Instructor_Guide_Math.pdf

7/28/2019 Instructor_Guide_Math.pdf

http://slidepdf.com/reader/full/instructorguidemathpdf 1/235

MATH IN AFTERSCHOOL

Produced for the U.S. Department of Education by the National Partnership for Quality Afterschool Learning

A Supplement to the

Online Afterschool

Training Toolkit

for 21st Century

Community Learning Centers

www.sedl.org/afterschool

AFTERSCHOOL

TRAININg TOOLkIT

AFTERSCHOOL

TRAININg TOOLkIT

An Instructor’s Guide to the



Contributors

Kathleen Dempsey

Dana Frazee

Kay Frunzi

Heather Martindill

Design and Production

Production

Laura Shankland

Deborah Donnelly

Catherine Jordan

Editorial

Leslie Blair

Suzanne Hurley

Debbie Ritenour

Designers

Shaila Abdullah

Ben Chomiak, Red Dog Creative

Jane Thurmond

Copyright © 2008 SEDL

SEDL

4700 Mueller Blvd.

Austin, TX 78723Voice: 512-476-6861

Fax: 512-476-2286

www.sedl.org

Mid-continent Research or Education and Learning

4601 DTC Boulevard

Suite 500

Denver, Colorado 80237

Voice: 303-337-0990

Fax: 303-337-3005

www.mcrel.org

This publication was produced in whole or in part with unds

rom the Oce o Academic Improvement and Teacher Quality

Programs, U.S. Department o Education under contract number

ED-03-CO-0048. The content herein does not necessarily refect

the views o the Department o Education, any other agency o the

U.S. government, or any other source.

Titles or names o specic sotware discussed or described in this

document are registered trademarks, trademarks, or copyrighted as

property o the companies that produce the sotware. Unless noted

otherwise, photos are © Jupiterimages Unlimited.

Please note that the World Wide Web is volatile and constantly

changing. The URLs provided were accurate as o the date o this

publication, but we can make no guarantees o their permanence.

Suggested citation in APA ormat:

Dempsey, K., Frazee, D., Frunzi, K., & Martindill, H. (2008).

Math in afterschool: An instructor’s guide to the Afterschool

Training Toolkit. Austin, TX: SEDL.



Lesso Overview ...................................................................... iv

Itroductio ............................................................................. 1

Practice 1: Fidig Math........................................................... 5

Lesson 1: Three Ms! Making Predictions, Measuring,

and Marshmallows .................................................. 8

Lesson 2: Largest Number Race ........................................... 14

Lesson 3: What’s the Best Snack? ......................................... 20

Lesson 4: Musical Notes and Math Fraction Drumming ........... 26

Lesson 5: Paper Airplane Gliders ........................................... 34

Practice 2: Math Ceters ........................................................ 43

Lesson 1: Measuring Hands and Feet .................................... 46

Lesson 2: Finding Pentominoes ............................................. 52

Lesson 3: Using Git Certifcates ........................................... 58

Lesson 4: What’s the Chance? .............................................. 64

Lesson 5: Pattern Block Percentages ..................................... 78

MATH IN AFTERSCHOOL

AFTERSCHOOL

TRAININg TOOLkIT

AFTERSCHOOL

TRAININg TOOLkIT

An Instructor’s Guide to the



MATH IN AFTERS CHOOL

ii www.sedl .org/afterschool

Practice 3: Math Games.......................................................... 85

Lesson 1: Race to the Finish ................................................ 88

Lesson 2: Math Football ...................................................... 94

Lesson 3: Number Concentration ........................................ 102

Lesson 4: Rational Number Bingo ....................................... 106

Lesson 5: Who Has? ......................................................... 112

Practice 4: Math Projects...................................................... 119

Lesson 1: Digital Math Storytelling ...................................... 122

Lesson 2: Stock Market Game ............................................ 128

Lesson 3: Learning Math and Art With Quilts ....................... 134

Lesson 4: Scale ................................................................ 144

Practice 5: Math Tools .......................................................... 151

Lesson 1: Tangrams .......................................................... 154

Lesson 2: Growing Rock Candy ........................................... 158

Lesson 3: Graphing Candy With Spreadsheets ...................... 164

Lesson 4: Learning Math and Musical Pitches

With Water Bottles .............................................. 172

Lesson 5: Geometric Shape Spotting ................................... 178



AN INSTRuCTOR’S GuIdE TO THE AFTERSCHOOL TRAINING TOOLkI T

McREL | National Partnership for Quality Afterschool Learning ii i

Practice 6: Math Tutorig...................................................... 185

Lesson 1: One-on-One Tutoring ........................................... 188

Lesson 2: Small-Group Tutoring .......................................... 192

Lesson 3: Learning With Tutorials ....................................... 196

Lesson 4: Homework Help: Ask an Expert! ........................... 200

Practice 7: Famil Coectios.............................................. 207

Lesson 1: Family Math Nights ............................................ 210

Lesson 2: Family Math Workshops ...................................... 214

Lesson 3: Grocery Store Math ............................................. 218

Resources............................................................................ 225

Planning Worksheet: Supporting Math Learning in Aterschool...225



MATH IN AFTERSCHOOL

iv www.sedl .org/afterschool

Lesson Overview

Lesso Grade

Level(s)

Duratio Subject Used Page

Three Ms! MakingPredictions, Measuring,and Marshmallows

K–2 1 hour Measurement 8

Largest Number Race 3–5 30–45minutes

Number/Operations 14

What’s the Best Snack? 3–5 1 hour Data and Probability 20

Musical Notes and MathFraction Drumming

3–5 90 minutes Number/Operations 26

Paper Airplane Gliders 4–8 90 minutesor 2 classperiods

Data and Probability,Measurement

34

Practice 1: Fidig Math 5

Measuring Hands and Feet 2–5 30–45minutes

Measurement 46

Finding Pentominoes 3–5 45 minutes Geometry, Algebra 52

Using Git Certifcates 4–5 45–60minutes


What’s the Chance? 6–8 1 hour Data and Probability 64Pattern Block Percentages 5–6 30 minutes Number/Operations, Geometry 78

Practice 2: Math Ceters 43

Race to the Finish K–2 10 minutesper round

Data and Probability,Number/Operations

88

Math Football 5–10 10–15minutes orone game

Number/Operations,Geometry, Measurement,Algebra

94

Number Concentration K–2 30 minutes Number/Operations, Geometry 102

Rational Number Bingo 4–8 5–10minutes orone game


Who Has? 4–8 5–10minutes orone game

All Strands 112

Practice 3: Math Games 85



AN INSTRuCTOR’S GuIdE TO THE AFTERSCHOOL TRAINING TOOLkI T

McREL | National Partnership for Quality Afterschool Learning v

Digital Math Storytelling 3–8 2–3weeks

All Strands 122

Stock Market Game 6–8 4 weeks Number/Operations,Data and Probability

128

Learning Math and ArtWith Quilts

K–2 Seven45-minutesessions

Number/Operations,Geometry, Algebra

134

Scale 6–8 Tensessionso 45–60minuteseach

Measurement, Algebra,Number/Operations, Geometry

144

Practice 4: Math Projects 119

Tangrams K–2 45–60minutes

Geometry 154

Growing Rock Candy 3–7 Oneweek orobservationand one1-hourlesson

Measurement, Data andProbability, Algebra

158

Graphing Candy WithSpreadsheets

5–8 45–60minutes

Data and Probability 164

Learning Math and MusicalPitches With Water Bottles

6–8 90 minutes Measurement, Number/ Operations

172

Geometric Shape Spotting K–2 Three1-hoursessions,with agallery

night orparents

Geometry 178

Practice 5: Math Tools 151

Lesso Grade

Level(s)

Duratio Subject Used Page




vi www.sedl .org/afterschool

One-on-One Tutoring K–12 Sessionso 15–20minutes

All Strands 188

Small-Group Tutoring K–12 20–30minutes

All Strands 192

Learning With Tutorials K–12 Sessionso 15–20minutes

All Strands 196

Homework Help:Ask an Expert!

2–12 Sessionso 15–20minutes

All Strands 200

Practice 6: Math Tutorig 185

Family Math Nights K–8 30 minutesto 2 hours

All Strands 210

Family Math Workshops K–8 30 minutesto 2 hours

All Strands 214

Grocery Store Math K–8 Varioustimes

All Strands 218

Practice 7: Famil Coectios 207

Lesson Overview, contine

Lesso Grade

Level(s)

Duratio Subject Used

Optional in Italics

Page



AN INS TRuCTOR’S GuIdE TO THE AFTERSCHOOL TRAINING TOOLkIT

McREL | National Partnership for Quality Afterschool Learning 1

Introction

The Aterschool Traiig ToolkitI you work in aterschool, you most likely know the challenge o oering aterschool academic

enrichment that will boost student perormance during the regular school day while making

sure activities are engaging enough to keep students coming back. Through a contract with

the U.S. Department o Education, the National Partnership or Quality Aterschool Learning

has developed tools to help you meet this challenge. National Partnership sta visited 53

aterschool programs, nationwide, that had evidence suggesting they had a positive eect on

student achievement.

With this research, the National Partnership developed the Aterschool Training Toolkit (www.sedl.org/aterschool/toolkits), an online resource that is available to aterschool proessionals

to help them oer engaging educational activities that promote student learning. The toolkit

is divided into sections that address six content areas: literacy, science, the arts, homework

help, technology, and the content area or this guide, math. Like the other content areas in

the toolkit, math is taught through promising practices, or teaching techniques with evidence

suggesting they help students learn important academic content.

The seven promising practices in aterschool math identifed in the Aterschool Training

Toolkit are as ollows:

• FindingMath• MathCenters

• MathGames

• MathProjects

• MathTools

• MathTutoring

• FamilyConnections




2 www.sedl.org/afterschool

When used with the Aterschool Training Toolkit, the lessons in this instructor’s guide will help

you master these promising practices. Once you become profcient at these practices, you

should be able to use them to develop other math lessons.

This instructor’s guide will help you

• understandhowtousethemathsectionoftheonlineAfterschoolTrainingToolkit;

• usemathtoofferfunlessonsthathelpstudentslearninafterschool;

• motivatestudentstoparticipateinafterschool;and

• usethelessonstobecomeamoreeffectiveafterschoolinstructor.

The Role o MathBeore you begin, you should know that this instructor’s guide is not a manual or dierent

types o math or or starting an aterschool math program. You do not need to be a math

expert to use this guide. In addition to the lessons on promising practices, a planningworksheet is available at the end o this guide. The planning worksheet will help you

accommodate your particular aterschool situation and plan or the best possible lesson.

How to Use This Istructor’s GuideThis guide will help you master the promising practices in aterschool math through the

ollowing steps:

• WatchingvideoclipsfromtheNationalPartnership’sonlineAfterschoolTrainingToolkit

• Teachingthelessonsincludedinthisinstructor’sguidetoyourstudents

• Reectingonthestudentlessons

Video Clips

The Aterschool Training Toolkit (www.sedl.org/aterschool/toolkits) includes video segments

showing outstanding aterschool programs across the United States. Watching these video

segments allows you to observe aterschool instructors in action as they use promising prac-

tices. Take notes on what you see and think o ways that you can use these practices in your

aterschool program.

Lessos

Ater you watch each video that illustrates a practice, you will fnd several lessons that usethe same practice. You can teach as many o these lessons as you think are appropriate to

your students, depending on their grade levels and math skills and the time available in your

aterschool schedule.





1 McEwan, E. K. (2002). Tentraitsofhighlyeffectiveteachers.Thousand Oaks, CA: Corwin Press, Inc.

Reectio

Ater each lesson, you will fnd a series o questions addressing the preparation, student en-

gagement, academic enrichment, and classroom management o that lesson. The purpose o

thereectionistoallowyoutobeintentionalinyourinstruction—tothinkaboutwhataspects

ofalessonworkedwellandwhatchangesyoumightwanttomakeforfuturelessons.Reec-

tion is an important part o becoming a successul instructor and will help you apply what you

learned rom one lesson to another.1

Thefollowingisanexampleofhowateachermightanswerthereectionquestionsafter

leading a lesson where students count the number o each color o M&Ms in a bag and make

charts to illustrate their fndings.

Reflection [Sample]

Preparatio• Howwelldidthelessonplanninghelpyouprepareforthisactivity?

• Whatcanyoudotofeelmoreprepared?

Overall,Ifeltverypreparedforthislesson.Ireadthroughthelessonseveraltimesandhad

mysuppliesreadyaheadoftime.IwishIwouldhavespentmoretimepracticingwiththe

spreadsheetapplicationsothatIwouldhavebeenreadytoexplainittothestudents.We

probablyshouldhavespentsometimereviewingExcelasaclassbeforewebegantheactivity.

Studet Egagemet• Howdidyouassessstudentengagement?

• Whatdidyounoticeaboutstudentengagementinthedifferentpartsofthelesson?

• Howsatisedwereyouwiththelevelofstudentengagement?

• Ifyouwerenotsatised,howcouldyouchangethelessontoincreasestudentinvolvement?

Iassessedstudentengagementbyobservingwhetherstudentswereontask.Iftheywere

talkingaboutsomethingunrelatedtothelesson,playingwiththecandyinsteadofcounting

it,orotherwisemessingaround,Iknewtheyweren’tengaged.Mostofthemwereprettyfocused.Itoldthemthattheycouldnoteatthecandyuntilthelessonwasnished,andthat

keptmanyofthemfocused.Someofthemwerecompletelydistractedbythecandy.Itwas

unbelievable,butIdidn’tknowwhattodoaboutit.Icouldswitchtosomethingelse,but

halfthefunisusingM&Ms.





Iwaspleasedwithhowengagedstudentswereformostofthelesson.Thingsfellaparta

littlewhenwestartedgraphingtheresults.Therangeofcomputerskillsvariessomuch.

Somestudentsknewexactlywhattodo,andotherswerecompletelylost.ThenexttimeI

teachthislesson,Iamgoingtodoamini-lessononusingelectronicspreadsheetsrstso

studentswillbemoreprepared—andthereforemoreengaged.

Academic Erichmet• Howdidthislessonsupportothercontentareas?

• Whatchangescouldyoumaketostrengthenacademicenrichmentandstillkeepthe

activity un?

Asidefromtheobviousmathenrichment,thislessonsupportstheuseoftechnology

inlearning.Oncestudentshavemasteredratiosandgraphingresults,guringoutthe percentageofeachcolorofcandywouldmakeagoodextensionactivity.

Classroom Maagemet• Whatstrategiesdidyouusetomakegosmoothly?

• Whatchangeswouldyoumakeifyoutaughtthelessonagain?

Myadvancedpreparationreallyhelpedthelesson,butoverallthelessondidnotgoas

smoothlyasIhadhoped.Nexttime,Iwilldenitelyspendmoretimehavingstudents

practiceusingExcel,andIwillalsoincorporateadditionalrewardstokeepstudentsengaged

andfocused.





Fining Math

What Is It?FindingMath involves using un problem-solving activities that bring math to lie. From

cooking to exercise, FindingMath lets students use everyday activities to make meaningul

discoveries, enhance their understanding o math, and build their enthusiasm or learning.

What Is the Cotet Goal?The key goals o FindingMath are to engage students in math through everyday activities

they already enjoy, build their problem-solving and collaboration skills, increase their desire

to learn, and ultimately extend their understanding o math. Specifc content goals should beconnected to what students are learning during the school day and to grade-level standards.

What Do I Do?Begin by talking to the day-school teacher to fnd out what math concepts students are

learning, the standards or each grade level, and the kinds o everyday, real-world activities

that illustrate math concepts and extend students’ learning.

For example, a cooking activity allows students to use math by measuring ingredients,

comparing measurements o liquids and solids, converting between standard and metric

systems, and reducing or enlarging how much a recipe yields. Next, consider the kinds o

activities that your students enjoy and how appropriate math concepts and skills can be

incorporated.

Once you have outlined the activities, develop a guiding question or problem to help students

discover math in an everyday activity. Figure out the learning goals and outcomes or each

activity, secure space, and gather any materials that you might need. As you introduce the

activity to students, emphasize a sense o un and discovery.

Use the planning worksheet at the end o this guide to begin thinking about how you can

incorporate math into aterschool activities.

Practice 1





Wh Does It Work?The aterschool setting provides a great opportunity to integrate math learning with activities

that students already enjoy. Research suggests that the best activities are based on students’

interests, incorporate physical activity, entail social interaction, and provide meaningullearning or students struggling with math. By honoring students’ need to learn in a dierent

setting, you can help build their understanding and increase their desire to learn.





video

Getting Starte

Go to the FindingMath practice ound in the math section o the Aterschool

Training Toolkit (www.sedl.org/aterschool/toolkits/math/pr_math_fnd.html).Click on the video “Rhythm and Beats” and watch as fth- and sixth-grade

students at the Champions aterschool program at Independent School No.

125, Woodside, Queens, in New York City, use counting and ractions to

compose and perorm percussion beats.

Use the beore, during, and ater writing prompts to write down your ideas on how you might

involve your students in math and music.

BEFORE yOU WATCH THE VIDEO, write down what you already know about students using

math in music.

DURInG THE VIDEO, consider the ollowing:

How does the instructor work with the students to lay the groundwork or the activity and get

them started?

How does the instructor interact with the kids? What does he or she do to keep them

engaged?

What academic skills, like reading or math are students reinorcing while they participate in

the activity? Be sure to give specifc examples.

AFTER yOU WATCH THE VIDEO, write what modifcations you might need to make to teach

this lesson in your own class.





Lesson 1

Three Ms! Making Preictions,Measring, an Marshmallows

In this lesson, students compare measuring cup sizes. They learn that how

much a measuring cup holds is called volume. Next, students learn the

meaning o the word prediction, as they predict how many marshmallows

will ft into a cup o orange juice and rozen yogurt.

Grade Level(s): K–2

Duratio:

1 hour

Studet Goals:

• Compareandordermeasuringcupsaccordingtovolume

• Usetoolstomeasure

• Makecomparisonsandestimatesamongdifferentmeasurements

• Makepredictions

Curriculum Coectio:

Science

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks). The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.

Stadard 1: Uses a variety o strategies in the problem-solving process

GradesK–2Benchmark 2: Uses discussions with teachers and other students to understand problems

Stadard 4: Understands and applies basic and advanced properties o the concepts o measurement

GradePreK

Benchmark 4: Orders objects qualitatively by measurable attribute

Benchmark 5: Knows the common language o measurement

Benchmark 6: Knows that dierent sized containers will hold more or less

GradesK–2

Benchmark 1: Understands the basic measures length, width, height, weight, and temperature





Imagie This!The room is flled with miniature dessert ches measuring orange juice into various-sized

measuring cups or a new and wonderul snack! As the young ches ponder and predict how

many marshmallows to set aside or the fnal touch, you fll their cups with tasty vanillayogurt. Once the ches have predicted the number o marshmallows necessary to fll up the

cup, they add the marshmallows one at a time and keep count until there is no more space in

the cup. They compare their predictions to the fnal count . . . and then eat their creation!

What you needp One set o measuring cups or each small group

p 50 small marshmallows or each small group

p One cup o orange juice or each student

pFrozenyogurt;enoughforeachstudenttohaveascoop

p Spoons

p Plastic cups

p Paper

p Pens

p Pencils

p Bags or supplies

Gettig Read• Assemblesupplybagswithmaterialsneededforeachstudent.

• Bepreparedtoreviewthemeaningoftheword prediction, which means to make a

reasonable guess about something that hasn’t happened yet. You may want to model

strategies or orming predictions with marshmallows or younger students.

Vocabulary

Measuremet: a comparison to some other known unit (e.g., length, width)

Predictio: a statement o what somebody thinks will happen in the uture

Volume: the space or size within a three-dimensional object




10 www.sedl .org/afterschool

What to Do• Dividestudentsintogroupsoffourorve,basedonwhowillworkwelltogether.Giveeach

student a bag o supplies and each small group a set o measuring cups.

• Askchildrentolineupthemeasuringcupsfromsmallesttolargest.• Askstudentstopredictwhichmeasuringcupwillholdthemostorangejuice.Trytoget

students to articulate that the bigger cups will hold more than the smaller cups. Tell them

that the amount each cup holds is called volume.

• Askstudentshowtheyfoundtheiranswersandhowtheyknowwhichcupholdsmore.

• Next,pourorangejuiceintothe1-cupmeasuringcupsandthenhavestudentspourthe

orange juice rom the measuring cups into their plastic cups.

• Askstudentstoobserveanysimilaritiesordifferencesinthejuiceineachcontainer.

What did they notice as they poured the juice? Younger students may think that there

are dierent amounts, based on how the juice flls each container. Ask them how they

know. It may help them to clariy the concept o volume by pouring the juice back into the

measuring cup to test their predictions.

• Addascoopoffrozenyogurtintoeachoftheplasticcupswithjuice.

• Next,askstudentstopredicthowmanymarshmallowswilltintothehalf-cupmeasuring

cups, write down their predictions, and then describe how they made their predictions.

• Havestudentstesttheirpredictionsusingthemarshmallowsandthendiscusstheir

answers. Answers will vary depending on how the cup was packed. Finally, students can

add marshmallows to their juice and yogurt and eat it!

Teaching Tips

I students haven’t used measuring cupsor learned about volume and measurementbeore this lesson, you may want to beginbyreviewingeachmeasuringcup;how

many halves, thirds, and quarters makeawhole;andansweranyquestionsthat

students have.





ExtedAs an extension piece, ask students to describe their process. What did they do frst? What

did they do second? Number the process on the board. Then ask students to write a how-to

piece. Younger students can draw pictures o the process.

Outcomes to Look orMuch o the assessment or this

lesson comes rom listening to and

watching the children. Listen or use

o vocabulary, acility with ordering

measuring cups, and estimation skills

and strategies.

• Studentparticipationand

engagement

• Usingmeasuringtoolsproductively

• Anunderstandingofdifferent

measurements and how to measure

• Answersthatreectan

understanding o size and volume

• Answersthatreectan

understanding o comparison and

prediction as well as strategies to

make and test predictions





Reflection

The questions below are prompts to help you record your ideas, but you can also write

additional observations about the lesson that the questions do not cover.









activity un?

Classroom Maagemet• Whatstrategiesdidyouusetomakethisactivitygosmoothly?










Lesson 2

Largest Nmber Race

In this lesson, students design a relay race to compare whole numbers and

then compete to create the largest 10-digit number. Teachers will need

a large space to set up this activity, which includes kinesthetic activities

such as jumping rope, relay races, basketball, and sack races.

Grade Level(s): 3–5

Duratio:

30–45 minutes

Studet Goals:

• Comparewholenumbers

• Understandtheplacevalueofdigitsinanumber

• Usespecicskillsinthecontextofavarietyofphysicalactivities

• Workcooperativelytosolveproblems

Curriculum Coectio:

Physical Education

Stadards:



Grades3–5Benchmark 7: Uses explanations o the methods and reasoning behind the problem solution todetermine reasonableness o and to veriy results with respect to the original problem

Stadard 2: Understands and applies basic and advanced properties o the concepts o numbers

Grades3–5

Benchmark 4: Understands the basic meaning o place value

Benchmark 5: Understands the relative magnitude and relationships among whole numbers,ractions, decimals, and mixed numbers





Imagie This!Laughing, obstacles courses, and math are all rolled into one lesson! Get ready or some

un with math as students work in teams to complete various obstacle-course races in the

shortest amount o time so they can obtain a number. Once they get a number, studentsmust decide where to place it on a 10-digit number line. Beware! Teams must use strategy

in deciding where to place the number on the line to create the largest number at the end o

the contest. The teams cannot move the numbers once they are placed. This exciting contest

repeats nine more times with students placing their numbers on the 10-digit number line ater

each race. Who will win?!

What you needp Two 10-sided number cubes

p Masking tape

p Paper

p Items or relay race (balls, jump ropes, etc.)

Gettig Read• Foreachteam,place10stripsofmaskingtapeontheoor,witheachstriprepresentinga

placeholder or a 10-digit number, and small pieces o tape or the commas. For example:

_____, _____ _____ _____, _____ _____ _____, _____ _____ _____

Vocabulary

Billio: one thousand million, written as 1 ollowed by 9 zeros

Digit: any one o 10 symbols between 0 and 9 that represent numbers

Millio: one thousand thousands, written as 1 ollowed by 6 zeros

Obstacle course: a sporting area where participants have to get pastvarious obstacles or objects to reach a goal





What to Do• Asaclass,designanobstacle-courserelaythatincorporatesatleasttwophysical

activities—jumpingropeandthrowingabasketballthroughahoop,forexample—while

moving toward a fnish line. The fnal activity in the relay involves receiving a randomlygenerated number between 0 and 9, and working together as a team to determine where to

stand in a string o 10 digits to make the largest number.

• Dividethestudentsintotwoteams.

• Chooseapersontobethenumberroller(someonewhocan’tparticipateinthephysical

activity or would preer not to is always a good choice). Each turn, this person will roll

the number cube, write the number on two pieces o paper, and hand them to the two

competing team members ater they fnish the other relay tasks. Both teams will receive

the same number each turn. The team members should then each write the number

somewhere on his or her team’s 10-digit number line.

• Tellstudentsthattherstteamtocompletealltasksandmakea10-digitnumbergetsonepoint. The team that makes the largest number also gets one point. Play can continue as

long as time allows. The team with the most points wins.

• Haveeachteamreaditsnumbertodeterminewhohaswon.Toreadthenumbers,youcan

havestudentsputtheirnumberedpiecesofpaperontheoor,standback,andlookatthe

number. You might ask, “How do you know which number is the largest?”

• Onceteamshavecompletedtheirrstround,discusshoweachteamcameupwithits

number, the strategies the students used, and what they learned.

• Beginbyreviewingtheobjectiveofthegameandmakingsurethatthestepsareclearto

students. The goal o the game is to come up with the largest number. See i students can

fgure out that larger digits should go at the beginning o the number and smaller digits at

the end. However, this is a game o chance and strategy. Students can’t move the digits

once they have placed them.

• Useguidingquestionstoencouragestudentstojustifyanddiscusshoweachteamcame

up with its number. Use the sample questions below or develop your own.

• Whatstrategydidyouusetomakethelargestnumber?Wasitagoodstrategy?Whyor

why not? What strategy would you like to try in the next round?

• Thistypeofquestioningshouldoccurseveraltimesthroughouttherelay.Studentsshould

refne their strategies once they understand the game better. Give each team time ater

each round to discuss a strategy or the next round.





Exted• Trythegamewiththefollowing:

- 2-digit multiplication, with the goal being to get the largest product

- 2-digit subtraction, with the goal being to get the smallest dierence- 2-digit addition, with the goal being to get the largest sum

- 2-digit division, with the goal being to get the largest quotient

Outcomes to Look or• Studentparticipationandengagement

• Studentsplayingtogetherfairly

• Studentsworkingtogethertoproblemsolve

• Anunderstandingofthevalueofwhole

numbers• Answersthatreectanunderstanding

o how base-10 (0–9) numerals can be

arranged to make the largest possible

number

Teaching Tip

Encourage students to come up withobstacle courses that include activitiesthat are un, challenging, and accessible

to all students. I students are physicallychallenged and can’t participate in theobstacle course, they can be the ones whoroll the dice.





Reflection











activity un?











Lesson 3

What’s the Best Snack?

In this lesson, students use nutritional inormation to analyze data about

dierent snacks and survey their peers to determine the best snack. To

organize their data, students make dierent charts or displaying the data

they collect. In the end, students decide which snack is the healthiest and

explain why they think so.


Duratio:1 hour

Studet Goals:

• Predictthebestsnack,meaningonethatishealthy,inexpensive,andtasty.Thentestthe

prediction by collecting data

• Organizedatabyusingabargraphandatable

• Findthemedian

• Writeanduseasurvey

• Understandthatdatarepresentspecicpiecesofinformation

• Drawaconclusion

Curriculum Coectio:

Science

Stadards:


Stadard 6: Understands and applies basic and advanced concepts o statistics and data analysis

Grades3–5

Benchmark 1: Understands that data represent specifc pieces o inormation about real-worldobjects or activities

Benchmark 3: Understands that a summary o data should include where the middle is and howmuch spread there is around it

Benchmark 6: Understands that data come in many dierent orms and that collecting,organizing, and displaying data can be done in many ways

Stadard 9: Understands the general nature and uses o mathematics

Grades3–5

Benchmark 2: Understands that mathematical ideas and concepts can be represented concretely,graphically, and symbolically





Imagie This!Every student in aterschool loves to have a snack, but are snacks good or them? What’s

in a snack? Are there empty calories or good nutrition? Let students investigate i a snack is

healthy beore they put that cracker or raisin in their mouths. Students collect data, surveytheir peers, and draw conclusions about three common snacks . . . and then, o course, they

get to eat the snacks!

What you needp Three dierent snack oods (raisins, pretzels, and peanut-butter crackers), enough or each

group o students

p Nutritional inormation or each snack

p Paper

p Pencils

p Butcher paper

p Markers

p Bags or snacks

p Copies o the data collection table and sample table (Handout 1)

p Poster paper, an overhead transparency, or a chalkboard

Gettig Read• Dividesnackfoodintobagsforeachgroupofstudents.

• Makecopiesofthenutritionalinformationandpriceforeachsnack.

Vocabulary

Calorie: aunitofenergy-producingpotentialinfood;iftheenergyisnot

used, it is converted to at

Fat: one o three main components o ood, the highest in energy and notwater soluble

Mea: a number that is ound by dividing the sum o two or morenumbers by the number o addends, e.g. an average

Sodium: a sot, silver, metallic element that reacts with other substancesandisessentialforthebody’suidbalance

Sugar: a simple carbohydrate that is sweet tasting, crystalline,and soluble in water





What to Do• Askstudentstopickapartnertoworkwith.

You may want to assign partners.

• Providespaceandhandoutmaterials(snacks and handouts) to each pair.

• Askstudentstothinkaboutthesnacksthey

have and to make a prediction about which

snack is best.

• Workingwithstudents,developalistof

criteria or evaluating the snacks. For

example, the best snack might be one

that is healthy, inexpensive, and tasty. Ask

about actors students might consider in

determining quality.

• Taketimetotalkaboutnutritionandhealthyamountsofcalories,fat,andsodium.

• Askeachpairofstudentstousethenutritionalinformationprovidedtocompletethedata

collection table and rate each snack. I the two students working together don’t agree, they

can fnd the average between the two ratings.

Teaching Tip

Get inormation ahead o time aboutcalories, at, sodium, and sugar soyou can have a discussion about howthey contribute or don’t contribute to ahealthy snack.





• Postalltheratingsononelargetableonposterpaper,anoverheadtransparency,ora

chalkboard. Reer to the sample table in the handout.

• Askstudentstodescribehowtheydeterminedtheratingforeachsnack.Forexample,if

one student rated a snack a 3 and the other student rated it a 4, the mean would be 3.5.

• Next,conductasurveytondoutwhatthemostpopularhighlyratedsnackwasamongall

students. Work with students to create a chart o the results.

• Askeachpairtousethedatafromthesurveycharttomakeagraphoftheresults.

• Usingthedata,decidewhichsnackisthebestchoice.Givestudentsachancetotalkwith

their partners, and then bring the class back together to share ideas. Each pair explains,

using the data, its decision about the best snack, and why the students made that choice.

Encourage students to use both sets o data when making a decision. Students can revisit

the predictions they made beore the data was collected.

• Askifanyoftheirideasaboutwhatbest means have changed. Ask, “What is the

relationship between the quality rating and your avorite snack?”

• Finally,discusswhythequalityratingeithermatchesordoesn’tmatchtheirfavoritesnack.

Outcomes to Look or• Answersthatreectanunderstandingofinformationasdata

• Anabilitytocollectandorganizedatainasensibleway(e.g.,bargraph,table)

• Answersthatreectanabilitytoexplainreasoningbasedonthedata

• Anabilitytondameasureofthemeanoraverage

• Studentsworkingtogethertosolveproblemsanddiscussstrategiesandsolutions





Data Collectio Table

SackFood

ServigSize

CaloriesperServig

Fat perServig

ProteiperServig

SodiumperServig

Price perServig

Qualit(1-low,5-high)

Raisis

Goldfsh® Crackers

Peaut-ButterCrackers

Sample Table

Pair Raisis Goldfsh® Crackers

Peaut-ButterCrackers

1 4 5 4

2 3.5 3 2

3 4 4 3.5

4 3 4.5 4

5 1 5 3

Hadout 1: Data Aalsis ad Probabilit: What Is the “Best” Sack?





Reflection









Academic Erichmet

• Howdidthislessonsupportothercontentareas?• Whatchangescouldyoumaketostrengthenacademicenrichmentandstillkeepthe

activity un?







Lesson 4

Msical Notes anMath Fraction drmming

In this lesson, students learn how whole, hal, and quarter ractions link

to musical whole, hal, and quarter notes and rests. Students decorate

drumsticks with the notes and ractions. They then practice drumming

various raction patterns.


Duratio:

90 minutes

Studet Goals:

• Learnbasicmusicalnotesconnectedtofractions

• Drumsimplefractionpatterns

• Performsimpledrummingsong

Curriculum Coectio:

Music

Stadards:These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks). The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.


Grades3–5



Grades3–5Benchmark 2: Understands that mathematical ideas and concepts can be represented concretely,graphically, and symbolically





Imagie This!Students learn about ractions while making music! Your room is flled with children engaged

in decorating drumsticks as you introduce each note and the raction that it represents. You

guide the students through drumming the various notes as you introduce the ractions andnotes to them. The students are ully engaged in practicing drumming simple raction patterns

in pairs. You pull them back into one group and lead them in drumming the raction patterns

in unison. They drum the raction patterns enthusiastically.

What you needp Paint stick or each student

p Paint-stick model or each group

p Markers or each group

p Handout 2: Notes, Rests, and Fractions (one copy per table)

p Handout 3: Simple Drumming Patterns (one copy per table)

p Poster or overhead transparency showing a simple drumming song

Gettig Read• Obtainapaintstickforeachstudent(freefromapaintstore).

• Makeamodelpaintstickdecoratedwithwhole,half,andquarternotesandrestsforeach

small group.

• Haveasetofmarkers,paintsticks,ahandoutwiththenotesandfractions,andahandout

with simple drumming patterns on each table.

Vocabulary

Beat: a rhythmic sound

Drummig patter: a regular, repetitive arrangement with the drumming

Measure: a unit o time by which a musical work is divided

notes: musical sound produced by a musical instrument





What to Do• Dividestudentsintogroupsoffourbasedonwhowillworkwelltogether.

• Giveeachstudentapaintstick,whichwillserveasadrumstick.

• Giveeachgroupasetofmarkersandthetwohandouts.

• Introducethewholeandhalfnotesandthefractions4/4and2/4=1/2.Seeexamplesat

endoflesson.

• Demonstratedrummingseveralmeasuresofwholeandhalfnotesandrests.

• Havestudentsdecoratetheirdrumstickswiththewholeandhalfnotesandfractions.

• Insmallgroups,practicedrummingthesimpledrummingpatternsofwholeandhalfnotes.

• Introducethequarternoteandrest,andthefraction1/4.

• Demonstratedrummingseveralmeasuresofquarternotesandrests.

• Insmallgroups,practicedrummingthesimplepatternsofwhole,half,andquarternotes

and rests.

• Inalargegroup,havestudentsusetheirdrumstickstodrumsimplenotepatternsthatthey

were practicing in small groups.

Exted• Introducestudentstoeighthandsixteenthnotes,rests,andfractions.

• Increasethecomplexityofthemusicalperformancebymakingitaround.

• Getsheetmusicandhavestudentswritetheassociatedfractionunderthenotes.

• Increasethecomplexityofthemusicalperformancebyhavingseveralgroupsplay

dierent beats.• Havegroupsofstudentswriteandperformtheirownmusic.


• Understandingofwholenumbers,fractions,

and decimals

Teaching Tip

Post and go over the expectations orbehavior:

•Drumstickscannottouchanyoneelse

•Drumonlywhenrequested•Putdowndrumstickwhennotbeingledin

a drumming activity









Hadout 2: notes, Rests, ad Fractios: Musical notes ad Math Fractio Drummig

Whole ote:

You hold a whole note for 4 beats:4

⁄ 4.You count 4 beats: 1, 2, 3, 4.

Each beat is 4 ⁄ 4 of a whole note.

Hal ote:

You hold a half note for 2 beats: 2 ⁄ 4.You count 4 beats: 1, 2, 3, 4.

Each beat is ½ of a whole note.

Quarter ote:

You hold a quarter note for 1 beat: ¼.You count 4 beats: 1, 2, 3, 4.

Each beat is ¼ of a whole note.

Musical Rests are used to show us whe we should ot make a oise.

Whole Rest: You do not make any noise for 4 beats: 4 ⁄ 4.

Half Rest: You do not make any noise for 2 beats: 2 ⁄ 4.

Quarter Rest: You do not make any noise for 1 beat: ¼.





Hadout 3: Simple Drummig Patters: Musical notes ad Math Fractio Drummig

1-2-3-4 1-2 3-4 1-2-3-4 1-2 3-4 1-2-3-4

1 ½ ½ 1 ½ ½ 1

1-2 3-4 1-2 3-4 1-2-3-4 1-2-3-4 1-2-3-4

½ ½ ½ ½ 1 1 1

1-2 3-4 1-2 3-4 1-2-3-4 1-2 3-4 1-2-3-4

½ ½ ½ ½ 1 ½ ½ 1

1-2-3-4 1-2 3 4 1 2 3-4 1-2 3-4

1 ½ ¼ ¼ ¼ ¼ ½ ½ ½





Hadout 3, cotiued

1-2 3-4 1 2 3 4 1-2 3 4 1-2-3-4

½ ½ ¼ ¼ ¼ ¼ ½ ¼ ¼ 1

1-2 3-4 1-2 3 4 1-2 3 4 1-2-3-4

½ ½ ½ ¼ ¼ ½ ¼ ¼ 1

Row, Row, Row your Boat

Row, row, row your boat gent- ly down the stream.

Mer- rily, Mer- rily Mer- rily Mer- rily

Life is but a dream.





Reflection









Academic Erichmet


activity un?







Lesson 5

Paper Airplane Gliers

In this lesson, students explore dierent paper airplane designs. They build

andypaperairplanesasawaytocollectdatatodeterminethebest

design based on the height and distance traveled.


Duratio:

90 minutes or two class periods

Studet Goals:

• Makepredictions

• Usetoolstomeasure

• Collectdatatoproveahypothesis

• Reinforceaveraging,estimation,androundingskills• Workwithgraphs

Curriculum Coectio:

Science

Stadards:


Stadard 3: Uses basic and advanced procedures while perorming the processes o computationGrades3–5

Benchmark 6: Uses specifc strategies to estimate quantities and measurements


Grades6–8

Benchmark 5: Uses data and statistical measures or a variety o purposes

Stadard 7: Understands and applies basic and advanced concepts o probability

Grades3–5

Benchmark 3: Understands that when predictions are based on what is known about the past,one must assume that conditions stay the same rom the past event to the predicted uture event





Vocabulary

Alot: intheair;inight

Glide: aviation aircrat descent using no engine power

Wigspa: space or expanse between the edges o the wing

Benchmark 4: Understands that statistical predictions are better or describing what proportiono a group will experience something rather than which individuals within the group willexperience something, and how oten events will occur rather than exactly when they will occur

Grades6–8

Benchmark 3: Understands how predictions are based on data and probabilities

Benchmark 4: Uses specifc strategies to estimate computations and to check the reasonablenesso computational results


Grades3–5

Benchmark 1: Understands that numbers and the operations perormed on them can be used todescribe things in the real world and predict what might occur

Imagie This!Can creating paper airplanes have an educational purpose? It may be hard to believe but

there’s math to be fgured and data to be collected in this creative lesson. Your students will

lovemakingandyingtheirveryowncreations.Whosedesignwillythelongestdistance?

Whose design will stay alot the longest? Does the design aect these numbers? Let’s fnd out!

What you needp

Graph paperp Unlined paper

p Tape measures

p Masking tape or sidewalk chalk

p Copy o data worksheet (Handout 4) or each student

p Pencils

p Stopwatches

p Markers (optional)





Gettig Read• Preparecopiesofthedataworksheetfor

each student. (See Handout 4 at end o

lesson.)• Designthelandingstripforthepaper

airplanes. It should be in a gym, hallway,

or other large indoor area to eliminate

wind eects. Label each oot and hal-oot

increment along a line on the landing strip

to use or data collection.

• Trythisactivitybeforeyoustartitwithyourstudentsandrecordyourdata.Useyourdata

worksheet as a model or your students.

What to Do• Asanintroductiontothisactivity,askthestudentsquestionssimilartothefollowingtohelp

them reach the desired hypothesis or their airplane test. Examples o student responses

that will lead to the next questions are in the parentheses.

- How do we know i a paper airplane is a good or bad paper airplane? (Ifitfallstothe

groundquickly,itisnotagoodairplane.)

- How can we tell i it alls quickly? (Wecount.)

- What do we count? (Wecountthesecondsormaybehowhightheplaneis.Wecount

howfaritgoes.)

- Do we count how ar or how long? (Theplaneisbetterifitiesfarther.Itisbetterifitieslonger.)

- So, is there a dierence? (Thatdepends.Inmostcases,planesthatylongerwillalso

yfarther.Theremightbesomecaseswheretheplaneieslongerbutdoessomething

likealoop.Inthatcase,itwon’tyfarther.)

- Will the shape o the airplane aect how quickly it alls? (No,Idon’tthinkitmatters.I

do!Ithinktheshapewillhelpitybetter.Well,maybe,Iguesswecouldtestthat.)

• Discusswithstudentsthattheynowhavetocomeupwithahypothesistotest.The

hypothesis should be similar to the ollowing: The shape o the plane aects how quickly it

sinks to the ground. The remainder o this activity is designed to help the students explore

this hypothesis.

• Lookatthedataworksheetwithyourstudentsandexplainhowtorecordthedataonthe

worksheet.

• Askstudentstodesignandconstructtheirownpaperairplanesoutofasingle8½x11

inch sheet o paper. Tell them they are going to use their airplanes to test their hypothesis

and determine the best design.

Teaching Tip

Tell students that they should try toduplicate the same launch angle and speedeach time.





Paper Airplae Desig Rules• Studentsuseonlyregular8½x11inchpaper.

• Notape,clips,orstaplescanbeused.

• Nocutsareallowedinthedesignoftheairplane;papermustremainintact.

• HavestudentschooseonepartnertoworkwithandtoidentifythemselvesaseitherPartner

A or Partner B. Each partner makes his or her own paper airplane. Each student’s plane

should be dierent.

• HaveallPartnerAstudentsytheirplanesoverthelandingstripsfve times, each time

trying or maximum distace. Then all Partner A students should do aother fve trials,

this time trying or maximum time alot.PartnerBcanhelptimeandmeasuretheights.

Both partners should record the distances and times alot and average the three longest

distances and the three longest times.

• Bothpartnersrecordthedataoneachightontheirdataworksheet.Theyshouldmeasure

the point at which the plane frst touches the ground (to the nearest hal oot) and not the

point at which it comes to rest.

• ThenstudentsswitchandrepeattheexercisewithallPartnerBstudentsyingtheirplanes

fve times or distace and fve times or time alot.

• Studentsrecordthedataandaveragethethreelongestdistancesandthethreelongesttimes.

• Afterstudentshaveowntheirplanes,theyneedtodeterminetheirplanes’wingarea.If

students are able, have them unold their planes and lay out basic geometric shapes to fll

the wing area.

- Older students can calculate the total area rom the sum o the areas o the shapes.

- I students are not able to calculate geometric areas, they could make a duplicate plane,cut o the wings, and lay the wings onto measured grids or pieces o graph paper and

count the total squares covered, estimating partial squares.

- A variation o this technique that eliminates a duplicate plane and cutting wings is to

draw or trace a grid on a blank transparency with a marker and then hold the clear grid

over the wings to count the squares covered.

• Havestudentsnishtheirdataworksheetandthenusetheirdatatocreatetwographsfor

theclass—onegraphcomparingtimealoftandwingareaandtheothercomparingdistance

and wing area.

• Aftertheyhavenishedthetests,havestudentsanswertheconclusionquestionsatthebottom o the data worksheet.





Exted• Repeattheightswithstudentsfactoringintheirheighttoseeifthatmakesadifferencein

the distance and time alot.

• Studentscanmakeaposteroftheirndingsorconclusions.


• Usingmeasuringtoolsproductively

• Anunderstandingofdifferentmeasurementsandhowtomeasure

• Answersthatreectanunderstandingofratio

• Answersthatreectanunderstandingofcomparisonandpredictionaswellasstrategiesto

make and test predictions









Hadout 4: Paper Airplaes Data Worksheet

M Hpothesis:

Parter A’s Plae

Area o Parter A’s Wigs=_____________

Average Time Alot (add the three best times together and divide by 3)=_______________

Average Distace Glided (add the three best distances together and divide by 3)=_____________

Parter A 1st ight 2d ight 3rd ight 4th ight 5th ight

Time aloft inseconds

Parter A 1st ight 2d ight 3rd ight 4th ight 5th ightDistance theplane glided

Parter B’s Plae

Area o Parter B’s Wigs=_____________

Average Time Alot (add the three best times together and divide by 3)=_______________

Average Distace Glided (add the three best distances together and divide by 3)=_____________

Parter B 1st ight 2d ight 3rd ight 4th ight 5th ight

Time aloft in

secondsParter B 1st ight 2d ight 3rd ight 4th ight 5th ight

Distance theplane glided

Coclusio Questios

What did ou lear about our hpothesis?

How do ou thik ou ca improve our airplae’s distace ad time alot without chagig the

size o the plae?

How do ou thik our height ma have aected the lot ad distace?

How would ou test to see i ou are right?

name__________________________________________ I am Parter (circle one) A B





Reflection









Academic Erichmet


activity un?











Math Centers

What Is It?The practice MathCenters eatures small-group stations that let students work together on un

math activities such as puzzles, problems using manipulatives, and brainteasers. Math centers

give students opportunities to problem solve a variety o activities, pace themselves, and work

independently or with their peers.

What Is the Cotet Goal?The key goals o MathCenters are to engage students in dierent math-related activities, build

their problem-solving and collaboration skills, increase their desire to learn, and ultimatelyextend their understanding o math. Specifc content goals should be connected to what

students are learning during the school day and to grade-level standards.

What Do I Do?Begin by talking to the day-school teacher to fnd out what math concepts students are

learning, the standards or each grade level, and the kinds o activities that extend students’

learning. For example, an activity involving money could help build students’ understanding

o number and operation, an important math standard. Next, consider activities that your

students already enjoy and how appropriate math concepts and skills can be incorporated.

Once you’ve outlined the activities, create space or small groups to work and secure any

materials or tools that will help them problem solve. Introduce the activity to the students,

with an emphasis on making it a un challenge. Math centers work best when students have

some choice in their activity, when they can approach an activity or problem rom dierent

angles, and when students work independently or with their peers to solve a problem.

Instructors act as acilitators. Circulate among the math centers, asking questions that guide

students toward a solution and providing eedback that encourages students’ understanding o

the math involved and their desire to learn.

Practice 2





Wh Does It Work?Research suggests that MathCenters encourage students’ independence and increase their

enthusiasm or learning by giving students opportunities to make choices, work together,

and talk about math. When students work in small groups, they are more likely and willingto explore dierent approaches to problem solving as well as to question, take risks, explain

things, and have their ideas challenged. Finally, centers help bring math content to lie

through un activities.





video

Getting Starte

Go to the MathCenters practice ound in the math section o the Aterschool

Training Toolkit (www.sedl.org/aterschool/toolkits/math/pr_math_centers.html).Click on the video “Math Centers: Choices and Challenges” and watch as

students at Purple Sage Elementary School in Houston, Texas, choose a variety

o center-based math games in small groups that help them better understand

and practice mathematical thinking.


involve your students in math and centers.


math in centers.



them started?


engaged?

What academic skills, like reading or math, are students reinorcing while they participate in








Lesson 1

Measring Hans an Feet

In this lesson, students predict i their hand or their oot is larger. They will

use a variety o measurement skills, tools, and strategies to fnd the area

o their handprints and ootprints.


Duratio:

30–45 minutes

Studet Goals:

• Understandlength,width,height,andarea,andhowtheyconnect

• Usespecicstrategiestoestimatemeasurements

• Selectanduseappropriatestandard(e.g.,inches)andnonstandard(e.g.,arbitrarylengthsof

string) units and tools o measurement

• Testpredictionsandcommunicatemathematicalreasoning

Curriculum Coectio:

Science

Stadards:These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks). The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.


GradesK–2

Benchmark 2: Uses discussions with teachers and other students to understand problems

Benchmark 3: Explains to others how she or he went about solving a numerical problem

Grades3–5

Benchmark 1: Uses a variety o strategies to understand problem situations

Benchmark 2: Represents problems situations in a variety o orms

Benchmark 3: Understands that some ways o representing a problem are more helpul than others

Benchmark 4: Understands and applies basic and advanced properties o the conceptso measurement


GradesK–2


Grades3–5

Benchmark 1: Understands the basic measures perimeter, area, volume, capacity, mass, angle,and circumerence





Vocabulary

Area: the space o the inside o a two-dimensional fgure

Legth: distance rom end to end


Width: distance rom side to side

Imagie This!Wiggle out o those socks and shoes! Get ready or bare eet and giggles as students make

predictions about the size o their own hands and eet. Ater predicting, they have to get downto business and gather data! Hmm, how might they do this? Let them ponder this with each

other or a ew minutes as they look at the supplies at their centers. Watch them fgure out

that tracing their hands and eet and measuring their drawings will lead them to a conclusion!

What you needp Graph paper

p Unlined paper

p Pencils or colored pencils

p Rulersp Protractors (optional)

p Geoboards (optional)

p Directions or each center

p Handout 5: Measurement and Geometry: Hands and Feet

Benchmark 2: Selects and uses appropriate tools or given measurement situations

Benchmark 4: Understands relationships between measures

Benchmark 5: Understands that measurement is not exact

Benchmark 6: Uses specifc strategies to estimate quantities and measurements





Gettig Read• Preparedirectionsandmaterialstocreateinvitingcenters.

• Printasamplehands-and-feetmeasurementimage(Handout5).

• Usethematerialsprovidedtotraceonehandandonefootonseparatepiecesofpaper.

• Predictwhetheryourhandoryourfoottakesupmorespace.

• Findoutifyourpredictioniscorrect.

• Bereadytomodelwhatyouhavedoneforyourstudents.

What to Do• Usethesamplehands-and-feetmeasurementimagetoreviewlength,width,andarea

with students.

• Askstudentstotraceonehandandonefootongraphpaper,andthentopredictwhichis

bigger in total area. Students may count the squares on the graph paper as a strategy ormaking predictions.

• Next,askstudentstomeasurethelengthandwidthoftheirhandprintsandfootprints.

• Whenstudentshavemeasuredlengthandwidth,askthemtocalculatetheareaofeach

one to test their predictions.

• Circulateandposequestionsasstudentsareworking.

Usig Guidig QuestiosAs students work together, the instructor should acilitate learning by asking questions that

encourage students to use what they know about math to solve the problem, as opposed tosimply giving them the answers. Use the sample guiding questions below or develop your own.

- I notice that you are counting spaces, represented by boxes on your graph paper, inside

your handprints and ootprints. Why might this method be useul in fnding out which

takes up more space?

- What method do you plan on using to solve the problem? What is your strategy?

- Can you restate this question in your own words?

- How are you keeping track o your calculations?

- Did you answer the question?

• Encouragestudentstoworktogethertoproblemsolve.• Finally,askstudentstoreportonwhichwasbigger,howtheycametotheiranswers,iftheir

predictions were correct, and what they learned.






• Studentsworkingtogetherandusingtools

to problem solve• Understandingofnonstandardunitsof

measurement (guessing size in terms

o a specifc student’s handprint or

ootprint, e.g.) as well as standard units

o measurement (measuring inches and

centimeters, calculating the area)

• Answersthatreectanunderstandingof

length, width, and area

• Abilitytomakeandtestpredictions


Teaching Tip

Stadard ad nostadard Uits o

Measuremet

Some students will understand length,width, and area quicker than others andmay not need guidance on the use o a ruleror protractor. Be sure that students maintainthe proper units o measurement as theyproceed (centimeters, inches) and that allmeasurements or one object are takenusing the same units. Students who aremeasuring will also need to use the ormulaor calculating area, or the space an objecttakesup(area=lengthxwidth).Allow

them to either come up with the ormulaon their own or have a conversation aboutwhat they might do with their measurementsbeore providing them with the ormula.

Students who are just learning theseconcepts may use nonstandard units omeasurement, such as counting the squareson the graph paper or simply guessingby comparing the size o their hands andeet. These students will need to estimatesome squares in portions (halves, quarters)and will also need to track what has been

counted in some way. Coloring or markingcounted spaces in some way will be helpul.However students decide to tackle theproblem, allow them to explore on their ownbeore oering a suggestion.





Hadout 5: Measuremet ad Geometr: Hads ad Feet





Reflection









Academic Erichmet


activity un?







Lesson 2

Fining Pentominoes

Students explore geometric relationships by arranging squares to orm

pentominoes, fgures that are made up o fve squares. Students work in

cooperative groups arranging shapes to orm 12 geometrical shapes. As a

group,theywillthenreectontheirmathematicalreasoning.

Grade Level(s):

3–5

Duratio:

45 minutes

Studet Goals:

• Understandbasicfeaturesofshapes,suchassidesandangles

• Exploregeometricrelationshipsbyarrangingobjects

• Understandwhatapentominoisandhowitisformed

• Worktogethertonddifferentpentominoesandproblemsolve

• Reectonandcommunicatemathematicalreasoning

Curriculum Coectio:

The Arts

Stadards:



Grades3–5


Stadard 5: Understands and applies basic and advanced properties o the concepts o geometry

Grades3–5

Benchmark 2: Understands basic properties o fgures

Benchmark 4: Understands that shapes can be congruent or similar

Benchmark 5: Uses motion geometry to understand geometric relationships





Imagie This!How can playing with squares and drawing the results be considered math? As early as 3000

B.C. in Mesopotamia, people were studying shapes and their relationships to each other in

surveying,architecture,measurements,areas,andvolumes.Drawingandbuildingshapes—thevisual,hands-onnatureofgeometry—makesgeometryveryaccessibleforallstudents!


p Unlined paper

p Pencils

p Pentomino blocks (optional)

p Dominoes (optional)

Gettig Read• Smallblocksortilesworkwellforthisactivity,butifyoudon’thavethem,studentscan

draw pentominoes on graph paper.

• Usethematerialsyouhavetocreateinvitingcenterswherestudentshaveaccesstoallthe

materials they may need.

• Reviewthepossibleshapesstudentscanmakewithuptovesquares(seetheexamples

on page 56). The bottom row shows you the 12 possible shapes students can make with

pentominoes. You can share this inormation with students ater they have completed

the lesson.

Vocabulary

Domio: asmallrectangulartilemarkedwithonetosixdots;usedin

various games

Petomio: a shape made up o fve squares connected on at least one side

Triomio: a shape with three squares connected on at least one side





What to Do• Creategroupsoffourtovestudentsforeachcenter.Youmaywanttoassignstudentsto

groups based on their needs and abilities or ask students to count o or random groups.

• Draworcongureapentominousingoneoftheimagesfromthehandout.Introducetheword to students and ask guiding questions about how many squares there are in this

new shape to create a group defnition. (A pentomino is a shape made up o fve squares

connected on at least one side.)

• Usingthepentominoyoucreated,turnitsothatthesquaresarestillinthesame

arrangement but are acing a dierent direction. Explain that this is not a dierent

pentomino because the combination o squares is the same.

• Explainthatthereare12possiblepentominoes,or12possibleshapesthatcanbecreated

by combining fve squares. You have already created one pentomino. Working in groups,

the students are to fnd the other 11.

• Now,askstudentstoworktogetheringroups,withmemberstakingturns,tondasmany

dierent pentominoes as they can. As the group creates a pentomino, each

student should draw it on his or her individual graph paper.

• Circulateamongthecenterstomakesureallstudentsareparticipating.Ask

questions and provide positive eedback to encourage learning.

• Aseachgroupnishes,checkintoseeifthestudentsfoundtheother11

pentominoes.

• Sharetheexamplesofpentominoesonpage56atthis

time. Have students compare their drawings with the

examples.• Discusstheactivitywiththewholegroup.Which

pentominoes were the easiest to fnd? Which were the

hardest? What did you learn?





Assessig PetomioesAs students work in centers to

fnd all 12 pentominoes, use the

ollowing guiding questions toassess students’ progress and

encourage them to think or

themselves:

• Canyoutellmehowyouknowthatthisshapeis

a pentomino?

• Howdoyouknowthateachpentominoyouhave

created is dierent?

• Howcanyougureoutifoneofyourpentominoes

is the same as another?

ExtedHow many combinations o quadraminoes,

hextominoes, and triominoes are there?

Outcomes to Look or• Studentparticipationandinterestintheactivity

• Studentsworkingandtalkingtogethertoproblemsolveandndpentominoes

• Answersthatreectanunderstandingofgeometricrelationships

• Answersandcongurationsthatreectanunderstandingofwhatapentominois

• Studentsusingdifferentstrategiestondotherpentominoes

• Students’abilitytoexplaindifferentshapesandhowtheyfoundtheiranswers





Geometr: Fidig Petomioes

Pentominoes are composed o fve squares, just as dominoes are made up o two squares. I

you are introducing pentominoes to students or the frst time, it may be helpul to begin by

reviewing dominoes or other simpler cases. Here are the “-ominoes” or one through fve.

1

2

3

4

5





Reflection









Academic Erichmet


activity un?







Lesson 3

using Gift Certificates

In this lesson, students use number and operation skills to fgure out how

best to spend a git certifcate at their avorite restaurant. They can spend

their money in many combinations, but they have to include all members

o their group.


Duratio:

45–60 minutesStudet Goals:

• Solvereal-worldproblemsinvolvingnumberandoperations

• Usemathematicaltoolseffectivelytosolveproblems

• Compute(add,subtract,multiply,anddivide)decimals

• Usespecicstrategiessuchasestimationandroundingtomakepredictions

• Understandandapplyavarietyofstrategiestosolveproblems

• Reectonandcommunicatemathematicalreasoning

Curriculum Coectio:

Lie Skills

Stadards:


Vocabulary

Strateg: a plan o action to get the answer





Stadard 1: Uses a variety o strategies in the problem-solving processGrades3–5


Benchmark 3: Understands that some ways o representing a problem are more helpul than others

Benchmark 4: Uses trial and error and the process o elimination to solve problems

Stadard 3: Uses basic and advanced procedures while perorming the process o computation

Grades3–5

Benchmark 1: Multiplies and divides whole numbers

Benchmark 2: Adds, subtracts, multiplies, and divides decimals

Benchmark 4: Uses specifc strategies to estimate computations and to check the reasonablenesso computational results

Benchmark 5: Perorms basic mental computations

Benchmark 8: Solves real-world problems involving number operations


Grades3–5

Benchmark 1: Understands that numbers and the operations perormed on them can be used todescribe things in the real world and predict what might occur.

Imagie This!Gits certifcates are cool gits i you know how to use them. You could spend them entirely on

yoursel or entirely on someone else, but in this class a $65 certifcate is being shared with

eachgroup—nowthat’scooperationatitsbest!Getoutthebase-10blocksorpapermoney

and have some un fguring out what people can eat. Maybe ater all those mouth-watering

choices, some real snacks might be available?!

What you needp Unlined paper

p Graph paper

p Calculators (optional)

p Pencils with erasers

p Base-10 blocks or play money

p Materials to set up a restaurant table (optional)

p A copy o the mission and menu or each center (Handout 6)





Gettig Read• Gathermaterialsandarrangecenterstogivestudentsaccesstomaterials.

• Makecopiesofthemissiondescription,menu,andguidingquestions.



• Studentsmayworkindependentlywithgroupsupportortogetherasagroup.Iftheywork

independently, have them compare and discuss their answers with each other when they

are fnished. For group work, ask each group to delegate one student to read the mission

description and guiding questions, and other students to be in charge o dierent materials

and tasks to ensure that everyone participates.

• Explaintostudentsthattheywillhave30minutestocompletetheactivity.

• Circulateamongthecenterstolistentostudents’conversationsandfacilitatediscussionby

asking guiding questions that guide students toward a solution. (See the questions on the

next page.)

Teaching Tip

Usig Base-10 Blocks

Base-10 blocks are wooden or plastic blocksthat represent units o 1, 10, or 100. Inthis lesson, students can use them, as theywould play money, to represent quantitiesas they calculate how to spend their gitcertifcate. Base-10 blocks are an exampleo a manipulative, a concrete object thathelps some students calculate amounts.





Usig Guidig QuestiosGuiding questions oer problem-solving prompts that encourage students to think or

themselves and use what they know to fgure out the answer. For example, students may

present an answer and ask you i it is right. Instead o simply saying yes or no, you mightwant to ask them how they got their answer, i it makes sense to them, and i they know how

to check their math to see i their answer is right. In this way, students are using what they

know to answer their own question and learning how to justiy their thinking.

Use the ollowing guiding questions or add your own.

• Canyourestatetheprobleminyourownwords?

• Whatdoyouknowabouttheproblem?Forexample,howmuchcanyouspend?Howmany

people are using the git certifcate? What does that tell you about how much each person

can spend?

• Whatmethoddoyouplanonusingtosolvetheproblem?Whatisyourstrategy?Howareyou keeping track o your thinking, and which strategies have you tried?

• Whatmaterialscouldhelpyousolvetheproblem?

• Howdidyoundyouranswer?Doesitmakesense?

• Didyouanswerthequestion?Gobackandcheck.

• Whatdidyoulearnfromotherstudentsthathelpedyousolvetheproblem?

• Finally,howcanyoushowthatyouransweriscorrect?

• Bereadytomodelproblemsolvingwithbase-10blocksorothermaterials.Providepositive

eedback to encourage students’ success.

• Whenstudentshavecompletedtheactivity,askeachgrouptopresentitssolutions(theremay be more than one) as well as the steps and mathematical reasoning involved. Allow

time or questions and answers.

Exted• Changethedollaramountofthegiftcerticateandredothecenter.

• Changethenumberofcoursespeoplewilleat.

Outcomes to Look or

• Studentparticipationandinterestinproblemsolving• Studentsusingavarietyofapproachesandstrategiestoproblemsolve

• Answersthatreectreasonablepredictionsandeffectiveuseoftools

• Adding,subtracting,multiplying,anddividingdecimalsaccurately

• Students’abilitytocommunicatehowtheyarrivedatthesolution





Hadout 6: number ad Operatio: Usig Git Certifcates

Missio Descriptio

You received a git certifcate to your avorite restaurant. The git certifcate is worth $65.You invite our o your closest riends to dinner. Each member o the group orders at least

one entree and at least one drink. Describe what each member o the group will order

and how much it totals. Good luck!

Meu

E n T R E E S

Spaghetti $8.00

Hamburger and ries $7.25Fish fllet $8.50

Soup and sandwich $6.50

Soup and salad $6.00

S I D E S

Salad $2.99

French ries $1.99

Baked potato $.99

Steamed vegetables $1.50

Applesauce $.75

D E S S E R T S

Brownie sundae $3.50

Ice cream sundae $2.50

Chocolate layer cake $2.50

Cherry pie $3.00

Lemon square $2.75

D R I n K SMilk $1.25

Juice $1.50

Soda $1.00

Lemonade $1.00

Iced tea $.75





Reflection









Academic Erichmet


activity un?







Lesson 4

What’s the Chance?

This lesson ocuses on developing students’ understanding o data and

probability, while they determine i the game they are playing is air.

Students are encouraged to engage in rich mathematical discussions while

testing their hypotheses.


Duratio:

1 hour

Studet Goals:

• Communicateaboutmathematics(e.g.,usemathematicallanguage,comparetheirthinkingwith

other students’ thinking, construct logical arguments to support their thinking)

• Usestrategiestounderstandnewmathcontent

• Selectandusethebestmethodofrepresentinganddescribingasetofdata

• Useexperimentalmethodstodeterminetheoreticalprobability

Curriculum Coectio:

Science

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: A

CompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks). The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.


Grades6–8

Benchmark 1: Uses a variety o strategies to understand new mathematical content and todevelop more efcient solution methods or problem extensions

Benchmark 4: Constructs logical verifcations or counter examples to test conjectures and tojustiy algorithms and solutions to problems

Vocabulary

Probabilit: the extent that something is likely to happen





Imagie This!

Have you ever wondered how likely you are to roll a pair o dice and get a seven? The study oprobability can help you fgure out the likelihood o that happening. In math, we call the thing

that is likely to happen an event. The word probability is used to mean the chance that a

particular event (or set o events) will occur expressed on a linear scale rom 0 (impossibility)

to 1 (certainty). As you roll the dice, keep a record o the impossibility and certainty scores in

thegameWhat’stheChance?toseeifyoucandetermineapattern—theprobability!

What you needp What’s the Chance teacher’s guide (see pp. 71–75)

p What’s the Chance student worksheet (Handout 7)

p Pencils

p Graph paper (and other paper as needed)

p Calculators

p Game board markers (e.g., coins, counters) or each team

p A number cube (die) with an even number o sides

Stadard 6: Understands and applies basic and advanced concepts o statistics and data analysisGrades6–8

Benchmark 1: Understands and applies basic and advanced concepts o probability

Benchmark 3: Uses experimental and simulation methods to determine probabilities

Benchmark 4: Understands the dierences among experimental, simulation, and theoreticalprobability techniques and the advantages and disadvantages o each


Grades6–8

Benchmark 1: Understands and applies basic and advanced concepts o probability

Benchmark 3: Uses experimental and simulation methods to determine probabilities

Benchmark 4: Understands the dierences among experimental, simulation, and theoretical

probability techniques and the advantages and disadvantages o eachStadard 9: Understands the general nature and uses o mathematics

Grades6–8

Benchmark 7: Understands that mathematics provides a precise system to describe objects,events, and relationships and to construct logical arguments

Benchmark 10: Understands that mathematicians commonly operate by choosing an interestingsetofrulesandthenplayingaccordingtothoserules;theonlylimittothoserulesisthatthey

should not contradict each other





Gettig Read• ReviewtheWhat’stheChanceteacher’sguide.

• CopytheWhat’stheChance?studentworksheet(Handout7)andfamiliarizeyourself

with the scenarios students will be involved with. I necessary, make time to share thelesson with a day-school mathematics instructor to converse about the standards and

mathematics involved.

• Decidehowyouwillorganizestudentsintopairs(allowingchoiceorassigningpartners).

• Makesureallmaterialsareavailableforallstudents.

• Prepareabriefintroductionofthegameandthestudents’missionduringthegame.

Students have probably had experiences playing dice games as well as games o chance.

What to Do

• Askstudentsiftheythinkboardgames,cardgames,andgameswithdicearefair.Encourage them to share some experiences and to think about whether they elt the games

were set up airly. Clariying the task and piquing students’ interest in the lesson are the

goals o this discussion.

• Askstudentstofamiliarizethemselveswiththeinstructionsandtogetstartedassoonas

their twosome is ready. Beore playing, students are asked to predict which player will

have the most wins. You can collect the predictions by putting tally marks on the board

or Player 1 or Player 2. Be sure to ask students to talk about the reasoning behind their

predictions.

• Circulateandstayinvolvedwhilestudentsplayandanswerthequestionsontheworksheet.

While talking with students, try to generate student thinking without giving away answersor leading students down a particular line o thinking.

• Forexample,youcanaskstudents,“Howdidyouarriveatthisanswer?”or“What

happened when you modifed the game board?”

• Ask,“Areyousurprisedbytheresults?Why?Whynot?Whatissurprisingtoyou?”

• OncestudentsrealizethatPlayer2winsmostofthetime,ask,“WhydoesPlayer2win

more oten than Player 1?”

• Togetstudentsreadytoanswerthequestionsonthetheoreticalprobabilityofthegame,

you can ask, “With what you know about probability, how oten do you think Player

2 should win? All the time? Hal the time? One fth o the time? How could you fgure

this out?”





• Asstudentsplaythegame,encouragethemtobounceideasaroundaboutwhoiswinning

and why. Student dialogue will enhance the richness o the game and the learning

experiences associated with playing it.

• Bepreparedforsomestudentstomoveforwardtotheextensionsortosavetheextensionsor another day. You may decide that some students can take the extensions home to work

on (and play with a amily member) i they have a desire to do so.

• Afterstudentshaveplayedthegameandansweredthequestions,leadaclassdiscussion

on airness in games and what it means. This will allow students to afrm their learning

by thinking through and comparing what they discovered (e.g., their thinking, their

discoveries, their theories, their ideas) while they played.

ExtedThe teacher’s guide has extension activities at the end.

Outcomes to Look or• Allstudentsengagedandactivelyseekinganswers

• Studentsusingstrategieseffectively

• Studentseffectivelyrepresentinganddescribingdata

• Studentsusingexperimentalmethodsanddeterminingtheoreticalprobability





Have you ever wondered i games are air? Here is a chance to play a game based on

probability and learn how to determine your chances o winning the game. What’s the Chance? is a game based on probability. Play this game with a partner. In

order to play, you will need to use a game board that looks like the one below, a marker,

and an even-sided number cube or die:

1 1 2 1Start Here

2 1 1

How to Pla:• Beginbyplacingthemarkeronthecenterbox,labeled1—StartHere.

• Player1beginsbyrollingthedie.Ifanevennumberisrolled,themarkerismoved

onespacetotheright;ifanoddnumberisrolled,themarkerismovedonespaceto

the let.

• Eachplayer’sturnconsistofthreerollsofthedieandthecorrespondingmarker

moves.

• Attheendofaturn(threerollsofthedie),apointisscoredbyoneoftheplayers.If

the marker ends on a white box, Player 1 receives a point. I the marker ends on a

purple box, Player 2 receives a point.

• Attheendofeachturn,returnthemarkertothe1—StartHerebox.

• Playersalternateturns.

A game consists o fve turns per player. The player with the most points is the winner.

Beore ou begi, think about whether the game appears to be air. Why do you think so?

Who do you predict will win?

You might want to use a table like the one below and tally marks to keep track o points.

Play at least 10 games to see i any patterns emerge. Your Game 1 row might look

something like this, where Player 1 is the winner:

Plaer 1 Plaer 2

Game 1

Hadout 7: What’s the Chace? STUDEnT WORKSHEET





Questios:

1. Based on your experimental data, do you think the game is air? Why or why not?

I you think the game is unair, how could you modiy the game to make it a air game?2. Create a list o all the dierent possible outcomes or Players 1 and 2. For example,

EVEN, EVEN, ODD is one possible outcome, and Player 2 would win.

3. What is the theoretical probability o Player 1 winning a game? How about Player 2

winning a game? Use a list or tree diagram to help you decide.

4. How does the theoretical probability compare to the experimental probability (your

results rom actually playing the game)? Explain why the experimental results might be

dierent than the theoretical probability.

Plaer 1 Plaer 2

Game 1

Game 2

Game 3

Game 4

Game 5

Game 6

Game 7

Game 8

Game 9

Game 10





Extesio Activities

Part 1. Add one square on either end o the game board, so that it looks like this:

2 1 1 2 1Start Here

2 1 1 2

Play the game as described above. However, each turn consists o our rolls o the die.

Agameisstill10turns—5turnsforeachplayer.Playersalternateturns.Ifthemarker

lands on a white box, Player 1 scores a point. I the marker lands on a purple box,

Player 2 scores a point. At the end o 10 turns, the player with the most points is the

game winner.

Beore you play the game, predict who you think will win the most games. Why do you

think so?

Play 10 games and record your results.

Questios:

1. Based on your experimental data, do you think the game is air? Why or why not? I

you think the game is unair, how could you modiy the game to make it a air game?

2. Create a list o all the dierent possible outcomes or Players 1 and 2. For example,EVEN, EVEN, ODD, EVEN is one possible outcome, and Player 1 would win.



4. How does the theoretical probability compare to the experimental probability (your

results rom actually playing the game)? Explain why the experimental results might

be dierent than the theoretical probability.

Part 2. Create your own game, based on ideas similar to What’s the Chance?

Hadout 7, cotiued





What’s the Chace? TEACHER’S GUIDE

This Teacher’s Guide is like the student version (Handout 7), but it includes answers. Have

you ever wondered i games are air? Here is a chance to play a game based on probability

and learn how to determine your chances o winning the game.

What’s the Chance? is a game based on probability. Play this game with a partner. In order

to play, you will need to use a game board that looks like the one below, a marker, and an

even-sided number cube or die:

How to Pla:• Beginbyplacingthemarkeronthecenterbox,labeled1—StartHere.

• Player1beginsbyrollingthedie.Ifanevennumberisrolled,themarkerismovedone

spacetotheright;ifanoddnumberisrolled,themarkerismovedonespacetotheleft.

• Eachplayer’sturnconsistofthreerollsofthedieandthecorrespondingmarkermoves.

• Attheendofaturn(threerollsofthedie),apointisscoredbyoneoftheplayers.Ifthe

marker ends on a white box, Player 1 receives a point. I the marker ends on a purple box,

Player 2 receives a point.

• Attheendofeachturn,returnthemarkertothe1—StartHerebox.

• Playersalternateturns.

A game consists o fve turns per player. The player with the most points is the winner.

Beore ou begi, think about whether the game appears to be air. Why do you think so?

Who do you predict will win?

You might want to use a table like the one below and tally marks to keep track o points. Play

at least 10 games to see i any patterns emerge. Your Game 1 row might look something like

this, where Player 1 is the winner:

Plaer 1 Plaer 2

Game 1

1 1 2 1Start Here

2 1 1





Questios:

1. Based on your experimental data, do you think the game is air? Why or why not?

I you think the game is unair, how could you modiy the game to make it a air game?The game is not a air game, although experimental results will vary. Player 2 has a 75% chance owinning, while Player 1 has only a 25% chance o winning.

Students will create various air games. The idea is to fnd a game where each player has an equalchance o winning.

2. Create a list o all the dierent possible outcomes or Players 1 and 2. For example, EVEN,

EVEN, ODD is one possible outcome, and Player 2 would win.

Teacher’s Guide, cotiued

Plaer 1 Plaer 2

Game 1

Game 2

Game 3

Game 4

Game 5

Game 6

Game 7

Game 8

Game 9

Game 10

Outcome Wier

EVEN, EVEN, EVEN Player 1

EVEN, EVEN, ODD Player 2

EVEN, ODD, EVEN Player 2

EVEN, ODD, ODD Player 2

ODD, EVEN, EVEN Player 2

ODD, EVEN, ODD Player 2

ODD, ODD, EVEN Player 2

ODD, ODD, ODD Player 1







The list created in Question 3 can be used or students to explain that, out o eight possible

outcomes, Player 2 will win six o the games, and Player 1 will win two o the games (theoretically).The tree diagram above shows the theoretical probability.

Each event is equally likely, with a probability o 1/8. Out o the eight events, Player 2 wins sixtimes, and Player 1 wins two times. This leads to our theoretical probabilities: the probability oPlayer 1 winning is 2/8, or 1/4. The probability o Player 2 winning is 6/8, or 3/4.

4. How does the theoretical probability compare to the experimental probability (your results

rom actually playing the game)? Explain why the experimental results might be dierent

than the theoretical probability.

Answers will vary with on the results o the experiments.

Player 1

Player 2

Player 2

Player 2

Player 2

Player 2

Player 2

Player 1





Extesio Activities

Part 1. Add one square on either end o the game board, so that it looks like this:

Play the game as described above. However, each turn consists o our rolls o the die. A

gameisstill10turns—5turnsforeachplayer.Playersalternateturns.Ifthemarkerlandson

a white box, Player 1 scores a point. I the marker lands on a purple box, Player 2 scores a

point. At the end o 10 turns, the player with the most points is the game winner.

Beore you play the game, predict who you think will win the most games. Why do you

think so?

Play 10 games and record your results.

Questios:

1. Based on your experimental data, do you think the game is air? Why or why not? I you

think the game is unair, how could you modiy the game to make it a air game?

The game is not a air game, although experimental results will vary. Player 1 has an 87.5% chanceo winning, while Player 2 has only a 12.5% chance o winning.

Students will create various air games. The idea is to fnd a game where each player has an equal

chance o winning.2. Create a list o all the dierent possible outcomes or Players 1 and 2. For example, EVEN,

EVEN,ODD,EVENisonepossibleoutcome;andPlayer1wouldwin.

Teacher’s Guide, cotiued

There are 16equally likelyoutcomes.

Outcome Wier

EVEN, EVEN, EVEN, EVEN Player 2

EVEN, EVEN, EVEN, ODD Player 1

EVEN, EVEN, ODD, EVEN Player 1

EVEN, EVEN, ODD, ODD Player 1

EVEN, ODD, EVEN, EVEN Player 1

EVEN, ODD, EVEN, ODD Player 1

EVEN, ODD, ODD, EVEN Player 1

EVEN, ODD, ODD, ODD Player 1

ODD, EVEN, EVEN, EVEN Player 1

ODD, EVEN, EVEN, ODD Player 1

ODD, EVEN, ODD, EVEN Player 1

ODD, EVEN, ODD, ODD Player 1

ODD, ODD, EVEN, EVEN Player 1

ODD, ODD, EVEN, ODD Player 1

ODD, ODD, ODD, EVEN Player 1

ODD, ODD, ODD, ODD Player 2

2 1 1 2 1Start Here

2 1 1 2







The list created in Question 3 can be used or students to explain that, out o 16

possible outcomes, Player 2 will win 2 o the games, and Player 1 will win 14 o the

games (theoretically).

Each event is equally likely, with a probability o 1/16. Out o the 16 events, Player

2 wins 2 times, and Player 1 wins 14 times. This leads to our theoretical

probabilities: the probability o Player 1 winning is 14/16, or 7/8. The probability o

Player 2 winning is 2/16, or 1/8.

4. How does the theoretical probability compare to the experimental probability (your results

rom actually playing the game)? Explain why the experimental results might be dierent

than the theoretical probability.Answers will vary with the results o the experiments.

Part 2. Create your own game, based on ideas similar to What’s the Chance?





Reflection









Academic Erichmet


activity un?











Lesson 5

Pattern Block Percentages

In this lesson, students use pattern blocks to learn about percentages and

represent percentages pictorially.


Duratio:

30 minutes

Studet Goals:

• Compareshapestodiscoverrelationshipsbetweendifferentpercentages

• Usetoolstoexploreandrepresentrelationships

• Deepenunderstandingoftherelationshipbetweenpercentagesandratios

• Workcooperativelywithpeers

Curriculum Coectio:

The Arts

Stadards:



Grades3–5

Benchmark 2: Understands equivalent orms o basic percents, ractions, and decimal and whenone orm o a number might be more useul than another

Grades:6–8

Benchmark 1: Understands the relationships among equivalent number representations and theadvantages and disadvantages o each type o representation

Benchmark 7: Understands the concepts o ratio, proportion, and percent and the relationshipsamong them


Grades3–5

Benchmark 1: Knows basic geometric language or describing and naming shapes

Benchmark 2: Understands and applies basic and advanced properties o the concepts onumbers





Imagie This!The room is flled with multiple locations or students to explore their mathematical thinking

and to reinorce skills learned during the school day. A group o students sitting around a

table scattered with pattern blocks is discussing how to best solve the problem at hand. Yourstudents can demonstrate their artistic side in this center.

What you needp One set o guiding questions per pair o students at the center

p One set o pattern blocks per pair o students at the center

p Unlined paper

p Colored pencils in the ollowing colors: blue, green, orange, red, tan, and yellow

Gettig Read• Assemblethecenterbyprovidingenoughpatternblocksforeachpairofstudents.Students

will also need access to unlined paper and colored pencils.

• Preparesheetsforeachpairatthecenterwiththefollowingguidingquestions:

- Use the pattern blocks to make two-color designs in which one color takes up 20% o

the whole. Illustrate these designs on the paper provided.

> Explain your strategy or creating a design that shows 20%.

> How can dierent designs all show 20%?

> Label the ractional part or each piece used in your design.

- Use the pattern blocks to create a design that is 20% one color, 30% a second color,and 50% another color.

> How many dierent designs can you come up with that ft this description?

> How can dierent designs all illustrate this description?

> Label the ractional part or each piece used in your design.

- What would a design showing colors with the ratio o 3:1 look like? How about the ratio

o 2:3? Sketch and justiy your answers.







• Studentsmayworkindependentlywithgroupsupportortogetherasapair.• Explaintostudentsthattheywillhave30minutestocompletetheactivity.

• Circulateamongthecenterstolistentostudents’conversationsandfacilitatediscussion

by asking questions that guide students toward a solution. Provide positive eedback to

encourage students’ success.

• Whenstudentshavecompletedtheactivity,askeachgrouptopresenttheirsolutions(there

may be more than one) as well as the steps and mathematical reasoning involved. Allow

time or questions and answers.

Exted• Askstudentstosketchseveralpossibledesignsofacircle,25%ofwhichisonecolor.

• Askhowtheprocessofsketchingthecirclecomparestoconstructingadesignwiththe

pattern blocks.

Outcomes to Look orMuch o the assessment or this lesson comes rom listening to and watching the students.

Listen or use o vocabulary, understanding o percentages, and students’ ability to illustrate

their discoveries.

• Studentparticipationandengagement

• Usingtoolsproductively

• Answersthatreectanunderstandingof

percentages

• Answersthatreectanunderstanding

o the relationships between ratios and

percentages

Teaching Tip

Settig Expectatios

Prior to having students work in centers,be sure to establish norms or working withtheir peers. Explain to students that centersare designed or them to spend as little oras much time as necessary to complete theactivity and gain an understanding o thematerials covered beore moving onto thenext center.





Vocabulary

Hexago: a two-dimensional fgure with six sides

Parallelograms: a two-dimensional geometric fgure with our sides inwhich both pairs o opposite sides are parallel and o equal length, andthe opposite angles are equal

Percetage: a proportion stated in terms o one-hundredths

Ratio: a proportional relationship between two dierent numbers orquantities

Rhombus: a parallelogram that has our equal sides

Square: a geometric fgure with our right angles and our equal sides

Trapezoid: a quadrilateral shape that has one pair o parallel sides and

one pair o sides that are not parallel

Triagle: a two-dimensional geometric fgure ormed o three sidesand three angles





Reflection









Academic Erichmet


activity un?













AN INSTR uCTOR’S GuIdE TO THE AFT ERS CHOOL TRAINING TOOLkIT


Math Games

What Is It?The practice MathGames eatures un activities that develop targeted math strategies and

skills. They can be competitive, cooperative, whole group, small group, or solitary. Math

Games can provide or structured play, in which students are highly motivated to engage in

mathematical thinking, have mathematical conversations, remember numerical combinations,

and develop problem-solving strategies.

What Is the Cotet Goal?

The goal o MathGames is to engage students in meaningul mathematical problem-solvingexperiences, build math knowledge and skills, and increase students’ desire to learn through

un activities. Specifc content knowledge will vary according to the game students play and

the connection to day-school learning and standards.

What Do I Do?Begin by talking to the day-school teacher to fnd out what math concepts and skills students

are learning, and what kinds o games can extend their knowledge. For example, i students

are learning to multiply and divide, a un game that lets students compete or solutions can

extend their learning. Select appropriate math games that target particular strategies and

skills, and tap students’ interests. Allow students to work together in small groups or as alarger group. Facilitate learning during the games by asking questions that encourage students

to use what they know about math to fnd the answer. Guide student thinking and highlight

important mathematical concepts through modeling, asking questions, and acilitating

conversations with and between students.

Practice 3





Wh Does It Work?In addition to tapping children’s natural motivation to play, MathGames oer several other

instructional advantages, including opportunities or choice, high concentration, and inormal

instruction. Choice promotes engagement while providing students with opportunities toincrease their understanding and application o math skills and concepts, gain computational

uency,andutilizecommunicationskillstojustifytheirmoves.Gamesalsoencouragesocial

interaction and immediate eedback





video

Getting Starte

Go to the MathGames practice ound in the math section o the Aterschool

Training Toolkit (www.sedl.org/aterschool/toolkits/math/pr_math_games.html). Click on Video 2, which shows rom Purple Sage Elementary School

in Houston. In this video, third-, ourth-, and fth-grade students engage in a

competitive physical game o bacon and egg that integrates math skill building.


involve your students in math games.


math games.



them started?


engaged?









Lesson 1

Race to the Finish

In this game, students roll number cubes to move a bicyclist toward the

fnish line. Each time they roll the number cubes, students record on a

data chart the requency o the numbers rolled. At the end o the game,

students analyze the requency o numbers to see which number they will

choose in the next game.


Duratio:At least 10 minutes per round

Studet Goals:

• Countwithunderstandingandrecognizehowmanyinsetsofobjects

• Developasenseofwholenumbersandrepresentandusetheminexibleways

• Understanddataandhowdatacanberepresentedinbargraphs

• Connectnumberwordsandnumeralstothequantitiestheyrepresentbyusingphysicalmodels

and representations on number cubes

• Developuencywithbasicnumbercombinationsforaddition

Stadards:



GradesK–2

Benchmark 4: Understands basic whole number relationships

Stadard 3: Uses basic and advanced procedures while perorming the processes o computation

GradesK–2

Benchmark 1: Adds and subtracts whole numbers


GradesK–2

Benchmark 1: Collects and represents inormation about objects or events in simple graphs


GradesK–2

Benchmark 1: Understands that some events are more likely to happen than others

Benchmark 2: Understands that some events can be predicted airly well but others cannotbecause we do not always know everything that may aect an event





Imagie This!People predicting winners! People cheering or their avorite number! Addition, probability, and

data all rolled into one. Students will be engaged as they play this probability game and keep

track o their data. Will they choose the same numbers to cheer or in the next game? Let’ssee—whatdoesthedatasay?

What you needpCopiesoftheRacetotheFinishgameboard(Handout8;laminatedifpossible)for

each group

p Markers (watercolor, dry erase, or overhead) or writing on laminated game boards

p Pair o dice or each small group

Gettig Read• Copythegameboard(Handout8).Laminateorcoverthecopywithclearcontactpaper.

• Ifyouplantointroducethegametothewholegroup,makeanoverheadtransparencyof

the game board.

Vocabulary

Data: inormation, numbers used or making calculations and drawingconclusions






What to Do• Setthegameup,makingsurethatallstudentscanseethegameboard(anoverhead

projector might prove useul).

• Havestudentschooseanumberbetween1and12thattheywillcheerfor;eachnumberrepresents a cyclist on the game board.

• Askstudentstopredictwhowillwinandwhy.

• Providetwodiceandhavestudentstaketurnsrollingthem.

• Aftereachroll,studentsaddthetwonumbersrolledandplaceanxintheemptyspace

above the bicyclist whose number corresponds with the sum o the two numbers rolled.

• Eachxrepresentsthebicyclistmovingclosertowardthenishline.

• Studentscontinuetakingturnsrollingthecubesandchartingtheoutcomeuntiloneofthe

bicyclists reaches the fnish line.

• Asstudentsplay,encouragethemtopredictwhotheythinkwillwin,whoisahead,andwhy. Ask guiding questions throughout and ater the game. See Guidig Questios below

or sample questions.

Guidig Questios

DuringPlay

• Whoisahead?Whichbicyclistisinrstplacerightnow?Whoisinsecondplace?Howfar

behind is the second-place bicyclist? How do you know?

• HowfarfromthenishlineisBicyclist5?

• Whichbicyclistmovesaheadthisroll?Howdoyouknow?• Howmanytimeshaveyourolleda5?Howdoyouknow?





AfterPlay

• Forwhomdidyoucheerinthisgame?Ifyouplaythegameagain,areyougoingtopick

this bicyclist to cheer on again?

• Whichbicyclistsaremoreorlesslikelytowin?Why?• WillBicyclist1everwin?Howdoyouknow?

Outcomes to Look or• Studentengagementandparticipation

• Commentsandanswersthatreectthatstudentscanusetheirchartstodiscussthe

bicyclists’ standings in the race

• Comments,answers,andchoicesthatreectanunderstandingofimpossibleandmoreor

less likely outcomes

• Studentscountingwithunderstandingandrecognizinghowmanyinsetsofobjects• Commentsandanswersthatreectadevelopingunderstandingofanduencyinaddition





Hadout 8: Data Aalsis ad Probabilit: Race to the Fiish





Reflection









Academic Erichmet


activity un?







Lesson 2

Math Football

In this game, students work as teams to solve mathematics problems

and gain yardage on the Math Football game board. Students compete to

determine which team can solve the problems more switly and score the

most touchdowns.

Grade Level(s):

5–10 (depending on difculty level o questions)

Duratio:

10–15 minutes per game

Studet Goals:

• Reinforcemathematicalvocabularyandskills

• Encourageteamworkandcollaboration

Curriculum Coectio:

Physical Education

Stadards:


The standards addressed depend on the questions the teacher writes and the grade level o thestudents. Below are the categories o math standards that could be addressed.

Number and Operations (includes Arithmetic and Number Sense)

Patterns, Relationships, and Algebraic Thinking

Geometry and Spatial VisualizationMeasurement

Probability and Statistics

Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!The aterschool instructor plays the music rom MondayNightFootball and asks, “Are you

ready or some ootball?” Students are eager to orm teams and put on their game aces.

Gameboards,questioncards,andmarkerpiecesaredistributed;andstudentswaitanxiouslyor the instructor to signal the start o the game. Students work in teams to solve problems

quickly and to see which team can score the most touchdowns.

What you needp A copy o the math ootball playing board (Handout 9)

p Question-and-answer cards prepared or the level o the learner (the cards can be prepared

on index cards)

p Game board markers (e.g., coins, counters) or each team

p Stopwatch

p Paper

p Pencils

Gettig Read• Duplicateamathfootballplayingboard(Handout9)foreachpairofteams.

• Preparequestion-and-answercardsforthelevelofthelearners(Seepage99

or examples.)

• Collectonegameboardmarkerforeachteam.

• Collectmarkersofvariouscolors,oneperteam.





What to Do• Dividestudentsintoteams.Teamsmaybecomposedofonetothreeplayers.

• Determinewhichteamswillcompeteagainsteachother.Studentsofsimilargradelevelor

mathematics experience should compete with each other.• Provideeachteamwithamarkerandeachpairofcompetingteamswithonemathfootball

playing board.

• Explaintherulestoplayers.

- Each team places its team marker on the 50-yard line.

- A set o question cards is distributed to competing teams.

- Teams may not start until the instructor calls or play to begin.

- When play begins, both teams try to solve the problem as quickly as possible. The frst

team to solve the problem accurately moves the team marker 10 yards on the playing

board. The answers or the problems can be ound on the reverse side o the questioncard so that players may sel-check.

- When a team reaches the end zone, it scores 7 points. Players record the points and

return team markers to the 50-yard line to begin another round.

- At the end o 10 minutes o play, the team with the most points wins the math

ootball game.

• Whenstudentsunderstandtherulesandarereadytoplay,theinstructorsignalsforplayto

begin and the action starts.

Outcomes to Look or• Increaseduencywithgrade-appropriatemathskills

• Teamworkandcollaboration

Teaching Tip

To keep play air or each team, rememberto place a blank question card on top o thestack. The time or each game (10 minutes)may be extended i doing so works best orthe students.





Hadout 9: Math Football Plaig Board

1 0

2

0

3 0

4 0

5 0

4 0

3 0

2 0

1 0

1 0

2 0

3 0

4 0

5 0

4 0

3 0

2

0

1 0





Sample Questio Cards

Math FootballQuestio Cards

Compute

5 + 6(15÷3) – 4

The Harrison’s dinner bill at a restaurant is $63.

How much money should be left as a tip if the

family plans to leave a 15% tip?

A tree casts a shadow 9 meters long.

At the same time, a building that is 54 meters

tall casts a shadow that is 27 meters long.

How tall is the tree?

A store advertisement reads,

“GoingOutofBusiness—Everything 5 ⁄ 8 off.”

What percent is this?

What value of d makes the following number

sentence true?d ⁄ 3=–27

Susan is ¼ John’s age.

If Susan is 2 years old, how old is John?

10 + 30 ÷ 5

28÷7•2

A circular plate has a radius of 7 inches.

What is the area of the plate

to the nearest whole inch?

Which measurement below

represents the greatest volume?

17 pints, 2 gallons, 35 cups, 9 quarts

greenapples—$1.48perlb. redapples—$1.02perlb.

If Jean buys 3½ pounds of each,

how much does she pay for the apples?

Which represents the greater value,2 ⁄ 11 or 1 ⁄ 9?

During basketball practice, Jena attempted

52 free throws and made 16 of them.

What is the probability that she will make

the next free throw that she attempts?

The ages of students in Martin’s

karate class are as follows:

8, 9, 7, 10, 9, 11, 6

Which age represents the mode?

––––––––––––––=





Sample Questio Cards, cotiued (Aswers)

Answer: 31Use order of operations

5 + 6(5) – 4

5+30–4=31

Math FootballQuestio Cards

Answer: 18 meterst ⁄ 9=54 ⁄ 27 t=18

Answer: $9.45

10% of $63.00 is $6.30

5% of $63.00 is $3.15

$6.30+$3.15=$9.45

Answer: –81

Use inverse operation

–27•3=–81

Answer: 62.5%5 ⁄ 8=5÷8=0.625•100=62.5%

Answer: 2

Use order of operations

10 + 6 16 –———=——=2

4•2 8

Answer: 8

4x2=8

Answer: 9 quarts

Convert all to cups

17pints=34cups,2gallons=32cups

35cups,9quarts=36cups

Answer: 154 sq in.

Area=π(r2)

π(72)=3.14x49=153.86=154

Answer: 2 ⁄ 11

2 ⁄ 11=18 ⁄ 99 and 1 ⁄ 9=11 ⁄ 99 so 2 ⁄ 11 is greater

Answer: $8.75

$1.48x3.5=$5.18

$1.02x3.5=$3.57

Answer: 9

The mode is the value represented most

often in a set of data.

Answer: 4 ⁄ 13

16 ⁄ 52=4 ⁄ 13





Reflection









Academic Erichmet


activity un?











Lesson 3

Nmber Concentration

In this game, students match Arabic numerals with their picture

representation. The students will use the classic game o concentration

to match the numbers they are learning during the school day to the

geometric representation o the same number.


Duratio:

30 minutes

Studet Goals:

• RecognizetheArabicnumerals(0,1,2,3,4,5,6,7,8,9)

• RecallthevalueoftheArabicnumeralsasrepresentedthroughpictures

• Namethegeometricshapesused

Curriculum Coectio:

Lie Skills (thinking and reasoning)

Stadards:

These standards and benchmarks are rom McREL's online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks). The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.

Stadard 2: Understands and applies basic and advanced properties o the concepts o numbersGradesK–2

Benchmark 1: Understands that numerals are symbols used to represent quantities or attributeso real-world objects

Benchmark 3: Understands symbolic, concrete, and pictorial representations o numbers


GradesK–2

Benchmark 1: Understands basic properties o and similarities and dierences between simplegeometric shapes





Imagie This!The room is flled with students working excitedly in small groups playing games. Who

could have imagined students would be so excited about math! Students are using the math

vocabulary o geometric shapes to explain why they are winning. As the students fnish theirgames, they beg you to let them play again and again.

What you needp Several sets o 22 concentration cards

Gettig Read• Preparetheconcentrationcardssothateachofthenumerals0,1,2,3,4,5,6,7,8,9is

represented numerically on a card and pictorially on a separate card. (See example below.)

• Usegeometricshapestorepresenteachnumberinpictures.Nametheshapesasyou

model the game.

• Havethestudentssaythenameoftheshapesafteryou.

Card Example

3





What to Do• Dividestudentsintogroupsoftwoorthree,basedonwhowillworkwelltogether.Give

each student group a deck o concentration cards.

• Askstudentstoplaceeachofthecardsprintsidedownonthetable.• Explaintothestudentsthebasicrulesofthegameofconcentration.

- Eachplayerwilltaketurnspickingacardandippingitover.

- Then the same player will pick a second card trying to make a match. A match is made

when the player picks a card that has an Arabic numeral that matches the picture

illustrated on the other card selected.

- I the player makes a match, he or she gets to keep both cards and go again.

- Iftheplayerdoesnotmakeamatch,heorsheturnsbothcardsover;andtheturngoes

to the next player.

- The game is over when all o the cards have been matched. The winner is the playerwho has the most matched cards at the end o the game.

Exted• Askstudentstocreatetheirownsetofconcentrationcardsthattheycantakehometo

play with.

Outcomes to Look orMuch o the assessment or this lesson comes rom listening to and watching the children.

• Studentparticipationandengagement

• Anunderstandingofnumeralsandtheircorrespondinggeometricpicturerepresentation

Teaching Tip

Modelig

I students haven't played concentrationbeore, the teacher might model thedirections or the large group with some

sample cards. When modeling how toplay, make sure to ask the large group oreedback as to whether the two cards turnedover are a match.





Reflection









Academic Erichmet


activity un?







Lesson 4

Rational Nmber Bingo

Teachers continually point to ractions as a stumbling block or students.

This game is a un way to provide practice with this important topic.

Whileplayingthisgame,studentsgainuencyreducingfractionstotheir

lowest terms and converting common percents and decimals into raction

orm. The game is played like a typical bingo game, but participants

must make mental conversions o rational numbers beore locating the

numerical value on their bingo card.


Duratio:

5–10 minutes or one game

Studet Goals:

• Reinforceskillswithreducingfractionstolowestterms

• Promoteuencywithconversionofcommondecimalsandpercentstofractions

• Promotestrategiesformentalmathematics

Curriculum Coectio:

Lie Skills (thinking and reasoning)

Stadards:


Stadard 2: Understands and applies basic and advanced properties o the concepts o numbersGrades3–5

Benchmark 2: Understands equivalent orms o basic percents, ractions, and decimals andwhen one orm o a number might be more useul than another


Grades5–8

Benchmark 1: Understands the relationships among equivalent number representations and theadvantages and disadvantages o each type o representation





Imagie This!The aterschool instructor holds up a bingo card and says, “Who wants to play bingo?”

Students naturally gravitate toward this un approach to learning and are eager to join the

un. Students prepare their own bingo cards and listen attentively as the instructor randomlyselects the frst number card rom the container. Students convert the number to its equivalent

raction and race to fnd the amount on their card. As more cards are selected, the tension

builds. Who will be the frst to call “Bingo!”?

What you needp A copy o the rational number bingo card or each player (See example rom pages

109–110)

p Equivalent rational number cards individually cut and placed in a container

Gettig Read• Duplicatearationalnumberbingocardforeachplayer.

• Cuttheequivalentrationalnumbercardsintoindividualpiecesandplacethem

in a container.

• Mixthenumberscardswellbeforebeginningthegame.

Vocabulary

Decimal: relating to the number 10 as a base

Fractio: a part o a whole, ormed by dividing one quantity into another

Percet: one part in 100

Ratioal umber: a whole number or the quotient o any whole numbers,excluding zero as a denominator





What to Do• Tellstudentsthattheywillbeplayinga

game o bingo.

• Directstudentstopreparetheirown bingo playing card.

• Directstudentstopreparesomethingto

use as a marker or their bingo card.

Since the card will be used multiple times,

it is best or students to use bits o paper or

manipulative pieces (cubes, counters, etc.)

to identiy the equivalent ractions on

their cards.

• Whenplaybegins,selectanequivalent

rational number card rom the container. Read aloud what is on the card and repeat it 2–3times. Try to maintain a brisk pace to keep students ocused as they play the game.

• Explaintoplayersthattheymustconvertthenumericalvaluetoitsfractioninlowestterms

and then fnd that raction on their bingo card. I the lowest-term raction is on the bingo

card, the player should cover it with a marker such as a bit o paper. The frst person to

complete a bingo (vertically, horizontally, or diagonally) wins the round.

• Makesurethecardsselectedfromthecontainerarekeptinaseparatepile.Thesecards

will be needed to check or accuracy o the bingo.

• Whenastudentcallsout“bingo,”makesurethatallotherstudentsmaintaintheirplaying

cards until accuracy is checked.

• Ifaplayergetsatruebingo,thatplayerwinstheround.Playersshouldthenremovethe

markers on their cards and prepare or another game o rational number bingo. Small

rewards may be provided to winners o each round as appropriate.

ExtedUse dierent math concepts or the bingo cards and questions.

Outcomes to Look or• Increaseduencyandcondencewithconvertingfractionstolowestterms

• Increaseduencyandcondencewithconvertingcommondecimalsandpercentstotheequivalent raction

• Activelisteningskills

Teaching Tip

Players should use mental math strategiesto play this game, but i some players havedifculty with the mental math, they canopt to use paper and pencil. Keep playersocused by maintaining a brisk pace as theequivalent cards are read. The pace shouldbe appropriate or the level o the learners.





Ratioal number Bigo Card

Directions

Each player will make his or her own bingo card by choosing a raction rom the list below

and placing it in one square on the bingo card. A raction may be used only once per card.

1 1 1 1 1 1 1 1 1 2 3 2 3 4 5 — — — — — — — — — — — — — — —

2 3 4 5 6 7 8 9 10 3 4 5 5 5 6

2 3 4 5 6 3 5 7 2 4 5 7 8 3 7 9 — — — — — — — — — — — — — — — —

7 7 7 7 7 8 8 8 9 9 9 9 9 10 10 10





Equivalet Ratioal number Cards or Bigo

50% 4—12

0.25 20% 3—18

5—35

0.1253—

2710%

8—

1275% 0.4

60%12—15

10—12

8—28

9—21

8—14

25—35

18—21

27—72

10—16

28—32

6—27

12—

27

15—

27

28—

36

16—

18

0.3 70%

0.9





Reflection









Academic Erichmet


activity un?







Lesson 5

Who Has?

This game is a un way to reinorce essential mathematics vocabulary

and skills. Students are provided clue cards that make a statement and

ask a question. As students answer correctly, the game proceeds in a loop

until all clues are read and answered orally. This game moves quickly and

can be used whenever a ew minutes are available. It is recommended to

record the time it takes the group to complete the loop o clues. Students

enjoy playing this game over and over and are motivated to beat their

previous times.

Grade Level(s):

4–8

Duratio:

5–10 minutes

Studet Goals:

• Reinforcemathematicsvocabularyandskills

• Increasemathematicaluency

• Promotelisteningskills

Curriculum Coectio:

Language ArtsStadards:


The standards addressed would depend on the questions the teacher writes and the grade level othe students. Below are the categories o math standards that could be addressed.


Patterns, Relationships, and Algebraic ThinkingGeometry and Spatial Visualization

Measurement


Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!The aterschool instructor holds the stopwatch, selects a student to begin, and says, “Go!”

The student begins to read his clue, as all other students listen careully. Students quickly

review their clue solutions or the correct response, and the student with that card reads theanswer and the next question. Students are eager to keep the pace brisk and work hard to

beat their best completion time. When the game is over, you can hear students say, “Can we

do this again?” The aterschool instructor smiles and says, “Certainly.”

What you needpCluecardsforeachstudent;studentscanbegivenmultiplecardsifneeded

p Stopwatch or clock with a second hand

Gettig ReadPrepare the clue cards beore the session. Clue cards should correspond to content that the

students are either currently studying in class or have previously studied. Duplicating the clues

on cardstock will make them last longer.

Example clues are given below.

I have a acuteagle. Who has atriagle with twocogruet sides?

I have a isoscelestriagle. Who has

a polgo withour sides?

I have a quadrilateral.Who has a agle

that measures moretha 90˚?

I have a obtuseagle. Who has a

triagle with ocogruet sides?





What to Do• Explaintherulesofthegametostudents.Distributeoneormorecluecardstoeach

student. (Make sure all clue cards are distributed.)

• Encouragestudentstolistencarefullyasthecluesarereadsothatthegroupcancompletethe list o clues as quickly as possible. A stopwatch or analog clock with a secondhand

should be used to record the time it takes or students to read and respond to all clues.

The rules are as ollows:

- Each player receives one or more clue cards.

- Players should not review their clue cards until all students receive clues.

- The instructor designates one student to read his or her clue to begin the game. The

instructor begins the stopwatch as the frst player begins reading.

- No player may speak except the one person reading the clue and the person who

responds to the clue. Players should not call out hints or the solution to help a student

who doesn’t realize he or she holds the correct response.

- Play continues until all clues have been read and answered. When the frst player rereads

the fnal response, the instructor should stop the watch and record the group’s time.

- Play may be repeated with students using the same clue cards, or students may

exchange cards beore playing again.

Teaching Tipnew Vocabular Terms

I some students are unamiliar with thevocabulary terms, allow them to work withthe clue cards between timed sessions.The students could work to arrange thecards to show clues and correct responses.Ater students understand this game, youmight consider having them make clue cardswith new questions (see samples at endo lesson).





Exted• Differentmathcontentcanbeusedforthisgame.

Outcomes to Look or• Activelisteningskills

• Increaseduseofmathematicalvocabulary

• Abilitytovisualize

• Solvingmentalmathproblems

Who Has? Clue CardsTo develop a set o clue cards or the WhoHas game, it is helpul to list the clues in order as

shown below. Clues can be developed or any topic or at any level as long as the student can

read and understand the clues.1. I have perpendicular lines. Who has a six-sided polygon?

2. I have a hexagon. Who has an angle that measures less than 90°?

3. I have an acute angle. Who has a triangle with two congruent sides?

4. I have an isosceles triangle. Who has a polygon with our sides?

5. I have a quadrilateral. Who has an angle that measures more than 90°?

6. I have an obtuse angle. Who has a triangle with no congruent sides?

7. I have a scalene triangle. Who has the product o 20 and 4?

8. I have 80. Who has an eight-sided polygon?

9. I have an octagon. Who has the quotient o 100 and 5?

10. I have 20. Who has a triangle with all sides congruent?

11. I have an equilateral triangle. Who has a polygon with fve sides?

12. I have a pentagon. Who has the sum o 55 and 45?

13. I have 100. Who has a pair o lines that do not intersect?

14. I have parallel lines. Who has a pair o lines that intersect at a 90˚ angle?





Reflection









Academic Erichmet


activity un?















Math Projects

What Is It?The practice MathProjects eatures experiences that connect mathematical concepts and

procedures to engaging real-world activities that extend or more than one lesson. Key to the

projectsconceptisthatthemathematics—contentandprocess—emergefromthestudents’

own investigation o an authentic situation, rather than a classroom exercise. This helps

students see ties between mathematics and real-lie experiences.

What Is the Cotet Goal?

The specifc content goals o MathProjects will vary depending on the math involved in theproject;butallprojectsengagestudentsinagiventopic,developproblem-solvingskills,and

increase students’ understanding o how to use math in real-world situations.

What Do I Do?Begin by connecting with the day-school teacher to fnd out what math concepts, skills, and

standardsstudentsarestudying;andwhatkindsofactivitiesmightlendthemselvestomath

projects. For example, building and racing model cars can extend what students are learning

about measurement, geometry, and algebra. Or, combine math and science activities by

working on an interdisciplinary project that requires data collection and analysis related to the

environment.

Practice 4





Work with students to choose an idea or project that interests them. Then, discuss the

project, identiy what students will do, make a project plan and time line, identiy resources

you will need, and fnally conduct the project. Projects work best when students can work on

them in a regular, ongoing way as some projects can take several days. You will also want to

determine how your students will present and evaluate their projects. A culminating activity,

such as a fnal product or presentation, is a typical way to wrap up a math project.

Wh Does It Work?Project-based learning in math works because students are directly involved in their own

learning as they develop problem-solving skills, learn new math content, and apply what

they learn in authentic, real-world situations. Through project work, students develop a need

to learn new mathematical content and applications. They also experience the connections

between the math they have learned in school and real-world situations, and gain skill in

transerring and applying this knowledge.





video

Getting Starte

Go to the InvestigatingScienceThroughInquiry practice ound in the science

section o the Aterschool Training Toolkit (www.sedl.org/aterschool/toolkits/ science/pr_investigating.html). Click on the “Exploring Trebuchets” video

and watch as frst- through sixth-graders at the Brighton-Allston Aterschool

Enrichment Program (BASE) in Boston, Massachusetts, work on a project

creating trebuchets (catapults). You will see math skills being used throughout the project.


involve your students in math projects.


math projects.



them started?


engaged?









Lesson 1

digital Math Storytelling

In this project, students create original math stories that include text,

drawings, photos, animation, audio, and video. They use math and

technology tools, such as digital cameras, computers, and manipulatives,

to bring their math stories to lie.


Duratio:

Several sessions over 2 to 3 weeks

Studet Goals:

• Enhancecommunicationskillsbyaskingquestions,expressingopinions,constructingmath

narratives, and writing or an audience

• Increasecollaborationskillsinagroupproject

• Usemathtotellastory

• Applyexistingmathknowledgetogeneratenewideas,products,orprocesses

Curriculum Coectio:

Technology, Language Arts

Stadards:





Geometry and Spatial Visualization

Measurement


Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!An aterschool instructor gathers a class o 20 students to work on a digital math project,

called “The Story o Math.” Students get to work in small groups fnding, creating, and

digitizing the stories o math in their everyday lives. They take photographs with digitalcameras, learn to use scanners to incorporate original math artwork, or even add music,

narration, and video to their stories.

What you needChoose the technology tools that are appropriate or the skill level o your students. The

supplies are the same or each session. Following are some basic recommendations:

p One computer or every 2–3 students

p Word processing sotware and presentation sotware such as PowerPoint

p Digital cameras

p Tool or voice recording (most computers have this eature)

p Sticky notes or index cards and poster paper to use or creating the storyboards

p Internet access or instructor and student computers (optional)

p Electronic projector or instructor computer (optional)

p Microphones (optional)

p Scanners (optional)

Gettig Read

Instructors should determine students’ computer skill levels and select appropriate technologytools. Instructors should also have amiliarity with multimedia sotware applications and

equipment or enlist the help o a volunteer who does.

• Becomefamiliarwiththedigitalstorytellingprocessbycompletinganonlinetutorial.Visit

the DevelopingSelf-ExpressionandCreativity practice o the technology section o the

Aterschool Training Toolkit, and click on the Resources tab (www.sedl.org/aterschool/

toolkits/technology/pr_developing.html).

• Consultwithday-schoolteacherstoseeifdigitalmathstorytellingmightenrichlearning

with a math concept being studied currently in class.

• Arrangeforvolunteerstoassiststudents.





What to DoSuggestions or breaking this lesson into sessions are provided, but eel ree to change the

sessions as needed.

Session1• Introducestudentstodigitalstorytellingbyshowingthemsomeofthedigitalstoriesfrom

the Resources section by projecting them on a screen or all to see and discuss. Note that

stories have a beginning, middle, and end. At this point you can begin to develop a rubric

with the students or their projects.

• Brainstormsomemathstoryideas.

Examples:

- Take a geometry walk around the classroom and show and tell what you ound.

- Math is all around the school. Where? Split up in groups and fnd out.

- Explain to others a concept like adding ractions using real-lie examples.- Portray math problems using various strategies.

- When do you use math in your personal lie?

• Aftercompletingthisbrainstormingsession,discusswhatstorythegroupwantstotell.

Constructing a story as a group about a math topic will help students learn both the math

process and the sotware needed to develop a digital story. This activity can be completed

as a whole-class group or small, three-person group. I this is the frst time your class has

created a story, a whole-class group eort may be easier to manage.

Sessions2and3

• Draftastory(onpaper)basedonthechosenidea.(Thiscanhappeneitherinawhole-classgroup or in small, three-person groups.)

• Remindtheclassthattheymaymakechangestothedraftatanytime.Foryounger

students in particular, review basic storytelling concepts, such as a story has a beginning,

middle,andend;orastoryhasatitleandauthors.

• Asyouguideyourstudentsthroughthestorytellingprocess,usethesevenmainelementsof

digital storytelling, created by Joe Lambert, coounder o the Center or Digital Storytelling.

• Rememberthatthemathstory—notthetechnology—shoulddrivethisproject.Although

audio and visual media may enhance certain aspects o a story, students should ocus on

how best to communicate what’s at the core o their math story.

• Withthewhole-classgrouporthethree-persongroups,differentstudentscandevelop

dierent parts o the story. Also, i this project is your students’ frst experience with digital

storytelling,keepthestoryshort—nomorethan3minutesinlength.

• Thiswouldbeagoodtimetolookattherubricagainandreviseitifnecessary.





Session4

• Introducestudentstostoryboarding.

• Handoutsmall,coloredstickynotesandsheetsofpaperwithblankstoryboards,which

are rows o empty boxes resembling an empty cartoon strip. Show students how to tell theirmathstoryframebyframebydiscussingthepicturesthroughwhich—andthesequencein

which—theywilltelltheirmathstory.

• Afterstudentshavedeterminedthetextandpicturesequence,discusstransitions,visual

eects (i any), and soundtracks. Always keep in mind the skill level o your students when

planning ways to represent their ideas.

Sessions5–9

• Helpstudentspreparetheirnaldraft.

- For a whole-class group project, break students into small groups, based on their ages

and skill levels. Ask each small group to develop one or two pieces o the storyboard.

One group will be in charge o assembling the pieces into one story using PowerPoint or

another sotware application. For the three-person group projects, students can assign

each other dierent tasks within their group project.

- I the group wishes to record narration, ask them to divide the story so that everyone

gets to read. Beore recording, demonstrate how to narrate eectively. Discuss

dierences between using emotion and no emotion in your speech, and what eect quick

or slow speech has on the story. Students need to practice narration beore recording.

- With the three-person groups, view their stories and use the rubric to help them assess

how they did.

• Haveeachgroupshareitsprojectwithotherstudents.• Youmightconsiderhavingthegroupsassesseachother’sprojectusingtherubric.

• Thesewouldbeexcellentprojectstoshareatafamilymathnight.

Session10

• Forthewhole-classproject,usetherubrictoassesstheprojecthelpstudentsunderstand

what they need to do next time in small-group projects. They will want to do this again!

• Discussthevalueofcollaborationincreatingadigitalmathstory.

• Haveeachstudentrelatetoapartnerthespecialcontributionheorshemadetotheproject

and why it was important. Discuss as a group what students learned about digital

math storytelling.


• Anunderstandingthatmediacanhelpmakemathlearningfarmorethanjustproblemsin

a book

• Demonstrationofmathknowledge





Reflection









Academic Erichmet


activity un?











Lesson 2

Stock Market Game

Students conduct research to determine stocks that they would like to

include in a fnancial portolio. Using a hypothetical budget o $100,000,

students track stocks over 4 weeks and devise a fnancial report to share

with the other class investors.

Grade Level(s):

6–8

Duratio:

4 weeks

Studet Goals:

• Understandthebasicsofhowstocksareboughtandsold

• Usemathematicalskillstotrackandcomputechangesinthevalueofstocksovera4-week

period o time

• Deviseanancialreportandpresentndingstootherclassinvestors

Curriculum Coectio:

Social Studies

Stadards:



Grades6–8

Benchmark 6: Uses proportional reasoning to solve mathematical and real-world problems

Stadard 9: Understands the general nature and uses o mathematicsGrades6–8

Benchmark 2: Understands that mathematicians oten represent real things using abstract ideaslikenumbersorlines;theythenworkwiththeseabstractionstolearnaboutthethingsthey

represent





Imagie This!An aterschool instructor engages a group o secondary students by posing the ollowing

scenario. Suppose you had $100,000 to invest in the stock market. Do you think that your

decisions would cause your fnancial portolio to increase in value? Or would your decisionsresult in fnancial losses? During the next 4 weeks you will have the opportunity to invest a

hypothetical $100,000 in the stocks o your choice. During the investing time rame, you

will keep weekly records indicating the percent o change (positive or negative) in the value o

each o your stocks. At the end o the time period, you will share your fnancial portolio with

theotherinvestorsinthisclassandreectonthedecisionsthatyoumade.

What you needpInformationtohelpstudentsresearchstocks—newspapers,periodicals,companyresearch

reports, access to the Internet (i available)

p Financial portolio worksheetp Graph Paper

p Pencils

p Calculators (optional)

Gettig Read• Collectnewspapers,periodicals,andcompanynancialreportstohelpstudentsresearch

companies and stocks.

• GainaccesstotheInternet,ifpossible,forstudentresearch.

• Makearrangementstohavecopiesofacurrentnewspaperavailableeachdayduringthe4-week game.

• Reviewthehistoryofstocksandgeneralinformationabouthowstockmarketsfunction.

Teacher support can be ound at the ofcial Stock Market Game Web site under Teacher

Support Center (http://smgww.org/).

• Makecopiesofthenancialportfolioworksheet.





What to Do• Introducethestockmarketgametostudentsbyusingthequestionsdescribedinthe

“Imagine This!” part o the lesson. Tell students that they will be tracking the stocks rom

companies o their choosing to see which student-investor team has the greatest gain instock value during the next 4 weeks.

• Groupstudentsinteamsof2to3.

• Startwithanintroductiontothebasicsofthestockmarket.

• Helpstudentsunderstandhowtolocateastockinthenewspaperandreportitsvalue.

• Providetimeforstudentstoresearchstocksanddecidewhichonestotrack.Studentsmay

purchase stocks rom 5 to 10 companies. Students should identiy why they decided to

select a certain stock. (For example, I will track the Tasty Ice Cream Company because it’s

getting warm and more people will be buying ice cream.)

• Attheendofeachweek,haveagroupdiscussionaboutgainsandlossesandother

observations related to the stock market. Students should complete the fnancial portolio

worksheet and graph the percent o change each week.

• Attheendofthe4weeksstudentsshouldreporttheirresultstothelargergroup.Results

will show which teams had the greatest gains and losses.

• Askstudentstoreectonthestockmarketgameexperience.Didtheyhavesurprisesalong

the way? What did they learn rom this experience?

Teaching Tip

Stock Iormatio

It’s important or students to know whycompanies issue stock. Companies issueshares o stock to raise money (fnancialcapital) or starting or expanding businessoperations. The Web site, Wally’s StockTicker (www.prongo.com/stock/index.pl),gives daily stock inormation in student-riendly terms.





Outcomes to Look or• Abetterunderstandingabouthowtheskillslearnedinmathclasscanbeusedbeyondthe

classroom

• Abetterunderstandingofhowcompaniesgainthefundsneededtogrowanddobusiness• Decision-making

• Teamwork

Vocabulary

Bear market: a nickname or a market where stocks all consistently over a

period o timeBull market: a nickname or a market where stocks rise consistently over

a period o time

Earigs: net income or a company during a certain time rame

Portolio: a collection o investments

Shares: units (certifcates or book entries) representing ownership ina corporation

Stock: ownership in a company as issued in shares

Stock market: an organized marketplace where shares o stock are boughtandsold;anexampleistheNewYorkStockExchange





Reflection









Academic Erichmet


activity un?











Lesson 3

Learning Math an Art With Qilts

In this project, students will learn about geometric shapes, patterns,

and measurement by making paper quilts. Each small group will create

square, rectangle, triangle, and circle quilt blocks by using measuring,

color combinations, and piecing skills. Students will conclude the project

by putting all the blocks together to make a large paper quilt.

Grade Level(s): K–2Duratio:

Seven 45-minute sessions

Studet Goals:

• Learntheconceptofpatterns

• Learnbasicgeometricpatterns

• Learnwhatshapesareformedwhendivided(forexample,asquarebecomestwotrianglesor two rectangles)

• Learnbasicmeasuringskills

• Increasene-motorcuttingskills

• Increasecollaborationanddecision-makingskills• Learncolorsandcolorcombinations

Curriculum Coectio:

The Arts, Language Arts

Stadards:


Stadard 4: Understands and applies basic and advanced properties o the concepts o measurementGradesK–2



GradesK–2


Benchmark 2: Understands the common language o spatial sense

Benchmark 3: Understands that geometric shapes are useul or representing and describing real-world situations





Benchmark 4: Understands that patterns can be made by putting dierent shapes together ortaking them apart

Stadard 9: Understands and applies basic and advanced properties o unctions and algebra

GradesK–2

Benchmark 1. Recognizes regularities in a variety o contexts (e.g., events, designs, shapes, setso numbers)

Benchmark 2. Extends simple patterns (e.g., o numbers, physical objects, geometric shapes)

Imagie This!Your room is flled with children making square shapes o paper quilt blocks. The small groups

o students are ully engaged in measuring, cutting, and piecing their colorul shapes into their

ownindividualquiltblockstocontributetothenalculminatingproduct—onelargegroup

quilt! Excitement permeates the room on the big day when they make their group quilt! The

groups o students take their group quilts on a quilt march to the other aterschool classes to

show them their beautiul products. The group quilts are displayed in the building later that

day. Families attend a amily night where the quilts are on display.

What you needSee individual sessions or other supplies needed.

p Quilting patterns rom the Internet

p Children’s books:

- ThePatchworkQuilt by Valerie Flournoy. Pictures by Jerry Pinkney. (New York: Dial

Books or Young Readers, 1985)

- Amina’sBlanket by Helen Dunmore. Illustrated by Paul Dainton. (New York: Crabtree

Publishers, 2003)

- TheKeepingQuilt by Patricia Polacco. (New York: Simon & Schuster Books or Young

Readers, 1998)

- TheQuiltStory by Tony Johnston. Pictures by Tomie dePaola. (New York: Putnam, 1985)

- TheBoyandtheQuilt by Shirley Kurtz. Illustrated by Cheryl Benner. (Intercourse, PA:

Good Books, 1991)

- TheMountainsofQuilt by Nancy Willard and Tomie dePaola. Pictures by Tomie dePaola.

(San Diego: Harcourt Brace Jovanovich, 1987)

- TheQuiltmaker’sGift by Je Brumbeau. Pictures by Gail de Marcken. (Duluth, MN:

Peier-Hamilton Publishers, 2000)

- SweetClaraandtheFreedomQuilt by Deborah Hopkinson. Illustrated by James

Ransome. (New York: Knop, 1993)





Vocabulary

Circle: a two-dimensional geometric fgure ormed o a curved linesurrounding a center point, every point o the line being an equaldistance rom the center point

Circumerece: the distance around a circle

Diagoal: a line that joins two points on a polygon but is not a side

Diameter: a line or chord through the center o a circle

Equal: the same amount

Lie segmet:partofaline;hasabeginningandanend

Measure: the size or extent o something

Patter: a repeated design

Quilt: a bedcover made o two layers o abric stitched together withpadding held in place by decorative intersecting seams

Radius: a line segment extending rom the center o a circle to its edge

Rectagle: fgure with our sides and our right angles

Reverse patter: opposite pattern

Square: a geometric fgure with our right angles and our equal sides

Smmetr: correspondence in size and shape o parts on opposite sides odividing lines

Triagle: a two-dimensional geometric fgure ormed o threesides and three angles





Sessio 1: Usig Square Patters

WhatYouNeed

p Ruler or each student

p Scissors or each student

p Enough dark blue and light blue sheets o paper so that each student can have fve 3 x 3

inch squares o each color

p Sample o pattern designs with two colors o 3 x 3 inch squares

p One sheet o white paper or each student

p Glue or each student

GettingReady

• Havematerials(ruler,scissors,paper,andglue)readyforeachstudent.

• Cut3x3inchdarkandlightbluesquaressoeachstudenthasveofbothcolors.

• Cuta36x36inchsquareforeachgroup.

• Have9x9samplesofvarioussquarepatterncombinations.

• Engageanotheradultorolderstudenttoassistyou.

WhattoDo

• Readabookaboutquiltstothestudents.(Seethelistin“WhatYouNeed.”)

• Talktostudentsaboutquilts.Showquiltsamplesorpicturesofquilts.

• Talktostudentsaboutsquaresandpatterns.Showthemsamplesquarepatterns.

• Discussthepropertiesofasquare.

• Dividestudentsintogroupsoffourbasedonwhowillworkwelltogether.

• Gooverdirectionsandbehaviorexpectationsforuseofglue,scissors,collaboration,etc.

• Reviewhowtomeasureobjects.Havestudentsmeasureoneofthesmallsquarestoensure

they know how to measure 3 x 3 inches.

• Demonstratehowtomeasureapieceofpapertocreatea9x9inchsquare.Show

students how to mark the 9 inches at the top and bottom and use their rulers to draw a

line across their paper to create a 9-inch square. Have students measure and cut their

paper into a 9 x 9 inch square. Rotate among students as they measure and cut their

square. (Accuracy is important.)

• Haveeachstudentselectvedarkblueandvelightblue,precut,3x3inchsquares.(Thestudents will not use one o the squares.)

• Havestudentsdesigntheirown9x9inchsquarepatternsandgluetheirpatternsonto

their 9 x 9 inch squares.

• Haveeachgroupcombineitssquarepatternstomakea36x36inchquiltsquare.

• Askgroupstoshareandtalkabouttheirquiltsquareswiththeothergroups.

• Markthenamesofeachgroupmemberonthebackofthelargesquareandcollectthe

quilt squares to save or the culminating event.





Sessio 2: Usig Triagle Patters

WhatYouNeed



p Enough dark green and light green sheets o paper so that each student can make fve

3 x 3 inch squares o each color

p Sample o triangle symmetry designs with two colors in a 9 x 9 inch quilt squares



GettingReady


• Cut3x3inchdarkgreenandlightgreensquaressoeachstudenthasveofbothcolors.

(Make extras in case students mess up when cutting the triangles).


• Have9x9inchsamplesofvarioussymmetricaltrianglecombinations.

WhattoDo

• Readanotherbookaboutquilts(optional).

• Discusswhatstudentslearnedaboutmakingtheirsquarequiltsintheprevioussession.

Review the vocabulary rom the beginning o the lesson.

• Modelforthestudentshowtomaketwotrianglesfromasquare.Showthemsample

triangle patterns.

• Discussthepropertiesofatriangle.

• Dividestudentsintothesamegroupsoffourfromtheprevioussession.

• Gooverdirectionsandreviewbehaviorexpectationsforuseofglue,scissors,andcollaboration.


they know how to measure 3 x 3 inches.

• Demonstrateandreviewhowtomeasureapapertocreatea9x9inchsquare.(Accuracy

is important.)

• Haveeachchildselectvedarkgreenandvelightgreen3x3inchsquares.(Theywill

not use one o the squares.)

• Demonstrateforthestudentshowtodrawadiagonallineonasquaretomaketwo

triangles. Circulate among the students as they draw and cut their squares into triangles.

(Accuracy is important.)

• Havestudentsdesigntheirown9x9inchsymmetricaltrianglepatternsandgluetheir

patterns onto their 9 x 9 inch squares.

• Haveeachgroupcombineitstrianglepatternstomakea36x36inchquiltsquare.








Sessio 3: Usig Rectagle Patters

WhatYouNeed



p Enough dark purple and light violet sheets o paper so that each student can make fve

3 x 3 inch squares o each color

p Sample o rectangle designs with two colors in a 9 x 9 inch quilt square



GettingReady


• Cut3x3inchdarkpurpleandlightvioletsquaressoeachstudenthasveofbothcolors.


• Have9x9inchsamplesofvariousequalrectanglepatterncombinations.

WhattoDo


• Discusswhatstudentslearnedaboutmakingtheirtrianglequiltsintheprevioussession.

• Reviewthevocabularyfromtheprevioussession.

• Modelforstudentshowtomaketworectanglesfromasquare.Showthemsample

rectangle patterns.

• Discussthepropertiesofarectangle.• Dividestudentsintothesamegroupsoffourfromtheprevioussession.





• Gooverdirectionsandreviewbehaviorexpectationsforcollaboration.


it measures 3 x 3 inches.

• Demonstrateandreviewhowtomeasureapapertocreatea9x9inchsquare.(Accuracyis important.)

• Haveeachchildselectvedarkpurpleandvelightviolet3x3inchsquares.(Theywill

not use one o the squares.)

• Demonstratehowtofoldthesquaretomaketwoequalrectangles.Circulateamong

students as they draw and cut their squares into equal rectangles. (Accuracy is important.)

• Havestudentsdesigntheirown9x9inchrectanglepatternandgluetheirpatternsonto

their 9 x 9 inch squares.

• Haveeachgroupcombineitstrianglepatternstomakea36x36inchquiltsquare.




Sessio 4: Usig Circle Patters

WhatYouNeed



p Enough yellow and orange sheets o paper so that each student can have fve 3 x 3 inch

squares o each color

p Enough yellow and orange sheets o paper so that each student can have fve circles with a

3-inch diameter

p Sample o circle designs with two colors in a 9 x 9 inch quilt square alternating the color o

background and circle



GettingReady


• Cutyellowandorangesquaresandcirclessoeachstudenthasveyellowandorangesquares and fve yellow and orange circles.


• Have9x9inchsamplesofcirclepatterncombinationsthatreversetheyellowandorange

background and circles.





WhattoDo


• Discusswhatthestudentslearnedabout

making their rectangle quilts in the previoussession.

• Reviewthevocabularyfromtheprevious

session.

• Discussthevocabularywordsforacircle.

• Modelforstudentshowtomakea

pattern by reversing the background and

circle. Show them sample reversed circle

background patterns.

• Dividestudentsintothesamegroupsfrom

the previous session.

• Gooverdirectionsandreviewbehaviorexpectationsforcollaboration.


it measures 3 x 3 inches.

• Demonstrateandreviewhowtomeasureapapertocreatea9x9inchsquare.(Accuracy

is important.)

• Haveeachstudentselectveorangeandveyellowcircles.(Theywillnotuseoneof

the circles.)

• Haveeachstudentselectveorangeandveyellowsquares.(Theywillnotuseoneof

the squares.)• Havestudentsdesigntheirown9x9inchreversedcirclepatternandgluetheirpattern

onto their 9 x 9 inch square.

• Haveeachgroupcombineitscirclepatternstomakea36x36inchquiltsquare.




Teaching Tip

Sessio Preparatio

Review directions and behavior expectationsbeore having groups start their work. Havematerials on the tables and posted when thestudents enter the room. Post a chart o thevocabulary words with a picture depictingeach word. Explicitly demonstrate each stepin each session. Review with students howthey will conduct themselves on the quiltmarch.





Sessio 5: Goig o a Quilt March

WhatYouNeed

p The quilt pieces that each group has made

p A paper (card stock or cardboard) that is 4-eet square or each group

p Glue or each group

p Various small cracker snacks

p Glue

GettingReady

• Havematerials(paper,glue,quiltpieces)readyforeachgroup

• Cuta4-footsquareforeachgroup

WhattoDo

• Readaculminatingbookaboutquiltstothestudents.• Reviewthevocabularywordsfromtheprevioussessionsandthepropertiesofalltheshapes.

• Dividestudentsintothegroupsfromtheprevioussessions.

• Gooverdirectionsandbehaviorexpectationsforcollaboration.

• Handouteachgroup’squiltpiecesandthe4-foot-squarepaper.

• Haveeachgroupcollaborativelyarrangeitsgroupsquare,triangle,rectangle,andcircle

patterns to make its fnal 4-oot-square quilt.

• Askgroupstoshareandtalkabouttheirquiltwiththeothergroups.

• Leadgroupsonaquiltmarch,duringwhichstudentssharetheirquiltswiththeolder

students in other classes.• Displaythequiltsthroughoutthebuilding.

Exted• Developcombinedquiltingdesigns.

• Usetilestomakepatterns.

• Usegridpapertodesignpatterns.

• Introducetessellations.

Outcomes to Look or• Studentsdiscussingandmakinggeometricpatternswithcolors

• Studentsknowinghowtomakedifferentsmallershapesfromonelargeshape

• Studentsmeasuringlengthsandwidthsproperly

• Studentsusingscissorsproperly

• Collaborationamongstudents





Reflection









Academic Erichmet


activity un?







Lesson 4

Scale

In this lesson students learn to draw to scale a perimeter o a room. They

will use various measuring tools, including an architect’s scale or ruler.

To draw a room to scale, students will have to use ractions and ratios to

reduce large space measurements down to a drawing that can be put on a

piece o paper.


Duratio:

1–2 weeks (ten sessions o 45–60 minutes)

Studet Goals:

• Understandthebasicelementsofmeasuringtheperimeterofaspace

• Learnhowtouseanarchitect’sscaleorruler

• Convertlargemeasurementsintoscaledmeasurements

• Workcooperatively

• Understandscaledrawing

Curriculum Coectio:

The Arts

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks). The mathematics portion o the database was developed

using National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.

Stadard 4: Understands and applies basic and advanced properties o the concepts omeasurement

Grades6–8

Benchmark 4: Solves problems involving units o measurement and converts answers to a largeror smaller unit within the same system





Imagie This!The rooms in your school are covered with beautiul scale drawings! Students sketch your

classroom—allofthedoors,windows,closets,andeventhefurniturealongthewalls.Then

you bring out tape measures as students work in pairs to measure the actual things in theirdrawings. On their sketches students write the exact measurements o each item. Now, how

do they convert those measurements into much smaller ones and stay accurate to scale?

Theyuseanewtool—thearchitect’sscale—tocreatescaledrawingsoftheirclassroom.Once

students understand how to make scale drawings, they’re ready to make a drawing completely

ontheirownofanotherroomintheschool—thelibrary,thecafeteria,theofce,andsoon.

The students can choose the room.

What you needThe supplies are the same or each session.

p Pencils with erasersp Colored pencils (optional)

p Tape measures

p Rulers

p Architects’ scales (a three-sided ruler)

p Graph paper

p 11 x 17 inch paper

Gettig Read• Purchasearchitects’scalesforyourclassroom.

• Sketchtheroomonplainpapersoyoucanuseitasamodel.Don’tputmeasurementson

this sketch.

• Copyyoursketchandnowmeasuretheroomandputyourmeasurementsonthecopied

sketch or later use.

• Practiceusingthearchitects’scaletoconvertalargemeasurementtoasmaller,scaled

measurement. Convert one o your actual room measurements into a scaled measurement.

• Onceyougetthehangofit,sketchyournaldrawingusingthescaledmeasurements.

• RyersonUniversityhasagoodexampleforyoutolookatbeforeyoubegindoingyourown

(http://www.ryerson.ca/arch/Gallery%202007/gallery.html)





Sessio 1: Sketchig Shapes

WhattoDo

• Havestudentsnoticetheperimeteroftheroom.Wherearethewindows,doors,closets,

and urniture against the wall? Where are the outlets?• Whereisnorth,south,east,andwest?

• Asagroup,havestudentsguesstimatetheroom’sdimensions.

• Haveeachstudentsketchonplainpapertheroomwithalltheitemsmentionedabove.

Have students check each other’s sketches to see i they have included everything. Some

students may have to start again to be sure to include all the items mentioned.

Sessio 2: Creatig Scaled Measuremets

WhattoDo

• Havestudentsworkinpairstomeasuretheperimeteroftheroom—thewalls,windows,closets,bookshelves,andso

on. As they obtain a dimension, they should write it on their

sketch o that item.

• Havethestudentsbeginconvertingtheirlargemeasurements

into scaled measurements.

• Checkstudents’mathbeforetheymoveontomakingtheir

fnal drawing.

Sessio 3: Drawig to Scale

WhattoDo

• Havestudentsnishtheirmathcalculations.

• Havestudentsworkindependentlyandbegintheirscaledrawingsoftheclassroom.

Theycanusegraphpaperorplainpaper.Theyshouldusepencilrst;and,later,when

they are sure they have everything correct, they can use colored pencils or pens to go

over the drawing.

Sessio 4: Sharig Sketches

WhattoDo

• Havestudentsnishtheirdrawings.Remindthemtoincludenorth,south,east,west,

and outlets.

• Postallthesketchesandhavestudentswalkaroundcomparingthedrawings.Ifyouwant

to use a rubric and have students assess each other, a sample is at the end o the lesson.

• Askstudentstoreectonwhattheylearnedinthisrstscaledrawing.Studentsmay

discuss their observations in groups or write them down individually.

3/32"=1'(1:128scale)

3/16"=1'(1:64scale)

1/8"=1'(1:96scale)

1/4"=1'(1:48scale)

1/2"=1'(1:24scale)

3/4"=1'(1:16scale)

1"=1'(1:12scale)

13/8"=1'(1:8.7scale)

11/2"=1'(1:8scale)

and3"=1'(1:4scale)





Sessio 5: Expadig the Desig

WhattoDo

• Leadstudentsonawalkaroundtheschooltolookatrooms—withscaledrawingsinmind!

Ask students to look or interesting challenges and what things might make a drawing easyor difcult.

• Haveeachstudentchoosearoomattheendofthewalk.

Sessios 6–9: Movig Beod the Classroom

WhattoDo

• Beforestudentsworkindependentlysketchingaroomintheschool,besuretogetapproval

rom other adults and be sure to go over behavior expectations or independent work. Set a

time or all students to be back in your classroom.

• Havestudentssketchtheirchosenroom.• Havestudentsmeasuretheirroom,calculatethescaleddimensions,andcreatetheir

scale drawing.

Sessio 10: Examiig the Sketches

WhattoDo

• Leadagallerywalkofthestudents’rstsketchwithmeasurements,theirmath

calculations, and their fnal scale drawings.

• Havestudentsusetherubrictoassesseachother’sdrawings.Youcandesignatewhowill

assess which drawings so that there is time or all the drawings to be assessed by someone.

Exted• Showoffthescaleddrawingsprojectatafamilynight.

• Goastepfurtherwiththemeasurementsandhavestudentsmeasureacompletewalland

fgure out how much paint they would need to paint it.

Outcomes to Look or• Cooperativeandindependentlearning

• Students’abilitiestoconvertlargemeasurementsintosmallermeasurements• Finishedproducts

• Peerreviewofnishedproducts





Sample Rubric or Scale Drawig

4 3 2 1

The drawing is nearly

perfect to scale.

The drawing is close

to scale.

The drawing

considers scale.

The drawing shows

little use of scale.

The labels meet

professional standards.

The labels are near

professional.

The labels show

minimum standards.

The labels do not

meet standards.

Checklist

p Measurements on the scale chart are accurate and complete.

p Scale is included on right-hand lower corner o the fnished drawing.

p All dimensions are labeled.





Reflection









Academic Erichmet


activity un?











Math Tools

What Is It?The practice MathTools includes pictures, rulers, symbols, technology, and concrete materials

such as beans, blocks, or other manipulatives that allow students to problem solve. Math

Tools can help students measure, count, sort, and evaluate math problems.

What Is the Cotet Goal?A central goal o MathTools is to help students learn to use tools and objects to problem solve

and enhance their understanding o targeted math concepts and skills. Specifc content will

vary depending on the lesson, learning goals, and connection to the day-school learning.

What Do I Do?Begin by talking to the day-school teacher. Find out what concepts and skills students are

learning, and how tools can enhance their learning. Develop activities that students will enjoy,

where they can play with dierent objects and learn to use tools to problem solve. Provide

an assortment o tools to tap students’ interest and help them see a variety o approaches to

problem solving. Make connections between the tools and the corresponding mathematical

idea you want students to learn. It is tempting to get out the manipulatives and show

students how to use them, but MathTools work best when students fgure out on

their own how the tools can help them solve a problem. Finally, allowstudents to discuss how specifc tools contributed to their

thinking about mathematics.

Practice 5





Wh Does It Work?When tools are used productively to teach and learn mathematics, students see connections

among objects, symbols, language, and ideas. Students who are provided with mathematical

tools use them to explore concepts and to build mathematical understanding.Additionally,toolshelpstudentsthinkexiblyaboutmathematics,usecreativitytosolvenew

mathematics problems, and explore mathematics with less anxiety. Because the nature o

aterschool is active and social, aterschool settings are ideal or allowing students to explore,

test, build, think, talk, connect, and reason with mathematical tools.





video

Getting Starte

Go to the FindingandSolvingProblems practice ound in the technology

section o the Aterschool Training Toolkit (www.sedl.org/aterschool/toolkits/ technology/pr_fnding_solving.html). Click on the “Hide and Seek with

Geocaching” video. Middle school students are working with a new tool that

will help them with longitude and latitude measurements.


involve your students in using math tools.


math tools.



them started?


engaged?









Lesson 1

Tangrams

In this lesson, students study geometric shapes. The shapes are puzzle

pieces or one large square. Students cut out the pieces and move them

around to fgure out how they go together to make a square. Once they

have fgured it out, students can color and paste their pieces together on

construction paper.


Duratio:

45–60 minutes

Studet Goals:

• Understandingofhowgeometricshapesttogether

• Improvedskillsatcuttingandpasting

• Understandingofthewordtangram

Curriculum Coectio:The Arts

Stadards:



GradesK–2

Benchmark 2: Understands the common language o spatial sense

Benchmark 4: Understands that patterns can be made by putting dierent shapes together ortaking them apart





Imagie This!Mixing arts and crats with math in aterschool will make learning geometry un! Ater

students cut out their geometric shapes, watch their minds puzzle through the shapes as

they visualize how to make them into one square. And then students get the opportunity tobeautiy their fnal product and take it home!

What you needp Scissors

p Glue

p Markers or paint

p Construction paper

p Tangram shapes (Handout 10)

What to Do• Havestudentscutouttheshapes.

• Thenhavestudentsmovetheshapesaroundinseveralcongurationstogureouthow

they ft together as a square.

• Havethestudentscolor(orpaint)thepiecesandpastethecompletedsquareonto

construction paper.

• Havethestudentslabeltheirnishedproduct“TangramPuzzle.”

• Havethestudentswrite(ortalk)abouttheprocesstheywentthroughtogureout

the puzzle.

Outcomes to Look or• Studentrecognitionofgeometricpatterns

• Enhancedcuttingandpastingskills

Vocabulary

Quadrilateral: a fgure with our sides and our angles

Tagram: a shape that consists o seven pieces, called tans, which fttogether to orm a shape o some sort

Triagle: a fgure with three sides and three angles





Hadout 10: Tagram Shapes





Reflection









Academic Erichmet


activity un?







Lesson 2

Growing Rock Cany

In this lesson, the instructor can either make the rock candy solution in

advance or incorporate cooking into the lesson. Students observe the

growth o rock candy over a given length o time, record data rom their

observations, and graph the changes they observe.


Duratio:

1 week o observation ollowed by a 1-hour lesson

Studet Goals:

• Recognizepatternsandtherulesthatexplainthem

• Usemathematicsvocabularytodiscussobservedgrowthpatterns

• Selectanduseappropriatetoolstomakemeasurements

• Organizeanddisplaydatainsimplechartsandgraphs

• Observegrowthpatternsfromatableandgraph

Curriculum Coectio:

Science

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks).The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.


Grades3–5



Grades3–5

Benchmark 5: Perorms basic mental computations

Stadard 4: Understands and applies basic and advanced properties o the concepts o measurementGrades3–5

Benchmark 2: Selects and uses appropriate tools or given measurement situations

Benchmark 5: Understands that measurement is not exact

Benchmark 7: Selects and uses appropriate units o measurement, according to type and size o unit


Grades3–5

Benchmark 1: Understands that numbers and the operations perormed on them can be used todescribe things in the real world and predict what might occur

Benchmark 2: Understands that mathematical ideas and concepts can be represented concretely,graphically, and symbolically





Imagie This!You have ound a way to make candy that grows! Students just won’t believe that something

they cook and can eat later actually will grow right beore their eyes. Their daily observations

will make it all real as they observe, collect data, and chart their data. You know they aredying to taste it ater all the calculations are done!


p Pencils (two per student)

p Ruler (cm)

p One 6-inch piece o string per student

p 3 cups o granulated sugar per student

p 1 cup o water per studentp One clean glass jar per student

p Food coloring

p Stove

p Saucepan

p Spoon

Gettig Read• Priortotheactivity,maketherockcandysolution.Or,youmightchoosetoincorporate

cooking into the activity.• Inamediumsaucepan,heatthe1cupofwaterand2cupsofsugar.Stiruntilthesugar

is completely dissolved. Gradually add a ew drops o the ood coloring and the additional

sugar, stirring continuously until all the sugar is dissolved.

• Designateanareawheretherockcandycangrowwithoutbeingdisturbedfor

approximately 1 week. Students will need access to this area to measure growth. Limit

movement o the rock candy once it has started growing.





What to Do• Usingtherockcandysolution,setupthegrowingareaforthecandy.Pourthesolutioninto

a clean glass jar, tie the string to the pencil, and suspend it across the mouth o the jar so

that the ends hang into the sugar water. See set-up illustration on page 161.• Havestudentsdevelopatablecontainingthreecolumns:Time(days),Height(cm),and

Change(cm).TheyshouldllintheinitialrowwithTime=0andHeight=0,leavingthe

Change row blank.

• OnDay2,givestudents10to15minutestomeasuretheirrockcandygrowth.The

students should remove the string rom the water and careully measure the height o the

rock candy. Students should enter this inormation on the next row o the chart and this

timecompletetheChangecolumn(change=today’sheight−yesterday’sheight).

• Continuehavingstudentschartgrowthovermultipledaysuntilmeasurablegrowth

has ceased.

• Onthenalday,havestudentsusegraphpapertocreatealinegraphofthecandygrowth.

One axis should be height, and the second axis should be time.

• Usingthisdata,studentsshoulddescribehowtherateofgrowthvariedovertime.

Encourage them to look not only at the height per day but at what has happened between

the recorded heights.

Outcomes to Look or• Useofvocabulary(suchas slow,fast,increase,decrease) to describe what has happened

between each measurement taken

• Students’abilitytofocusnotsimplyontheheightmeasurementbutonwhathashappenedbetween the recorded heights

• Commentsandanswersindicatingthatstudentsarelisteningto,monitoring,andapplying

the problem-solving strategies o their peers





Set-up illustration:

Sample table or rock candy growth:

A line graph illustrating the growth o rock candy:





Reflection









Academic Erichmet


activity un?











Lesson 3

Graphing Cany With Spreasheets

In this lesson, students predict how many M&Ms are in a bag, then collect

data and graph their fndings in Excel. They learn how to log data on a

data chart and make a graph rom the data.


Duratio:

45–60 minutes

Studet Goals:

• Collectdatathroughobservations

• Representdatausingtablesandgraphs(bymeansofExcel)

• Usedataforavarietyofpurposes(formulatinghypotheses,makingpredictions,testingconjectures)

• Determineprobabilityusingsimulationsorexperiments• Enterdataintoaspreadsheet,useformulastoupdatesolutionsautomatically,andcreateapiegraph

• Useratiosandproportionstorepresentrelationshipsamongquantities

• Explainandjustifytheirthinking

Curriculum Coectio:

Science, Technology

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004; www.mcrel.org/standards-benchmarks).The mathematics portion o the database was developed

using National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.


Grades5–8

Benchmark 5: Knows the dierence between pertinent and irrelevant inormation whensolving problems

Benchmark 6: Understands the basic language o logic in mathematical situations

Benchmark 7: Uses explanations o the methods and reasoning behind the problem solution todetermine reasonableness o and to veriy results with respect to the original problem





Stadard 2: Understands and applies basic and advanced properties o the concepts o numbersGrades5–8

Benchmark 7: Understands the concepts o ratio, proportion, and percent and the relationshipsamong them


Grades5–8

Benchmark 4: Selects and uses appropriate computational methods a or a given situation

Benchmark 6: Uses proportional reasoning to solve mathematical and real-world problems


Grades5–8

Benchmark 5: Uses data and statistical measures or a variety o purposes

Benchmark 6: Organizes and displays data using tables, graphs, requency distributions, and plotsStadard 7: Understands and applies basic and advanced concepts o probability

Grades5–8

Benchmark 2: Determines probability using simulations or experiments

Benchmark 5: Understands the relationship between the numerical expression o a probabilityand the events that produce these numbers

Imagie This!Computers and candy sound like a good combination or aterschool students. Ater making

predictions and writing ratios about M&Ms, students navigate through an Excel spreadsheet.

And i you give them permission, they’ll munch on those M&Ms while they chart their data.

What you needp One computer or every two to three students

p An electronic spreadsheet application, such as Excel, and word processing sotware, such

as Word, or writing summaries o fndingsp Internet access or instructor and student computers (optional)

p Small bags o M&Ms (one bag per student)

p Copies o Handout 11: Graphing Candy With Spreadsheets





Gettig Read• Makesurethatstudentshavebasickeyboardingskills;knowhowtoopen,close,and

savedocuments;andknowhowtoopenandnavigatesoftwareapplicationssuchasExcel

and Word.• Makesurethatyouknowhowtoopen,close,andsavedocuments,andhowtocreatean

Excel worksheet (including using ormulas) and use Word.

What to Do• Tobeginthislesson,havestudentsestimatethenumberandcolorofcandiesinsidetheir

small bags.

• Aftertheestimationshavebeenmade,studentsopentheirbagstosort,classify,count,and

record the M&Ms. Direct students to write ratios to represent their fndings.

• Technologyplaysanintegralpartintheremainderofthislesson.Followingthecollection

o data, have students use an electronic spreadsheet to create a graph o their fndings.

Review and print the detailed description in Handout 11: Graphing Candy With

Spreadsheets.

• Whenstudentsnishcollectingdata,havethemcompileasetofeveryone’sndingsto

estimate the number and color o M&Ms in a mystery bag.

• Inordertowinthemysterybag,studentsmustnotonlymakeaconjecturebutalsoexplain

their reasoning using the data sets.





Teaching Tip

Ratios

A ratio is a comparison between twonumbers, usually represented by twonumbers separated by a colon. Students canfnd multiple ratios with the colored candies.For example, you may ask them to fnd theratio o yellow candies to brown candies.I there are seven yellow candies and ninebrown candies the ratio o yellow to browncandies would be represented by 7:9. Whenusing ratios, the order o numbers and wordsis important. The numbers should be writtenin the same order as stated. For example,

in the ratio o yellow to brown candies thenumber o yellow candies is written in ronto the colon while the number o browncandies is written behind it.

To compare ratios, change the ratio to araction, with the frst number becoming thenumerator and the second the denominator.Using the example above, the ratio 7:9would become 7/9. The ratios are equal ithefractionsareequal;forexample,7:9=14:18because7/9=14/18.


• Answersthatreectanunderstanding

o prediction• Abilitytoexplainmathreasoning

• Ratiosthatrepresenttheactualndings

• Reasonableconjecturesbasedonthe

class set

• Appropriateuseofaspreadsheettocreate

a graph





The M&M candy makers claim there is a certain percentage o each color in every bag.

Let’s see i they are right. Make a spreadsheet to calculate the number o each color thatshould be in each bag, based on the percentages that the candy maker tells us. Then you

will open a bag o M&Ms, count them, and make a comparison to see i the M&M candy

makers are right.

1. First open up your spreadsheet application (Microsot Excel).

2. Click on Start…Programs…Microsot Excel.

3. When Microsot Excel opens, a blank spreadsheet will appear like the one below. I it

does not automatically appear, you can click on File…New…New Workbook to start a

new spreadsheet fle.

4. The M&M candy makers say that a bag contains the ollowing color o candies:

10% blue 30% brown 10% green 20% red

10% orange 20% yellow

5. Create a spreadsheet to do some counting and comparisons.

Set up your table by ollowing the steps below:

Coutig ad Comparig:

1. Create a title in A1 (M&M Color Comparisons)

2. Create a label or cell A2 (Total M&Ms) total

number o M&Ms in your bag in cell B2

(don’t eat any yet!)

3. Create and label columns A3 (color) and B3 (% o total).

4. Enter the colors and the company percentage in the

columns and rows (A4–A9 and B4–B9).

Hadout 11: Graphig Cad With Spreadsheets





Next, fgure how many o each color should be in your bag (Column C) based on the

company’s ormula. For example, to determine the number o blue, multiply the totalnumber—intheexampleshown,thetotalis65(B2)—bythepercentageofblues

(.10or10%—showninB4).PlaceyourcursorincellC4andtypethisformula:

=sum($B$2*B4)andpresstheReturnkey.ThecorrectsumwillappearinC4.Usethe

same procedure to determine the number o other colors. Be sure to use the correct cell

numbers in your calculations.

Now, count the actual number o each color and enter those numbers as comparison

with what the candy maker said should be in the bag.

Determie the actual percetage o each color i our bag o M&Ms.1. Use this ormula, which will divide the number o an individual M&M color by the

totalnumberofM&Ms(todetermineitspercentofthetotal)=SUM(E4/E10)

2. Use the same ormula or each color. Be sure to use the correct cell number in your

calculations.

3. Create a new column to display your results.

4. Were the percentages the same?

5. Create another column to calculate the dierence.

6. What ormula did you use to do this?7. What might explain the dierence?

Explore o our ow1. Create a chart rom your data. To do this go to “Insert” and then “Chart” and then

ollow the instructions that appear.

2. Change the look o your spreadsheet with Word Art, borders, or clip art.

3. Remember to save your work.





Reflection









Academic Erichmet


activity un?











Lesson 4

Learning Math an Msical PitchesWith Water Bottles

In this activity, students put dierent amounts o water into glass beverage

bottles to make various musical pitches to create a musical instrument.

They learn how to relate volume to tones and pitches, and measure water

volume by standard systems. Next, students learn to create and use a

mathematical ormula to calculate the volume o the air in the bottles. They

convert the standard unit measuring system to the metric system and fgure

out the percentage o air and o water in each bottle. The session ends with

a concert using the musical instruments that the students made.


Duratio:

90 minutes

Studet Goals:

• Createamusicalinstrumentusingwaterinbottles

• Measurethevolumeofwaterineachbottle

• Createanduseamathematicalformulatomeasurethevolumeofairinthebottles

• Calculatethepercentageofwaterandofairineachbottle

• Convertthevolumeofwaterfromuidouncestomilliliters

• Playasimplesongwiththebottles

Curriculum Coectio:

The Arts

Stadards:



Grades6–8

Benchmark 3: Understands the relationships among linear dimensions, area, and volume and thecorresponding uses o units, square units, and cubic units o measure

Stadard 8: Understands and applies basic and advanced properties o unctions and algebra

Grades6–8

Benchmark 1:. Knows that an expression is a mathematical statement using numbers and symbolsto represent relationships and real-world situations





Imagie This!Your room is flled with water bottles, water, measuring devices, and recording charts! As

students make a musical instrument by putting specifed amounts o water in each bottle,

you circulate among them. Once the students have successully created the specifed musicalinstrument, they measure and record the amount o water in each bottle. Groups collaborate

to fgure out a ormula or calculating the amount o air in a bottle. They then use their

ormula to calculate and record the amount o air in each bottle and convert their volumes o

ounces into milliliters. For the fnal activity, each group will perorm a short musical melody.

What you needp Five identical glass beverage bottles per group (each group may have a dierent set o

identical beverage bottles to compare sounds o the various groups’ bottles in the class).

p Water or each group

p Measuring cups with the standard unit o measure or each group

p Rulers

p Paper

p Pencils

p Recording chart and water markers or each group

p One permanent marker or each group

Gettig Read• Assemblematerialsforeachstudent(ruler,paper,andpencil).

• Assemblematerialsforeachgroup(veglassbeveragebottles,water,measuringcupswith

standard unit o measure, recording chart, and markers).

• Postamountofwatertoputineachwaterbottleasfollows:(19oz/570ml);(13oz/390

ml);(11oz/330ml);(8oz/240ml);and(6oz/180ml).

• Postthestepsinthedirectionsforthegroupstofollow.

• Postthestructureofthechart(waterinoz,waterinml,airvolume).





What to Do• Dividestudentsintogroupsofvebasedonwhowillworkwelltogether.

• Gooverexpectationsforbehaviorandconductforthelesson.

• Giveeachstudentaruler,paper,andpencil.Giveeachsmallgroupglassbeveragebottles,a measuring cup, water, ruler, recording chart, and markers.

• Postthedirectionsbelowandgooverthedirectionsforthelesson:

- Students fll their beverage bottles with the posted amount o water.

- Using permanent markers groups number the bottles rom 1 to 5, with 5 or the largest

amount o water and 1 or the smallest amount.

- Groups record the amount o water in each bottle in ounces on the group chart.

- Groups use the ormula to calculate and record the amount o air in each bottle. (Air

equalsthetotalVolumeinbottleminusWater)or(A=V−W).

- Groups convert the standard unit measure o ounces to milliliters in the metric system.- Groups fgure out the percentage o water and the percentage o air in each bottle.

• Havegroupsfollowthedirectionsasyoucirculateamongthem.

• Asalargegroup,comparethegroups’calculationoftheamountofairandwaterineach

bottle and the percentage o air and water.

• Havestudentsarrangetheirbottlesofwaterinorderfromlargestamountofwaterto

smallest.

• Haveeachofthevestudentsinthegroupsalignhimselfofherselfbehindabottle.

• Now,forthenalactivity,havestudentsusetheirrulerstoplaysimplenotepatterns,

progressing to simple songs.

Teaching Tip

Go over directions and behavior expectationsbeore having group members start theirworktogether.Brieyreviewtheformulafor

fguring out the volume o air in the bottles,the standard units and metric units o

measurement, and percentages. Answer anyquestions that students have.





The Data Studets Record• Groupsrecordtheamountofwaterineachbottleonthegroupchartinounces.

Answersare19oz,13oz,11oz,8oz,6oz

• Groupsutilizeaformulatodeterminetheamountofairinthebottles.

(Formulais:Air=totalVolumeinbottle–Water)(A=V−W)

Answerswillvarydependingonthesizeoftheirbottles.

• Groupsconvertouncestomilliliterinthemetricsystem.(1uidoz=29.6milliliters)

Answers:19oz/562ml;13oz/385ml;11oz/326ml;8oz/237ml;6oz/178ml

• Groupsgureoutthepercentageofwaterandthepercentageofairineachbottle.(Addthe

volume o the air and water. Divide the air by the total to get the percentage o air. Divide

the water by the total to get the percentage o water.)

Exted• Providestudentswiththreeadditionalbottles.Havestudentspredicthowmuchwaterit

will take in each additional bottle to make a whole octave. Have them fll their bottles with

the amount o water they predicted to see i their predictions are correct.

• Askstudentstoconvertthepercentageofwaterandairinthebottlestodecimals.

Outcomes to Look or• Increasedknowledgeofhowmathisusedinmusic

• Increasedknowledgeofpitchandvolume

Vocabulary

Customar sstem:a system o measurement used in the United States(thebasicuidounceorcup)

Metric sstem: A system o measurement based on tens (the basic unit ocapacity is the liter)

Octave: A musical interval o eight notes

Ouce (oz): a customary unit o weight equal to 1/16 o a pound

Pitch: the level o a sound

Volume: the number o cubic units it takes to fll a solid





Reflection









Academic Erichmet


activity un?











Lesson 5

Geometric Shape Spotting

In this lesson, students work to identiy common shapes in their everyday

lives. They use a digital camera to record the shapes they have spotted

around the school.


Duratio:

Three 1-hour sessions, with a gallery night or parents

Studet Goals:

• Recognizethree-dimensionalshapesintherealworld

• Learnthetwo-dimensionalrepresentationofthree-dimensionalshapes

• Reviewthevocabularyofthree-dimensionalshapes

• Workcooperativelywithpeers

• Useanewtool,adigitalcamera

Curriculum Coectio:

The Arts, Technology

Stadards:



GradesK–2


Benchmark 3: Understands that geometric shapes are useul or representing and describing realworld situations





Imagie This!Youngphotographersareseekinggeometricshapes—circles,triangles,squares,and

rectangles—aroundtheclassroomandtheschoolbuilding.Astheytakeashapewalk,

students write the name and picture o the shapes on index cards, so they can place the cardsin ront o the shapes they fnd in the school. Once a shape is ound and identifed with an

index card, the young photographers are ready to take a digital picture o the shape! As true

photographers, they will showcase their photo-geometric art in a class gallery or parents to

come to see.

What you needp Three-dimensional physical models o a triangular prism, rectangular prism, cube, sphere,

and cone

p Shape cards with two-dimensional pictures o the geometric solids, triangular prism,

rectangular prism, cube, sphere, and conep Name cards with the names o the geometric shapes, triangular prism, rectangular prism,

cube, sphere, and cone

p Digital camera(s)

p Index cards

p Markers

p Printer with a new color cartridge

p Copy paper

p Construction paper

Gettig Read• Createthenamecardsandshapecardspriortotheactivity.Createatleastfoursets.You

will use these as a model or students to copy later.

• Priortotheshapewalk,allowstudentstopracticeusingthedigitalcamerassothatduring

the shape walk they are learning about the shapes and not about how to use the cameras.

• Determineanareaintheschoolorbuildingthathasmanyoftheseshapesforthestudents

to take a walk through and take pictures.

• Enlistthehelpofotheradultsorolderstudentsfortheshape-walksession.

• Takeafewpicturesofyourowntoprovideasmodels.

• Mountthepicturesonconstructionpapertomodelhowtodothisforthegallery.





Sessio 1: Reviewig Shapes

WhattoDo

• Usingthephysicalmodelsoftheshapes,

review with students the names o theseshapes. Say the name o the shape and

have students repeat the name. Show them

the name o the shape in print.

• Thenreviewwiththestudentswhatthe

two-dimensional sketches o these shapes

look like. Show students the cards that you

made as well as other two-dimensional

pictures o these shapes.

• Askthestudentstolookaroundtheclassroomtondexamplesoftheseshapes.Asthe

students point out examples, have them label the object using either the two-dimensionalsketch or a name card that you have prepared.

• Allowallstudentsachancetosuccessfullyndanexamplewithintheclassroom.

• Next,havethestudentscreatetheirownshapelabelsusingtheindexcards.Theshape

labels should have a two-dimensional sketch o the shape along with the name o the shape.

Sessio 2: Takig a Shape Walk

WhattoDo

• Reviewschoolrulesandbehaviorrulesbeforestartingtheshapewalk.

• Practiceusingdigitalcamerasbeforethewalk.Makesureeveryonehasachancetotryout

a camera beore you begin.

• Breakthestudentsintosmallergroupsfortheshapewalk.Oneadultshouldbewitheach

small group. Group size will be determined by the number o digital cameras available but

should be no larger than our students per group.

• Allowstudentstowalkaroundtheschoolorbuildingandndthefourgeometricshapes

you have been studying. The shapes can be either artifcial or natural.

• Havestudentslabelandtakepicturesofdifferentshapes.Studentsshouldincludethe

shape labels in the pictures to indicate what shapes they are photographing.

Teaching Tip

Help students understand that they can

recognize shapes even when the objectsthey see are not exactly like the shapes theyimagine. For students who are strugglingwith this task, give them only one shape tolook or during the walk.





Sessio 3: Preparig a Galler Show

WhattoDo

• Beforethenextclass(orduringtheclass,ifyouwish),printthestudents’pictures.(Printing

them on copy paper is fne.)

• Havestudentspreparetheirpicturesforagalleryshowoftheirworkbygluingtheirphotos

on construction paper.

• Decidewherethegalleryofstudents’workwillbeshowcasedandhavethestudentsmount

their photos in that spot.

Exted• Inviteparentstocomeandseethegallery.Studentscantaketheirparentsonashapewalk

around the school and show them the geometric shapes they ound and photographed.

Juice and cookies would round out the evening!


• Usingtoolsproductively

• Answersthatreectanunderstandingofshapesintherealworld

• Correctuseofmathematicaltermswhendescribingshapes

• Studentrecognitionofgeometricshapesintheworld

Vocabulary

Circle: a two-dimensional fgure ormed by a curved line surrounding acenter

Cube: a solid fgure with six square aces

Rectagle: a two-dimensional fgure with our right angles and our sides

Rectagular prism: a solid fgure with six rectangular aces

Solid fgure: a three-dimensional fgureSphere: an object similar in shape to a ball

Square: a two-dimensional fgure with our right angles and our equal sides

Triagle: a two-dimensional geometric fgure ormed o three sides andthree angles

Triagular prism (pramid): a solid fgure with our triangular acesand a rectangular base





Reflection









Academic Erichmet


activity un?















Math Ttoring

What Is It?MathTutoring involves working with students on specifc math skills. This work can take place

in ongoing one-on-one or small-group sessions. Tutors, students, and day-school teachers

work together to identiy skills or areas where students need help and design activities and

review sessions to build specifc math skills.

What Is the Cotet Goal?The key goal o MathTutoring is to provide problem-solving experiences that build students’

understanding o specifc math acts and skills. The content o MathTutoring draws rom theday-school learning and the specifc concepts and skills identifed or each student.

What Do I Do?Begin by talking to the day-school teacher to fnd out what math concepts and skills students

are learning, the standards or each grade level, and which students need help. For each

student, identiy with the day-school teacher the specifc math acts or skills that are difcult,

examples o problems that the student struggles with, and activities that could help clariy

a concept and build understanding. Talk to the individual students as well and ask them

what math skills are difcult or them, what their strengths are, and what kinds o activities

they are interested in. Fun activities engage students and increase their desire to learn. Oncespecifc skill areas have been identifed, determine short- and long-term goals. For example,

i a younger student is struggling to add two-digit numbers, a short-term goal would be to

master equations using base-10 blocks or other manipulatives. A long-term goal would be or

the student to be able to add without using manipulatives. Provide regular, positive eedback

to encourage students to succeed. At the end o each tutoring session, allow time to discuss

what was learned and what skills and activities require more practice.

Practice 6





Wh Does It Work?Research indicates that regular, high-quality one-on-one tutoring may be the most eective

aterschool activity or improving academic achievement. One-on-one and small-group

mathematics tutoring rom well-trained sta allows aterschool programs to target students’individual strengths, weaknesses, and interests by providing direct, diagnostic mathematics

instruction and mentoring. This type o tutoring is most eective when tied to the day-school,

which allows children to practice and reinorce what they are learning in the classroom.





video

Getting Starte

Go to the One-on-OneandSmall-GroupTutoring practice ound in the

literacy section o the Aterschool Training Toolkit (www.sedl.org/aterschool/ toolkits/literacy/pr_tutoring.html). Click on the video “One-on-One Tutoring”

taken at Delaware Elementary School in Indiana. In addition, you can go to

the Tutoring,MentoringandBuildingStudySkills practice in the homework

section o the Aterschool Training Toolkit (www.sedl.org/aterschool/toolkits/homework/pr_

study_skills.html) to see a video or math tutoring.


involve your students in math tutorials and tutoring.

BEFORE yOU WATCH THE VIDEO, write down what you already know about one-on-one

tutoring and math tutorials or both.



them started?

How does the instructor interact with the kids? What does he or she do to keep them engaged?









Lesson 1

One-on-One Ttoring

This lesson provides a starting point or how one-on-one tutoring can

be used to enhance student learning in aterschool. Using day-school

teachers’ recommendations, the aterschool instructor provides a student

with tutoring that either targets math skills where the student needs

support or involves enrichment activities that enhance math strengths.


Duratio:

Sessions o 15–20 minutes

Curriculum Coectio:

Various Connections

Stadards:







Measurement


Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!Your class is busy working in small, cooperative groups on homework today. This gives you

the opportunity to pull one student at a time out o the groups or 15 minutes apiece so that

you can work one-on-one with each student on a math skill that the day-school teacher hasasked you to address. In the space o a 90-minute class, you have time to work with six

students individually.

What you needp Pens and pencils

p Writing materials

p Computer (optional)

p Manipulatives (optional)

p

Materials and assignments rom day school

Gettig Read• Meetwithday-schoolteacherstoidentifystudentswhoneedsupportorenrichment

activities;learnmoreaboutthestandardsandbenchmarksateachgradelevel;andidentify

specifc skill areas, strengths, and learning goals or each student.

• Workwithday-schoolteacherstodevelopanassessmenttoolforeachstudent’slearning

goals. Discuss and design projects and activities that will give students opportunities to

practice specifc skills and that will indicate that students are learning.

• Findaquiet,comfortableroomwherestudentscanfocusonthetaskathand.

What to Do• Begintutoringsessionswithadiscussionoftheday’sgoalstomakesurethatstudents

understand what they are supposed to do. You might ask, “How will we know you learned

this?”

• Previewthestepsinvolvedinthatday’ssessionandworkwithindividualstudentson

each step. Encourage students to ask questions as they move through each problem. Ask

questions that encourage students to talk about their approach to the problem.

• Occasionally,teachersrequestthattutorsspendtimeworkingthroughhomeworkduring

tutoring sessions. Balance homework help with other eorts to keep students interested inand ocused on independent learning projects.

• Providepositivefeedbacktoencouragestudents’success.

• Debriefwhatwasaccomplished.Eachsessionshouldendwiththetutorandstudent

discussing what was accomplished and what needs to be done to prepare or the next

session. Tutors should be willing to allow students to pursue new questions or ideas i this

exploration will contribute to deeper understanding o the content.






• Progressinidentiedskillareas

• Increasedcondenceinidentiedskillareas

• Answersthatreectincreasedunderstandingoflearninggoals

• Studentscommunicatingaboutwhattheyhavelearnedandhowtheylearned





Reflection









Academic Erichmet


activity un?







Lesson 2

Small-Grop Ttoring

This lesson provides a starting point or how small-group tutoring can

be used to enhance students’ learning in aterschool. Using their day-

school teachers’ recommendations, the aterschool instructor has students

work in small groups either on activities that target specifc math skills

and areas where students need support, or on enrichment activities that

enhance their strengths.


Duratio:

20–30 minutes

Curriculum Coectio:

Various Connections

Stadards:







Measurement


Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!Your classroom is humming with small cooperative groups o students helping each other in

math concepts and skills. Older students can be your teachers or younger students by guiding

them through ractions or multiplication, while at the same solidiying their own math skills.

What you needp Pens and pencils

p Writing materials

p Computer (optional)

p Manipulatives (optional)

p Materials and assignments rom day school

Gettig Read• Meetwithday-schoolteacherstoidentifystudentswhoneedsupportorenrichment

activities;learnmoreaboutthestandardsandbenchmarksateachgradelevel;andidentify

specifc skill areas, strengths, and learning goals or each student.

• Workwithday-schoolteacherstodevelopanassessmenttoolforeachstudent’slearning

goals. Discuss and design projects and activities that will give students opportunities to

practice specifc skills and that will indicate that students are learning.

• Groupstudentsbasedoncommonlearninggoalsandskills.

• Selectmaterialsandprepareactivitiesforeachstudenttoworkon.





What to Do• Denetheday’sgoalsandskills.Begintutoringsessionswithadiscussionoftheday’s

goals. Ensure that the learning goals are ones that the students are invested in achieving by

asking a question such as, “How will we know you learned this?”• Groupstudentsandmonitorbothcollaborationskillsandlearningprogress.

• Encouragestudentstoworktogether;askquestions;andcommunicateabouttheactivity,

how they are approaching the problem, and what they are learning.

• Balancehomeworkhelpwithothereffortstokeepstudentsinterestedinandfocusedon

small-group activities and independent learning goals.

• Providepositivefeedbackandencouragestudents’success.

• Debriefwhatwasaccomplished.Eachsessionshouldendwithadiscussionofwhatwas

accomplished and what needs to be done to prepare or the next session. Tutors should be

willing to allow students to pursue new questions or ideas i this exploration will contribute

to deeper understanding o the content.











Reflection









Academic Erichmet


activity un?







Lesson 3

Learning With Ttorials

You can increase both students’ math knowledge and technology skills

with a computer arrangement. Using age-appropriate tutorials rom the

Internet, CDs, and DVDs, you can set up a study center where students

learn rom tutorials. In your ongoing conversations with your students’ day-

school teachers, ask which areas o math students need the most help

with or tutorials in aterschool.

Grade Level(s):

K–12

Duratio:


Studet Goals:

• Enhancestudents’understandingofmathconcepts

• Increasetechnologyskills

• Increasestudents’abilitiestondanswersthemselvesandworkindependently

Curriculum Coectio:

TechnologyStadards:


The standards addressed would depend on the content and the grade level o the students. Beloware the categories o math standards that could be addressed.


Patterns, Relationships, and Algebraic ThinkingGeometry and Spatial Visualization

Measurement


Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!In an aterschool class, each student needs individual help with his or her learning. The

schedule and class size make it difcult to tutor each student individually during the

aterschool session. However, the class has access to two computers, one with Internet accessand the other without. The class also has access to the school library computers.

What you needp Student computers with multimedia capability

p Internet access or instructor and student computers

p Adult volunteers

Gettig Read• Discussthestudents’needswiththeday-schoolteacherstodeterminethemost

appropriate tutorials.

• Whenselectingtutorials,considercontent,age,andgenderappropriateness,and

compatibility with your computer and operating system.

• Reviewyourafterschoolprogram’sInternet-usepolicyandrules,andreviewthesewith

your students. Post these rules where they can see them.

• Arrangeforanadultvolunteertohelpyouontutorialdays.

• ConsiderusingsomeofthefollowingWebsites:

- Learn 4 Good Kids’ Corner: ree access to hundreds o educational games, activities,

worksheets, and lessons (www.learn4good.com/kids)

- Pitsco’s Ask an Expert (http://askanexpert.com)

- Ask Dr Math (http://mathorum.org/dr.math/dr-math.html)

- TheMathTutor(www.iegler.com/mathman.htm)

- Math.com (www.math.com/)





What to Do• Directstudentstoappropriatecomputers.

• Explainthefocusoftheactivity.

• Showstudentshowtoaccessthesitesyouhavechosenandthenhavethemtry the tutorials.

• Ifseveralstudentshavethesameneed,thenconsiderhavingthemworkasateam.

• Monitorthetimestudentsspendworkingonthetutorials.Helpstudentsstayfocusedon

the tutorials and use the Web sites appropriately.

Exted• Checkwiththeday-schoolteachertoseeifcomputerenrichmentactivitiesareavailableas

part o the supplementary textbook materials students use during the day.










Reflection









Academic Erichmet


activity un?







Lesson 4

Homework Help: Ask an Expert!

With only one computer and Internet access, you can provide your

students with math homework help. Using the best ask-an-expert Web

sites, set up a cyber study center where students ask online experts

questions related to their homework assignments. In your ongoing

conversations with your students’ day-school teachers, ask which topics

students should discuss with experts.


Duratio:


Studet Goals:

• Completeandturninhomeworkontime

• Correctlyaddresshomeworkinstructions

• Evaluateinformationprovidedfromonlinesources

• Expressquestionsbywritingaccuratelyandresponsibly

Curriculum Coectio:

TechnologyStadards:






Measurement


Problem Solving

Reasoning and Proo

Communication

Connections





Imagie This!It’s homework time in the aterschool program. As students get out their books and

notebooks, two eighth-grade girls gather at a computer to help each other with their math

homework. They are struggling with a geometry problem on perimeters. Ater logging on toa math-mentoring Web site, they search the orum archives or questions and answers about

perimeters. They fnd some messages that help them answer most o their problems but

remain stumped on two questions. They post a question to the online math expert and log on

the next day to see what responses they have received.

What you needp Instructor computer with Internet access and projector

p Student computer(s) with Internet access

p Bookmarked ask-an-expert Web sites

p Adult volunteer or student aide

Gettig Read• Lookoverthefollowingask-an-expertWebsites:

- Pitsco’s Ask an Expert (http://askanexpert.com)

- Ask Dr. Math (http://mathorum.org/dr.math/dr-math.html)

- Jiskha Homework Help (www.jiskha.com)

- AllExperts (http://allexperts.com)

- Inoplease Homework Center (www.inoplease.com/homework/hwhelper.html)

• Arrangeforanadultorolderstudentvolunteertoassiststudentswiththeask-an-

expert process.





Sessio 1: Gettig Read

WhatYouNeed

p Instructor computer with Internet access and projector

p Bookmarked list o ask-an-expert Web sites

WhattoDo

• Tellyourstudentsthatyouaregoingtoshowthemhowtondanswerstotheirmost

challenging homework questions.

• Showstudentsthelistofask-an-expertWebsitesandhowtoaccessthosesites.

• Reviewrulesonaskingaquestion.Theserules,suchasthosefoundonPitsco’sAskan

Expert Web sites (http://askanexpert.com), should be common to most o these sites.

• Remindstudentsthattheseexpertswillnotdotheirhomeworkforthembutarerather

resources to help students do their own work and to learn rom that eort.

• Atthemiddleschoolandhighschoollevels,studentsmayconsulttheseexpertsas

resources or a paper or project. Remind students to cite appropriately these people’s

contributions.

• Youwillalsowanttoreviewyourprogram’sorschool’sInternet-usagepolicyandrules,and

post a copy close to the student computers.

Teaching Tip

Whe to Ask a Expert

As you implement your ask-an-expertonline homework help program, take sometime to consider how it will ft into yourexisting homework sessions. I you have alimited number o computers available oronline help, you might consider having asign-up sheet. For more inormation abouthomework help in aterschool, see thehomework section o the Aterschool Training

Toolkit (www.sedl.org/aterschool/toolkits/ homework/index.html).





Sessio 2 ad Beod: Askig Experts

WhatYouNeed

p Student computer(s) with Internet access

p Bookmarked ask-an-expert Web sites

p Adult volunteer or older student aide

WhattoDo

• Havethestudentsconsultexpertsforhelpwiththeirhomeworkbyusingtheask-an-expert

Web sites.

• Ifseveralstudentshavethesamequestion,allowthemtoworkasateamtogetananswer

rom the experts.

• Assignanaidetothisstationtomonitorandhelp.

Exted• Ifyouhavemorethanonecomputeravailableforstudentuse,broadenthescopeof

your cyber study center. Stock an additional computer with appropriate, high-quality

learning activities.

• Checkwithday-schoolteacherstoseeifcomputerenrichmentgamesareavailablewiththe

textbooks students are using during day-school. Additionally, Web sites such as Fun Brain

and Gamequarium provide links to many un, ree online learning games.

Outcomes to Look or

• Studentengagementandparticipation• Progressinidentiedskillareas









Reflection









Academic Erichmet


activity un?















Family Connections

What Is It?FamilyConnections describes methods to support amily and community involvement in and

enthusiasm or math in aterschool. Examples include planning and oering parent workshops,

amily nights, or amily visits to the program. Family math events are planned times when

parents can visit their child’s aterschool program or participate in an event sponsored by the

aterschool program. The aterschool sta can lead these events, or they may choose to fnd

local experts or community members to lead them.

What Is the Cotet Goal?The goal o FamilyConnections is to engage parents, caretakers, and students in meaningul

math experiences and problem-solving activities that help support students’ math learning

both in day school and aterschool.

What Do I Do?Use surveys (or involve an aterschool advisory committee) to gather inormation rom your

familiesandcommunitytogetasenseoftheirinterests,needs,andpreferences;andtohelp

maximize participation in the events. Involve day-school and aterschool teachers to select a

specifc outcome and an appropriate design or the event. For example, a workshop might be

the best way to help parents learn powerul strategies or helping students with mathematicshomework, whereas a amily mathematics air with game booths might be oered to teach

parents un activities they could re-create at home.

Practice 7





Involve day-school teachers rom the regular day program and parents in the planning o these

events. Parents can highlight issues and challenges they ace in supporting their children’s

mathematical learning. Teachers bring knowledge o the day-school program curriculum as

well as a wealth o ideas or supporting learning at home. Speaking with both groups will

allow you to plan an event that is benefcial and supported by both the parents and teachers.

For specifc considerations or planning parent workshops, amily nights, or amily visits to the

program, visit the resources section o the FamilyConnections practice.

Wh Does It Work?Parental interest and support are primary actors in a student’s educational success.

Many parents do not become involved in their children’s schooling because they see ew

opportunities to be involved, sense an indierent attitude o the school personnel, are

intimidated by the educational jargon, or have transportation, saety, or childcare issues. Many

parents who do not have these problems still do not eel equipped to help their children,

especially since mathematics content becomes increasingly difcult as students get older, and

the parents might not have the content knowledge to assist their children. There have also

been changes in the way that mathematics is taught, which can present some conusion and

rustration or parents. Parents might also carry their own negative mathematical experience

with them. By taking these items into consideration, aterschool practitioners can build an

environment where parents eel knowledgeable and comortable to help their children succeed

in mathematics.





video

Getting Starte

Go to the InvolvingDaySchools,Families,andCommunities practice in

the homework section o the Aterschool Training Toolkit (www.sedl.org/ aterschool/toolkits/homework/pr_amilies_communities.html). Click on

the video or involving schools and amilies in the aterschool program.

Parents are involved with conerences in aterschool, just as they are with

day-school conerences.


involve amilies in the aterschool program.

BEFORE yOU WATCH THE VIDEO, write down what you already know about involving

amilies in aterschool programming.



them started?


engaged?









Lesson 1

Family Math Nights

Family math nights are nights set aside at aterschool where parents,

guardians, and community members are invited to experience math with

their children. Participants have the opportunity to attend a variety o

math events and to explore content, activities, and games that support

mathematical learning.


Duratio:

30 minutes–2 hours

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004;

www.mcrel.org/standards-benchmarks).The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.





Measurement


Problem SolvingReasoning and Proo

Communication

Connections





Imagie This!Parents, guardians, and community members are playing math games and learning math with

students and instructors! That’s a amily math night! Children guide their amily members

through a variety o math centers, math stations, or events. How about Rational NumberBingo or Measuring Hands and Feet? Family members play games or complete math centers

with their children while learning strategies, games, and activities they can use at home to

support their children.

What to DoPlanning is an integral step or a successul amily math night. Key planning steps include:

• Establishinggoals(Isthereaparticulartopicorlearningstrategythatwillbetaught?Willit

be a celebration o student work?)

• Location(Willtheeventbeheldintheschoolcafeteria,classrooms,gymnasium,ina

community center, etc.?)

• Attendance(Howmanypeoplewillbeinvited?Acertaingraderange?Theentire

aterschool program?)

• Dateandtime(DoesaneveningorSaturdayworkbetterforparents?Makesuretocheck

communityandschoolcalendarsforconicts.)

• Stafng(Doyouneedasteeringcommitteetohelpintheplanningandexecution?Where

will the volunteers come rom?)

- A steering committee can help with the planning o the event. You might consider

individuals who could fll roles such as event coordinator, publicity coordinator, activities

coordinator (plans and makes sure materials are present or learning activities), ood andprize coordinator, community coordinator, volunteer coordinator, and so on.

- Volunteers can be aterschool sta, day-school teachers, parents, students, school

administration, or community members. Volunteers will be useul to serve as greeters,

registration help, activity acilitators, and such the day o the event.

• Timeallotmentduringevent(Howwillthetimeduringtheeventbebrokenup?If

discussing a particular learning strategy, one suggestion might be to establish activity

centers that parents and students visit and participate or the frst 30 to 45 minutes o

the night. Then allow 30 minutes or all o the participants to reconvene and discuss their

experiences with the activities, the learning that occurred, and how this might be used in

the home setting.)• Promotionofevent(Howwillnewsoftheeventspread?Letterstovolunteers?

Announcementsorierstofamilies?Letterstoteachersdescribingtheeventandrequesting

support? Press releases? Hearing about the event many times and in many ways tends to

increase attendance.)





Outcomes to Look or• Parentresponsivenessandattendance

• Parentandstudentengagementinlearning

• Increasedparentalinvolvement

• Increasedparentalawarenessaboutmathematics

• Increasedparentalawarenessaboutmathhomeworkhelp

• Newideasfromparents

• Increasedcommunicationbetweenhomeandschool





Reflection









Academic Erichmet


activity un?







Lesson 2

Family Math Workshops

Family math workshops are ormal opportunities or parents or caretakers

to learn about the types o mathematics that their children are learning in

the classroom, the activities that can be used at home, and the strategies

to help with children’s homework. Workshops might be led by an invited

speaker, teacher, or other expert in the selected topic.


Duratio:

30 minutes–2 hours

Stadards:

These standards and benchmarks are rom McREL’s online database, Content Knowledge: ACompendiumofContentStandardsandBenchmarksforK–12Education(4thedition,2004;

www.mcrel.org/standards-benchmarks).The mathematics portion o the database was developedusing National Council o Teachers o Mathematics (NCTM) standards in addition to other nationallyrecognized standards documents.





Measurement


Problem SolvingReasoning and Proo

Communication

Connections





Imagie This!Your school library is flled with parents or guardians o your students. All are ready to learn

how to teach math to their children! You have brought in an engaging acilitator who will lead

your participants in practicing and talking about math concepts. Participants will develop theirown mathematical thinking, increase their knowledge o general math skills, and gain a better

understanding o how they can tutor their children at home.

What to DoThe frst step in planning amily math workshops is to determine the challenges that parents

and caretakers ace when they help their children with their mathematical learning. It is

important that the parents see the workshop as benefcial to their own ability to help their

children learn. Establishing a small group o parents who can assist in the workshop planning

will allow you the opportunity to make sure the needs o the parents are being met.

Ater establishing the needs, key considerations in planning the event include:

• Establishingfrequency(Howoftenshouldworkshopsbeheld?Monthly?Quarterly?)

• Establishingadateandtime(Whenwillmostparentsbeabletoattend?Anevening?

Saturday?)

• Establishingaplace(Wherewilltheeventbeheld?Intheschool?Communitycenter?)

• Selectingatopicandorspeakertofacilitatetheagenda

• Examiningchildcareneeds(Doweneedtoofferchildcareduringtheeventtoencourage

attendance? What activities will the children do?)

• Selectingfacilitators(Whoisknowledgeableonthetopicstobecovered?Aretheyavailable

to speak?)

• Preparingmaterials(Whatsupplementalmaterialsmighttheparticipantsneed?)

• Creatinganagenda(Howwillthetimebelaidout?All-grouplecture?Small,breakoutwork

groups? Grade-level discussions?)

Outcomes to Look or• Parentresponsivenessandattendance

• Increasedparentalinvolvement

• Increasedparentalawarenessaboutmathematics

• Increasedparentalawarenessaboutmathhomeworkhelp

• Newideasfromparents

• Increasedcommunicationbetweenhomeandschool





Reflection









Academic Erichmet


activity un?











Lesson 3

Grocery Store Math

Unlike the previous sections o this manual, this section does not list

detailedandcompletelessonsforchildren;rather,itprovidesmanyideas

that parents and guardians can implement beore, during, and ater

the grocery shopping experience. Each suggested idea is ollowed by

standards reinorced with the activity.

Like the standards throughout the manual, these standards and

benchmarks are rom McREL’s online database, Content Knowledge:

A Compendium o Content Standards and Benchmarks or K–12

Education(4thedition,2004;www.mcrel.org/standards-benchmarks).

The mathematics portion o the database was developed using National

Council o Teachers o Mathematics (NCTM) standards in addition to othernationally recognized standards documents.

The grocery store is a great place or amilies to help students

reinorce their math skills. Many times parents are hesitant

to take their children to the store out o ear they will

misbehave. By giving them

a task at the store or

upon returning home,

children will be more

willing to help with this

weekly chore and learnsome math, too!





Imagie This!You are having un grocery shopping with your kids! Yes, that’s right! There are many, many

mathematical ways you can have a good time at the grocery store while teaching your child

math and shopping at the same time. Check out some o the ideas below and have un!

Idea 1: Shoppig BigoGrade Level(s):

K–2

• Usingtheweeklyads,helpyourchildcreateabingocard.Takean8½by11inchpieceof

paper and old it in hal and then in hal again. Repeat until the old lines create 16 squares.

• Lookthroughthegrocerystoreierinthenewspaper,andwithyourchildcutoutnumbers

that are seen in the advertisements. For example, you might cut out “3 or $1,” a picture o

a dozen eggs, or the math term 1gallon.

• Withyourchild,pasteeachoftheseexamplesintoadifferentsquareonthepage.Youcan

reinorce the page by gluing it on cardboard.

• Takethecardwithyoutothestoreandhaveyourchildmarkoffasquareifheorshespots

those numbers, words, or measurements during the trip to the store.

• Makesuretorewardyourchildattheendofthetripforhisorherhardworkinplaying

shopping bingo!

Stadard: Understands and applies basic and advanced properties o the concepts o numbers

Idea 2: How Ma Do We need?

Grade Level(s):K–2

• Whenpreparingforatriptothegrocerystore,haveyourchildhelpwiththelist.

• Writetheitemsonthelistandthenencourageyourchildtoplacemarksnexttotheitems

representing how many o each item is needed at the store. This will help to reinorce the

idea o collecting and organizing data.

Stadard: Collects and represents inormation about objects or events in simple graphs





Idea 3: How Are These Alike?Grade Level(s):

K–2

• Uponreturningfromthestore,unpackabagofitemsandaskyourchildtosorttheitemsinto categories. It is important that the child chooses his or her own categories.

• Oncethechildisnished,askhimorhertoexplainhowtheitemsineachgrouparealike.

Stadards: Orders objects qualitatively by measurable attribute

Sorts and groups objects by attributes

Idea 4: How Much Does It Hold?Grade Level(s):

K–2

• Foryoungerstudents,reinforcetheircountingskillsbyhavingthemcountthenumberofitems in a bag as you unpack the groceries ater a trip to the store.

• Youmayaskthemtoestimatethenumberofitemstheythinktheywillndinthebag

beore they begin to unpack the bag.

Stadards: Counts whole numbers

Estimates quantities in real-world situations

Idea 5: Pouds o ProduceGrade Level(s):

3–5

• Reinforcethechild’sabilitytoaccuratelymeasureandestimateweightwhileinthe

produce section.

• Tellyourchildtheweightyouwouldlikeofaparticularitemandaskhimorhertoestimate

how much o that ruit or vegetable they think that weight will be.

• Oncethechildhasmadeanestimate,havehimorherusethegrocerystorescaleto

measure the actual weight o the object.

• Askthechildifthereistoomuchortoolittleandhowheorsheknowsthat.

• Thenaskyourchildtoestimatehowmuchorhowmanymoreofthatobjectheorshewill

need to add or subtract to reach the desired weight.

Stadards: Uses specifc strategies to estimate quantities and measurements

Selects and uses appropriate units o measurement, according to type and size o unit





Idea 6: How Much Is It?Grade Level(s):

3–5

• Allowchildrentogureouthowmuchtheactualgrocerybillwillbebylookingattheitemspurchased.

• Ifyouhavemorethanonechildwithyou,createafriendlycompetitionwherethechildren

try to get the closest to the actual dollar amount spent.

• Youwillneedtoprovideeachchildwithpaperandpenciltowritedowntheamountof

each item.

• Youmayalsowanttoprovideeachchildwithacalculatorforthisactivity.

• Forolderstudents,remindthemtoaddintaxandsubtracttheappropriateamountfor

coupons or other discounts that you will receive.

Stadards:Uses explanations o the methods and reasoning behind the problem solution to determinereasonableness o and to veriy results with respect to the original problem

Adds, subtracts, multiplies, and divides decimals

Solves real-world problems involving number operations (e.g., computations with dollarsand cents)

Idea 7: What’s the Better Deal?Grade Level(s):

6–8

When shopping on a budget, you pay careul attention to how much each item costs and want

to make sure that you get the best deal possible. Older children can help you fgure out thebest deal possible while also reinorcing their math skills. While shopping at the store, you

oten come across multiple brands o the item you want to purchase.

• Askthechildtogureoutwhichitemhasthebestunitpriceandthereforewouldbethe

best deal.

• Childrenwillneedtotakeintoaccountthesizeoftheobject(oz,lbs,etc.)aswellasthe

cost o the object.

• Manytimesthisexercisecanbedeceiving,especiallyifanitemisonsale,somakesure

the child takes into account any sales or coupons that might come into play.

• Onceyourchildhasguredoutthebestdeal,makesuretohavehimorherrationalizewhy

he or she chose that item.

Stadards: Constructs inormal logical arguments to justiy reasoning processes and methods o solutionsto problems

Uses proportional reasoning to solve mathematical and real-world problems





Reflection









Academic Erichmet


activity un?















L

e a r n i n g G o a l 1. Write the math content standards or learning goals in your own words:

S u p p o r t i n g K n o w l e d g e a n d S k i l l s

2. Now break the learning goal(s) into more specifc and manageable pieces:What will students need to know to meet the goal? Tip:Thinkaboutspecicfacts,concepts,vocabulary,rules,principles,and/ortimelinesthatstudentsneedtoknowtomeetthegoal.

What will students need to do to meet the goal? Tip:Thinkaboutspecicprocesses, procedures,orotherskillsthatstudentsneedtoknowhowtodotobesuccessfulwith

thegoal.

A c t i v i t i e s

3. What activities will provide students with opportunities to learn or practice using thisknowledge or skills? Tip:Thinkintermsofexistingactivitiesthatyoucouldmodifyornewonesthatyoucouldcreate.

In what ways do these activities support other goals (youth development, workingtogether, presenting ideas) that you have or your students? Tip:Thinkaboutspecicphysical, social,moral,emotional,and/orbehavioralknowledgeandskillsthatstudentsneedtobe

successfulwiththeactivity.

A s s e s s m e n t s

4. How will you know i students learn what you want them to learn?Tip:Explainwhatyouwillseeandhearthatindicatesthatstudentsacquiredthespecic

knowledgeandskillsyouidentiedinStep2.

Planning Worksheet: Spporting Math Learningin Afterschool

Begin by connecting with the day-school teacher to fnd out more about the math standards

and grade-level benchmarks. Then identiy the skills, standards, or learning goals toincorporate in aterschool.

Grade Level:

Skill/Standard/Learning Goal:



Acknowledgments

This resource was developed with the support of the U.S.

Department of Education as part of the National Partnership for

Quality Afterschool Learning project. It was designed to support

21st Century Community Learning Center instructors who

wish to create quality learner-centered environments for their

afterschool programs.

The content of the Afterschool Training Toolkit is based on more

than 4 years of research and observations at 53 afterschool

programs with evaluation data suggesting an impact on

student learning. The content also draws from a review of

relevant research studies and the experience and wisdom that

each of the developers brought to the project. The collective

experience of the developers includes afterschool programming,

professional development, educational research, program

development, program management, and direct instructional

experience with students.

The developers believe that these practices and materials will

help afterschool leaders and educators create high-quality

programs that will motivate, engage, and inspire students’

learning and participation.

We extend our appreciation to our site schools and thank the

parents of the children in these classrooms for allowing us to

showcase their children at work in the toolkit videos.

In addition we would like to acknowledge Chris Briggs-Hale,

Maggie Cooper, Jodi Holzman, Sarah LaBounty, and Danette

Parsley for their work in initially conceptualizing and creating

the online content that supports this guide.



u.s. Department of eDucationTechnical Assistance and Professional Development for

21st Century Community Learning Centers

Documents

Instructor_Guide_Math.pdf