Investigating Patterns

7/25/2019 Investigating Patterns

1/43

Investigating Patterns

For the Love of the Game

Materials needed:

Graph paper, map pencilsand/or highlighter, IAB


2/43

Homewor

For each of the patterns:!" #raw the ne$t % shapes in the se&'ence

(" )reate a ta*le with the shape n'm*er in the first col'mn and the

n'm*er of addition shapes added to get to the ne$t shape, do this for

the ne$t % shapes

%" #escri*e in words how the pattern changes

+" )reate an e$pression for the data" Graph -o'r res'lts from the ta*le

.hape ! .hape ( .hape % .hape ! .hape ( .hape %


3/43

he Springboard Informer

is pleased to *ring -o' an

e$cl'sive snea pee at

Level 0 .t'dio's1'pcoming m'ltipla-er

game, Modus Operandi2


4/43

he game is set for a #ecem*er

release2 Level 01s lead designer,

Flo-d )astle, sat down with 's for a

one3on3one interview2


5/43

Before we get into thegame, tell 's a little

a*o't the compan-

itself2 Is there an-

significance to the

name4

here is, act'all-2 I pla-ed a ton of

video games while I was growing 'p2

I1d spend ho'rs and ho'rs tr-ing to

fig're o't how to *eat certain levels2

hat all changed when I too Alge*ra2


6/43

Alge*ra4

hen I made

the

connection

*etween m-approach to

a partic'lar

level in a

video game

and the

process ofcompleting

an Alge*ra

pro*lem2

he rest is

histor-,

Level 0.t'dios was

*orn2

At first, Alge*ra didn1t interest

me that m'ch *eca'se it 5'st

seemed lie a *'nch of steps

str'ng together that I wass'ppose to memori6e2

I preferred video games

*eca'se I felt challenged

to see o't a pattern and

felt confident in nowing

that there was often

more than one wa- to

complete a level2


7/43

7o' started a video

game design

compan- in -o'r

Alge*ra class4

Hehehehe2 8ell, not

reall-, *'t I did design the

logo in st'd- hall one da-2

he logo represents a

s-m*ol of that

connection I made,

and it has *ecome the

*asis for the design

principles of o'r

games2


8/43

First I

started *-

looing for a

pattern

Here I will

wal -o'

thro'gh the

steps

Begin *-

cop-ing this

design on graphpaper2

)olor the

s&'ares lie I

did, it will mae

it easier2

! 9 ; 0( +%

L < = < L


9/43

! 9 ; 0( +%

L < = < L

Level > ofs&'aresadded

Perimeter otalArea

! ! + !

(

%

+

9

;

0

Investigate the

patterns in the logo*- completing the

ta*le2

H %


10/43

! 9 ; 0( +%

L < = < L


Perimeter otalArea

! ! + !

(

%

+

9

;

0

Investigate the


ta*le2

H!


11/43

! 9 ; 0( +%

L < = < L


Perimeter otalArea

! ! + !

(

%

+

9

;

0

Investigate the


ta*le2

M8 !st


12/43

!2

(2

%2

+2

2

92

2


Perimeter otalArea

! ! + !(

%

+

9

;

0

8hat patterns do

-o' notice in the

col'mns and rows

of the ta*le4

H!


13/43

!2

(2

%2

+2

2

92

2


Perimeter otalArea

! ! + !(

%

+

9

;

0

8hat patterns do

-o' notice in the

col'mns and rows

of the ta*le4

H%


14/43

!2

(2

%2

+2

2

92

2


Perimeter otalArea

! ! + !(

%

+

9

;

0

8hat patterns do

-o' notice in the

col'mns and rows

of the ta*le4

M8!


15/43

?ow 'se -o'r pattern to

predict the val'es for a

tenth level in the design2

)ompare -o'r

answer with -o'r

partner2


16/43

@, I see that the

logo has plent- of

different patterns in

it, *'t how does that

translate to gamedesign4

8ell, as in all video games, the wa- to

s'rvive is *- collecting health points,

or gold coins, or lives at each level2 In Modus Operandi, a

character can

regenerate health

points at each level2


17/43

ae a loo at the

Perimeter )ol'mn2

he n'm*er of health

points regenerated at

each level follows the

same pattern as the

n'm*ers in thePerimeter col'mn2

@ne pro*lem we

had was that

characters in o'r

game can reach 'p

to level 2 atherthan writing a

program that does

repeated

calc'lations, we

decided to come 'p

with an e$pression

for finding the

n'm*er of health

points regenerated

at an- level2


18/43

How does the perimeter of

each level compare to the

n'm*er of the level itself4

)ompare -o'r

answer with -o'r

partner2


19/43

Cse the varia*le DLE to

represent the level n'm*er

of a character in the game2

)ompare -o'r

answer with -o'r

partner2

8rite an e$pression

that co'ld *e 'sed to

determine the n'm*er

of health pointsperimeter"

regenerated at an-

level in the game2


20/43

?ow let1s see how the

e$pression wors2

)ompare -o'r

answer with -o'r

partner2

Cse the e$pression -o'

wrote to determine the

n'm*er of health points

regenerated for acharacter at level 2


21/43

Let1s loo at another

col'mn


22/43

Cse the varia*le DLE to

represent the level

n'm*er of a character

in the game2

est -o'r e$pression

*- 'sing Levels %, 9,

and ; and solving2

#o -o'r answersmatch what is in

those col'mns4

8rite an e$pression for

finding the total n'm*er

of s&'ares added at

each level2


23/43

?ow let1s 'se -o'r

e$pression to predict2

)ompare -o'r

answers with -o'r

partner2

#etermine the n'm*er

of gold coins

ac&'ired at the

following levels:a" Level !

*" Level %9

c" Level


24/43

Finall-, let1s loo at the

+thcol'mn, it shows the

total area for each level2

Cse the varia*le DLE

to write an

e$pression for

finding the total area

of the logo *ased on

the level n'm*er2


25/43

.o -o' can 'se ta*les and

e$pressions to show the

same information2

B't that1s not all, 7o' can

also 'se graphsa*les, e$pressions and

graphs are among the

m'ltiple representations for

dealing with a pro*lem2

Let me show

-o'2


26/43

Let1s graph the data from the

ta*le on the appropriate grid2

8e will mae % graphs2 In

all % the level n'm*er will

*e the independent

varia*le *eca'se the more

games we win the higherthe level we o*tain2


27/43

@n the !st

graph we will

show the

relationship*etween the

Level ?'m*er

and the > of

.&'ares Added2

@n the (nd

graph we will

show the


Level ?'m*er

and the

Perimeter2

@n the %rd

graph we will

show the


Level ?'m*er

and the otal

Area2


28/43

?ow we m'st decide on what

n'm*er scale we will 'se2

?e$t, mae s're we la*el

o'r $ and - a$is according

to o'r pro*lem and then

plot the points2


29/43

Loo at -o'r graphs2 #o an-

of them represent a Linear

Model4


30/43

7o' spoe earlier a*o'tm'ltiple representations2 Are

there other wa-s the logo

represents this4

@ooooohhhh2 Good

&'estion2Let1s tae another loo at

the > of .&'ares Added

col'mn2

hese n'm*ers

represent the n'm*er

of gold coins ac&'ired

at each level2 8e

alread- have one

e$pression for finding

the n'm*er of coins at

each level2 Let1s loo at

the logo in a different

wa-2


31/43

he diagrams *elow show the

First fo'r levels of the logo as

individ'al fig'res2

Beginning with the second

level, what ind of shape

appears to *e DmissingE

from each fig're4

How does that

answer compare

to the vales inthe otal Area

col'mn4


32/43

How can -o' 'se the val'es in

the otal Area col'mn to

generate the n'm*er of

s&'ares added in a given level4

Get the e$pression -o'

wrote for the otal Area

col'mn and the e$pression

-o' 5'st wrote and

generate anothere$pression for the n'm*er

of s&'ares added in a

given level2

hen 'se -o'r new

e$pression to find then'm*er of s&'ares added in

Level 9 and Level !2


33/43

Are the val'es the same or

different4

8h- do -o' thin this

happened4

8ell game design is an


34/43

.ome of -o'r previo's

titles have received mi$ed

reviews from the gaming

comm'nit-2 How are -o'

addressing this in -o'r

new game4

8ell, game design is an

interesting field of st'd-2As gamers we want to *e challenged,

*'t we also need to feel as tho'gh

we1re *eing rewarded appropriatel- for

o'r efforts2

From a development

standpoint, that1s easier

said than done2


35/43

@'r first game,

Realm of Empires,

had a great stor-2 B't

it was too eas- and

pla-ers felt the- didn1tget mone-1s worth2

@'r last game, Rube Goldbergs Lab,

ended 'p *eing too comple$ and

alienated man- cas'al gamers, who

gave 'p and &'it pla-ing the game2

8ith Modus Operandi,

we thin we1ve hit the

sweet spot2

@f co'rse Part of achieving


36/43

I1m g'essing

there1s

something in the

logo that

e$plains that

too4

@f co'rse Part of achieving

the appropriate *alance

involves two varia*lestime

and rewards2

For instance, we now we want it to

tae a certain amo'nt of time " to

reach the ma$im'm level or complete

the game2

8e also now that

earl- levels need to *e

completed or gained

&'icl-, with the later

levels *ecoming more

comple$ and tainglonger to complete2


37/43

o *alance the additional time

and comple$it- of each level,

the rewards sho'ld alsoincrease accordingl-2

Let me show -o'2


38/43

Loo at the following

graphs2#o either one represent a

linear model4

8hich set of data wo'ld

*e *est represented *-

each4 8h-4

Graph A Graph B

)ompare and )ontrast:


39/43

)ompare and )ontrast:the process of designing and/or pla-ing a

video game to completing a math pro*lem2

Process of designingand/or pla-ing a video

game

)ompleting a mathpro*lem


40/43

opic: Investigating Patterns

ool Bo$:?'meric and graphic representations of data

Linear vs2 non3linear data

Pattern recognition

Predictions *ased on patterns

How do I loo

for patterns4

8hen looing for a pattern compare the n'm*ers in the !st

col'mn to all the other col'mns2 Loo for n'm*ers changing'sing addition, s'*traction, m'ltiplication or division2

8hat is a

varia*le4A varia*le is a letter or s-m*ol 'sed to

represent one or more n'm*ers2

How is ane$pression

'sed4

An e$pression can *e 'sed to solve for an- given val'e2'st s'*stit'te the given val'e for the varia*le2


41/43

opic: Investigating Patterns

How do I

graph data4

After deciding what data will *e graphed, decide what n'm*er

scale will *e most appropriate2 8hat is the lowest and highest

n'm*ers that occ'r in -o'r data, can I co'nt *- !1s, (1s etc2 hen

mae s're to la*el the $ and - a$is correctl- 'sing the titles of the

col'mns2 hen plot -o'r points2

8hat does a

Linear Model

loo lie4

A Linear Model is a set of data that has a constant rate of

change slope" and a graph that loos lie a line2

8hat are

e&'ivalent

e$pressions4


42/43


43/43

Activit- !2!

! % % %

( 9 !( %

% 0 ( %

+ !( +; %

!" #escri*e an- patterns -o' notice in the ta*le of

val'es

(" Ass'me the pattern in each col'mn contin'es2 If

-o' were given a random n'm*er, how wo'ld -o'

determine if the n'm*er wo'ld appear in one of

the col'mns2

%" Based on -o'r investigation of the ta*le of val'es,

how co'ld -o' la*el the col'mns4

Investigating Patterns

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