Post on 25-Feb-2018
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Investigating Patterns
For the Love of the Game
Materials needed:
Graph paper, map pencilsand/or highlighter, IAB
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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 %
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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
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he game is set for a #ecem*er
release2 Level 01s lead designer,
Flo-d )astle, sat down with 's for a
one3on3one interview2
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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
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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
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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
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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
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! 9 ; 0( +%
L < = < L
Level > ofs&'aresadded
Perimeter otalArea
! ! + !
(
%
+
9
;
0
Investigate the
patterns in the logo*- completing the
ta*le2
H %
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! 9 ; 0( +%
L < = < L
Level > ofs&'aresadded
Perimeter otalArea
! ! + !
(
%
+
9
;
0
Investigate the
patterns in the logo*- completing the
ta*le2
H!
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! 9 ; 0( +%
L < = < L
Level > ofs&'aresadded
Perimeter otalArea
! ! + !
(
%
+
9
;
0
Investigate the
patterns in the logo*- completing the
ta*le2
M8 !st
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!2
(2
%2
+2
2
92
2
Level > ofs&'aresadded
Perimeter otalArea
! ! + !(
%
+
9
;
0
8hat patterns do
-o' notice in the
col'mns and rows
of the ta*le4
H!
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!2
(2
%2
+2
2
92
2
Level > ofs&'aresadded
Perimeter otalArea
! ! + !(
%
+
9
;
0
8hat patterns do
-o' notice in the
col'mns and rows
of the ta*le4
H%
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!2
(2
%2
+2
2
92
2
Level > ofs&'aresadded
Perimeter otalArea
! ! + !(
%
+
9
;
0
8hat patterns do
-o' notice in the
col'mns and rows
of the ta*le4
M8!
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?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
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@, 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
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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
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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
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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$pression
that co'ld *e 'sed to
determine the n'm*er
of health pointsperimeter"
regenerated at an-
level in the game2
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?ow let1s see how the
e$pression wors2
)ompare -o'r
answer with -o'r
partner2
Cse the e$pression -o'
wrote to determine the
n'm*er of health points
regenerated for acharacter at level 2
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Let1s loo at another
col'mn
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Cse the varia*le DLE to
represent the level
n'm*er of a character
in the game2
est -o'r e$pression
*- 'sing Levels %, 9,
and ; and solving2
#o -o'r answersmatch what is in
those col'mns4
8rite an e$pression for
finding the total n'm*er
of s&'ares added at
each level2
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?ow let1s 'se -o'r
e$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
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Finall-, let1s loo at the
+thcol'mn, it shows the
total area for each level2
Cse the varia*le DLE
to write an
e$pression for
finding the total area
of the logo *ased on
the level n'm*er2
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.o -o' can 'se ta*les and
e$pressions to show the
same information2
B't that1s not all, 7o' can
also 'se graphsa*les, e$pressions and
graphs are among the
m'ltiple representations for
dealing with a pro*lem2
Let me show
-o'2
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Let1s graph the data from the
ta*le on the appropriate grid2
8e will mae % graphs2 In
all % the level n'm*er will
*e the independent
varia*le *eca'se the more
games we win the higherthe level we o*tain2
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@n the !st
graph we will
show the
relationship*etween the
Level ?'m*er
and the > of
.&'ares Added2
@n the (nd
graph we will
show the
relationship*etween the
Level ?'m*er
and the
Perimeter2
@n the %rd
graph we will
show the
relationship*etween the
Level ?'m*er
and the otal
Area2
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?ow we m'st decide on what
n'm*er scale we will 'se2
?e$t, mae s're we la*el
o'r $ and - a$is according
to o'r pro*lem and then
plot the points2
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Loo at -o'r graphs2 #o an-
of them represent a Linear
Model4
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7o' spoe earlier a*o'tm'ltiple representations2 Are
there other wa-s the logo
represents this4
@ooooohhhh2 Good
&'estion2Let1s tae another loo at
the > of .&'ares Added
col'mn2
hese n'm*ers
represent the n'm*er
of gold coins ac&'ired
at each level2 8e
alread- have one
e$pression for finding
the n'm*er of coins at
each level2 Let1s loo at
the logo in a different
wa-2
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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
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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
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Are the val'es the same or
different4
8h- do -o' thin this
happened4
8ell game design is an
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.ome of -o'r previo's
titles have received mi$ed
reviews from the gaming
comm'nit-2 How are -o'
addressing this in -o'r
new game4
8ell, game design is an
interesting field of st'd-2As gamers we want to *e challenged,
*'t we also need to feel as tho'gh
we1re *eing rewarded appropriatel- for
o'r efforts2
From a development
standpoint, that1s easier
said than done2
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@'r first game,
Realm of Empires,
had a great stor-2 B't
it was too eas- and
pla-ers felt the- didn1tget mone-1s worth2
@'r last game, Rube Goldbergs Lab,
ended 'p *eing too comple$ 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
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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
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o *alance the additional time
and comple$it- of each level,
the rewards sho'ld alsoincrease accordingl-2
Let me show -o'2
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Loo at the following
graphs2#o either one represent a
linear model4
8hich set of data wo'ld
*e *est represented *-
each4 8h-4
Graph A Graph B
)ompare and )ontrast:
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)ompare and )ontrast:the process of designing and/or pla-ing a
video game to completing a math pro*lem2
Process of designingand/or pla-ing a video
game
)ompleting a mathpro*lem
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opic: Investigating Patterns
ool Bo$:?'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
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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
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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