THE BIOMECHANICS OF SKELETAL SYSTEMS: A STUDY OF IMPOSSIBILITIES AND THE

ADAPTATIONS THAT MAKE THEM A REALITY

Susan Kirking

Jenifer Junior High School Lewiston, ID

&

Tracy Coburn Washington State University

Pullman, WA

Washington State University Mentors Dr. David Lin

School of Chemical Engineering and Bioengineering

&

Kasey Schertenleib Research Associate

July 2005

The project herein was supported by the National Science Foundation Grant No. EEC-0338868: Dr. Richard I. Zollars, Principal Investigator and Dr. Donald C.

Orlich, co-PI. The module was developed by the authors and does not necessarily represent an official endorsement by the National Science Foundation.

Summary

Overview of Project. This module was designed to introduce students to bioengineering

and its applications in science and engineering, using scaling relationships and modeling, but it

was also constructed with the objective of allowing the students to have fun and express creative

license within given parameters. In putting together this module, we came to the agreement that

the appeal of cartoon characters would increase student interest and participation, thus increasing

the amount of knowledge gained by the individuals. While meeting the objectives of this

program by introducing the concept of engineering to the K-12 science classroom, we also strove

to incorporate mathematics in a manner which allowed the students to see how math is a core

concept in science and engineering and cannot be separated. Using cartoon skeletal drawings as

an example, students will follow guided inquiry techniques which will allow them to generate a

working model of the head-neck system and demonstrate a basic understanding of relationships

within skeletal structures. Cartoon characters were chosen for their extreme disproportion

between the head and neck, as well as their appeal and commonality. Students will use their

newfound knowledge to reflect on other aspects of body relationships such as the stability

generated through interactions between the skeleton, muscles, and tendons. It is intended that

students will be able to brainstorm and experiment to form neck adaptations which would be

capable of supporting the cartoon head, and then be able to present their findings to their

classmates in an assessed presentation.

Intended audience. This module was designed for an upper-middle-school Life Science

course (7th or 8th grade), but is easily adaptable for the high school level. It is not suggested that

1

this module be attempted at a lower grade level than the second half of seventh grade due to the

large amount – and level – of math involved.

Estimated duration. The module was designed to run on a 90-minute period schedule for

6 class days. Adaptations for the upper levels will take less time, but a minimum of 3 days will

be needed. It is suggested by the authors that the day of model construction and paper Mache

fall on a Friday so as to give the model time to dry.

Introduction

Many fields of employment involve aspects of engineering rarely considered by students

faced with choosing a career path. The word engineering often evokes images of large quantities

of math and physics. This module is designed to not only provide a valuable life-science lesson,

but to also expose students to the options available to them within engineering. It is important

that students realize creativity is a driving force in engineering, and that it is utilized in many

different fields from bridge- and car-design, to the discovery of new medications and earth-

friendly products, to animation and computer graphics. Students interested in art, science, math,

and computers, among others, are all equally exposed to some aspect of engineering, and it is the

teacher’s job to guide them towards understanding this aspect of their interest.

Rationale

Engineering, as a discipline, has seldom been explored or considered by students in the

traditional K-12 education system. The study of body systems is an integral unit to Life Science

during the middle school experience, but students rarely get the opportunity to study how those

2

systems interact with and support one another. This module will give students the opportunity to

study the engineering factors which demonstrate how skeletal and muscular systems function

together, and how they fail when acting independently.

Over the course of this module activity, students will gain knowledge which will allow

them to be able to describe the science and engineering behind their understanding of why and

how skeletal relationships work.

Science

Why? This question is addressed on a daily basis by scientists studying our surroundings,

our world, and our universe. It has allowed us to better understand the relationship between

living and non-living things, the cycles found in nature, and the forces which affect our everyday

lives. Science has made the terms “double helix”, “environmental impact”, and “gravity” part of

our everyday jargon. Advancements in medicine have increased life span, lowered infant

mortality, and given us the means by which to manage our rate of population growth.

Engineering

Although scientific discoveries have long served to promote humanity out of our

primitive origins, it has taken the creativity and inventiveness of engineers to construct the tools

which have allowed those scientific discoveries to be put to use. From concepts as functional as

the wheel, which propelled us into mobility, to those as convenient as cell phones, engineers

have continually provided physical manifestations of scientists’ discoveries.

3

Goals

The student will be able to:

Perform mathematical measurements and scaling conversions including volume, area, circumference, and weight. (ID Math 327.01.b, 327.02.a, 329.03.a, 331.01, 339.01; WA Math EALR 1.1, 1.2, EALR 2.2.2)

Calculate proportional up-scaling of figures based on measurements taken from drawings (ID Math 327.01.b, 327.02.a, 328.01.a, 329.03.a, 331.01, 339.01, 341.01; WA EALR Math 1.1, 1.2, 2.2)

Create physical models based on mathematical findings from up-scaling (ID Math 328.03.c, 331.01 Science 633.02; WA Math EALR 1.1, 1.2, 2.2; Science EALR 3.1, GLE 2.1.3, 2.1.4, 3.1.2)

Test findings according to the scientific method

(ID Science 633.02, 643.01; WA Science EALR 2.1, 3.1, GLE 3.1.2) Explain their findings in a presentation using illustrations/models/diagrams/available

technology such as power point (ID Science 633.02, 643.02; WA Science EALR 3.2, GLE 2.1.3, 2.1.4, 3.2.3)

Prepare a written self-analysis of findings and how they agreed with/conflicted with

group analysis. (ID Science 633.01, 633.02, 637.01.b, 643.01, 643.02; WA Math 4.2, 5.2, 5.3, Science EALR 3.2, GLE 2.1.3, 3.1.2)

Gain an appreciation of engineering.

(WA Math EALR 5.2, 5.3; Science EALR 2.1, 3.1, 3.2, GLE 3.1.2, 3.2.3)

4

Idaho State Standards for Grade 7

Math

327.01.b. Expand the use of percents and ratios to solve problems

327.02.a. Add, subtract, multiply, and divide fractions and decimals

328.01.a. Use a variety of strategies including common mathematical formulas to

compute problems drawn from real-world situations

328.03. c. Select appropriate models to represent mathematical ideas.

329.03.a. Develop the use of proportions, ratios, and scales

331.01 Apply concepts of size, shape, and spatial relationships

339.01 Understand and use U.S. customary and metric measurements

Science

633.01 Understand systems, order, and organization

633.02. Understand concepts and processes of evidence, models, and explanation.

637.01.b. Know that species may become extinct when the environment changes and their adaptive characteristics are insufficient to allow their survival

643.01 Understand that interpersonal relationships are important in scientific endeavors

643.02 Understand technical communication

5

Washington State Standards for Grade 7

EALR (Essential Academic Learning Requirements)

MATH

1.1 Understand and apply concepts and procedures from number sense.

1.2 Understand and apply concepts and procedures from measurement.

2.2. Apply strategies to construct solutions.

3.2. Make predictions, inferences, conjectures, and draw conclusions.

4.1. Gather information.

4.2. Organize, represent, and share information.

5.2. Relate mathematical concepts and procedures to other disciplines.

5.3. Relate mathematical concepts and procedures to real-world situations.

SCIENCE

2.1. Investigating Systems: Develop the knowledge and skills necessary to do scientific

inquiry.

3.1. Designing Solutions: Apply knowledge and skills of science and technology to

design solutions to human problems or meet challenges.

3.2. Science, Technology, and Society: Analyze how science and technology are human

endeavors, interrelated to each other, society, the workplace, and the environment.

GLE (Grade Level Expectations)

MATH

1.1.4. Understand the concept of direct proportion.

2.2.2. Apply mathematical tools to solve the problem.

SCIENCE

2.1.3. Apply understanding of how to construct a scientific explanation using evidence

and inferential logic.

odels are used to investigate objects, events, systems, and processes 2.1.4. Analyze how m

3.1.2. Apply the scientific design process to develop and implement solutions to

problems or challenges.

science, mathematics, and technology within

3.2.3. Analyze the use of

occupational/career areas of interest.

6

Equipment

Head Construction

• Chicken wire

• Lengths of wire or twist ties

• Wire cutters

• Gardening gloves

• First Aid kit

• Permanent markers

Paper Mache

• Flour

• Newspaper

• Shallow pans/bowls

• Plastic bags for drop-cloths

Decoration of Head

• Paint – liquid and spray

• Markers

Weighting the Head

• Felt or thick fabric (to line inside of

head and prevent punctures)

• Scale

• Weight (we suggest lead shot) for

head, divided into tear-proof bags of

varying weight)

• Bags – we suggest Ziploc baggies for

the shot, reinforced by placing them in

paper lunch sacks (this keeps the

students from opening the baggies)

Neck Construction (suggestions – you can use

anything that comes to mind)

• No-slip rug backing

• Bubble wrap – varying sized bubbles

• Wrapping paper (or similar) tubes

• Straws

• ¼ thick inch Foam

• Construction paper

• Rubber bands

• Toothpicks

Measuring Tools

• Rulers – one for each student

• Tape measures – regular and soft (one

soft tape per group)

• Calculators – one for each student

Clean-up

• Water – easy access to a sink/clean-up

facilities

• Paper towels

7

Resources/Technology

jector

oard/smartboard

rkers/chalk/stylus

Camera or video camera

Pre q ledge

teachers should re e s of skeletal structures

ased mammals) to make sure stud t t some understanding of

weight vs. strength and the adaptations which have ure.

ill be best equipped for this exercise t of

o make conversions from metric s

pro rt for volume, iameter, using

provide so be able to accu te rs,

tape measures, and scales.

• Computers

• Printer

• LCD projector

• Overhead pro

• Whiteboard/chalkb

• Dry-erase ma

• Textbooks

• Digital

re uisite Student Skills/Know

Prior to starting this module, vi w different type

(e.g. aerial vs. land-b en s have at leas

been made in nat

Students w if hey have a basic understanding

algebra and are able t to tandard and vise versa, calculate

circumference, and dpo ional scaling, and make computations

d formulas. Students must al ra ly use measuring tools such as rule

8

Information for the Teacher

Safety. Students should be aware of proper laboratory conduct and the teacher should

rem d the hazards of this activity. Hazards include possible cuts from the wire and

inju f eights on toes, among others.

in them of

ry rom dropping w

Instructional Strategies. Instructor will utilize the following three strategies to maximize

stud t ts will respond to questions posed by the teacher in

written and oral format; as well as record any questions they may have for the instructor;

(2) i ing in think-pair-share format; (3) flow chart, directing

udents through the procedures of the lab and indicating key objectives

en learning: (1) journaling – studen

ind vidual/pair/classroom brainstorm

st

Grouping of Students. Students will work independently and in pairs, and will share

ideas/findings as a class.

Family Interactions. Parents/guardians will assist in homework worksheet, and will be

require on

f

Supplemental Material

d to sign homework for full student credit. There will be an open line of communicati

between the teacher and parents/guardians, and parents/guardians are welcome to

observe/contact the teacher at any time. The teacher will keep the parents/guardians notified o

their student’s progress, both good and bad.

. Worksheets, grading rubrics, and presentation guidelines have

een included at the back of the module, as has an answer key for the Marvin Worksheet.

b

9

Construction of Wire Frame Head. Cut a 12.5-inch-wide strip by 25-inch-long strip from

a roll o

ect

together using wire or twist-ties. Bend the

edges until your model head is roughly circular, making cuts if necessary to create more round-

ness. C

ecipe for Paper Mache

f chicken wire (it is suggested that if the wire roll is 25 inches long, you cut the 25-inch-

long strip along the length of wire, as it gives a better surface to wire together a circle). Conn

the two 12.5-inch-long edges and secure the two ends

ut a “hatch” into the top or side of your model head, through which you will place your

weights. Be sure to cover the hatch as well as the main head when paper Mache-ing, being

careful to mark the hatch edges or covering it separately.

25” long cut 25” wide Roll 12.5” wide cut Direction of Wire Roll

R . Rip (DO NOT CUT) the newspaper into 1-1.5” wide strips of

paper.

newspaper

edges and covering all the wire completely. Using

ng str s of paper Mache for more complete coverage and less work in the long run! Allow to

dry in a

Avoid using shiny or thick-papered inserts. Mix flour with water until it reaches a runny

paste-like consistency. Be sure to work out all the lumps by squeezing them until they are

dissolved. This will ensure more rapid and even drying. Working quickly, dip the

into the paper Mache “soup” and squeegee off excess liquid using your fingers. Drape the moist

paper over the chicken wire, overlapping the

lo ip

warm, dry area overnight before painting.

10

Parameters for Model Neck. Model Neck must be constructed according to the sizes

calculated by the students when scaling up their drawings for construction of the 25 inch tall

model. An example of how to do this scaling is included on page 29. Model neck

circumference will be calculated using model neck diameter (measurement F in the Marvin

Worksheet on page 27). In the even that multiple groups have successful model necks which do

not collapse under the head weight, the most successful group will be that which constructed

their model neck with the lowest weight.

11

Daily Activities

Day 1

Introduction – KWL (What I Know, What I Want to know, W

What do you know about engineering?

What does an engineer do?

T-P-S (Think, Pair,

hat I Learned) journal questions

What do you know about science?

What is the relationship between engineering and science?

Share) activity

List as many jobs as you can think of which involve engineering.

Lecture – present new math material

What is volume? What is surface area? What is the relationship between volume and surface area? How do you scale something up? How do you scale something down?

Marvin Worksheet and homework (see Supplemental Materials, pages 27- 28 and 23-24, respectively)

The authors have generated a worksheet (Marvin Worksheet) for the students to practice measuring lengths of different parts of the body, then scale those measurements up to 25” tall models. Also included is a homework worksheet with different story problems for students to practice calculating weights and taking measurements, making conversions (from cm to in, etc), taking averages, and scaling. Students should be sure to obtain parent/guardian signature at bottom, along the indicated line, to promote discussion of the project at home.

Review Marvin worksheet

Choose partners

Closure and exit activity (finish KWL card)

20-25 min

10 min

15 min 20 min 10 min 5 min 10 min

12

Day 2

Journal questions

Review homework worksheet (Supplemental Materials pp. 23-24 Measur cumference and neck length. average sed when students begin constructing their m el of an entire neck - muscles, tendons, etc. - rather than the

in with).

selection. Note to teacher: the website for cartoon skeleton drawings is e suggest that the entire class creates

models of the same drawing so results can be properly compared between

Make mcompar essary.

lecture-how to do conversions

r stud t character, checked by teacher. Studenof the hheight weight

Day 3

5-10 min

0-15 min

0 min

m

5 min

How have structures in nature come to exist? Why? 1 2 5

e partner’s head circumference, neck cir Collect measurements on the board. Record and find class s (this information will be u

odvertebrae-only models they will beg

Get cartoon character from teacher and get 2 paper copies of your final in 1 1

included at the end of this module. W

groups.

easurements independently then get with partners and e measurements. Re-measure if nec

0 min Review Size and weight conversions fo en

ts will scale up their model to a 25” tall model, adding the lengths ead, neck, torso, and legs in order to determine the overall

of the drawing. If necessary, finish as homework. Calculate of head based on calculations outlined on p29.

artoon character’s proportions so different from yours and mine? How do cartoon characters make you feel?

Construction and paper Mache of model head (for details, see Information for the Teacher, p10; for photos, see Supplemental Materials pp.31-33)

30 min

5-10 min 80-85 m

Journal questions

Why are c

in

13

Day 4

acher, be o not have access to their model heads at this time

Journal

body – for example, what factors allow for a giraffe to have such

r?

nformation for the Teacher, 11; photos, Supplemental Materials, pages 31-33)

2) model necks #1(scaled-up version) (2) model necks #2 (proportional version - according to

em

(1) model neck - conversions based on the measurements taken of

Cut spongy material for between vertebrae

Clean-up and wrap-up

***Te sure the students d

questions – bone structure/composition 10-15 min

0-50 min

5-20 min

20-30 min 5 min

4 1

What factors other than bones contribute to the stability of a

a long neck? What changes you could make to bones to make them strongeWhat are the advantages/disadvantages of these changes?

Construction of model necks (for details, see Ip

***Number of model necks to be constructed will be determined by the individual teacher – the numbers mentioned are only suggestions. (

measurements of adult human male head-vertebrae systincluded on page 29)

classmates on day 2

Weigh model head + weight using a bathroom scale or some scale capableof measuring in pounds

Paint model head

14

Day 5

Journal questions

Use all the steps in the scientific method to design the experiment you will perform in testing your necks. Be sure to state what

happen

Set up

Prepareagree w questio

Day 6

5-10

5-30 min

0 min

0 min

min

question you are trying to address and your hypothesis of what will.

for and perform head/neck trial experiment, with thorough observations for each of the 5 necks

Work on presentations (***teacher: hand out guidelines, Supplemental Materials p.25)

a written self-analysis of their individual findings and how they ith/conflict with their group analysis. Address the following ns: 1. How could you make a more stable skeleton? 2. What initial characteristics caused your model to work/fail?

Bugs Bunny be as big as Dumbo? Support your answer using numerical relationships (this involves surface area and

help to make calculations to see this)

Student group presentations

Wrap-up discussion

Day 7

1 6 1

5 Journal questions -10 min

75-80 min 5-10 min

Why can’t

volume – it may

This day has not been included in the total outline, but we encourage that you take half a period

or so to discuss the students’ findings. The discussion would also be useful for leading into the

next unit portion, if you were to follow the skeletal system with the muscular system.

15

Evaluation Protocols (Assessment)

ssessmenPre-A t. Teacher will pose KWL questions to students to evaluate prior

kno ledge about the topic. A

students in a spiral notebook,

discussing the questions as a class. Spiral notebooks will be kept in the classroom and accessible

to the teacher for individual re

Formative-Assessment.

w nswers, along with any student questions, will be recorded by the

and the first 5-10 minutes of each class period will be spent

sponse.

Teacher will frequently check for understanding on an individual

basis by wandering th n

their project. This time can also be used to quick-check students’ responses to the pre-

assessment questions and add

Summative-Assessment.

e classroom and posing questions to the students as they are working o

ress any questions/concerns at that time.

Students will be asked to create a working model and each

partner must be able to explain their findings in a presentation using

illu rations/models/diagrams/available technology such as power point. Students will be

provided a Presentatio ssary

vocabulary words (Supplemental Materials p.30), a flow chart to help them keep on-track

(Supplemental Materials p.26), and they will be evaluated according to the attached rubrics

(Supplemental Materials pp.19-22). Students will also be asked to prepare a written self-analysis

of their individual findings and how they agree with/conflict with their group analysis.

st

ns Guidelines worksheet (Supplemental Materials p.25), a list of nece

16

Accommodations for Special Needs Students

Physical Disabilities. The classroom will be arranged in such a manner as to mak

maneuverable to all wheelchair-bound students. To accommodate sight-impaired students,

materials presented in overhead format will also be provided in written format and text wil

enlarged for those with limited vision. All instruction will be provided in written format for

hearing-impaired students and read to s

e it

l be

ight-impaired students when necessary. Time extensions

ill be considered on a student-by-student basis.

w

Learning Disabilities. Students with learning disabilities will be accommodated

according to their IEP, with one-on-one attention provided by the instructor, as well as

with non-disabled students when possible and beneficial to the student.

pairing

Time extensions will be

onsidered on a student-by-student basis.

c

ESL. ESL students will be paired with a bilingual student wh

with whom they work well if no bilingual students are present in the classroom, or will be

provided with an aide from the school district. Whenever necessary, instructions will be

provided for the student in their native language, but coursework will be required to be

completed in English. Time extensions will be considered on a student-by-student basis

en possible, with a student

17

18

Supplemental Materials

19

Area of Focus 5 points 3 points 1 point 0 points Points earned

Teamwork Students work well in pairs and each person contributes equally to

project

Students work together but one student

contributes more than the other. Project is

completed

Students do not cooperate

manage to c rt of the

Students fail to work together to complete

any portion of the project

well but

omplete paproject

Conversions All conversion work is shown and problems

are correctly set up and answered

Conversions are set up correctly and work is

shown, but answers are incorrect

not show

Conversions are not set up correctly/work not shown/ answers are

incorrect/student fails to attempt conversions

Conversions are set up correctly, but work is

n and/or answers are incorrect

Model Head Model head is properly proportioned – in size

and weight – according to calculations

Model head is properly proportioned in either

size or weight according to calculations

Model head ut No model was constructed

is made, bproportions are incorrect

Model Neck Model necks are properly proportioned –

in size and weight - according to

calculations and given limits

Model necks are properly proportioned in either size or weight

according to calculations and given

limits

Model neck , b

proportions s are inc

No model necks were constructed

s are madeut /limitationorrect

Number of necks

numb

outlined in t re

Students failed to construct the number of model necks outlined in

the procedure

Students constructed the er of model necks

he procedu

Continued on next page…

Project Rubric, Page 1

Project Rubric, Page 2

Area of Focus 5 points 3 points 1 point 0 points Points earned

Use of Scientific Method

St fic m d,

All steps of the scientific method were followed in the order

outlined in the procedure

All steps of the scientific method were followed, but not in the

order outlined in the procedure

eps of the scientiethod were followe

but not all of them and not in the order outlined

in the procedure

The student failed to follow the scientific

method in any manner

Flow Chart Students followed all steps of the provided flow chart, in order

Students followed the order but skipped some steps of the flow chart

Student failed to follow the flow chart in the

given order

Calculations calcu rrect calcu rrect

More than 76% of the lations are co

and all work is shown

51-75% of the lations are co

and some work is shown

Less than 50% of the calculations are correct and no work is shown

No calculations are correct and no work is

shown

Journal Questions

tho

journal questions are addressed and/or

are addressed and/or answers show no

Journal questions are all addressed and show

thought process

More than ¾ of the journal questions are addressed and show

ught process

Less than half the

Student shows no organized thought

process

No journal questions

consideration on the student’s part

Accuracy

following:

Data lacks thoroughness, accuracy, and organization, or is

Data are recorded thoroughly and accurately in an

organized manner

Data are recorded but lacks one of the

following: thoroughness, accuracy

or organization

Data are recorded but lacks two of the

thoroughness, accuracy or organization

not recorded at all

Creativity Students show some creative effort

Students fail to show creativity

Total points: /45

20

Paper Rubric

21

us oints ints nt Area of Foc 3 p 2 po 1 poi 0 points Total points

Vocabulary words All vocabulaare used, and use

the proper cont

ry words d ex

of thee r

b. e

d in

t

75% or greatervocab. words ar

used, in the propecontext

50-74% of the vocawords are used, in th

proper context

Less than 50% of thevocab. words are use

Grammar an 3 al errors a

present

More than 10 Less thgrammatic re errors present

4-6 grammatical 7-10 grammatical errors present grammatical errors

present Spelling Less than 3 spelling

t rs

errors presen4-6 spelling erro

t presen7-10 spelling errors

present More than 10 spelling

errors present Data All data are prese

accurately and iorganized manner

nn

nt,

r on

t, ted an

All data are presebut either lacks

accuracy o

Some data are presenbut lacks accuracy and organization

organizati

No data are included in the paper

Data analysow

ughtthe student’s part

s is t is s a

e, rather than individual, idea

s ght

is Data analysis ipresent and sh

individual tho

s s on

Data analysipresent, bupresented a

collaborativ

Data analysis is simply presented a

data, without thouof why things

occurred

Data analysis is not present at all

Thoroughness all ect,

ions n

%

Paper addresses aspects of the proj

from calculatthrough model testi

g

Paper addresses >50of the project, fromcalculations through

model testing

Paper fails to address at least 50% of the

project

Length or longer

h s Paper is 5 paragraphs Paper is 4 paragrap s Paper is 3 paragraph Paper is less than 3 paragraphs

Total points: /20

22

Pre ic

0

sentation Rubr

Area of Focus 5 points 3 points 1 point points Total Points

Technology Students use technology

appropriately and have at least 3 visual aids as well as their model components

Students use technology

ppropriately with at least 2 visual aids and a

components present

have their model components

Students either use technology

appropriately with at least 1 visual aid OR

have their model components

Student fails to use technology or have

their model

Professionalism

a anw

Students take their presentation seriously nd use minimal filler

words such as um, ah, like

Students take their presentation seriously

d use multiple filler ords such as um, ah,

like

Students joke around while making their

presentation and fail to provide all their

findings

Students do not take the presentation

seriously and do not present any useful

findings Time Use

sinf

m

present any useful Students use the time

to present all their information

Students present ome of their

ormation, but notall of their

presentation pertains to the experiment

Students spend minimal time

presenting their information, and

any components are missing

Students fail to

information

Thoroughness Inform d

represented

I Presentation does not ation presenteis thorough and

accurately

nformation presented lacks some

components but contains main points

Presentation conveys little information pertain to the

experience

Questions Students leave time

questions asked answer most

questions asked of them once reminded

answer most of the questions asked of

them once reminded asked of t

remi

for students to ask

questions of them and can answer most

Students fail to ask if there are any

questions, but can

Students fail to ask if there are any

questions and cannot

Students fail to ask if there are any

questions and cannot answer any questions

hem once nded

Total points: /25

Homework Worksheet

Perfo calculations using the provided formulas. Show all work and circle answers. Ymay use a calculator. Formulas: f a h rea o π r h) 2.54 d = 1 f a s fa rea o π renc a le: 2π r π ~ 3.14

1. A c c C the e area t nsw tric it

2. s erence

of th ph 3. Johnny’s dog weighs 75 lbs. Pete’s dog weights 34 kg. Which boy’s dog weighs less?

Name:________________

rm the ou

Volume oSurface a1 inch = 2.2 pounVolume oSur ce aCircumfe

cylinder: π r2

f a cylinder: 2cm kg phere: 4/3 π f a sphere: 4e of circ

(π r

2) + (2

r3

r2

ylinder is 3 incheshe entire cylinder s.

tall and 1.3(assume it has

m in diameter. top and bottom li

alculateds). A

volume and surfacers should be in meof

un

A phere is 10 inchese s ere.

in diameter. Solve for the surface area, volume, and circumf

23

4. Bobby the architect was building a replica of the White Hous30 foot wide marble staircase and is the entire building is 90 feet tall. Bobby’s entire

model volcano for science fair. Her model is 1/50th of the real mountain’s height. How tall is the real volcano if her model is 61 cm tall? In the U.S.

answer in cm)?

e. The real building has a

model is only 24 inches tall and made of paper. How tall is his staircase?

5. Sally is making a

we measure height in feet, so make sure to adjust your answer accordingly.

6. The cylinder in question 1 needs to be cut into four equal-height segments. How tall is

each segment (

Parent/guardian: lease sign to indicate your student has discussed their work with you. Thank you, eacher.

PT ____________________________________________________

24

Pre

* Ques

What worked? Why did it work?

What didn’t work? Why didn’t it work?

How did you improve your head-neck system?

* Minimum of 3 digital pictures or illustrations of your experiment to support your data

* E

* Avoi

* Minimum 5 minutes in length

* Be sure to ask if there are any questions when you are finished

* Be prepared to answer questions posed by the class or teacher – you are the teacher of this

“lesson”

* Describe the science behind your experiment

* D r

Name:________________ sentation Guidelines

tions to be addressed

ach partner must present some of the material

d slang and filler words such as “ah, um, like…”

esc ibe the engineering behind your experiment

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Flow Chart

Marvin Worksheet with parent signature

and tner

Have measurements checked by teacher

Construct head and decorate

Construct necks according to given parameters

Experiment with head-neck system and make necessary adjustments

Presentation

Final Paper

Choose partners

Re-test system

Homework worksheet

Make measurements of cartoon character

Compare with par

Name:________________

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Marvin Worksheet

n ach of the d body. Record each of your measurements – in inches – in th o the assigned letter. Marvin’s total height is the sum of lines A, E, G, and H. Use your measurements to calculate the lengths of lines A-H if Marvin were 25 inches tall. Use the back

on a sheet of lined paper. SHOW ALL WORK FOR SCALING CA ULATIONS!

Name:________________

structions: Using a ruler, measure along e lines transecting Marvin’s head, neck, ane appropriate spot according t

I

of this worksheet OR attach your calculationsLC

Lengths A:

B:

C:

D:

E:

F:

G:

H:

A+E+G+H:

Lengths if Marvin as 25” tall:

A:

B:

C:

D:

E:

F:

G:

H:

A+E+G+H:

B A

CD

E F

G w

H

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Teacher Answer Key for Marvin Worksheet

: 0.69” H: 3.00”

Total Height: 8.13”

Scaled to 25” tall

A: 8.27”

B: 9.99”

C: 3.66”

D: 2.12” 9.23”

A: 2.69” E: 0.56”

B: 3.25” F: 0.38”

C: 1.19” G: 1.88”

D

Head/neck height: 3.25”

E: 1.72”

F: 1.17”

G: 5.78”

H:

28

Calculations

How to set up the conversion calculation:

Height of measured part = Height of theoretical part

25” body

ad (as an example):

X / 25”)

= (2.69” * 25”) / 8.13” = 8.27”

which is equal to the diameter of the head.

ou can then use to calculate your volume, and, with the average human brain density (density is equal to mass over volume) of

ws:

Volume of the head = 4/3 π r

(Volume of head in cubic inches

Height of entire measured body

So for the height of the he

(2.69” / 8.13”) = (

X

This gives you X,

Dividing the diameter in half gives you the radius, which y

1.071g/cm3, you can calculate the weight of the head as follo

3

) x (16.39 cubic centimeters) = cubic centimeters of head

Cubic inches

timeters(Cubic cen of head) x (1.071 g) = weight of head in grams Cubic Centimeter

(Weight of head in grams

) x 1 kg = weight of head in kilograms 1000 g

eight of head in kilograms(W ) x 2.2 pounds = weight of head in pounds

1 kg

Adult male human vertebrae are approximately 2 5/16 inches in diameter and the head is

pproximately 3.22 inches in diameter. Use this information to scale up your cartoon neck to the

me proportions as a human head-neck system.

a

sa

29

Name:________________ Vocabulary Sheet

olume

daptation

Science

Engineering

Model

Proportional

Scaling

V

System

A

30

31

Figure 1. (A) The wire model should be roughly circular in shape and the student should be sure to leave a hole in the top or upper back through which they can pass the weight of the head. (B) Once paper Mache’d, the model head should roughly resemble the example above. This step is followed by painting and

n. The neck (C) is included to give a representation of the size difference. decoratio

Our scaled-up model of Marvin the Martian’s head, next to one of the experimental neck designs. This model head is larger in diameter than the one outlined in the lesson, and the weight was 29 pounds.

Figure 2. Model neck with the “disk” layers in place (we used the no-slip backing for rugs).

ck (buckling).

Figure 4. Deformed model neck “vertebrae” after model neck failure.

Figure 3. Failure of the model ne

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Figure 5. Another neck model, this time without separate vertebrae. This model neck is already under stress, as the head aced upon it. You can note this stress through the slight bon the right vertical edge of the model neck.

has been plowing effect

Figure 6. The head/neck model interaction as shown above in Figure 5, but from a wider angle. Although the neck appears stressed (note the slight curve in the right vertical edge), it is not completely collapsing under the weight of the head.

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Resources

http://michaelpaulus.com/gallery/character-Skeletons

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