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Katie Costello	

K-5 Intervention	

kcostell@somsd.k12.nj.us	

973-476-8440	

Kimberly Beane	

K-5 Supervisor of Math & Science	

kbeane@somsd.k12.nj.us	

973-769-2413	

K-5 Math & Science	

New Teacher Institute	

Welcome!
We re excited to do
math & science with you!
Think of a
number that
has meaning to
you. Build it
with
manipulatives.
Agenda	
  &	
  Goals	
  
•  Favorite	
  Numbers	
  and	
  Describing	
  Numbers	
  
•  Instruc9onal	
  blocks	
  and	
  minutes	
  
•  Singapore	
  Math	
  &	
  Math	
  in	
  Focus	
  
•  Lesson	
  Structure	
  
•  Curriculum	
  Documents	
  and	
  Pacing	
  
•  Assessment	
  and	
  Progress	
  Reports	
  
•  Mee9ng	
  individual	
  student	
  needs	
  
Use	
  chips	
  to	
  show	
  7	
  
Math	
  Instruc,onal	
  Blocks	
  and	
  Minutes	
  
K-­‐1	
  
2-­‐5	
  
Pedagogy:	
  C-­‐P-­‐A	
  
	
  	
  
•  Concrete	
  (manipula9ves)	
  to	
  	
  
•  Pictorial	
  (visual	
  models	
  or	
  drawings)	
  to	
  
•  Abstract	
  representa9ons	
  (numbers,	
  symbols)	
  
Jerome	
  Bruner’s	
  research	
  proved	
  that	
  instruc9onal	
  strategies	
  
build	
  understanding	
  for	
  students	
  when	
  they	
  move	
  from…	
  
Pedagogy:	
  Rela9onal	
  Understanding	
  
Richard	
  Skemp’s	
  research	
  proved	
  that	
  for	
  long	
  term	
  learning	
  to	
  
occur	
  rela,onal	
  understanding	
  is	
  more	
  successful	
  than	
  
instrumental	
  learning.	
  
Rela,onal	
  Understanding	
   Instrumental	
  Understanding	
  
Conceptual	
  
WHY	
  before	
  HOW	
  
One	
  to	
  One	
  Correspondence	
  
Quan99es	
  and	
  Values	
  
Anchoring	
  to	
  10	
  or	
  Tens	
  
PART-­‐WHOLE	
  models	
  
	
  
	
  
Reading	
  with	
  understanding	
  
Procedural	
  
How	
  
Oral	
  Coun9ng	
  
Wri9ng	
  numbers,	
  Spelling	
  numbers	
  
Isolated	
  steps	
  or	
  steps	
  without	
  meaning	
  
	
  
	
  
	
  
Phone9c	
  or	
  word	
  calling	
  
Pedagogy:	
  Perceptual	
  Variability	
  
Zoltan	
  Diene’s	
  research	
  proved	
  that	
  children	
  gain	
  the	
  most	
  
conceptual	
  understanding	
  when	
  they	
  are	
  exposed	
  to	
  a	
  concept	
  
through	
  a	
  variety	
  of	
  materials	
  or	
  experiences.	
  
Perceptual	
  Variability	
  
p! /!
q!
z!
?
"
;!
Number Lines
make
Number Sense
[wwwwwwwwwwwwwwwwwwwwww]!
y u r!
Reflec9ng	
  On	
  Pedagogy	
  
v Concrete-­‐Pictorial-­‐Abstract	
  (Bruner)	
  
v Rela9onal	
  Understanding	
  (Skemp)	
  
v Mul9ple	
  Representa9ons	
  (Dienes)	
  
Turn	
  &	
  Talk:	
  Summarize	
  each	
  with	
  a	
  partner	
  
Kindergarten	
  
Anchor	
  to	
  5.	
  	
  Bonds	
  to	
  5.	
  
K	
  &	
  1st	
  
Anchor	
  to	
  10.	
  Bonds	
  to	
  10.	
  
Visualiza,on:	
  Anchor	
  to	
  10	
  
Anchoring	
  to	
  10	
  
New Teacher Institute 2013
Decomposing	
  Numbers	
  
Composing	
  Numbers	
  
V!
C!
Visualiza,on:	
  Parts	
  and	
  Whole	
  
1st	
  Grade	
  Number	
  Bonds	
  
Number	
  Bonds	
  in	
  Upper	
  Grades	
  
Visualiza,on:	
  Parts	
  and	
  Whole	
  
3rd	
  Grade	
  Number	
  Bonds	
  
ternational(Singapore)PrivateLimited.Copyingispermitted;seepageii.
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Grade	
  1	
  Singapore	
  Math!	
  
Please	
  solve.	
  
Place	
  Value	
  Strips	
  
1.	
  	
  Find	
  a	
  partner	
  to	
  compose	
  one	
  of	
  these	
  numbers:	
  
	
  	
  61	
  	
  	
  	
  42	
  	
  	
  	
  	
  23	
  	
  	
  	
  	
  35	
  	
  	
  	
  14	
  	
  	
  	
  56	
  
	
  
	
  
2.	
  	
  With	
  your	
  partner	
  say	
  these	
  about	
  your	
  number:	
  
a.	
  	
  ____	
  tens	
  and	
  ____	
  ones	
  make	
  _____	
  
b._____	
  +	
  _____	
  =	
  _______	
  
	
  
	
  
Place	
  Value	
  Strips	
  
3.	
  	
  Find	
  another	
  pair	
  to	
  add	
  these	
  numbers	
  mentally:	
  
	
  	
  61	
  +	
  35	
  =	
  
	
  	
  42	
  +	
  23	
  =	
  
	
  	
  56	
  +	
  14	
  =	
  
	
  
	
  
4.  Use	
  the	
  hundreds	
  around	
  the	
  room	
  (and	
  a	
  partner)	
  
	
  	
  	
  	
  	
  	
  	
  to	
  make	
  these	
  numbers…	
  
142	
  
361	
  
523	
  
435	
  
614	
  
256	
  
	
  
	
  
Place	
  Value	
  Strips	
  
5.  Come	
  to	
  the	
  front	
  of	
  the	
  room	
  and	
  put	
  the	
  	
  
	
  	
  	
  	
  	
  	
  3-­‐digit	
  	
  numbers	
  in	
  order	
  from	
  least	
  to	
  greatest.	
  
	
  
	
  
6.	
  	
  	
  Find	
  another	
  pair	
  to	
  add	
  these	
  numbers	
  mentally:	
  
	
  	
  435	
  +	
  361	
  =	
  
	
  	
  523	
  +	
  142	
  =	
  
	
  	
  256	
  +	
  614	
  =	
  
	
  
	
  
Place	
  Value	
  Strips	
  
Build	
  two	
  	
  3-­‐	
  digit	
  numbers	
  
Lesson	
  Structure	
  &	
  	
  
the	
  Teacher’s	
  Guide	
  
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!
•  Teacher	
  Modeling	
  
•  Guided	
  Prac9ce	
  
•  Independent	
  Prac9ce	
  
Kindergarten	
  
	
  
Inves9gate	
  
	
  
	
  
	
  
	
  
Discover	
  
(Teacher	
  
Model)	
  
	
  
	
  
Explore	
  
(Guided	
  	
  
Prac9ce)	
  
	
  
	
  
	
  
Apply	
  
(Indep)	
  
C-­‐P-­‐A	
  &	
  Tradi9onal	
  Algorithms	
  
Linking	
  Cubes	
  &	
  Base	
  Ten	
  Blocks	
  
Solve	
  these	
  problems	
  using	
  base	
  ten	
  blocks…	
  
	
  
	
  	
  	
  124	
  
	
  +315	
  	
  	
  
	
  
	
  
	
  	
  	
  579	
  
	
  -­‐	
  432	
  	
  	
  
	
  
	
  
	
  	
  	
  33	
  
x	
  	
  	
  4	
  
	
  
	
  
	
  	
  	
  323	
  
	
  -­‐	
  265	
  	
  	
  
	
  
	
  
	
  	
  	
  267	
  
	
  +145	
  	
  	
  
	
  
	
  
Place	
  Value	
  Discs	
  Gr.	
  3-­‐4	
  
Solve	
  these	
  problems	
  using	
  base	
  ten	
  blocks…	
  
	
  
	
  	
  	
  124	
  
	
  +315	
  	
  	
  
	
  
	
  
	
  	
  	
  579	
  
	
  -­‐	
  432	
  	
  	
  
	
  
	
  
	
  	
  	
  33	
  
x	
  	
  	
  4	
  
	
  
	
  
	
  	
  	
  323	
  
	
  -­‐	
  265	
  	
  	
  
	
  
	
  
	
  	
  	
  267	
  
	
  +145	
  	
  	
  
	
  
	
  
Homework	
  
K-­‐1	
  
•  Number	
  Sense	
  Games	
  or	
  Hands-­‐on	
  Tasks	
  
•  Fact	
  Games	
  
•  ST	
  Math	
  
	
  
Gr.	
  2-­‐5	
  
•  FACT	
  PRACTICE	
  Online	
  Games	
  and	
  Tasks	
  (LiveBinder,	
  Math	
  in	
  Focus)	
  
•  Extension	
  word	
  problems	
  of	
  what	
  has	
  been	
  taught	
  
•  ST	
  Math	
  
	
  
New Teacher Institute 2013
New Teacher Institute 2013
Bar	
  Models	
  Gr.	
  2-­‐5	
  !"#$%&
Part-­‐Whole	
  
Part-­‐Whole	
  Bar	
  Models	
  
Introducing	
  Bar	
  Models	
  
Addi9on	
  Part-­‐Whole	
  Bar	
  Model	
  
1.	
  	
  Allison	
  jogs	
  6,860	
  meters	
  and	
  Calvin	
  jogs	
  5,470	
  
meters.	
  	
  How	
  far	
  do	
  they	
  jog	
  altogether?	
  
	
  
2.	
  Mr.	
  Michaels	
  has	
  $1,685.	
  Ms.	
  Kajy	
  has	
  $2928	
  more	
  
than	
  Mr.	
  Michaels.	
  	
  How	
  much	
  money	
  does	
  Ms.	
  Kajy	
  
have?	
  
Subtrac9on	
  Part-­‐Whole	
  Bar	
  Model	
  
1.	
  Brad	
  has	
  1,300	
  stamps.	
  He	
  has	
  938	
  Canadian	
  stamps	
  
and	
  the	
  rest	
  are	
  Malaysian.	
  	
  How	
  many	
  Malaysian	
  
stamps	
  does	
  Brad	
  have?	
  
2.	
  There	
  are	
  3,160	
  books	
  in	
  a	
  shop.	
  	
  1,226	
  are	
  in	
  
English.	
  817	
  books	
  are	
  in	
  Spanish	
  and	
  the	
  rest	
  are	
  in	
  
French.	
  	
  How	
  many	
  French	
  books	
  are	
  there?	
  
	
  
Mul9plica9on	
  Part-­‐Whole	
  Bar	
  Model	
  
1.	
  A	
  refrigerator	
  costs	
  5	
  9mes	
  as	
  much	
  as	
  a	
  television.	
  	
  
The	
  televisions	
  costs	
  $429.	
  	
  How	
  much	
  do	
  they	
  cost	
  all	
  
together?	
  
2.	
  Lilian	
  sold	
  114	
  9ckets	
  to	
  the	
  fair.	
  	
  Rohani	
  sold	
  2	
  9mes	
  
as	
  many	
  9ckets	
  as	
  Lilian.	
  Daquan	
  sold	
  3	
  9mes	
  as	
  many	
  
9ckets	
  as	
  Lilian.	
  	
  How	
  many	
  9ckets	
  did	
  they	
  sell	
  all	
  
together?	
  
	
  
Division	
  Part-­‐Whole	
  Bar	
  Model	
  
1.	
  	
  Desmond	
  and	
  Melissa	
  collect	
  cards.	
  	
  They	
  have	
  92	
  
cards	
  in	
  all.	
  	
  Melissa	
  has	
  three	
  9mes	
  as	
  many	
  cards	
  as	
  
Desmond.	
  	
  How	
  many	
  cards	
  does	
  Desmond	
  have?	
  
	
  
2.	
  	
  The	
  florist	
  buys	
  4	
  boxes	
  of	
  carna9ons.	
  There	
  are	
  21	
  
carna9ons	
  in	
  each	
  box.	
  	
  The	
  florist	
  puts	
  the	
  carna9ons	
  
into	
  bouquets	
  of	
  6	
  carna9ons	
  each.	
  How	
  many	
  
bouquets	
  of	
  carna9on	
  are	
  there?	
  
	
  
Frac9on	
  Part-­‐Whole	
  Bar	
  Model	
  
1.	
  	
  Rachel	
  bakes	
  a	
  pie	
  for	
  her	
  friends.	
  	
  Priscilla	
  eats	
  2/6	
  
of	
  the	
  pie	
  and	
  gives	
  the	
  rest	
  to	
  Tom.	
  	
  How	
  much	
  pie	
  did	
  
Tom	
  get?	
  
	
  
2.	
  Three	
  friends	
  share	
  a	
  grapefruit.	
  Elena	
  at	
  1/3	
  of	
  the	
  
grapefruit.	
  	
  Lee	
  at	
  1/9	
  of	
  the	
  grapefruit.	
  Sara	
  at	
  4/9	
  of	
  
the	
  grapefruit.	
  	
  What	
  frac9on	
  of	
  the	
  grapefruit	
  did	
  they	
  
eat	
  altogether?	
  	
  	
  	
  	
  	
  
	
  
Scoring	
  and	
  Progress	
  Reports	
  
Differen,a,on	
  vs.	
  Individualiza,on	
  
60	
  Minute	
  	
  
Math	
  Lesson	
  
30	
  Minute	
  
	
  Individualized	
  Math	
  Instruc9on	
  
	
  
Follows	
  curriculum	
  
	
  
Covers	
  all	
  standards	
  
	
  
New	
  content	
  
	
  
Similar,	
  ,ered	
  tasks	
  
	
  
Same	
  concept	
  for	
  all	
  
	
  	
  
	
  
Meets	
  child	
  where	
  he/she	
  is	
  
	
  
Focuses	
  on	
  founda,onal	
  skills	
  
	
  
Familiar	
  content	
  
	
  
Individualized	
  tasks	
  
	
  
Concepts	
  individualized	
  
	
  
Kim’s	
  Math	
  PD	
  Resources	
  
Find	
  ALL	
  of	
  Kim’s	
  PowerPoints	
  by	
  searching	
  Kbeane	
  
on	
  SlideShare.net.	
  
hjp://www.slideshare.net/KimberlyBeane/presenta9ons	
  
	
  
Find	
  ALL	
  of	
  Kim’s	
  STEM	
  LiveBinders	
  by	
  searching	
  
Kbeane	
  on	
  LiveBinders.com	
  
hjp://www.livebinders.com/shelf/search_display_author?
terms=KBeane	
  
	
  
Follow	
  Kim’s	
  educa9onal	
  research,	
  policy,	
  and	
  STEM	
  
tweets	
  @KimberlyLBeane	
  
	
  
For	
  	
  STEM	
  updates,	
  PD	
  discussions,	
  and	
  general	
  
collegiality	
  friend	
  Kimberly	
  Beane	
  on	
  Facebook	
  

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New Teacher Institute 2013

  • 1. Katie Costello K-5 Intervention kcostell@somsd.k12.nj.us 973-476-8440 Kimberly Beane K-5 Supervisor of Math & Science kbeane@somsd.k12.nj.us 973-769-2413 K-5 Math & Science New Teacher Institute Welcome! We re excited to do math & science with you! Think of a number that has meaning to you. Build it with manipulatives.
  • 2. Agenda  &  Goals   •  Favorite  Numbers  and  Describing  Numbers   •  Instruc9onal  blocks  and  minutes   •  Singapore  Math  &  Math  in  Focus   •  Lesson  Structure   •  Curriculum  Documents  and  Pacing   •  Assessment  and  Progress  Reports   •  Mee9ng  individual  student  needs  
  • 3. Use  chips  to  show  7  
  • 4. Math  Instruc,onal  Blocks  and  Minutes   K-­‐1   2-­‐5  
  • 5. Pedagogy:  C-­‐P-­‐A       •  Concrete  (manipula9ves)  to     •  Pictorial  (visual  models  or  drawings)  to   •  Abstract  representa9ons  (numbers,  symbols)   Jerome  Bruner’s  research  proved  that  instruc9onal  strategies   build  understanding  for  students  when  they  move  from…  
  • 6. Pedagogy:  Rela9onal  Understanding   Richard  Skemp’s  research  proved  that  for  long  term  learning  to   occur  rela,onal  understanding  is  more  successful  than   instrumental  learning.   Rela,onal  Understanding   Instrumental  Understanding   Conceptual   WHY  before  HOW   One  to  One  Correspondence   Quan99es  and  Values   Anchoring  to  10  or  Tens   PART-­‐WHOLE  models       Reading  with  understanding   Procedural   How   Oral  Coun9ng   Wri9ng  numbers,  Spelling  numbers   Isolated  steps  or  steps  without  meaning         Phone9c  or  word  calling  
  • 7. Pedagogy:  Perceptual  Variability   Zoltan  Diene’s  research  proved  that  children  gain  the  most   conceptual  understanding  when  they  are  exposed  to  a  concept   through  a  variety  of  materials  or  experiences.   Perceptual  Variability   p! /! q! z! ? " ;!
  • 9. Reflec9ng  On  Pedagogy   v Concrete-­‐Pictorial-­‐Abstract  (Bruner)   v Rela9onal  Understanding  (Skemp)   v Mul9ple  Representa9ons  (Dienes)   Turn  &  Talk:  Summarize  each  with  a  partner  
  • 10. Kindergarten   Anchor  to  5.    Bonds  to  5.  
  • 11. K  &  1st   Anchor  to  10.  Bonds  to  10.  
  • 17. Visualiza,on:  Parts  and  Whole   1st  Grade  Number  Bonds  
  • 18. Number  Bonds  in  Upper  Grades  
  • 19. Visualiza,on:  Parts  and  Whole   3rd  Grade  Number  Bonds  
  • 20. ternational(Singapore)PrivateLimited.Copyingispermitted;seepageii. ( * " +,$-!./!-,&!0.//.12!1304&#( 5 ! 6! 7 ! )! 8 ! 9! : ! ; /." <==>!$-!-,&!1304&#!4=1%/? " @ * ' A " +,$-!./! ( " 5 ! B! 7 ! *! 8 ! A! : ! '6 Grade  1  Singapore  Math!   Please  solve.  
  • 21. Place  Value  Strips   1.    Find  a  partner  to  compose  one  of  these  numbers:      61        42          23          35        14        56       2.    With  your  partner  say  these  about  your  number:   a.    ____  tens  and  ____  ones  make  _____   b._____  +  _____  =  _______      
  • 22. Place  Value  Strips   3.    Find  another  pair  to  add  these  numbers  mentally:      61  +  35  =      42  +  23  =      56  +  14  =       4.  Use  the  hundreds  around  the  room  (and  a  partner)                to  make  these  numbers…   142   361   523   435   614   256      
  • 23. Place  Value  Strips   5.  Come  to  the  front  of  the  room  and  put  the                3-­‐digit    numbers  in  order  from  least  to  greatest.       6.      Find  another  pair  to  add  these  numbers  mentally:      435  +  361  =      523  +  142  =      256  +  614  =      
  • 24. Place  Value  Strips   Build  two    3-­‐  digit  numbers  
  • 25. Lesson  Structure  &     the  Teacher’s  Guide  
  • 26. !"#$%"$#&'()'*'!"#$%&'%()*+,'+&,,-.' /#01&,'234' !"#$%&$'$()*#$ !"#'+,&$,$()*#$ $ -."($/0$ • 123)24$0"23)567$82775*$5"$"2823.*9$:5*92*9$ • %+;$0"5<82(7$5"$=6279)5*7$ • !"#$%$>)7:677$0"23)567$82."*)*?$)*792.@$5A$"23)24$0"5<82(7$ $ !"#$%&$,$()*#$ !"#'+,&$%,$()*#$ $ pB2.:C2"$D5@28)*?$ • >)"2:9$)*79"6:9)5*$ • -C582$:8.77$ • /72$(.*)068.9)327$4C2*$0):96"2@$)*$9C2$92E9$ $ !"#$%&$'F$()*#$ !"#'+,&$'F$()*#$ $ w$!6)@2@$G".:9):2$ • H96@2*97$45"I$)*$0.)"7J$4)9C$(.*)068.9)327$4C2*$*22@2@$ • B.7I7$:5(2$A"5($9C2$796@2*9$92E9$$ • H5869)5*7$676.88K$32"<.8$5"$5*$@"K$2".72$<5."@7$ • L88547$A5"$2""5"7J$728A$:5""2:9)5*J$.*@$@)7:677)5*$ • B2.:C2"$(5*)95"7$796@2*9$6*@2"79.*@)*?M"2.@)*277$$ $ !"#$%&$,$()*#$ !"#'+,&$%F$()*#$ $ ! N*@202*@2*9$-5"I$ • H96@2*9$@2(5*79".92@$6*@2"79.*@)*?$@6")*?$0".:9):2$ • H96@2*9$"2.@K$95$45"I$)*@202*@2*98K$ • B.7I7$:5(08292@$)*$9C2$796@2*9$45"I<55I$ • L7727727$)*@)3)@6.8$796@2*9$6*@2"79.*@)*?$.*@$"2.@)*277$A5"$9C2$*2E9$ 82775*$ $ '+;$()*#$ $ O8576"2$ • H6((.")P27$9C2$<)?$)@2.$5A$9C2$82775*$ • -C582$:8.77$@)7:677)5*$ $ !
  • 27. •  Teacher  Modeling   •  Guided  Prac9ce   •  Independent  Prac9ce  
  • 28. Kindergarten     Inves9gate           Discover   (Teacher   Model)       Explore   (Guided     Prac9ce)         Apply   (Indep)  
  • 30. Linking  Cubes  &  Base  Ten  Blocks   Solve  these  problems  using  base  ten  blocks…          124    +315                579    -­‐  432                33   x      4            323    -­‐  265                267    +145          
  • 31. Place  Value  Discs  Gr.  3-­‐4   Solve  these  problems  using  base  ten  blocks…          124    +315                579    -­‐  432                33   x      4            323    -­‐  265                267    +145          
  • 32. Homework   K-­‐1   •  Number  Sense  Games  or  Hands-­‐on  Tasks   •  Fact  Games   •  ST  Math     Gr.  2-­‐5   •  FACT  PRACTICE  Online  Games  and  Tasks  (LiveBinder,  Math  in  Focus)   •  Extension  word  problems  of  what  has  been  taught   •  ST  Math    
  • 35. Bar  Models  Gr.  2-­‐5  !"#$%& Part-­‐Whole  
  • 38. Addi9on  Part-­‐Whole  Bar  Model   1.    Allison  jogs  6,860  meters  and  Calvin  jogs  5,470   meters.    How  far  do  they  jog  altogether?     2.  Mr.  Michaels  has  $1,685.  Ms.  Kajy  has  $2928  more   than  Mr.  Michaels.    How  much  money  does  Ms.  Kajy   have?  
  • 39. Subtrac9on  Part-­‐Whole  Bar  Model   1.  Brad  has  1,300  stamps.  He  has  938  Canadian  stamps   and  the  rest  are  Malaysian.    How  many  Malaysian   stamps  does  Brad  have?   2.  There  are  3,160  books  in  a  shop.    1,226  are  in   English.  817  books  are  in  Spanish  and  the  rest  are  in   French.    How  many  French  books  are  there?    
  • 40. Mul9plica9on  Part-­‐Whole  Bar  Model   1.  A  refrigerator  costs  5  9mes  as  much  as  a  television.     The  televisions  costs  $429.    How  much  do  they  cost  all   together?   2.  Lilian  sold  114  9ckets  to  the  fair.    Rohani  sold  2  9mes   as  many  9ckets  as  Lilian.  Daquan  sold  3  9mes  as  many   9ckets  as  Lilian.    How  many  9ckets  did  they  sell  all   together?    
  • 41. Division  Part-­‐Whole  Bar  Model   1.    Desmond  and  Melissa  collect  cards.    They  have  92   cards  in  all.    Melissa  has  three  9mes  as  many  cards  as   Desmond.    How  many  cards  does  Desmond  have?     2.    The  florist  buys  4  boxes  of  carna9ons.  There  are  21   carna9ons  in  each  box.    The  florist  puts  the  carna9ons   into  bouquets  of  6  carna9ons  each.  How  many   bouquets  of  carna9on  are  there?    
  • 42. Frac9on  Part-­‐Whole  Bar  Model   1.    Rachel  bakes  a  pie  for  her  friends.    Priscilla  eats  2/6   of  the  pie  and  gives  the  rest  to  Tom.    How  much  pie  did   Tom  get?     2.  Three  friends  share  a  grapefruit.  Elena  at  1/3  of  the   grapefruit.    Lee  at  1/9  of  the  grapefruit.  Sara  at  4/9  of   the  grapefruit.    What  frac9on  of  the  grapefruit  did  they   eat  altogether?              
  • 43. Scoring  and  Progress  Reports  
  • 44. Differen,a,on  vs.  Individualiza,on   60  Minute     Math  Lesson   30  Minute    Individualized  Math  Instruc9on     Follows  curriculum     Covers  all  standards     New  content     Similar,  ,ered  tasks     Same  concept  for  all         Meets  child  where  he/she  is     Focuses  on  founda,onal  skills     Familiar  content     Individualized  tasks     Concepts  individualized    
  • 45. Kim’s  Math  PD  Resources   Find  ALL  of  Kim’s  PowerPoints  by  searching  Kbeane   on  SlideShare.net.   hjp://www.slideshare.net/KimberlyBeane/presenta9ons     Find  ALL  of  Kim’s  STEM  LiveBinders  by  searching   Kbeane  on  LiveBinders.com   hjp://www.livebinders.com/shelf/search_display_author? terms=KBeane     Follow  Kim’s  educa9onal  research,  policy,  and  STEM   tweets  @KimberlyLBeane     For    STEM  updates,  PD  discussions,  and  general   collegiality  friend  Kimberly  Beane  on  Facebook