Math and Science Activities in the Context of Baseball from the Event-Based Science Institute Teacher Version Mathematics
Math and Science Activities in the Context of Baseball from the Event-Based Science Institute Teacher Version - Mathematics The secret to real learning learning that lasts is total engagement. When students are fully engaged in their work working in a real-world context, using vocabulary, skills, and concepts familiar to experts in the field learning happens naturally. When students are truly absorbed in meaningful work, memorization, drill and practice, and worksheets become unnecessary. The trick is not just to engage students in the first place, that is the easy part. The trick is to keep students engaged. The activities in this module are designed for use in middle school science and mathematics classrooms. They use baseball as their real-world context. The stories that you find in the Background section of each activity are true. They tell about real things that happen to real baseball and softball players. From the context of the story flows a challenging task that requires students to design and conduct an experiment or use a mathematics concept. This strategy is called Total Engagement Learning. Placing a learning activity in the context of something real gives students an authentic reason to learn. An authentic activity works too. It engage students for three reasons: CONTEXT A real-world context makes learning meaningful. PURPOSE An authentic activity gives students a reason to learn and use concepts and skills. DIFFERENTIATION Authentic activities demonstrate how people with different skills, interests and jobs can all use and apply the things we are learning in school. In the classroom this means role playing, and role playing means natural differentiation. Each activity comes in an online Student Version (http://www.mcps.k12.md.us/departments/eventscien ce/baseball/ebs.baseballactivities.html) and a Teacher Version. Make a copy of the Student Version for each student to use. You may want to make just enough copies for one class and place them in sheet protectors to preserve them. The Teacher Version provides instructions on conducting the activity as well as references to the National Standards covered by the activity. Activities are also accompanied by readings. These readings come in two forms: Fundamentals - a brief discussion of the concepts (science or mathematics) dealt with in the activity. The Teachers Version will tell you how many copies you will need to make. Skills - a brief discussion of techniques and skills needed to conduct the experiment. The Teachers Version will tell you how many copies you will need to make. Some activities are also provided with resources. Resources are charts and tables that contain additional information for students to use as they complete the activities. The Teachers Version will tell you how many copies you will need to make. In a few cases, forms accompany the activities. If an activity has a form, you must print a copy of it for each student. The Event-Based Science Institute, with a generous grant from the Cal Ripken, Sr. Foundation, created the activities contained herein. They are intended for the use of science and mathematics teachers in both public and private schools. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the Event-Based Science Institute, Inc. and do not necessarily reflect the views of the Cal Ripken, Sr. Foundation. This publication was supported by grant number 2003-DR-FX-0024 from the Office of Juvenile Justice and Delinquency Prevention (OJJDP).The opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of OJJDP or the U.S. Department of Justice. Copyright 2004 Event-Based Science Institute, Inc. However, these online activities were designed to be used with appropriate duplicating equipment to reproduce copies for use with students. Permission is hereby granted to teachers for that purpose. For all other purposes, you may request permission in writing from the Event-Based Science Institute, Inc., 6609 Paxton Road, Rockville, MD 20852. Event-Based Science is the registered trademark of the Event-Based Science Institute, Inc. Copyright 2004 - Event-Based Science Institute 2
Math Activities TABLE OF CONTENTS BASE RUNNING BASEBALL CARDS DESIGNING REPLICA BALLPARKS HOME RUN DISTANCE TIME TO CELEBRATE Copyright 2004 - Event-Based Science Institute 3
Base Running Teacher Version Objective Students will use measuring instruments to mark a specific distance, to clock running times for that distance, then use proportional reasoning to predict running times over a longer distance. National Council of Teachers of Mathematics Standards A whistle might also be helpful if more than 1 student is running at the same time. A whistle will also help you get the attention of everyone. While two students are measuring distance, have the player manager lead the rest in stretching and warming up. All Major League athletes warm up and stretch before every game. This warm up should not be optional. Any child refusing may be given the option of researching the benefits of stretching before strenuous activity! Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand and use ratios and proportions to represent quantitative relationships. Compute fluently and make reasonable estimates. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. Description Preparation Obtain cones or other fieldmarking devices. If your school has access to a Babe Ruth League Field or Little League Fields ask permission to use the field and maybe even ask to borrow some of their bases. If someone asks, "Why don't we just run 90 feet instead of estimating our times over 90 feet?" Tell them that the 60-foot distance is more proportioned to the size of a middle school student. A student who is running at full speed for 90 feet will most likely tire and slow down during the last third of the longer distance. Work with your class to create a data table. Then Things that may go wrong and what you can do: have each student prepare a data table before going outside. It could rain schedule to use the gym if needed Gather all of the materials that are listed below. You go outside and forget a crucial If you do not have access to stop watches, a piece of material (i.e. stop watch) digital watch or a watch with a second hand can assign kids duties and responsibilities work. (i.e. equipment manager) so you, the teacher, do not have to remember everything. A checklist will help. Class Organization Organize students in small teams. If you have time, let your students decide how many people should be on each team and what job each student should have. Jobs can include timer (I student), recorder (1 student), distance measurers (2 students), referee (1 student to call starts), equipment manager(s) (1 or 2 students), player manager (1 student who makes sure that runners are in order and ready to go). Materials For each team 1 stop watch 1 measuring device (measuring wheel, tape measure, yard sticks, rulers, etc.) 1 clipboard 1 data table To help your students know when it is their time to run, names should be listed in order on the data table. To avoid arguments, jobs and responsibilities should also be listed. For individuals pencils sport shoes or baseball cleats Copyright 2004 - Event-Based Science Institute 4
For the teacher whistle extra staff, if available Scoring Rubric The student has completed a Major League Baseball Scouting Form. All information is provided, a Box-and-Whisker plot correctly reflects the distribution of running times in the class tested. The names and correctly calculated running times of the fastest (upper quartile) boys and girls are displayed in the table. The overall appearance of the form is neat and professional, the form is signed, and the data table is attached. 3 Points The student has completed a Major League Baseball Scouting Form. Most information is provided, a Box-and-Whisker plot correctly reflects the distribution of running times in the class tested. The names and running times of the fastest boys and girls are displayed in the table. Most times have been calculated correctly. The form is signed and the data table is attached. 2 Points The student has completed a Major League Baseball Scouting Form. Most information is provided, a Box-and-Whisker plot is included. The names and running times of the fastest boys and girls are displayed in the table. Most times have been calculated correctly. The form is signed and the data table is attached. No work completed. Extending the Activity 1 Point 0 Point Option 1: Use the internet and other sources to find other baseball players who have broken base running records or for Rookies who are having an excellent start like Esix Snead, of the New York Mets. Research to find their running times. Make a chart comparing and contrasting the new player to Rickey Henderson and to an individual in your class. Option 2: Research to find a training program to build speed and endurance in sprinting / running. Include any drills, exercises, and dietary needs of fast-running athletes. Make a list of the things these athletes have in common and come up with a training schedule for your classmates. Be sure to include dietary recommendations. Copyright 2004 - Event-Based Science Institute 5
Baseball Cards Teacher Version Objective(s) Students will use data from a simulated baseball game to compute batting averages and calculate proportions. National Council of Teachers of Mathematics Standards Work flexibly with fractions, decimals, and percents to solve problems. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand and use ratios and proportions to represent quantitative relationships. Description This activity is designed to provide your students with practice with decimal fractions in the context of a simulated baseball game. Step 1: After reading the Background section, discuss with your class how it is possible for one player can have a better batting average than another player who has more base hits. As an example, you can compare Barry Bonds and Manny Ramirez (Resource - 2002 Batting-Average Leaders). Ask your students to divide hits by at bats (AB) for Bonds and Ramirez. When working with a partner, each student continues to spin until there are three outs and then the other student spins. Students take turns spinning the spinner and recording the results in a chart until nine innings have been completed. In this simulated game, there is no way to track the score. The purpose is to establish a batting average for each student. Once students have completed 9 innings, each should complete the Game Statistics chart with their personal data from the game. Step 4: Students should use their data from the simulated game to estimate how many hits they would get if they were at bat as many times as their favorite player was in the regular 2002 season. To do this, have students set up a proportion like this: student data favorite-player data hits = x at bats at bats Step 5: Create a baseball card: Give your students some sample baseball cards. Have them discuss the kinds of information that appears on every card. Tell them that they are about to make their own baseball card. You will need to explain to your students that an official at bat is a turn at bat in which a player either makes an out or a base hit, or reaches base on an error or a force out. Base on balls, hit by pitch, sacrifice hits, or catcher's interference do not count as an official at bat. (For other baseball definitions, give your students copies of Fundamentals - Baseball Terms.) For the purpose of the simulated game in this activity, an official at bat is a turn at bat in which a player makes an out or a base hit. A walk does not count as an official at bat. Step 2: Give your students a copy of the 2003 Batting Statistics (Student Version). Together with your class, calculate the first batting average as a decimal fraction rounded to the thousandths place value. Let students work in pairs to find the missing batting average for each remaining player. Step 3: Playing the game: Have your students simulate a baseball game using a spinner. They can work with a partner, to play a simulated game. Distribute materials for the rough draft of the back of a baseball card. Have students fill in their personal data as if they were their favorite Major League player (using their own average, the at bats from the Major League player, and the hits they would have had if they batted as many times as their favorite player). After your students have finished the rough draft and you have approved it, give them the final copy to complete in ink. They can either draw their own picture on the front of the card or you can use a digital camera to produce a real picture for the front of the card. Copyright 2004 - Event-Based Science Institute 6
Materials For the class: Transparency of 2002 Batting-Average Leaders Transparency of 2003 Batting-Statistics (Student Version) Example Baseball Cards (a collection of real baseball cards for students to examine) Scoring Rubric Baseball card includes correct statistics and all other parts are included. 3 Points Baseball card has minor mistakes in the statistics and/or minor parts are missing. 2 Points Baseball card has several mistakes both in the statistics and parts are missing. 1 Point For Groups: One Baseball Spinner Resource - Baseball-Card Format Resource - Game Worksheet Resource - Game Statistics For individuals: Resource - 2003 Batting-Statistics Worksheet Resource - Game Worksheet Resource - Baseball-Card Format (Optional) No work completed. Extending the Activity More advanced students can create spinners for their favorite players by creating circle graphs. The graph should be broken up into these categories: outs, hits, and walks. First, find the total plate appearances (PA) by finding the sum of walks and at bats. Next, find the percentages for the circle graph using these formulas: Walks= Walks/PA Hits= Hits/PA Outs= AB-Hits/PA Copyright 2004 - Event-Based Science Institute 7
Designing Replica Ballparks Teacher Version Objective(s) Students will measure angles using a protractor and use proportional relationships to create scale drawings. National Council of Teachers of Mathematics Standards Apply appropriate techniques, tools, and formulas to determine measurements. Apply transformations and use symmetry to analyze mathematical situations Description This activity is designed to provide students with practice in preparing scale drawings. Students must have an understanding of proportional relationships in order to be successful with this activity. create a scale drawing that includes the outfield fence, the pitcher s mound, and the base paths. Students will create proportions by using values in Table 1-1 Major League vs. Babe Ruth League. It is recommended that you set up and solve one proportion problem to model the procedures for your students. Upon completion of the scale drawing, students must create a worksheet that features their computations. Also, the chart comparing MLB fields with Babe Ruth League fields provides measurements for different distances and they are not all in the same proportion. Therefore, instruct students to base their calculations of the distance to the outfield fence on the ratio of base distances. In the second part of their proposal, students provide the justification for their scale drawing. Students must explain each computation in order to prove to the Board of Trustees that their proposal is mathematically sound. The final part of the proposal is a written rationale of student s selection of their particular ballpark. Students are encouraged to include some interesting facts about the ballpark, share any personal experiences about the ballpark, and explain why other children would enjoy playing on a replica field of that ballpark. This section is intentionally placed as the third component. It is of primary interest that students complete the mathematical components of the activity before investigating their ballpark. Materials It is recommended that students work in pairs to promote mathematics communication and to ensure a quality product. Students will work cooperatively to create a proposal for the construction of a Babe Ruth League replica baseball field. You may want to explain that a replica baseball field is a scaled down version of its Major League counterpart. Begin the activity by asking, If you could play on any Major League baseball field, which would it be? The finished product for this activity is a threepart proposal. Students will use the dimensions of the Major League baseball field that they select and Babe Ruth League base distances to For each team Major League Ballpark Information Sheet Table 1-1 Major League vs. Babe Ruth League Fundamentals - Terms and Definitions Skills -Scale Drawings Graph paper Ruler Protractor Scoring Rubric See the Babe Ruth League Ballpark Information Sheet Answer Key for accurate Babe Ruth League measurements for each Major League Ballpark. Copyright 2004 - Event-Based Science Institute 8
All measurements and labels on the scale drawing are correct according to the selected scale. Explanations of all calculations are complete and accurate. Several historical and/or personal facts about the ballpark are present in the rationale for selecting the stadium. 3 Points Most measurements and labels on the scale drawing are correct according to the selected scale. Explanations of most calculations are complete and accurate. A few historical and/or personal facts about the ballpark are present in the rationale for selecting the stadium. 2 Points Many measurements and labels on the scale drawing are incorrect according to the selected scale. Explanations are incomplete, inaccurate, or not presented at all. A single historical and/or personal fact about the ballpark is present in the rationale for selecting the stadium. No work completed. Extending the Activity 0 Point Junior Groundskeeper: Students determine how much it will cost to maintain their Babe Ruth League field. Students can calculate the cost of seeding the grassy areas and providing dirt for the infield areas by calculating the areas represented by each. Assistant Coach: One of the jobs of an assistant coach is to determine if their catcher throws hard enough to prevent opposing players from stealing bases. Students will assume the role of assistant coach and, in small teams, determine their throwing speed from home plate to second base. Students will have to use the Pythagorean Theorem to determine the distance between home plate and second base in order to complete speed calculation. 1 Point Copyright 2004 - Event-Based Science Institute 9
Homerun Distance Teacher Version Objective Students will convert metric units to customary units in the context of baseball. National Council of Teachers of Mathematics Standards Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Understand measurable attributes. Understand both metric and customary systems of measurements.. Convert from one unit to another within the same system. Description This is a two-day activity in which your students work together to measure how far they can hit a baseball and convert customary measurements to metric measurements. The first part of the activity requires a baseball field or other space outside. Bats and balls (tennis balls or baseballs) are needed during this activity. Although students are told to develop their own procedures, it is important to make sure that everyone conducts the experiment the same way. First let your students work in teams of two or three to brainstorm ideas for the procedures to use. Then discuss all of the ideas and decide on one set of procedures that is a composite of the best ideas from all of the teams. Be sure to offer suggestions of your own that insure the safety of your students. Also make sure that the final procedures include recording of all measurements in customary units (yards, feet, and inches). When your students come in from outside have them find a distance in the school (or their neighborhood) that is similar to the distance they personally hit the ball. Find another distance that is the same as the distance of the Barry Bonds homerun from the Background. These real-life measurements can include both long and very short comparisons from football field lengths, to candy bar lengths or anything in between. The next step in this activity is converting all measurements from customary to metric. Instruction and practice are provided in a number of forms: Fundamentals - Converting Measurements (Customary to Metric) Fundamentals - Converting Measurements (Metric to Customary) Skills - Practice Converting (Customary to Metric) Skills - Practice Converting (Metric to Customary) Worksheet - Home run Hitters Use one or all of these sheets to ensure that all students find success. Once all conversions have been successfully completed, have your students prepare for the evening sportscast. Print one Script-and-Shot Form for each student. Instruct your students to complete the form by making sure that they say and show everything that the producer wants. Make sure that everything fits a two-minute spot. The producer hopes that by using real-life measurements the audience will be better able to better visualize the distances. Materials For each pair Fundamentals - Converting Measurements (Customary to Metric) Fundamentals - Converting Measurements (Metric to Customary) Skills - Practice Converting (Customary to Metric) Skills - Practice Converting (Metric to Customary) Worksheet - Home run Hitters Baseball Bat Baseball (or tennis ball) Yardstick or measuring tape (customary units) Calculator Script-and-Shot Form Copyright 2004 - Event-Based Science Institute 10
Scoring Rubric A Script-and-Shot Form has been completed in a "professional" manner. The news story includes home run distances in both Customary and Metric units and gives meaningful real-life distances that correspond to home run distances. Everything fits the two minutes allocated for the spot. 3 points A Script-and-Shot Form has been completed. The news story includes home run distances in both Customary and Metric units and gives meaningful real-life distances that correspond to home run distances. 2 points A Script-and-Shot Form has been attempted. The news story includes home run distances but the use of Customary and Metric units demonstrates a lack of understanding. Real-life distances that correspond to home run distances may or may not be included. No work completed Extension Activity 1 point 0 points Students will select a hometown Major League Baseball player and find out 3 or 4 homerun distances. Have them convert to Metric units and write a short news story comparing the player to any of the three from the worksheet. Copyright 2004 - Event-Based Science Institute 11
Time to Celebrate Teacher Version Objectives Students will write, simplify, and evaluate expressions to represent real life situations. National Council of Teachers of Mathematics Standards Description National Council of Teachers of Mathematics, 2000, pages 222, 256, 268, 274, and 280 In this activity, students will work individually as they plan the awards banquet for their local Babe Ruth League softball team. But first, students use the think/pair/share strategy as they investigate the number of ways that they could spend $10.00 to buy hot dogs, French fries, and sodas. Algebra Standard: In grades 6-8 all students should: Have your students work independently for 2 Understand patterns, relations, and minutes. In those 2 minutes, they should functions calculate several ways that they could spend the Relate and compare different forms of $10.00. Then, have them share with a partner for representation for a relationship 2 minutes. Finally have your students share with Represent and analyze mathematical the class. Try to find all 22 options. situations and structures using algebraic symbols Discuss with your students how to organize their work so that their thinking is ordered. Also, have Develop an initial conceptual your students discuss how to communicate their understanding of different uses of findings to others. variables Use symbolic algebra to represent Students need to understand the terms used in situations and to solve problems, this lesson. The terms are important for students especially those that involve linear to communicate effectively. The correct use of relationships these terms will show that students can use their Problem Solving Standard: algebraic skills. If students need support in these In grades 6-8 all students should skills, have them read: Build new mathematical knowledge through problem solving Fundamentals - Vocabulary Terms Solve problems that arise in mathematics and in other contexts This resource will help students understand the Communication Standard differences between terms. The goal is to In grades 6-8 all students should correctly use the terms in their activity. Working Organize and consolidate their with the correct vocabulary will allow them to be mathematical thinking through used correctly in their plan. communication Communicate their mathematical The opening activity then looks at expressions thinking coherently and clearly to peers, and equations. Students will write an expression teachers, and others to represent the cost of buying food. Next, they Use the language of mathematics to will write an equation to represent two equal express mathematical ideas precisely expressions. We have provided these resources Connections Standard that you can use to help your students with these In grades 6-8 all students should concepts as well: Recognize and apply mathematics in contexts outside of mathematics Fundamentals - Expressions versus Equations Representation Standard Fundamentals - Simplifying versus Solving In grades 6-8 all students should Skills - Evaluating Expressions Create and use representations to organize, record, and communicate Be sure that your students see the importance of mathematical ideas identifying variables for the expressions. Use representations to model and interpret physical, social, and mathematical phenomena Principles and Standards for School Mathematics, Have the students investigate the difference in the number of solutions between the expression (22) and the equation (5). Copyright 2004 - Event-Based Science Institute 12
In order for your students to understand how mathematics is used in everyday life, they need to be able to translate between words in English and expressions/equations in mathematics. Students who need additional support can read: Skills -Translating English Terms into Math Expressions Before you move to the last part of this activity, you may wish to help your students think about how they can meet the $10.00 requirement and at the same time meet other needs. One of those other needs might be setting a minimum requirement of buying at least one hot dog, one order of French fries, and one soda. (This exercise will allow students to start thinking about meeting the different requirements of their banquet their menu.) Next, students begin to examine how to create a menu. The menu will meet different needs and stay within the $400 budget. Students will work individually (allow 4 minutes), then together (allow 2 minutes), to help them to understand the project. You should circulate among your students to check on their understanding and progress. Once students understand the task, let them begin to work. Be sure that they include an explanation of the benefits of their menu. Materials Answers For each team Copies of each of Fundamentals and Skills essays For individuals Copies of Worksheet - Ballpark Costs Information Calculator For the opening activity on spending $10.00, the possibilities are (22 ways): Hot Dogs $4.00 French fries $3.00 Soda $2.00 Total 0 0 1 $2.00 0 0 2 $4.00 0 0 3 $6.00 0 0 4 $8.00 0 0 5 $10.00 0 1 0 $3.00 0 1 1 $5.00 0 1 2 $7.00 0 1 3 $9.00 0 2 0 $6.00 0 2 1 $8.00 0 2 2 $10.00 0 3 0 $9.00 1 0 0 $4.00 1 0 1 $6.00 1 0 2 $8.00 1 0 3 $10.00 1 1 0 $7.00 1 1 1 $9.00 1 2 0 $10.00 2 0 0 $8.00 2 0 1 $10.00 Copyright 2004 - Event-Based Science Institute 13
The expression for the cost of the food would be 4h + 3f + 2s where h is the cost of a hot dog f is the cost of an order of French fries s is the cost of a soda The equation would be 4h + 3f + 2s = 10 There are 5 ways to spend exactly $10.00 Scoring Rubric The student's plan to the local Babe Ruth League includes a menu that costs less than $400. The plan includes the expression that they used to determine the cost of the menu. All variables in the expression have been identified and all mathematical vocabulary has been used correctly. The plan also includes a discussion of the nutritional and other benefits of the menu chosen. 3 Points The student's plan to the local Babe Ruth League includes a menu that costs less than $400. The plan does not include the expression that they used to determine the cost of the menu. All variables in the expression have been identified and all mathematical vocabulary has been used correctly. The plan does not include a discussion of the nutritional and other benefits of the menu chosen. 2 Points The student's plan to the local Babe Ruth League only includes a menu. No work completed. Extending the Activity 1 Point Students who are capable of extending the activity can create a spreadsheet for their plan. Additional challenge can be offered by lowering the budget to $300 or $350. Different teams of students could be given different budgets. Students could then compare the challenges presented to them by having less money. Copyright 2004 - Event-Based Science Institute 14