making - Applying logic in analyzing graphs and abstract concepts.

T and A Other: (Describe) N/A

Major Products and/or Performances:

Group – Written paper, data collection, 2 task problems, and graphical representations

Presentation Audience:

x Class

School

Individual –Journal entries, 1 task problem Expert

Community Other:

Launch: Event or experience used to engage the students interest and inquiry:

Balloon rocket video clip. http://www.sciencebob.com/experiments/balloonrocket.php

Evaluation: Formative

Assessments (During the Unit)

Interview Practice Presentations

Mathematicians Journal x Notes

Preliminary

Plans/Outlines/Prototypes

Checklists x

Rough Drafts Concept maps

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 Summative

Assessment (End of Project)

Written Products, with a rubric x Peer Evaluation, with

a rubric

x

Oral Presentation with a rubric Self Evaluation, with

a rubric

x

Other Product(s) or

Performance(s), with a rubric

Other:

Resources Needed: On-site people, facilities:

Teacher

Equipment/Technology: calculator, computer, projector

Materials: Balloons (long and round), rolls of kite string, fishing line, yarn, drinking straws cut to short and longer lengths, stopwatches (IPod w/ app), tape measures, masking tape, and graph paper

Community Resources:

Reflection Methods: Individual, Group, and/or Whole Class

Mathematicians Journal x Small/Focus Groups

Whole Class Discussions x Fishbowl Discussions

Survey Other:

Material Adapted From:

http://www.sciencebob.com/experiments/balloonrocket.php http://www.youtube.com/watch?v=A7wrEWfV6TY

http://www.green-planet-solar-energy.com/balloon-rocket-experiment.html http://www.exeter.edu/academics/72_6539.aspx

http://www2.uwstout.edu/content/profdev/rubrics/secondaryteamworkrubric.html

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 Virginia’s Senior Level Capstone Course

Instructional Plan Unit Title: The Amazing Balloon Race

Driving Question: What gets shorter as time drags on? P.S--It’s not your patience.

Task: You will become a rocket engineer and launch an exploration into data collection, graph analysis, and the logic of time, distance, and speed.

ENGAGE

How will student’s interested be peaked so they want to engage in the inquiry in this unit?

Number of hours-10 min

Present video clip of a balloon rocket.

http://www.youtube.com/watch?v=A7wrEWfV6TY

Discuss with the class the concepts of speed, time, and distance and their initial thoughts on how they are related. What math do the students see in these relationships?

Mathematician Journal

Prompts

Where do you see examples of speed, distance, and time in your daily life? EXPLORE Teacher provides guidance for the explorations to prepare students with the knowledge and skills to engage in the task. Students will self-assess on the prior knowledge and skills assumed for the unit

Exploration 1: Rocket Balloon Teacher Demonstration: Materials: String, fishing line inserted in a straw, balloon, tape, a stopwatch/timer that records tenths of a second and a ruler/measure.

Teacher inserts the string through a straw, blows up a balloon and tapes it to the straw facing the other end line. 2 students have pulled the string tight. Teacher asks another student to use a timer to record time while the balloon travels. After it travels, distance will be measured to see how far it traveled. (Example data: 22 ft in 1.7 seconds) The class graphs this data on HO #1.

The teacher leads a discussion with the class to investigate how to use the data to find the speed.

Speed = Distance / Time

Speed = 22 ft/ 1.7 sec = 12.9 ft/sec

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 Number of

hours 1-2

Students are shown how to convert this to miles/hour.

5760 / 12.9 (3600) = 8.1 m/hr

Exploration 2: Sandy’s Journey Problem Sheet HO #2.

Students are challenged with a real world problem where they create a narrative story to explain graphical data.

Students, working in groups of 2-3, analyze, interpret, and predict while writing a narrative to describe what is

happening on Sandy’s car trip based on a graph. They should be encouraged to be creative in their writing. The goal is for them to connect to the demonstration graph an understanding that speed is a relationship or a rate that describes how far you can travel per unit of time so distance can be calculated by dividing distance by time.

Project or post the graph shown on HO #2 and read: “Sandy lives in Heathsville and heads out at 12 noon for a 210 mile trip. Encountering road construction and a seeing a UFO sighting slowed her down. She only traveled 30 miles during the first hour.”

Discuss with students whether the narrative matches this part of the graph and have them express reasons to support their thinking. Then call on a few students to make up their own story for this first part of the journey. Ask, “Can you think of another interesting scenario?” and have a few volunteers respond. At this point have each student develop a story for the graph. Have students post their stories on chart paper to share with the group in gallery walk.

A suggested rubric for teacher formative assessment of how well students collaborate is found on HO #3. Teachers may want to allow students to self assess also.

Exploration 3: Allie’s Bike Ride Problem

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 EXPLAIN

Teacher introduces the main task of the unit and prepares students for small group independent work. Number of Hours 1/2

Balloon Launch Activity: HO 5 a-b.

Introduction of the Task: During this outside activity, each group gathers data including time and distance during a rocket race. First, the preparation time and distance is recorded, next the rocket travel time and distance are recorded, and finally a student runs and slides the deflated rocket to the end. This entire series is conducted 3 times providing each group with ample data to graph and analyze. The materials available to the students include: Balloons, kite string cut in 100 foot lengths, drinking straws, stopwatches, tape measures and masking tape.

Students are provided with websites to research how to build their rocket and set up the experiment.

http://www.sciencebob.com/experiments/balloonrocket.php http://www.green-planet-solar-energy.com/balloon-rocket-experiment.html

Goal of this task: Students understand that speed is

dependent on distance and time. Time never stops, so if no distance is traveled, then there is no speed. Our speed is hindered by lack of movement. Students learn, as in Sandy’s Journey, that breaks in travel reduce overall speeds.

Students work in groups of 4.

Teacher brainstorms with students the tasks that need to be done and discuss with students how the groups may decide to share the work. Teachers review safety procedures for working outside to launch the rocket.

Teacher reviews the following steps:

 Reinforce collaborative group norms and checklist.  Review Launch Checklist and Data Collection Form

HO #5 a-b and make sure students understand what is expected. Remind them of the websites they need to review to learn how to build their rockets.

 Review the product expectations for this task and go over HO #7 Group Presentation to prepare students for final product.

 Remind the students that they are to complete the peer evaluation for how well they worked together

Prompts

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 using HO# 3

ELABORATE The student groups are working independently with teacher consultations. Number of Hours 2 1/2

Balloon Launch Activity: HO # 5a-b

Students research how to build the rockets on the internet at the following sites.

http://www.sciencebob.com/experiments/balloonrocket.php http://www.green-planet-solar-energy.com/balloon-rocket-experiment.html

Groups of 4 students build rockets (outside or in a large open area) using knowledge they acquired in research.

Using HO #5 a-b students create balloon rockets outside and gather data using a table to organize their information. The table data is used to create a graph.

Provide materials to build the rockets and graph paper and rulers will be necessary.

Prepare for partner presentations HO # 7.

Complete the peer evaluation rubric for collaboration HO #3

Mathematician Journal Prompts Post-activity: Describe your thoughts about rocket building. Would you make any changes if you were to do it again? EVALUATE Working groups submit products or make presentations Number of Hours 1

Final evaluation includes sharing of balloon data in graph form where one pair meets with another pair to explain their results to each other using their graphs.

Each pair collaboratively completes the final rubric for the presenting group. [HO#7]

Optional: Afterwards, each individual can extend their learning by solving the Pendulum Task HO #6.

Prompts

What

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 Map the Unit

What do students need to know and be able to do to complete the task/project/problem successfully? How and when will they assess their own necessary knowledge and skills? How will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major task for the unit and analyze the tasks necessary to produce a high-quality product.

Task:

You become a rocket engineer and launch a discovery into data collection, graph analysis, and the logic of time, distance, and speed.

KNOWLEDGE AND SKILLS NEEDED

Assumed already learned

Students will self-assess

Will be taught during the unit

1. Analyze, interpret, and predict x x

2. Create a graph and plot data x

3. Create a table of data x x

4. Identify relationships x

5. Apply logic to practical problems x

What project tools will student’s use?  Know/need to know lists  Daily goal sheet

X Mathematician’s Journals

 Briefs/Memos

 Task lists

 Planning Calendar

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 HO #1

Use class data from Exploration 1.

Balloon Rocket Demonstration

Speed = Distance / Time

Speed =

Convert to miles/hour

D

ist

ance

i

n Fe

et

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Sandy’s Journey

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 HO #2 Suggested Solutions

Time Hours Miles

0-1 1 30

1-2 1 60

2-3 1 0

3-5 2 120

Example of story: Sandy lives in Heathsville and headed out at 12 noon for a 210-mile trip. Encountering road construction and a UFO sighting slowed her down. She only traveled 30 miles during the first hour. Relieved by hitting the highway at 1 pm, she zoomed for 60 miles and stopped at a rest area at 2 pm. She got herself a healthy and delicious lunch from a vending machine and rested for an hour. Full of energy, she drove 60 miles per hour and completed her 210-mile trip at 5 pm. Her average speed while driving was 52.5 miles per hour.

The entire trip lasted 5 hours and she traveled 210 miles, thus, we could reason that her average speed was 42 mph. However, the question states, “In particular, identify the speed at which Sandy spent most of the afternoon driving.” Therefore, we subtract the 1 hour she did not travel and divide distance (210) by 4.

MPE Addressed: Understand and Applying Functions

Transfer between and analyze multiple representations of functions, including algebraic formulas, graphs, tables, and words. Select and use appropriate representations for analysis, interpretation, and prediction.

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Allie’s Bike Ride

At noon one day, Allie left home to make a long bike ride to the family camp on Mud Lake, a distance of 100 km. Later in the day, the rest of the family packed some things into their van and drove to the lake along Allie’s bike route. They overtook Allie after driving for 1.2 hours,

stopped long enough to put Allie and the bicycle in the van, and continued to the camp. Refer to the graph as you answer the following questions about the day’s events:

a.) Allie pedaled at two different rates during the biking part of the trip. What were they?

b.) After biking for a while, Allie stopped to take a rest. How far from home was Allie then? How long was the rest?

c.) How far from home was Allie when the family caught up?

d.) At what time did the family arrive at the camp?

e.) At what time would Allie have arrived if left to bicycle all the way?

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 HO #4 Solutions

Time km km/hour

2 40 20

.5 0 0

3.2 32 10

a. 20 km/hr and 10 km/hr

b. 40 km from home and 30 minutes rest

c. 72 km

d. 6 pm

e. 8:24 pm

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 HO #5a

Balloon Launch Activity

During this activity, students gather time and distance data so that speed can be determined and graphical representations produced.

Supplies: 5 balloons, kite string measured in 100 ft. length, 1 drinking straw, 1 stopwatch, distance marker (hat, flag, or any item that can be dropped at location of

rocket landing), 1 tape measure, rulers for graphing and masking tape.

Group Members: Each group should have 4 members: two people to pull string tight, one person to operate timer and record data, and a last person to blowup balloon and run rocket to the end. Teams may rotate duties during the 3 different races. See directions below.

HO #5b Balloon Launch Activity

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Partnership Grant Program NCLB Title II Part B Revised 8/14/12 HO #5b

Directions for Data Display: Use the data from your chart to graph your results in terms of time and distance traveled. For each trial, the data should be recorded on your graph in a

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Pendulum Problem

The graph shows how the length (measured in cm) of a pendulum is related to the time (measured in sec) needed for the pendulum to make one complete pendulum back-and-forth movement (which is called the period). Find the length of a pendulum that swings twice as often as a 30-cm pendulum.

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