ETHNOMATHEMATICS
STANDARD BENCHMARKS AND VALUES
SOLVE REAL-WORLD PROBLEMSUSING ENGINEERING DESIGN PROCESS
BY ELIZABETH FRILLES
HIGH SCHOOL NINTH - TENTH GRADETIMEFRAME APPROXIMATELY ONE MONTH
NĀ HOPENA A‘O:• Strengthened Sense of Hawai‘i• Strengthened Sense of Belonging • Strengthened Sense of Responsibility• Strengthened Sense of Excellence
THE COMMON CAREER TECHNICAL CORE (CCTC): CAREER READY PRACTICES1. Act as a responsible and contributing citizen and employee.2. Apply appropriate academic and technical skills.3. Attend to personal health and financial well-being.4. Communicate clearly, effectively and with reason.5. Consider the environmental, social and economic impacts
of decisions.6. Demonstrate creativity and innovation.7. Employ valid and reliable research strategies.8. Utilize critical thinking to make sense of problems and
persevere in solving them.9. Model integrity, ethical leadership and
effective management.10. Plan education and career path aligned to personal goals.11. Use technology to enhance productivity.12. Work productively in teams while using cultural/
global competence.
NEXT GENERATION SCIENCE STANDARDS (NGSS): SCIENCE AND ENGINEERING PRACTICES:1. Asking questions (for science) and defining problems
(for engineering).2. Developing and using models.3. Planning and carrying out investigations.4. Analyzing and interpreting data.5. Using mathematics and computational thinking.6. Constructing explanations (for science) and designing
solutions (for engineering).7. Engaging in argument from evidence.8. Obtaining, evaluating, and communicating information
COMMON CORE STATE STANDARDS (CCSS)• RST.11-12.7, RST.11-12.8, RST.11-12.9; • HS-ETS1-1, HS-ETS1-2, HS-ETS1-3, HS-ETS1-4;• HS-LS2-1, HS-LS2-2, HS-LS2-6, HS-LS2-7, HS-LS2-8,
HS-LS4-6;• HSG.MG.A.1, HSG.MG.A.2, HSG.MG.A.3, HSS.ID.A.2;• WHST.9-10.4, WHST.9-10.5, WHST.9-10.6, WHST.9-10.7,
WHST.9-10.8, WHST.9-10.9
What is Engineering and Engineering Design Process (EDP)?What is the difference between Engineering Design Process (EDP) and the Scientific Method?
How do engineers or designers help solve real-world problems, overcome technological challenges, and improve products?
How can we use the Engineering Design Process to solve design challenges?How can the Engineering Design Process help us to solve problems in our daily lives?
ETHNOMATHEMATICS
2Solve Real-World Problems Using Engineering Design Process
ENDURING UNDERSTANDINGEngineering Design Process is a method that is used to solve real-world issues, overcome technological challenges, and improve products for sustainability.
CRITICAL SKILLS AND CONCEPTS:Student(s) will be able to • list and explain the steps of the Engineering Design
Process (EDP).• explain the design involves a set of steps that
can be performed in different sequences and repeated as needed.
• describe how engineers, scientists, and others who engage in design and technology use scientific knowledge to solve practical problems.
• connect the importance of the Science and Engineering Practices, Math Practices, and Career and Technical Education (CTE) Practices when solving design challenges in creating prototypes of the products.
AUTHENTIC PERFORMANCE TASK: A technical report or display board that will include applied mathematics, technical or scientific data, and a written summary of the design challenge for presentation and evaluation.
AUTHENTIC AUDIENCE(S): Fellow students, other teachers, and science/engineering fair attendees.
ETHNOMATHEMATICS
3 Ethnomathematics
LEARNING PLANTEACHER PREPARATION• Create pre-test to hand out to students to assess prior knowledge.• Search for and bookmark video clips about Engineering Design
Process (EDP).• Prepare a Powerpoint presentation that covers the essential
questions and ask students open-ended questions to check for understanding.
• Research current issues in Hawai‘i.• Experiment with Tagxedo (www.tagxedo.com) in order to better
instruct students.• Provide copies of EDP graphic organizers and rubrics for
each student. • Prepare materials that inform students of safety protocols.• Provide examples of how to write a technical report or create a
display board that summarizes findings.
INSTRUCTIONS1. Have students discuss the essential questions in groups.2. Show the students a video about EDP (https://www.youtube.
com/watch?v=fxJWin195kU); next have each student write down their own definition of EDP and take turns sharing them as a class.
3. Students will brainstorm critical issues in Hawai‘i that could be solved with technology and use Tagxedo(http://www.tagxedo.com/) to create a word cloud.
4. Group students into teams, and have each team select an issue to research and solve.
5. Students will be provided with an EDP graphic organizer and rubric. Give them time to read the materials and ask clarifying questions.
6. Students will use the EDP graphic organizer to help them design their solutions with reference to the rubric.
7. Give students time in class to prepare materials and create prototypes of products (always keeping safety in mind).
8. Once each group has a prototype, provide class time for students to compose their technical reports or create display boards that summarize their design solution.
9. Have student groups present their projects and evaluate each other using the rubrics provided earlier.
10. Finally, allow students to reflect on the process.
ETHNOMATHEMATICS
4
REFERENCES/RESOURCES:English Language Arts Standards » Science & Technical Subjects » Grade
9-10. (n.d.). Retrieved from http://www.corestandards.org/ELA-Literacy/RST/9-10/English Language Arts Standards » Writing » Grade 9-10. (n.d.). Retrieved
from http://www.corestandards.org/ELA-Literacy/WHST/9-10/High School: Geometry » Modeling with Geometry. (n.d.). Retrieved from
http://www.corestandards.org/Math/Content/HSG/MG/. High School: Modeling. (n.d.). Retrieved from http://www.corestandards.org/Math/Content/HSM/.High School: Statistics & Probability » Interpreting Categorical &
Quantitative Data. (n.d.). Retrieved from http://www.corestandards.org/Math/Content/HSS/ID/.Nā Hopena A‘o Learning Outcomes in Hawai‘i | EPIC. (2015, September
24). Retrieved from http://www.epiconline.org/na-hopena-ao-learning-outcomes/
Next Generation Science Standards. (n.d.). Retrieved from http://www.nextgenscience.org/Standards for Mathematical Practice. (n.d.). Retrieved from http://www.
corestandards.org/Math/Practice/. The Career Ready Practices | Advance CTE. (n.d.). Retrieved from http://
www.careertech.org/career-ready-practicesEngineering Design Processhttp://www.sciencebuddies.org/engineering-design- process/engineering-
design-process-steps.shtml https://www.teachengineering.org/k12engineering/designprocess Engineering Design Process versus Scientific Method http://www.sciencebuddies.org/engineering-design- process/engineering-
design-compare-scientific-method.shtml NASA Engineering Design Processhttps://www.nasa.gov/audience/foreducators/best/edp.html VIDEOS What’s an Engineer? Crash Course Kids #12.1 https://www.youtube.com/watch?v=owHF9iLyxic The Engineering Process: Crash Course Kids #12.2https://www.youtube.com/watch?v=fxJWin195kU
Solve Real-World Problems Using Engineering Design Process
6 Ethnomathematics
ETHNOMATHEMATICS
ENGINEERING DESIGN PROCESS (EDP)
NAME DATEPERIODSUBJECT
STEP DESCRIPTION, EXPLANATION, DRAWING, ILLUSTRATION OR DIAGRAM
1. IDENTIFY THE PROBLEM• Re-state the problem• Identify the criteria or constraints
How can I design a _________ that will __________?
2. RESEARCH THE PROBLEM• Examine the current state of the issue and current
solutions• Explore the other options via internet, library,
interviews, etcetera
3. BRAINSTORM SOLUTIONS • Develop possible solutions• Draw on mathematics and science• Articulate possible solutions in two or three dimensions• Sketch ideas with Labels and arrows to identify parts
and function 4. CHOOSE A SOLUTION
• Develop possible solutions• Draw on mathematics and science• Articulate possible solutions in two or three dimensions• Sketch ideas with Labels and arrows to identify parts
and function5. CREATE & DEVELOP A PROTOTYPE
• Model the selected solution(s) in two or three dimensions
• Construct a full-size or scale model based on their drawings
6. TEST AND EVALUATE THE PROTOTYPE• Does it work?• Does it meet the original design criteria or constraints?
7. IMPROVE & REDESIGN • Does it work?• Does it meet the original design criteria or constraints?
8. PRESENTATION• Communicate the solution(s) by making an engineering
presentation that includes a discussion of how the solution(s) best meet(s) the needs of initial problem, opportunity, or need
• Discuss societal impact and tradeoffs of the solutions
7Solve Real-World Problems Using Engineering Design Process
ENGINEERING DESIGN PROCESS (EDP)
STUD
ENT
NAM
E (I
NIT
IALS
ON
LY)
SUBJ
ECT
TEAC
HER
/FAC
ILIT
ATO
RPE
RIO
DDA
TE
STEP
WEL
L-BE
LOW
(1-P
OIN
T)AP
PRO
ACH
ING
(2-P
OIN
T)M
EETS
(3-P
OIN
T)EX
CEED
S (4
-PO
INT)
STUD
ENT
SELF
-AS
SESS
MEN
T
TEAC
HER
ASSE
SSM
ENT
1 - I
DEN
TIFY
TH
E PR
OBL
EM
Stud
ent(s
) can
not s
tate
the
chal
leng
e pr
oble
m in
his/
her
own w
ords
.
Stud
ent(
s) se
ek h
elp
from
thei
r PBL
Fa
cilit
ator
to st
ate
the
chall
enge
pro
blem
in
his/h
er o
wn w
ords
.
Stud
ent(
s) c
an s
tate
the
chal
leng
e pr
oble
m
in h
is/h
er o
wn
wor
ds w
ithou
t any
hel
p fr
om
PBL F
acili
tato
r.
Stud
ent(
s) c
an in
depe
nden
tly st
ate
the
prob
lem
in h
is/he
r wor
ds p
reci
sely
and
expl
icitl
y usin
g hi
gher
leve
l of v
ocab
ular
y.
2 - R
ESEA
RCH
TH
E PR
OBL
EM
Stud
ent(
s) w
rite
a sh
ort 5
-sen
tenc
e su
mm
ary o
f the
rese
arch
whi
ch
inclu
des 1
relia
ble
sour
ce.
Stud
ent(
s) w
rite
a sh
ort 1
0-se
nten
ce
sum
mar
y of t
he re
sear
ch w
hich
inclu
des 2
re
liabl
e so
urce
s.
Stud
ent(
s) w
rite
a br
ief 1
5-se
nten
ce su
mm
ary o
f th
e re
sear
ch w
hich
inclu
des 3
majo
r ref
eren
ces
or re
liabl
e so
urce
s.
Stud
ent(
s) w
rite
a cle
ar a
nd c
onci
se
20-s
ente
nce
sum
mar
y of t
he re
sear
ch w
hich
in
clude
s 4 o
r mor
e re
liabl
e so
urce
s.
3 - B
RAIN
STO
RM
SOLU
TIO
NS
Stud
ent(
s) c
anno
t ske
tch
or d
raw
th
eir i
deas
. No
label
s and
arr
ows
pres
ent o
n hi
s/her
not
es. N
o st
uden
t pa
rtic
ipat
ion
is ob
serv
ed.
Stud
ent(
s) se
ek h
elp
from
PBL
faci
litat
ors
how
to sk
etch
or d
raw
his/
her i
deas
. Som
e lab
els a
nd a
rrow
s are
miss
ing.
Stud
ent(
s)
rare
ly pa
rtic
ipat
e in
the
disc
ussio
n.
Each
stud
ent i
n th
e gr
oup
can
sket
ch h
is/he
r ow
n id
eas a
s the
gro
up d
iscus
ses w
ays t
o so
lve
the
prob
lem
. Lab
els a
nd a
rrow
s sho
uld
be
inclu
ded
to id
entif
y par
ts a
nd h
ow th
ey m
ight
m
ove.
The
stud
ent(
s) a
ctive
ly pa
rtic
ipat
ed in
the
disc
ussio
n gu
ided
by t
he P
BL fa
cilit
ator
.
Stud
ent(
s) c
an in
depe
nden
tly b
rain
stor
m
the
desig
n’s s
peci
ficat
ions
, lim
its a
nd
requ
irem
ents
pre
cise
ly an
d ex
plic
itly a
s a
grou
p. S
tude
nt(s
) can
inde
pend
ently
reco
rd
pros
and
con
s of e
ach
desig
n id
ea d
irect
ly on
the
pape
r nex
t to
the
draw
ings
.
4 - C
HO
OSE
A
SOLU
TIO
N
Stud
ent(
s) d
id n
ot a
ttem
pt to
sp
ecify
des
ign
limita
tions
and
re
quire
men
ts. M
easu
ring
tool
s and
un
its a
re n
ot u
sed
appr
opria
tely.
No
safe
ty m
easu
re is
obs
erve
d.
Stud
ent(
s) h
as li
mite
d kn
owle
dge
on th
e sp
ecifi
catio
ns a
nd c
onst
rain
ts o
f the
de
signs
. Mea
sure
men
ts a
re n
ot p
reci
se.
Tool
s are
use
d in
appr
opria
tely
. Saf
ety
is vi
olat
ed b
y on
e or
two
stud
ents
in
the g
roup
.
Stud
ent(
s) c
an sp
ecify
the
desig
n re
quire
men
ts
(crit
eria)
. Stu
dent
(s) c
an lis
t the
limits
on
the
desig
n du
e to
ava
ilabl
e re
sour
ces a
nd th
e en
vi-ro
nmen
t (co
nstr
aints
). Dr
awin
gs a
re n
eat,
usin
g ru
lers
to d
raw
stra
ight
lines
and
to m
ake
part
s pr
opor
tiona
l. Par
ts a
nd m
easu
rem
ents
shou
ld b
e lab
eled
cle
arly
and
prec
isely.
Saf
ety i
s pra
ctice
d by
the
entir
e gr
oup.
Stud
ent(
s) d
evel
op tw
o or
mor
e id
eas
thor
ough
ly an
d ca
n cr
eate
new
dra
win
gs
that
are
ort
hogr
aphi
c pr
ojec
tions
(mul
tiple
vie
ws s
how
ing
the
top,
fron
t and
one
side
) an
d iso
met
ric d
raw
ings
(thr
ee-d
imen
siona
l de
pict
ion)
. Saf
ety i
s str
ictly
obs
erve
d.
5 - C
REAT
E &
DEVE
LOP
A PR
OTO
TYPE
Stud
ent(s
) cho
ose
a des
ign
to so
lve
the
prob
lem
how
ever
lack
ing
in
reas
ons t
o w
hy it
was
cho
sen.
Mod
el
or p
roto
type
is in
com
plet
e. Sa
fety
is
not o
bser
ved.
Stud
ent(
s) so
mew
hat i
dent
ify th
e be
st
desig
n to
solv
e th
e ch
alle
nge
prob
lem
. St
uden
t(s)
writ
e th
e re
ason
why
he/
she
chos
e th
e so
lutio
n bu
t lac
king
in d
etai
ls.
Mod
el o
r pro
toty
pe is
con
stru
cted
po
orly
show
ing
inco
rrec
t mea
sure
men
ts.
Safe
ty is
loos
ely
obse
rved
dur
ing
the
cons
truc
tion
proc
ess.
Stud
ent(
s) ca
n id
entif
y the
des
ign
that
appe
ars t
o so
lve th
e pr
oble
m th
e be
st. S
tude
nt(s
) can
writ
e a
stat
emen
t tha
t des
crib
es w
hy h
e/sh
e ch
ose
the
solu
tion
whi
ch in
clude
s so
me
refe
renc
e to
the
cr
iteria
and
cons
train
ts. S
tude
nt(s
) can
cons
truc
t a f
ull-s
ize o
r sca
le m
odel
bas
ed o
n th
eir d
raw
ings
. Th
e PB
L Fa
cilit
ator
will
help
iden
tify
and
acqu
ire
appr
opria
te m
odel
ing
mat
erial
s an
d to
ols.
Safe
ty
is ob
serv
ed d
urin
g th
e co
nstr
uctio
n pr
oces
s.
Stud
ent(
s) c
an in
depe
nden
tly id
entif
y th
e be
st d
esig
n to
solve
the
prob
lem
an
d w
rite
the
ratio
nale
of t
he so
lutio
n in
a 5
-par
agra
ph e
ssay
. Stu
dent
(s) c
an
inde
pend
ently
iden
tify t
he a
ppro
priat
e to
ols a
nd m
ater
ials n
eede
d to
con
stru
ct th
e m
odel
or p
roto
type
. Pre
cise
mea
sure
men
ts
and
safe
ty a
re a
dher
ed th
roug
hout
the
cons
truc
tion p
roce
ss.
6 - T
EST
& EV
ALUA
TE
PRO
TOTY
PE
Stud
ent(
s) d
id tr
y to
exam
ine
and
evalu
ate
the
mod
el o
r pro
toty
pe.
Stud
ent(
s) so
mew
hat e
xam
ine
and
evalu
ate
the
mod
el o
r pro
toty
pe w
ith a
lot o
f hel
p fro
m th
e PB
L fa
cilit
ator
.
Stud
ent(
s) c
an e
xam
ine
and
evalu
ate
his/
her p
roto
type
or d
esig
n ba
sed
on th
e cr
iteria
an
d co
nstr
aints
with
som
e he
lp fr
om th
eir
PBL f
acilit
ator
.
Stud
ent(
s) c
an in
depe
nden
tly e
xam
ine
and
evalu
ate
work
ing
mod
el o
r pro
toty
pe a
nd
pres
ent i
t tho
roug
hly t
o ot
her t
eam
s.
7 - I
MPR
OVE
&
REDE
SIGN
The
pres
enta
tion
is po
or a
nd th
e br
ainst
orm
ing
with
oth
er te
ams
lack
det
ails.
The
prob
lem
s are
not
id
entifi
ed a
nd n
o cl
ear p
ropo
sal
is cr
eate
d.
Stud
ent(s
) pre
sent
the fi
ndin
gs to
oth
er te
ams
but n
ot th
orou
gh. B
rain
stor
min
g is p
oorly
co
nduc
ted
due t
o lac
k of d
etail
s, th
e pro
blem
is
not c
learly
iden
tified
and
the p
ropo
sal t
o th
e so
lutio
n is
weak
.
Stud
ent(
s) w
ill pr
esen
t the
ir wo
rkin
g m
odel
or
prot
otyp
e to
oth
er te
ams.
Stud
ent(
s) w
ill en
list
othe
r stu
dent
s to
revie
w th
e so
lutio
n an
d he
lp
iden
tify c
hang
es th
at n
eed
to b
e m
ade.
The
team
m
ust i
dent
ify a
ny p
robl
ems a
nd p
ropo
sed s
olu-
tions
.
Stud
ent(
s) c
an b
rain
stor
m u
sing
high
leve
l cr
itica
l thi
nkin
g qu
estio
ns w
ith o
ther
team
s. St
uden
t(s)
or t
eam
(s) c
an id
entif
y the
main
pr
oble
ms a
nd p
ropo
se so
lutio
ns st
rong
ly in
deta
ils.
TIM
E M
ANAG
EMEN
TSt
uden
t(s)
did
not
use
tim
e we
ll. Ti
me
was
was
ted
durin
g ph
ase
2-5
of th
e ED
P.
Stud
ent(
s) so
met
imes
use
d tim
e we
ll. Th
ere
were
tim
es w
hen
the
grou
p go
t off
task
du
ring
phas
e 2-
5 of
the
EDP.
Stud
ent(
s) u
sed
time
appr
opria
tely,
a fe
w ti
mes
th
e gr
oup
got o
ff ta
sk, b
ut fo
r the
majo
rity o
f th
e ta
sk ti
me
was
wel
l spe
nt d
urin
g th
e ED
P.
Stud
ent(
s) u
sed
time
wise
ly. T
he g
roup
stay
ed o
n ta
sk d
urin
g ea
ch p
hase
of t
he E
DP.
TOTA
L &
COM
MEN
TS
ENGI
NEE
RIN
G DE
SIGN
PRO
CESS
(EDP
) 4-P
OIN
T RU
BRIC