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