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Helping ng All Children en Become e Part
f the Whole
Rate this presentation on the mobile conference app! All presentation surveys are available five minutes before the conclusion of each presentation! www.nctm.org/confapp Download available presentation handouts from the Online Conference Planner! www.nctm.org/planner Join the conversation! Tweet us using the hashtag #NCTMBOSTON
Tr
Trish sh Al Alex exander nder: :
s experi erience ence teachin hing g middl dle e school
urricul culum um team for r 15 years rs
Table ble Le Leader er for state e assessme ssment nt trainin aining g
Joann
nn Ba Barnett: ett:
s experi erience ence teachin hing g middl dle e school
lped ed deve velo lop p EMS S course rse work rk and presently ently facilit cilitating ting Elementary entary Math Sp Specialist ialist program
Misso sour uri i St State e Univer versi sity. y.
tructor
velo lopmental pmental Math classes sses at Ozark k Comm mmuni unity ty Coll llege ege
Our challeng
nge e is to design our lessons s so studen ents ts can articulat ate e important nt ideas.
Tomlinson, C. A. (2014). Differentiated classroom: Responding to the needs of all learners. Ascd.
Stu
"St
Stud udents ents joini ning ng your ur classroom ssroom have ve va vari ried d conception nceptions s of what it means s to do mathematic ematics.
is imp mporta
nt to establi blish sh imm mmediately diately that mathemat hematic ics s is about ut ideas, s, that all the students ents in the class s are capable ble of havi ving ng ideas s in mathemati matics, cs, and that all are expected cted to contrib tribute ute to the deve velopmen lopment t of the class' ss' ideas.
Students udents must st le learn rn that id ideas s need not be fu full lly y fo form rmed ed to be expres ressed; sed; tentative ative id ideas as provide vide im importa rtant nt begi ginnings nings." ."
(P (Page e 10 10)
Russell, Susan Jo, Deborah Schifter, and Virginia Bastable. Connecting arithmetic to algebra: Strategies for building algebraic thinking in the elementary grades. Heinemann, 2011.
An abil
ilit ity to p perceiv ive the ordered pair ir in in a a fra ract ction ion symbo bol l as a c conce ceptual tual unit it (ra rather er than n two in indiv ividua idual l number bers) s) has been found nd to b be an in indic icato tor for successful ssful perf rform rmance ance wit ith ra ratio ional l numbe bers. rs.
Behr,
, Wachsmu muth, th, Post, and Lesh (1984) ask, “what meaning, for example, do 2/3 × 5/6 or
2/3 + + 5/ 5/8 h have for chil ildren n who la lack a well ll-in inte ternal rnaliz ized ed concept of the big igness ss
Chil
ildren ren have dif ifficul iculty ty in internal aliz izing ing that the symbol
r a fr fract ctio ion n re repre resents ents a si singl gle entit ity.
Kinder
dergarten garten
Whe
hen n cou
ntin ing g ob
jects, ts, say th the e nu numb mber er na name mes s in n th the e sta tandard ndard or
r, pairing ring each h
ject ct wi with th on
and on
nu number er na name and nd each h nu number er na name wi with th on
and
Transition from Whole Number to Fraction Notation
Grade 1 Partit ition ion and describ ibe e two a and four equal al shares es of cir ircle les and rectangl gles es …recognize that decomposing into more equal l shares s created d sim imil ilar fig igures es Gr Grade 2
four equal l shares s of cir ircle les and rectangles, …recognize that equal shares es of id identica ical l whole les s need not have e the same shape
Wh
Look at all the 6’s in the two numbers
belo low: What does each 6 m mean, , and why do th the ci circ rcle le pie iece ces lo look so di differ ferent ent for r the two numb mber ers? s?
How can
3 5 8 5
What do you know about the fractions below?
Ba
Activity adapted from John Van de Walle’s
“Teaching Student-Centered Mathematics, Grade 3-5.” Pearson Education, 2006. Pages 138-140.
The connecti
ection
ween en the comparison rison of fracti tions
evel elopm
ent of numb mber er sen ense se is clear. . Comparing aring fractions ions is necessa ssary ry for
ining an intuiti tive ve feel of the size of fracti tions.
tional
ber is recogn gnized zed to be e close e to 1/ 1/3 3 or 1/ 1/2, 2, for ex examp mple, e, one e has s a better er feel for its magn gnitude.
fracti tional
ber sense se is parti ticul cular arly y imp mportant rtant wh when en es estimati mating ng wi with fractions.
(Sowd wder er)
In support of this, Post et al. (1986) noted
that “children who do not have a workable concept of rational number size cannot be expected to exhibit satisfactory performance across a set of tasks which varies the context in which the number concept of fraction is involved” (p. 2). Further, Behr, Wachsmuth, Post, and Lesh (1984) ask, “what meaning, for example, do 2/3 × 5/6 or 2/3 + 5/8 have for children who lack a well-internalized concept
Wr
Write e the followi wing g fractions
r from lea east st to gr grea eates est.
Wr
Write e the followi wing g fractions
r from lea east st to gr grea eates est.
Wr
Write e the followi wing g fractions
r from lea east st to gr grea eates est.
Wr Write e the fo follow lowing ing fr frac actio ions ns in ord rder er fr from m le leas ast to gr great atest. st.
Whic
Pa
Game on…. Quiz each other Tra
Pa
Each
ch time e a digi git t is rolle lled, d, place ce it in one of th the boxes. es.
A digi
git t that t is rol
led d may y be placed ced in the SAVE E Stars ars at any point int durin ring g the ga game. e.
After
er we have ve rolled led all 14 digi gits, ts, the numb umbers ers in the SAVE E Stars rs may replace lace any two digi gits ts on the e number mber line ne IF doing ing so will ll help lp you create ate a more re accurate rate fraction. tion.
Afterw
erwards, ards, check k fractions tions with h partner tner and circle rcle any y fracti tion
you created ated on
mber line ine that has the appr propriate
value. ue.
Ple
lease se email il Jo Joann n pers rsonally ally at the email il above e if if you would ld li like a co copy
ing fractio ions ns activ ivit ity y usin ing the Hands Up Up/Pair ir Up Up activ ivity ity .
Rate this presentation on the mobile conference app! All presentation surveys are available five minutes before the conclusion of each presentation! www.nctm.org/confapp Download available presentation handouts from the Online Conference Planner! www.nctm.org/planner Join the conversation! Tweet us using the hashtag #NCTMBOSTON