Mathematics Senior Level Capstone Course Unit Overview
Title of Unit: Swing, Batter Batter! Unit Designers:
Javornda Ashton/Northumberland Sharon Daniel /Middlesex
Editors, Amy Lamb /Northumberland & Diane Leighty/ UVA-SCPS Office of Mathematics Outreach
Context:
Summary of the issue, challenge, investigation, or problem.
You are a new baseball player and you’ve heard that the pitcher on the opposing team can throw at an above average speed. You have decided that you need to develop a plan to ensure that you swing at the right time.
Therefore you will need to know the time that it will take for the ball to reach the plate.
Number of Class Hours:
4 – 5 Hours Unit
Design: _X_Task Based ___Project Based Other Subject
Areas/Disciplines Addressed:
Physics
Driving Question: When should I swing the bat? Mathematics Content
Addressed:
Solve practical problems involving rational numbers, ratios and proportions. MPE Addressed:
Problem Solving, Decision Making, and Integration Assumption of Prior
Knowledge:
Students will need to have a basic understanding of the operations of rational numbers as well as how to write and solve proportions.
College and Career Readiness/21st Century Skills to be taught (T) during this unit or expectation (E) for student use during this
Collaboration – Students will work in pairs or a group of three if needed
E Research – N/A
Communication (Oral and/or Written) – Write a summary to compare findings with the actual solution
T & A Technology – Microsoft Word and Graphing calculator
E
unit and assessed (A): Determine the procedure to find the time it takes for a pitch to reach home plate. Major Products and/or
Performances:
Group – Develop a written procedure for determining the time that a pitch takes to reach home plate. This procedure must include your complete process of discovering your solution
Presentation Audience: x Class
School Individual – Mathematician’s Journal entries Expert
Community Other: Launch: Event or
experience used to engage the students interest and inquiry:
http://www.youtube.com/watch?v=yjbAYAeb7xc- Aroldis Chapman story video
http://www.youtube.com/watch?v=f3wJ-HgsnCg&feature=related –Chapman’s 105 mph pitch video
Evaluation: Formative Assessments (During the Unit)
Interview X Practice Presentations
Mathematicians Journal X Notes
Preliminary
Plans/Outlines/Prototypes
Checklists
Rough Drafts Concept maps
Field Tests X Other:
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: Facilitator/Teacher
Community Resources: None
Reflection Methods: Individual, Group, and/or Whole Class
Mathematicians Journal X Small/Focus Groups X Whole Class Discussions X Fishbowl Discussions
Survey Other:
Material Adapted From: (Provide credit for any materials or activities adapted from other sources.) - http://www.exeter.edu/academics/72_6539.aspx - Phillips Exeter Academy
http://www.popularmechanics.com/outdoors/sports/physics/how-the-105-mph-fastball-tests-the-limits-of-the-human-body- Aroldis Chapman article
http://math.about.com/library/blrubric1.htm -rubric
http://www.portical.org/creating_tables.doc- creating tables
Virginia’s Senior Level Capstone Course Instructional Plan
Unit Title: Swing Batter Batter!
Driving Question: When should I swing the bat? Task:
You are a new baseball player and you’ve heard that the pitcher on the opposing team can throw at an above average speed. You have decided that you need to develop a plan to ensure that you swing at the right time.
Many major-league baseball pitchers can throw the ball at 90 miles per hour. At that speed, how long does it take a pitch to travel from the pitcher’s mound to home plate, a distance of 60 feet 6 inches? Give your answer to the nearest hundredth of a second.
ENGAGE How will student’s interested be peaked so they want to engage in the inquiry in this unit? Number of hours __1/4
Chocolate Bar problem
The goal of the activity is for students to activate their prior knowledge about adding and subtracting fractions.
Using the Chocolate Bar word problem, the students will use a candy bar that is divided into fourths to demonstrate how to solve the problem statement.
Present this situation to the students and have them record their thinking in their journal.
Problem: Show/Remind students of a Hershey Chocolate Bar. The purpose of the problem: You want to eat the entire Chocolate Bar. Before you are able to take a bite of your new chocolate bar, a friend comes along and takes ¼ of the bar. Then another friend comes along and you give this person 1/3 of what you have left. Make a picture or diagram in that shows the part of the bar left for you to eat. Work with your shoulder partner and share diagrams, explaining what part of the bar is left.
Mathematician Journal Prompts –
EXPLORE Teacher provides guidance for the explorations to prepare students with the
knowledge and skills to engage in the
exploration task.
Number of hours__1_
The teacher can demonstrate how solve the chocolate bar problem using the table feature in Word to make tables with various numbers of columns and how to shade the columns. Students can use Attachment Handout #3 Creating Tables in Word to practice this skill if needed before working on the explorations below.
Provide students with Handout #1.
Students may work in pairs to answer these problems. Exploration 1: Plebe Pie Problem
Students will use prior knowledge of fractions to complete this problem using a Microsoft Word table to create diagrams to solve the problem.
Exploration 2: A Journey of 1,000 miles
The goal of this activity is to refresh the student’s prior knowledge of ratios and conversions as applied to a practical problem. Students should work in partners and use the online graphing calculator science tools application to convert units as needed. See the link below. The students apply these conversions to proportions to solve the problem.
Have two pairs meet to discuss their solutions and how they determined the answer for the Journey of 1,000 miles.
The teacher checks with each group of pairs on the method of solution and the accuracy of the student work. The teacher can identify different solution methods and ask student pairs to display their work for class discussion to identify the connections between the different methods.
The journal prompt should be displayed for students to answer at the end of this activity.
Notes: Handout #2 is an answer key of possible solutions for the teacher. Handout #3 can be copied and given to students who need help with creating tables in Microsoft Word.
Optional - TI-83 Science Tools Applications: Use Unit Converter Tool http://education.ti.com/downloads/guidebooks/apps/ 83science_tools/83p_sciencetoolsapp_eng.pdf Mathematician Journal Prompts
– Discuss the
EXPLAIN Teacher introduces the main task of the unit and
prepares
students to work in small group independently.
Number of Hours__1
The teacher should show the following YouTube video clips to engage students in the task about Aroldis Chapman
http://www.youtube.com/watch?v=f3wJ-HgsnCg&feature=related –Chapman’s 105 mph pitch video
http://www.youtube.com/watch?v=yjbAYAeb7xc- Aroldis Chapman’s story video
Put students in pairs or groups of three as necessary.
The student task is presented on handout #4 and handout #5. There are two versions for differentiation for the levels of student understanding.
Tell students that they are taking on the role of a new baseball player facing a pitcher who throws at an above average speed. As the hitter against this pitcher you want to determine if there is a way to figure out the best time to swing to increase your chances of getting a hit.
Give students one of the handouts below and remind them of how to work in a group. You may want to have a student read the problem and the instructions for the whole class before beginning. Clarify instructions for the students, what the expected product is, and how group’s work will be evaluated.
Teachers may want the group to work together on Part 1 and each individual student to complete Part 2.
Swing Batter Batter (Basic) –Handout #4 Swing Batter Batter (Modified)-Handout #5
When students have completed the task you can ask students to respond to one or more of the journal prompts.
Mathematician Journal Prompts
– What challenges did you face as you began this task?
What questions did you have you worked on this task? ELABORATE The student groups are working independently with teacher consultations.
Each student pair is given the problem statement and pairs begin brainstorming on ways to solve the problem so they can find a reasonable solution for the time of the pitch. The pair draws diagrams as needed and writes down each step to solving the problem as stated on the task sheet.
The teacher serves as facilitator and interviews each pair to monitor their progress.
Number of Hours__1.5__
See attachment HO#4 Swing Batter Batter/Rubric
See attachment HO #5 Swing Batter Batter/Rubric (Modified with hints)
between mathematics and baseball?
EVALUATE Working groups submit products or make
presentations Number of Hours__.75_
Students turn in their problem statement, solution steps and conclusion either typed or neatly handwritten.
Complete teacher assessment using the rubric included on the task sheet.
Mathematician Journal Prompts
Compare your final solution to the results of the information in the
introduction on Chapman. Was your solution reasonable?
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.
KNOWLEDGE AND SKILLS NEEDED Assumed already learned
Students will self-assess
Will be taught during the unit
1. Simplifying fractions x x
2.Solving for a variable in a proportion x x
3.Converting units using graphing calculator (TI-83/84 plus/silver edition)
x x
4.Ratios and proportions x x
5. Solving linear equations x x
6.Ability to compare reasonable solutions x 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
□ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ ________________________________ □ _____________________________
__
Attachments: Handouts With Title and Numbered Sequentially as Handouts 1-5
HO #1
Exploration 1: Plebe Pie
At West Point, the “plebe” (first year cadet) who brings dessert to the table must divide it into pieces that are exactly the size requested by the cadets at the table. One night, the two seniors assigned to the table requested 1/5 of the pie and 1/6 of the pie, respectively. How much of the pie did that leave for the younger cadets? How do you know your answer is correct?
Exploration 2: A Journey of 1,000 miles
HO #2
Exploration Solutions
1. Plebe Pie Problem ( solution using Microsoft Word Table feature)
19/30 of the pie is left.
2. A Journey of 1,000 miles
Information given/Solution: Need to know:
Number of steps in a mile
Average stride length
Conversions
Calculations [will vary depending upon average stride length]
Average stride- 3ft.
1 mile= 5,280 ft. or 1,760 yards.
1 mile = 1,760 steps
1,000 miles= 1,760,000 steps
1 kilometers= .6213712 miles
1 kilometers= 1, 093, 613 steps
Elaboration Problem: Swing Batter Batter
1. 90 mph/1hr. = 475, 200 ft/3,600 s
Setup a ratio to convert 60.5 ft to seconds. 475,200 ft = 60.5 ft
3,600 s x seconds
x = ( 3600s *60.5ft)/475, 200 ft.
HO #3 Creating a Table in Word
Introduction : This HO can be omitted if you are using a different version of Word than is used here.
Tables can be inserted anywhere in a document. If the document is going to be filled out by a user it works better if the entire document is one table. For our problem, we will be making a table document to show some of the powerful and time saving formatting capabilities available.
Get Ready
Before you create a Table, you need to make sure that the Gridlines (the lines around the cells) are visible. Go to Table, then click on Show Gridlines as shown to the right.
The Task
Here’s our task. We need to create four columns to represent the candy bar problem.
Creating a Table
Click on Table, then on Insert, then on Table as shown to the left.
A screen will appear that will allow you to change the number of rows and columns that are needed, shown here. You will need to
Note: Making sure there are enough columns is more important than if there are enough rows. Rows can be added and removed easily. This is what a four column table looks like to represent the candy bar at each phase of giving pieces away.
HO #4
Swing Batter Batter!
Aroldis Chapman, a 22-year-old Cuban defector pitching for the Cincinnati Red, pitched at a speed of 105 mph. Chapman’s pitch was one of the fastest ever recorded; one that pushed his body to the limit of human ability. The speed of the 105-mph pitch is measured from where the pitcher releases the ball in which the batter, Matt McBride of the opposing Columbus Clippers had 0.35 seconds to react to Chapman’s pitch.
You’re a new baseball player and you’ve heard that the pitcher on the opposing team can also throw at an above average speed. You’ve decided that you need to develop a plan to ensure that you swing at the right time. Therefore you will need to know the time that it will take for the ball to reach the plate so that you will know when to swing….
Problem: A major-league baseball pitcher can throw the ball at 90 miles per hour. At that speed, how long does it take a pitch to travel from the pitcher’s mound to home plate, a distance of 60 feet 6 inches? Give your answer to the nearest hundredth of a second.
What do you need to know?
Instructions:
1. Display step by step procedures and diagrams if used to solve the problem. The final product must be typed or neatly hand written.
2. Is your answer reasonable? Explain. Compare your answer to the information in paragraph 1 on Aroldis Chapman.
Assessment Rubric
Benchwarmer (1pt) Rookie (3 pts) MVP (5 pts) Understanding of
Concept
Demonstrates little understanding of the main concept.
Demonstrates partial understanding of the main concept.
Demonstrates thorough
understanding of the main concept. Organization Very weak evidence
of organization, a few correct answers.
Organization needs to improve, most answers are correct.
Well organized with correct answers.
Analysis Very little evidence of analysis. Some educated guesses. Accuracy is weak.
Analyzes the problem with some success, accuracy needs to improve.
HO #5
Swing Batter Batter!
Aroldis Chapman, a 22-year-old Cuban defector pitching for the Cincinnati Reds, pitched at a speed of 105 mph. Chapman’s pitch was one of the fastest ever recorded; one that pushed his body to the limit of human ability. The speed of the 105-mph pitch is measured from where the pitcher releases the ball in which the batter, Matt McBride of the opposing Columbus Clippers had 0.35 seconds to react to Chapman’s pitch.
You’re a new baseball player and you’ve heard that the pitcher on the opposing team can also throw at an above average speed. You’ve decided that you need to develop a plan to ensure that you swing at the right time. Therefore you will need to know the time that it will take for the ball to reach the plate so that you will know when to swing….
Problem: A major-league baseball pitcher can throw the ball at 90 miles per hour. At that speed, how long does it take a pitch to travel from the pitcher’s mound to home plate, a distance of 60 feet 6 inches? Give your answer to the nearest hundredth of a second. There are 5280 feet in a mile.
What Information is given?
~ Speed of the ball = 90 mph
~1mile = 5,280 ft. .
What do I need to know? ~ Time it takes a pitch to travel ~ Convert 60 feet 6 inches to feet
~ Set up a proportion to convert the previous answers to seconds
Instructions:
Display step by step procedures and diagrams if used to solve the problem. The final product must be typed or neatly hand written.
Is your answer reasonable? Explain. Compare your answer to the information in paragraph 1 on Aroldis Chapman.
Assessment Rubric
Benchwarmer (1pt) Rookie (3 pts) MVP (5 pts) Understanding of
Concept
Demonstrates little understanding of the main concept.
Demonstrates partial understanding of the main concept.
Demonstrates thorough
understanding of the main concept. Organization Very weak evidence
of organization, a few correct answers.
Organization needs to improve, most answers are correct.
Well organized with correct answers.
Analysis Very little evidence of analysis. Some educated guesses. Accuracy is weak.
Analyzes the problem with some success, accuracy needs to improve.
