Math Academy Mall

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MahAcaemyLes Go o he Mall!Explorations in Combinatorics


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A Tank Yo to Or Cororate Sonsors

The Actuarial Foundation would like to thank theollowing sponsors or their generosity in unding the

production o the Math Academy booklet.

By providing fnancial support or this project they are

assisting The Actuarial Foundation in its pursuit o one o

its many aspirationsto provide students with enrichedlearning opportunities that can help them succeed in

their educational and proessional endeavors.

The Actuarial Foundation and the companies listed

below are collectively ensuring math educationremains strong and enjoys a prosperous uture.

2008 The Actuarial Foundation

the Acuaal founaons msson: To develop, fundand execute education and research programs that servethe public by harnessing the talents of actuaries.


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Congratulations! Youve just ound your answer to the

question, What can I do to create real enthusiasm or

mathematics in all my students?

Created by teachers or teachers, the Math Academy tools

and activities included in this booklet were designed to create

hands-on activities and a un learning environment or the

teaching o mathematics to our students. On Math Academy

days I oten ound that I couldnt make it rom my car to my

classroom without being stopped by enthusiastic students

wanting to know every detail o the upcoming days events.

Math Academy days contributed to a positive school-wide

attitude towards mathematics on our campus.

This booklet contains theMath Academy Lets Go to the Mall!

Explorations in Combinatorics, which you can use to enhance your

math instruction while staying true to the academic rigor required

by the state standards ramework.

This eort would not have been possible without support rom

The Actuarial Foundation. With the help o the Foundations

Advancing Student Achievement (ASA) grant program, whichis committed to unding projects that enhance the teaching o

mathematics, this Math Academy program came into being.

I sincerely hope that you enjoy implementing theLets Go to the

Mall! Math Academy with your students. When you do, you will

nd that your students engage with mathematics on a whole

new level. The Actuarial Foundation is truly a great partner in

urthering mathematics education!

For the kids!

Kmberly Rmbey, M.Ed., NBCT (Mat)Mathematics Specialist

Phoenix, AZ

I you wish to fnd out more about my experiences with this

and other Math Academies, eel ree to contact me via e-mail

[email protected].

A Letter from te Ator


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When the Math Academy concept was rst developed, it was designed as a hal-day or ull-day evenwhich allowed students to deepen their understanding o math while interacting with volunteersrom the community (see page 26 or ideas on working with community volunteers). The activities

we selected or these events were hands-on, standards-based lessons which applied mathematicalprinciples in real-world scenarios. Each student experienced three to ve activities during the courseo the event.

Each Math Academy began with a brie school assembly eaturing a guest speaker who representedthat days particular theme. Themes included math related to restaurants, sports, nature, shopping,ne arts and other topics, as well as ocusing on math-related careers. Ater the assembly, studentsrotated to dierent classrooms where they engaged in various activities related to mathematics andthe days coordinating theme.

Included in this booklet is the Math Academy Lets Go to the Mall! Explorations in Combinatorics,which has all the activities we used or the combinations and permutations Math Academy. ThisMath Academy is designed to help students understand the connection between various kinds ocombinations (multiplication principle and choose numbers) and permutations. You may choose toimplement a grade-level or school-wide Math Academy as we originally designed it, or you may preerto implement these activities in your own classroom. Whichever ormat you use, keep in mind thatthe goal is to help your students see the relevance o mathematics in real-lie contexts. I you wouldlike more inormation on the set-up or a school-wide or grade-level Math Academy event, visit The

Actuarial Foundations Web site atwww.actuarialfoundation.org/grant/mathacademy.html

Wat s a Mat Academy?


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Math Academy Format

You may choose to conduct your Math Academy as a school-wide event, as agrade-level rotation, or as a single-classroom experience. I you will be holding

your Math Academy or a single classroom, you may want to invite a guestspeaker to speak with your class about how mathematics is used in his/her job(rather than putting on a school-wide or grade-level assembly as described below).

Math Academy Schedule

Schedule and times may vary depending on format being used.

Opening assembly (optional) 15 minutes

Directions and Math Journals 15 minutes

Activity Rotations 3045 minutes per activity

Assessment and Closure 15 minutes

Opening Assembly/Directions

To build enthusiasm and to ocus attention, have everyoneparticipate in the Math Academy Chant(or younger students):

You and me, we all agree Math is un as you will see!It makes us think, it makes us strong,It helps us learn even when were wrong.

You and me, we all agree

Math is un at the Math Academy!inoucon

Announce to the students that today they will be workingon projects dealing with combinations and permutations.

Gues Seake pesenaon (oonal)

Beorehand, arrange or someone in the sales industry to talk to thestudents about the mathematics in the mall (they may or may notconnect to combinations and permutations, but encourage them todo so). Possible guest speakers may include someone rom the mall,ice cream shop, clothing shop, or any retail store. Although thisguest speaker will primarily be ocused on the shopping side o

this Math Academy theme, you may want to work with him/herahead o time to assist with tying in mathematical ideas to the talk.

Use o Math Journals

Students record their ndings in their Math Journals during each activity.These journals should contain all recording sheets or the activities as wellas blank paper or the extension activities. Beore beginning the ActivitiesRotation, students should spend about 10 minutes writing in their math jour-nals, including their refections rom the assembly as well as briefy describing

what they already know about combinations and/or permutations.

Gettng Started

Theme

Combinations and Permutations Using ideas rom the mall to acilitatediscussions ocused on combinatorics

Objective

Students will build, describe, and usenumerical operations to determinecombinations and permutations.


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Use the Procedures section in each activity as a skeleton or the lesson.

Look through the Suggestions or Customizing This Activity section.

Select the suggestion(s) which best ts with the combinatoricsconcepts on which you want your students to ocus.

TEAChER TipS: CuSTOMiziNG ThESE ACTiviTiES

Activities Rotation

I multiple classes are participating in the Math Academy, eachclassroom should host a dierent activity so students will rotaterom classroom to classroom in order to complete each activity.I only one class is participating, the students may rotate romone activity to the next around the room, or they may do eachactivity as a whole class, one activity ater the other. Activitiesbegin on page 7. For best results, plan on three to ve activitiesor your Math Academy.

Closure and Assessment

Once all activities are completed, the students may return to theirhomeroom classes or nal refections and assessment. See pages 22and 24 or sample quiz and survey.

Key VocabularyCombinatorics

Combinations

Permutations

MultiplicationPrinciple

Choose Numbers

Factorials

Gettng Started (continued)

We asked our students to use

graphic organizers to recordtheir thoughts and ndingsin their math journals. Thiscreates a great connection toour language arts curriculum.

The best results are achievedwhen 45 minutes are allowedin each classroom about 30minutes or the activity and15 minutes or clean-up andrefection. The students can

use their math journals torecord their ndings during theactivities and write refectionson the journals blank pages.

Following the combinationsand permutations activitiesin this booklet, you will nda student quiz as well assample surveys or studentsand teachers so that you canevaluate the success o yourMath Academy. The Actuarial

Foundation would love to hearall about your success and willsend a $50 Git Certicateto the rst 100 teachers whoimplement these activities andsubmit the results. For moreinormation and to downloadthe evaluation orm, go towww.actaralfondaton.org/grant/matacademy.tml.

TEAChER TipS


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Mat Actty 1:Its a Wrap with Combinations

Objective The students will determine combinations using the multiplica-tion principle and then model the results using a tree diagram.

Materials Pencils

Clear bags or paper manipulatives

Paper manipulatives copied, cut and placed in plastic bags(see page 8)

Its a Wrap combinations sheet or each student(see page 9)

Procedures 1. Optional: Set the stage or the wrapping paper store puta sign on the outside o your door, decorate your room,

wear an apron, make a choices sign, etc.

2. Prepare the paper manipulatives and put in clear bags.NOTE: Be sure to include more o each item than isneeded so that students must think about when to stopputting combinations together.

3. Discuss the problem with the students (see Its a Wrapcombinations sheet).

4. Demonstrate how to make wrapping paper/bowcombinations using exactly one paper and one bow.

5. Have students work in groups to create all o thepossible wraps using exactly one paper and one bow.

6. Once groups are nished, demonstrate how to representall o the combinations using a tree diagram.

7. Have students create their own tree diagrams to matchtheir wrapping creations.

8. Closure discuss why there are exactly nine possible wrapcombinations using only one paper and one bow.

SuggestionsorCustomizing

This Activity

This problem is set up to include three kinds o paper andthree kinds o bows (9 possible combinations). Put in morepapers and/or more bows to add an extra challenge.

Add a third set o objects (in this case, ribbons or stickers).

Discuss the multiplication principle (determining thenumber o combinations by multiplying the number oitems in each set) and have students relate it directly to theirdiagrams and/or pictures (in this case, 3 3 = 9 possiblecombinations).

Have students create an organized list, table, or array modelto illustrate their combinations rather than a tree diagram.


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Mat Actty 1:Its a Wrap Cut-Outs

Sol Sol Sol Sol Sol

Ses Ses Ses Ses Ses

polka dos polka dos polka dos polka dos polka dos

Smle Bow Smle Bow Smle Bow Smle Bow Smle Bow

Culy rbbon Culy rbbon Culy rbbon Culy rbbon Culy rbbon

roun Bow roun Bow roun Bow roun Bow roun Bow

Copy the wrapping paper and bows below. Cut apart to be used with Its a Wrap.


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Mat Actty 1:Its a Wrap Combination Sheet

Maria is getting her mothers git wrapped at the mall. The sign below shows that the price rangeshe is looking at has three wrapping paper choices and three bow choices:

Wang pae Choces Bow Choces

Solid

Stripes

Polka Dots

Simple Bow

Curly Ribbon

Round Bow

What are all the dierent combinations that can be made using exactly one wrapping paper andone bow?

Make a tree diagram below to show all the possible combinations. Use words, numbers, and pic-tures to demonstrate/explain how you arrived at your answer.


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Teachers Answer Key

Mathematical Patterns in this problem:

I there are 3 papers and 3 bows, there are 9 possible combinations using exactly

one paper and one bow.

Tree Diagram:

Note:

You may choose to have the students use the ollowing models as well.Organized List/Table

paer Bow

Solid Simple

Solid Curly

Solid Round

Stripes Simple

Stripes Curly

Stripes Round

Polka Dots Simple

Polka Dots Curly

Polka Dots Round

Array

BOWS

Smle (S) Crly (C) Rond (R)

pA

pERS

polka

Dots(p)

P-S P-C P-R

S

tries

(St) St-S St-C St-R

Solid(S)

S-S S-C S-R

Multiplication Principle:

3 3 = 9

Mat Actty 1:Its a Wrap with Combinations

Solid Stripes Polka Dots

Simple Curly Round

paes:

Bows: Simple Curly RoundSimple Curly Round


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Mat Actty 2:Be a Sport with Combinations

Objective The students will determine combinations using choosenumbers while discovering, identiying, recording, and

verbalizing the arithmetic patterns or various choose-numbercombinations. The students will model their results as anorganized list on a chart.

Materials Pencils


Paper manipulatives copied, cut and placed in plastic bags(see page 13)

The Big Sale combinations sheet or each student(see page 14)

Procedures 1. Optional: Set the stage or the Be a Sport store put asign on the outside o your door, decorate your room, and/or dress up like someone working at a sports apparel store.

Copy and cut apart the paper manipulatives and put in2.clear bags. Note: Be sure to include more o each item thanis needed so that students must think about when to stopputting combinations together.

Discuss the problem with the students (see Be a Sport3.combinations sheet). Explain that the store is having a2-item special. Each customer may select exactly two items(must be dierent) and put them in a bag. Their job is to

discover how many dierent bags can be made when select-ing two items rom six choices.

Demonstrate how to select exactly two items rom the six4.choices. Emphasize that the two items may never be identical(e.g.: they cannot select two baseball hats at the same time).

Have students work in groups to create all o the possible5.2-item specials by selecting exactly two unique items oreach bag.

Once groups are nished, demonstrate how to represent all6.o the combinations using a chart or organized list.

Have students create their own charts and/or organized7.lists to demonstrate their results.

Closure discuss why there are exactly 15 possible8.combinations.


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Ideas orCustomizing

This Activity

Have students create a tree diagram to illustrate theircombinations rather than an organized list.

Change the number o items being used and/or the num-

ber o items being chosen (start with 6 items and choose 1,2, 3, 4, 5, or 6; start with 5 items and choose 1, 2, 3, 4, or5; start with 4 items and choose 1, 2, 3, or 4; start with 3items and choose 1, 2, or 3; start with 2 items and choose1 or 2; start with 1 item and choose 1).

Ask students to create a chart or diagram to show the patternsor each o the combinations created in the above option.

Discuss how choose number combinations dier romthe multiplication principle combinations (lessons one inthis booklet).

Ask students to look or patterns when organizing their

combinations.

Ask students to derive an algorithm or determining thenumber o combinations possible.

Change the number o items available.

Advanced: Develop the ormula or nding choose num-bers. The ormula or nding choose numbers is rarelytaught in middle school. The beauty o this problem ormiddle school students is in allowing the students theopportunity to visualize, identiy, and verbalize patterns.However, i you choose to introduce the ormula, you will

want to be sure they are already very amiliar with actorials.

In= number o items available and t= how many itemschosen, then the ormula will be as ollows:

n!

(t!)(nt)!

Te Famos handsake problem

This widely-used scenario has beenused in mathematics classes ormany years. Ask the student: I agroup o people got together andeach person shook the hand oevery other person in the groupexactly one time, how many hand-shakes would take took place? Thetable below shows the answers:

# of eole

n gro # of andsakes2 1 (1)

3 3 (2+1)

4 6 (3+2+1)

5 10 (4+3+2+1)

6 15 (5+4+3+2+1)

This is another example o choosenumbers. In this case, no matterhow many people are in the group,two people are chosen at a timeto shake hands. You may want tohave the students act this out.

TEAChER TipS


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Jesey Jesey Jesey Jesey Jesey

Baseball Ca Baseball Ca Baseball Ca Baseball Ca Baseball Ca

Shos Shos Shos Shos Shos

t-sh t-sh t-sh t-sh t-sh

runnng Shoes runnng Shoes runnng Shoes runnng Shoes runnng Shoes

Swea pans Swea pans Swea pans Swea pans Swea pans

Mat Actty 2:Be a Sport Cut-Outs


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The sports apparel store at the mall, Be a Sport, is having a great sale this weekend!Each customer may choose exactly two items rom the list and purchase them bothor a great price. The trick is that each 2-item special must have two dierent items

(or example, they may not purchase two T-shirts at the same time).

What are all the dierent combinations that can be made by choosing exactly two items?

Use the paper items to discover how many combinations are possible (remember, you may not put two o the sameitem together). Then make an organized list in the chart below to show all the possible combinations. Use words,numbers, and pictures to demonstrate/explain how you arrived at your answer.

JerseyBaseball capShortsT-shirt

Running shoes

Sweat pants

SALE!

iem 1 iem 2

Mat Actty 2: The Big Sale Combination Sheet


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Teachers Answer Key

Chart/organized list for choosing two items from six choices (6 choose 2):

Note to teachers: order will vary, but look or patterns

Frst item Second item

Jersey Baseball cap

Jersey Shorts

Jersey T-shirt

Jersey Running shoes

Jersey Sweat pants

Baseball cap Shorts

Baseball cap T-shirt

Baseball cap Running shoes

Baseball cap Sweat pants

Shorts T-shirt

Shorts Running shoes

Shorts Sweat pants

T-shirt Running shoes

T-shirt Sweat pants

Running shoes Sweat pants


Choose 2: When there are 4 items and they are choosing 2, there is a 3 + 2 + 1

pattern; When there are 5 items and they are choosing 2, there is a 4 + 3 + 2 + 1pattern; When there are 6 items and they are choosing 2, there is a 5 + 4 + 3 + 2 + 1pattern; etc.:

4 coose 2 3 + 2 + 1 = 6 combinations

5 coose 2 4 + 3 + 2 + 1 = 10 combinations

6 coose 2 5 + 4 + 3 + 2 + 1 = 15 combinations

7 coose 2 6 + 5 + 4 + 3 + 2 + 1 = 21 combinations

8 coose 2 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 combinations

Choose 3: When there are 4 items and they are choosing 3, there is a 2 + 1 pattern;When there are 5 items and they are choosing 3, there is a 3 + 2 + 1 pattern; Whenthere are 6 items and they are choosing 3, there is a 4+3 + 2 + 1 pattern; etc.:

4 coose 3 2 + 1 = 3 combinations




8 coose 3 6 + 5 + 4 + 3 + 2 + 1 = 21 combinations


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Teachers Answer Key (continued)

Choosing dierent amounts rom the same original number o items:

4 coose 1 4 combinations



4 coose 4 1 combination












Using the formula: The ormula or nding 6 choose two will include actorial or the

number o items available, the actorial or the number o items chosen, and the actorial orthe number o items NOT chosen. It will look like this:


6!

(2!)(62)!REMiNDER:

n!

(t!)(nt)!


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Mat Actty 3:Ice Cream Cone Permutations

Objective The students will determine permutations while discover-ing, identiying, recording, and verbalizing the arithmeticpatterns or various amounts.

Materials Paper ice cream scoops (3 to 6favors cut rom construction paper)

Paper triangles to represent conesonto which to place the paperscoops

Blank Paper

Pencils

Colored pencils,crayons, or markers

Procedures 1. Optional: Set the stage or the ice cream shop youmay want to put a sign on the outside o your door to leteveryone know they are going into the Ice Cream Shop.

I you wish, you can even decorate your room and/orwear apparel appropriate or an ice cream shop worker.

Discuss the problem with the kids.2.Today everyone will get a 3-scoop ice cream cone.

The big decision is this: in what order do you want yourscoops arranged on your cone?

Use the paper ice cream to discover all o the possibleorders your three scoops can be arranged.

Organize the paper ice cream cones so that patterns canbe easily detected.

Record all o the possible

permutations(order in whichthey can be arranged) in an organized ashion using atree diagram, organized list, table, picture, etc.

Have students work in groups or individually to use the paper3.scoops and cones to nd all o the orders in which threescoops can be arranged.

Have students record their results as a tree diagram, orga-4.nized list, chart, etc., on the blank paper. Its important thatthe students see a connection between the manipulatives andthe diagrams they create.

Discuss the mathematical patterns that exist in this problem5.

(see teacher answer key or examples).6. Just For Fun: Provide real ice cream or a 2 or 3-scoopspecial with your class ollowing the activity.


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Ideas orCustomizing

This Activity

Introduce the concept o actorials Annos MysteriousMultiplying Jarby Mitsumasa Anno is a great literatureselection which explains actorials using several models

Repeat this activity using 1 scoop, 2 scoops, 4 scoops, etc.Place the results on a chart in order to detect arithmeticpatterns (see Teachers Answer Key or examples).

Repeat this activity using a dierent context in whichstudents may order items into dierent arrangements.Possibilities may include:

children standing in line (e.g., In how many dierentorders can Anna, Brock, Char, and Dave stand in line atthe Ice Cream Store?)

placing digits in dierent orders (e.g., How many di-

erent 3-digit numbers can you make given the digits 7,8, and 9?)

Teachers Answer Key


1 scoo 1! = 1 permutation

2 scoos 2! = 2 1 = 2 permutations

3 scoos 3! = 3 2 1 = 6 permutations

4 scoos 4! = 4 3 2 1 = 24 permutations

5 scoos 5! = 5 4 3 2 1 = 120 permutations

6 scoos 6! = 6 5 4 3 2 1 = 720 permutations

Mat Actty 3:Ice Cream Cone Permutations

Annos Mysteros

Mltlyng Jar

by Mitsumasa Anno

This amazing book demon-strates the concept o actorialsin such a concrete way! It startswith a jar, and inside the jar isone island. On that island aretwo countries. In each countryare three mountains, etc. Eachpage shows the multiplicativegrowth in pictures and num-bers, all the way to 10!


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Mat Actty 4: Create-a-Bear Permutations

Objective The students will determine permutations while discover-ing, identiying, recording, and verbalizing the arithmeticpatterns or various amounts.

Materials Blank Paper

Pencils

Colored pencils, crayons, or markers


Paper manipulatives copied, cut and placed in plastic bags (see

page 17)

Procedures Set the stage or the students as i they are working at the1.Create-a-Bear store in the mall. Their job is to make aposter showing all o the possible ways the bears can beplaced in a line (permutations).

Discuss the problem with the kids.2.Today the students will be working at the Create-a-Bearstore in the mall. They will be creating a display to showall o the little children how they can dress the bears.

The big decision is this: in what order do you want toline the bears up in the display?

Use the paper bears to discover all o the possible ordersin which you can put them in line. Suggestion: usethree bears to begin with, then more or less.

Organize the dierent arrangements so that patternscan be easily detected using a chart, organized list, orother model.

Record all o the possible permutations (order in whichthey can be arranged) in an organized ashion using atree diagram, organized list, table, picture, etc.

Have students work in groups or individually to use the3.

paper bears to nd all o the orders in which the bears canbe arranged in line i there are 3 bears. (You may change thenumber as desired.)

Have students record their results as a tree diagram, orga-4.nized list, chart, etc., on the blank paper. Its important thatthe students see a connection between the manipulatives andthe diagrams they create.

Discuss the mathematical patterns that exist in this problem5.(see teacher answer key or examples).


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Teachers Answer Key


1 bear 1! = 1 permutation (order in which to line up the bear)

2 bears 2! = 2 1 = 2 permutations (orders in which to line up the bears)

3 bears 3! = 3 2 1 = 6 permutations (orders in which to line up the bears)

4 bears 4! = 4 3 2 1 = 24 permutations (orders in which to line up the bears)

5 bears5! = 5 4 3 2 1 = 120 permutations (orders in which to line up thebears)

6 bears6! = 6 5 4 3 2 1 = 720 permutations (orders in which to line upthe bears)

Ideas orCustomizing

This Activity

Introduce the concept o actorials Annos MysteriousMultiplying Jarby Mitsumasa Anno is a great literatureselection which explains actorials using several models (seepage 18 or a description).

Repeat this activity using 1 bear, 2 bears, 4 bears, etc.Place the results on a chart in order to detect arithmeticpatterns (see Teachers Answer Key or examples).

Repeat this activity using a dierent context in whichstudents may order items into dierent arrangements.Possibilities may include

children standing in line (e.g., In how many dierentorders can Anna, Brock, Char, and Dave stand in line attheCreate a Bear Store?)

placing digits in dierent orders (e.g., How many di-

erent 3-digit numbers can you make given the digits 7,8, and 9?)

See Ice Cream Cone Permutations in this booklet.



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Geen Geen Geen Geen Geen

Geen Geen Geen Geen Geen

re re re re re

re re re re re

Blue Blue Blue Blue Blue

Blue Blue Blue Blue Blue

Copy the bears below. Cut apart to be used with Create=a-Bear Permutations


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Name ________________________________________

1. Draw a tree diagram which shows the possible outts which can be created rom 3 pairs o shortsand 4 shirts. How many combinations were possible?

2. The pet store at the mall is oering a special on ood and water bowls. There are 9 dierent oodbowls and 6 dierent water bowls rom which to choose. I each set must contain exactly one oodbowl and one water bowl, how many dierent combinations are possible? (Show your work.)

3. The stir-ry restaurant at the mall is oering a special on 2-item stir-ries. I there are 5 items tochoose rom, how many 2-item combinations are possible? (Show your work.)

Samle Q


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4. The jewelry store at the mall just put 7 items in the sale bin. They are selling them in sets o three.How many combinations o three dierent items can be put together (no duplicates in any set)?

(Show your work.)

5. Four students are standing in line to go to the movies at the mall. In how many dierent orderscan they stand in line? (Show your work.)

6. The toy store at the mall is setting up a new display. There are six dierent toys they are putting inthe window. In how many orders can the toys be placed? (Show your work.)

Samle Q (continued)


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1. What job would you like to have when you grow up?

2. What kind o math skills do you think you will need to do that job?

3. Rank each o these statements on a scale o 1 to 5 (1 being lowest rank):

I like math in school. 1 2 3 4 5

I use math outside o school. 1 2 3 4 5

The math I learn at school is helpul. 1 2 3 4 5

I am good at math. 1 2 3 4 5

I liked participating in the Lets Go to the Mall!Math Academy 1 2 3 4 5

I learned a lot about math during the Math Academy. 1 2 3 4 5

I would like to participate in Math Academiesagain in the uture. 1 2 3 4 5

4. The best thing about the Math Academy was:

5. The worst thing about the Math Academy was:

6. Do you know what an actuary is?

Samle Stdent Srey


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1. What ormat did you use or this Math Academy?

m classroom m all classrooms in grade level m school-wide to all grade levels

2. What grade-level(s) used this Math Academy lesson?

3. Which Math Academy activities did you utilize with your students? 1 2 3 4 5 6

4. For the ollowing two questions, please use a ranking scale o 1 through 5(5 = great; 3 = mediocre; 1 = poor).

Overall, how would you rank this Math Academy?

How would you rank the activities you presented/taught?

5. Would you recommend these activities be used again?m Yes m No

Comments:

6. Do you think your students now have a better understanding o combinations and permutations?

m Yes m No

Comments:

7. Would you like to participate in another Math Academy?

m Yes m No

Comments:

8. Please let us know how well your Math Academy went.

9. Comments, ideas, suggestions:

Samle Teacer Srey


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One o the most benecial aspects o our Math Academy program is theactuarial mentors/volunteers who interact with our students during each

Math Academy activity. Our actuarial mentors take time away rom theirusual work responsibilities on the days o our events so they can help out inthe classrooms. Please take the t ime to contact The Actuarial Foundation [email protected] nd out i actuaries are available in your area.

I you do not have actuaries available in your community, you may want toconsider requesting the assistance o parents, community members, or businesspartners who would be willing to work with the students during the activities.

Ater securing your mentors/volunteers, it is critical to identiy a Lead Mentorwho will serve as the liaison between you and the other mentors. The Leadshould e-mail all communications rom the teachers to the mentors, set up

schedules, send reminders beore each event, etc.

Mentor Training Session

Distribute the Math Academy schedule.

Distribute copies o the Math Academy activities.

Pedagogy Discuss some simple teaching techniques.

Management Assure mentors that the teachers willhandle all discipline. Discuss preventative managementtechniques such as proximity and having activities

well-prepared to avoid student down-time.

Brainstorm Allow some time during your trainingto take any ideas or suggestions rom your mentors.

Allow time or questions and answers.

Assigning mentors Assigning mentors to the sameclassroom throughout the year will help build strongerrelationships with the students and teachers.

E-mail exchange Collect everyones e-mail addresses oreasy communication between mentors and teachers.

School tour End your training with a school tour. Be sureyour mentors know the key locations o your school includingthe sign-in book (and procedures), restrooms, principals oce,

and classrooms. I possible, include a map in their take-homematerials so they can nd their teachers classrooms oncethey receive their assignments.

Commnty inolement

An actuary is an expertwho deals with numbersand percentages, also knownas statistics. Actuaries provideadvice to businesses, govern-ments, and organizations tohelp answer questions aboutwhat to expect in planningor the uture.

To nd out more aboutthe actuarial proessionvisit BeAnActary.org.

WhAT iS AN ACTuARY?

The number o volunteer mentorsyou have will depend upon the

ormat and number o studentsinvolved in the program.Although you dont needvolunteer mentors at the class-room level, students nd thesevolunteer mentors to be un.

TEAChER TipS


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The unit included in thisLets Go to the Mall! booklet draws rom theeld o discrete mathematics. According to the NCTMPrinciples andStandards, the main topics o discrete mathematics are distributedacross the Standards instead o receiving separate treatment, and theyspan the years rom pre-kindergarten through grade12. As an activebranch o contemporary mathematics that is widely used in business andindustry, discrete mathematics should be an integral part o the schoolmathematics curriculum, and these topics naturally occur throughout theother strands o mathematics.

Although the content or combinatorics is integrated throughout theNCTM content standards, the ollowing pK-12 process standards arespecically addressed in this booklet:

Problem Solving:

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety o appropriate strategies to solve problems

Monitor and refect on the process o mathematical problem solving

Connections:

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and

build on one another to produce a coherent whole

Recognize and apply mathematics in contexts outside o mathematics

Representation:

Create and use representations to organize, record, and communicatemathematical ideas

Select, apply, and translate among mathematical representations to solveproblems

Use representations to model and interpret physical, social, and mathemati-

cal phenomena

You will want to check with your own state ramework

to select perormance objectives which are specifc

to your students.

Algnment wt Standards


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Lets Go to the MallMath AcademyChecklist

Determine the date, time,and schedule or yourMath Academy

Identiy the objectives tobe reinorced through thisMath Academy

Plan the opening assembly,i applicable

Conrm the schedule andcontent with guest speaker,i applicable

Customize the activitiesenclosed in this booklet

Make copies o the activities,quiz and surveys

Purchase and/or gathermaterials

Note: Most hands-on materi-als or these activities can becreated by copying the black-line masters throughout thebooklet. In addition, your willneed the ollowing items:

small, clear bags to organizepaper manipulatives

colored paper

colored pencils, markers,and/or crayons

Make math journalsor all students

Distribute materialsto other participatingteachers, i applicable

Notes


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More Resources romTeActaral Fondaton

BEST PRACTICES GUIDE

Students achieve with ASA grants

Students and Mentors:

A Powerful Combination

Octavio,

Grade8AllAbout

Algebra

Erica,Grade11

PumpedAbout

Probability

Katie,Grade5Having Fun

With Fractions

Expect the Unexpected with Math

Shake, Rattle, & Roll and Bars, Lines, & Pies, educational pro-grams unded by the Foundation and developed and distributedby Scholastic, the global childrens publishing education and mediacompany, are designed to provide teachers and students withmath literacy-based materials that meet national standards andare in alignment with core school curriculum. These skill-buildingprograms provide lesson plans, activities and other teachingresources while incorporating and applying actuaries naturalmathematics expertise in real world situations.

To learn more about the program, or to download a copy, visit

www.actaralfondaton.org/grant/ndex.tml.

Advancing Student Achievement GrantsAdvancing Student Achievement helps support your eorts inthe classroom by integrating hands-on, practical mathematicsskills brought to lie by practicing proessionals into youreveryday curriculum.

As part o that program, The Actuarial Foundation oers undingo mentoring programs that involve actuaries in supporting yourschools teaching o mathematics.

For inormation on this program and to nd out how you can applyor an ASA grant, visit www.actaralfondaton.org/grant/.

Best Practices Guide

This guide eatures a compilation o research on the valueo mentoring, combined with 15 case histories o programsunded by the Foundation, each o which includes inormationon program design and results.

To request a hard copy o the Best Practices Guide, sendan e-mail to [email protected] or to download a copy, visitwww.actaralfondaton.org/grant/bestractces.tml.

Math

Math Academy Series

Real-lie applications o mathematics while having un? Isit possible? Yes! Created by teachers or teachers, the MathAcademy tools and activities included in these booklets weredesigned to create hands-on activities and a un learning envi-ronment or the teaching o mathematics to students. You canuse Math Academy activities to enhance your math instructionwhile staying true to the academic rigor required by the statestandards ramework. To download other booklets visit:www.actaralfondaton.org/yot/matacademy.tml.

MathAcademyAre You Game?Explorations in Probability

SUPPLEMENTALMATHMATERIALSFORGRADES36


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PH: 847.706.3535FX: 847.706.3599

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Documents

Math Academy Mall