Alice’s Adventures in Wonderland and
Exponents
By:
Enriqueta Ramirez and
Johnny Reyes
Acknowledgments
• Susan B. Taber. Using Alice in Wonderland to
Teach Multiplication of Fractions
• Kat Cain. Lesson Template. Exponents in
Wonderland
• Heather Preciado. Classroom Video and
Lesson Development
• Diane Kinch, Greisy Winicki and Minh Kim.
Lesson Development
• Nicole Wickler, Director. Cal Poly Pomona
CEMaST
A Lesson on Exponents
Mrs. Preciado’s class video
Les so n 1 Ğ Exp o n en ts i n W o n derl an d I
(2 Da y s)
Grade : 7
E mb e d d e d asse ss men t tas k : Ho w Doe s A lice C han g e
worksheet , n o teb o ok e n trie s an d in for m al teac h er q u estion ing in
smal l group s .
Le n gth of Les s on : 1 0 0 mi n utes
P lac e m e nt o f less o n i n u nit : 1
st
o f 3 les s on s o n ex p on e nts (d ay s 1 & 2 )
Cali f or n ia M ath Con t ent St a nd a rd s re lev a nt to th is lesson:
Ma in le a rn in g go a l: Stu d ent s wi ll s tar t to g et a n in tu itive fe el fo r ho w quickly
object s gro w an d shrink w h en m u ltiplie d b y a sca le fac tor m ul tipl e time s .
Expone n tia l n ot a tio n (pos itiv e in tege r expo n ents ) wil l b e use d w ith e m p hasis
on its mea n in g o f repe a te d mu ltip licat ion . Zer o expon e nts w ill be int r oduce d
in co n tex t.
Fo c us ques t io n f o r th e le s s o n: Whe n w e chang e a n objectÕs he igh t by a
particula r scal e fa c to r m u ltipl e time s , w ha t is th e o u tc o me ? H o w ca n w e
represen t th e cha n ge u s ing m a th e m a tica l n o ta tion?
Ide al stu d en t re s po n se t o t he f ocu s q ues t io ns: W h e n w e m u ltiply by a
scale facto r b e tw ee n 0 an d 1 , the o bjec t g e ts s ma ller . When we mu ltip ly b y a
scale facto r gre a ter tha n 1 , th e obje c t get s large r . I f w e mu ltipl y by a scal e
facto r m ul tipl e tim es , we c a n repres e n t the res u lting s c ale facto r w ith a n
exponen tia l expressio n .
Math em atic s c ont e nt st o ry lin e : Co n tin u in g idea s de v elope d in un its o n
mu ltip licat ion by fracti o ns a n d scal e draw ings . Whe n the scal e fa c to r is less
tha n 1 , eve n thoug h the res u lt is s ma ller tha n w e be ga n w ith , the oper a tio n is
stil l m ul tiplic a tio n . In a sca le dra w in g if th e heig ht cha n ges by a pa r ticu lar
scale facto r , s o wi ll th e wi d th an d al l o ther measur e m e nts .
Repea ted mu ltip lica tio n can be re present e d b y expo ne nts a n d g iven an
exponen tia l expressio n (w ith p osi tive inte g er exp o ne n t) we c a n re lat e it t o a
contex t o f re p ea ted mu ltip lic a tio n .
Grade 7 Measur e me n t an d Ge o m e try
1.2 Constru c t and re ad drawin g s an d m odel s m ade t o scale.
Cali forni a C o mm o n Cor e S tandard s releva n t t o th is le s son:
Grade 7 Ge o metry
Draw, c o nstruc t, an d describ e ge o m e trica l figures a nd describe
the r el a tionsh ips b e twee n th e m.
1. S o lve pr o bl e ms in v olvin g scal e drawing s o f g eo m etr ic fi g ures
includin g c o mp u tin g ac tua l len g ths an d areas fr o m a s c ale
drawing an d reproduci n g a scal e drawi n g a t a d iffere n t scale.
Grade 8 Expression s an d E qu a tions
Work w ith ra dical s an d in tege r expone n ts
1. Kn o w a n d a pply th e prope r tie s o f in te g er expo n ent s to
generat e e q uivale nt n u merica l expression s .
Mate r ia ls N e ed e d: N e ws p rint R o ll, s c is s or s (teach e r a n d
stud e nt) , m arke r s , mea s u r in g d ev ices ( ru ler s , y ar d/ mete r
sticks ) . H o w Do e s A lice Gr o w wo r ksh e et , A lic e in
Wo n de r la n d vi de o c lip ( ht tp: //www .trai lerad dic t.c om /cl ip/a lic e -inwon der la nd - 195 1/d r ink - m e )
Zero Produ c t Pro p erty ( if th e pr o duc t o f 2 n u mbers is z ero the n on e or th e
othe r mu s t be zero ) an d its co n trapo s titive (if ne ithe r fa ctor is zero tha n the
produc t can n o t b e zero) . Thi s is a previ e w o f a p r incip le use d in fa c torin g .
Opt ion a l: C al c u lators
Alice’s Adventure in Wonderland
Alice Shrinks or Grows
• Alice is 5 ft. 4 in. or 64 inches
tall.
• Potion labeled 1/2 or biscuit 2
(scale factor)
• Drinks 1, 2 and 3 times.
• Write an expression using
Exponential Notation:
64 x (1/2)1, 64 x (1/2)2, 64 x
(1/2)3
• Write an expression using
Exponential Notation:
64 x 21, 64 x 22, 64 x 23
Materials
• Video clip of Alice in Wonderland (You Tube)
• Handouts - Instructions
• Butcher paper, measuring tape,
color markers
• Calculators
• Lessons for days 1-5
Activity
• Get into groups of 4
• Secure materials
– Worksheet
– Poster paper
– Colors
– Measuring tape
1
Na m e _________ _ _____ _ _____ _ _____ __ _________
P e riod __ _ __ Date ________ __
H o w D o es Alice Gr o w ?
Directi on s: I n thi s pr o ject yo u w ill be dra wing a Òlif e-sizedÓ Ali ce (as a st ick -Ş gu re)
be fore sh e dr in ks her pot ion a n d ag ain a fte r s h e dr in ks o n ce, tw ice, an d t hree tim es .
1. Yo u r Ali ce is 6 feet ta ll . S h e dr in ks a pot ion labe led 1 . T hi s is the sca le factor. If
2
she dr in ks fro m thi s pot ion 3 tim es, how can we represe nt her Ş n al h eigh t u sing
expo n en tial n otat io n?
2.Co m plete th e foll ow ing tab le.
Starting
H eight
6 feet
Scal e Fact o r
# of D r inks
Exponen
t ia l Notation
Standard F
o rm
First
1
2
6 feet
Second
1
2
6 feet
Thi rd
1
2
1. We do n Õt wa n t a te lescop ing Ali ce, so w e need to keep o ur draw ing o f h er prop o rt ion al.
T h e m ost pro m in en t feat u re on o u r st ick Ş g u re is th e head. Meas ure th e h ead size o f
so m eo ne in y ou r gro up an d co m p a re thi s to hi s or h er h eigh t. If yo u r Ali ce starts w ith a
h eigh t of 6 feet, how long a n d how w ide sh oul d h er head be ?
E ith er wr ite a se n te nce or a m at h em at ic al e xpress ion that sh ows how y ou foun d this.
4
Na m e _________ _ _____ _ _____ _ _____ __ _________
P e riod __ _ __ Date ________ __
H o w D o es Alice Gr o w ?
Directi on s: I n thi s pr o ject y o u w ill be dra wing a Òlif e-sizedÓ Ali ce (as a st ick -Ş gu re)
be fore sh e dr in ks h er pot ion a n d a g ain a fte r s h e dr in ks o n ce, tw ice, an d th ree tim es .
1. Yo u r Ali ce is 2 in ch es ta ll . S h e dr in ks a po tion labe led 3. T hi s is th e scale factor. If
sh e dr in ks fro m thi s pot ion 3 tim es, how can we represe n t h er Ş nal h eigh t using
ex po n en tial n otat io n?
2.Co m plete th e foll ow ing tab le.
Starting
Scal e Fact o r
# of D r inks
2 inches
H eight
3
First
2 inches
3
Second
2 inches
3
Thi rd
Exponen
t ia l Notation
Standard F
o rm
1. We do n Õt wa nt a te lescop ing Ali ce, so w e need to keep o u r draw ing o f her prop o rt ion al.
T h e m ost pro m in en t feat u re o n o ur st ick Ş g u re is th e head. Meas u re th e h ead size of
so m eo n e in y o u r g ro up an d co m p a re thi s to hi s or h er h eigh t. If y ou r Ali ce starts w ith a
heigh t o f 2 in ch es, h ow lo ng a n d h ow w ide sh o ul d her h ead be ?
E ith er wr ite a se n te nce or a m at h em at ic al e x press io n that shows how y o u fo un d this.
Alice Posters
• The names of group
members.
• A blurb on whether Alice is
shrinking or growing.
• The exponential notation of
Alice's size change.
• 4 stick-figure Alices.
• Color-coding with a key or
labeling to show which Alice
is 1st, 2nd, 3rd, 4th.
• Exponential notation for
Alice's growth.
Gallery
Thank You!
• Our current direction 2013
Surface Area and Volume
• Future lesson 2014 Probability
• Access to our Lessons:
– Enriqueta.ramirez@pusd.org
– Johnny.reyes@pusd.org
• Closing Video: Our Incredible
Universe from an Exponential
View.