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ì	  Engaging	  Students	  in	  Learning	  CPSB	  High	  School	  Mathema2cs	  Inservice,	  2012	  
Organized	  Chaos	  
COMPASS	  «  Se#ng	  Instruc-onal	  Outcomes	  (1c):	  	  Establishing	  clear,	  rigorous	  	      objec2ves	  that	  de...
Standards	  of	  Mathematical	  Practice	  «  Make	  sense	  of	  problems	  and	  persevere	  in	  solving	  them.	  « ...
Attention	  Getter	  
Marshmallow	  Challenge	  «  20	  s2cks	  of	  spagheN	  «  1	  yard	  of	  tape	  «  1	  yard	  of	  string	  «  1	  ...
Marshmallow	  Challenge	  «  The	  winning	  team	  is	  the	  one	  that	  has	  the	  tallest	      structure	  measure...
Marshmallow	  Challenge	  
Marshmallow	  Challenge	  50	  40	  30	  20	  10	                             Height	  (Inches)	    0	  
Marshmallow	  Challenge	  
Marshmallow	  Challenge	  «  Why	  do	  kindergarteners	  create	  taller	  and	  more	              interes2ng	  structu...
Mix-­‐N-­‐Match	  «  Each	  student	  is	  given	  a	  card	  with	  some	  type	  of	  problem	      or	  informa2on	  o...
Mix-­‐N-­‐Match	                 Name	  the	  property	                                                                   ...
Line-­‐Ups	  «  Each	  student	  is	  given	  a	  card	  with	  some	  type	  of	      problem	  on	  it.	  «  Students	...
Line-­‐Ups	  «  Line	  up	  in	  order	  from	  the	  teacher	  who	  has	  taught	      the	  most	  years	  to	  the	  ...
Line-­‐Ups	  «  Frac2ons,	  Decimals,	  &	  Percents	  «  Sta2s2cs	  «  Order	  of	  Opera2ons	  «  Algebraic	  Expres...
Inside-­‐Outside	  Circle	  «  Students	  form	  two	  concentric	  circles,	  with	      equal	  numbers	  of	  students...
Inside-­‐Outside	  Circle	  «  Structure	  works	  best	  when	  the	  problems	  being	      solved	  do	  not	  require...
Rally	  Coach	  «  Students	  pair	  up	  and	  decide	  who	  is	  Person	  A	  and	      who	  is	  Person	  B.	  There...
Rally	  Coach	  «  Mul2-­‐Step	  problems	  «  Comple2ng	  worksheets	  «  Genera2ng	  lists	  «  Constructed	  respon...
Round	  Table	  «  Similar	  to	  Rally	  Coach	  but	  involves	  four	      students	  instead	  of	  two.	  «  Studen...
Round	  Table	  «  Given	  three	  points,	  A	  (4,	  -­‐7),	  B	  (3,	  1),	  and	  C	  (-­‐2,	  0)…	  «  Person	  1	 ...
Mix	  Pair	  Rally	  Coach	  «  Each	  student	  is	  given	  a	  card	  containing	  some	      informa2on.	  «  Studen...
Showdown	  «  Teacher	  selects	  one	  student	  from	  each	  group	  to	     be	  the	  Showdown	  Captain.	  «  The	...
Showdown	  «  The	  Showdown	  Captain	  leads	  the	  checking.	  «  If	  correct,	  the	  team	  celebrates;	  if	  no...
Classroom	  Setup	  
Stations	  «  Sta2on	  1:	  Students	  will	  be	  given	  eight	  index	  cards	      with	  func2ons	  and	  func2on	  ...
Stations	  «  Sta2on	  3:	  Students	  will	  be	  given	  a	  calculator	  to	      help	  them	  solve	  a	  real-­‐wor...
Questions	  
References	  «  Kushnir,	  Dina.	  (2001).	  Coopera*ve	  learning	  and	     mathema*cs:	  High	  school	  ac*vi*es.	  S...
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2012 CPSB High School Math Inservice

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Transcript of "2012 CPSB High School Math Inservice"

  1. 1. ì  Engaging  Students  in  Learning  CPSB  High  School  Mathema2cs  Inservice,  2012  
  2. 2. Organized  Chaos  
  3. 3. COMPASS  «  Se#ng  Instruc-onal  Outcomes  (1c):    Establishing  clear,  rigorous     objec2ves  that  describe  what  students  will  learn.    «  Managing  Classroom  Procedures  (2c):  Establishing  a  smoothly   func2oning  classroom  through  the  management  of  instruc2on  and   transi2ons  to  allow  for  maximum  learning  for  all  students.  «  Using  Ques-oning  and  Discussion  (3b):  Strategically  using  a  varied   set  of  ques2ons  to  engage  all  students  in  discussion  around  rigorous   content.  «  Engaging  Students  in  Learning  (3c):  Asking  all  students  to  do  work   that  is  rigorous  an  intellectually  challenging.  «  Using  Assessment  in  Instruc-on  (3d):  Using  clear  assessment  criteria   to  drive  instruc2onal  choices  throughout  the  lesson  and  at  the  end.  
  4. 4. Standards  of  Mathematical  Practice  «  Make  sense  of  problems  and  persevere  in  solving  them.  «  Reason  abstractly  and  quan2ta2vely.  «  Construct  viable  arguments  and  cri2que  the  reasoning  of   others.  «  Model  with  mathema2cs.  «  Use  appropriate  tools  strategically.  «  ALend  to  precision.  «  Look  for  and  make  use  of  structure.  «  Look  for  and  express  regularity  in  repeated  reasoning.  
  5. 5. Attention  Getter  
  6. 6. Marshmallow  Challenge  «  20  s2cks  of  spagheN  «  1  yard  of  tape  «  1  yard  of  string  «  1  marshmallow  
  7. 7. Marshmallow  Challenge  «  The  winning  team  is  the  one  that  has  the  tallest   structure  measured  from  the  table  top  surface   to  the  top  of  the  marshmallow.  «  The  en2re  marshmallow  must  be  on  top.  «  Use  as  much  or  as  liLle  of  the  kit.  «  Break  up  the  spagheN,  string,  or  tape.  «  The  challenge  lasts  for  18  minutes.  
  8. 8. Marshmallow  Challenge  
  9. 9. Marshmallow  Challenge  50  40  30  20  10   Height  (Inches)   0  
  10. 10. Marshmallow  Challenge  
  11. 11. Marshmallow  Challenge  «  Why  do  kindergarteners  create  taller  and  more   interes2ng  structures  than  business  graduates?  «  The  marshmallow  is  a  metaphor  for  the  hidden   assump2ons  of  a  project.  «  What  are  your                                                                                       assump2ons  this  school                                                                       year?  
  12. 12. Mix-­‐N-­‐Match  «  Each  student  is  given  a  card  with  some  type  of  problem   or  informa2on  on  it.  «  Students  ‘mix’  and  find  the  person  with  a  card  that   ‘matches’  theirs.  «  As  students  pair  up,  they  move  to  the  outside  perimeter   of  the  classroom  and  stand  together  as  a  pair.  «  Once  everyone  has  found  their  match,  students  confer   with  another  nearby  pair  to  double  check  that  they  do   indeed  make  a  match.  «  Redistribute  if  desired.  
  13. 13. Mix-­‐N-­‐Match   Name  the  property   In  simplest  radical  form,  find  the   demonstrated:   distance  between:     7! 9!5 = 7!9 !5   ( ) ( ) (1, !3), ( 7, 2) Simplify  (posi2ve  exponents):   Sketch  the  graph  of:    !3 2 6x y   ( ) y = 2sin x 7 x Find  the  remainder  when   Evaluate  the  determinant:   3   2 " 1 !4 % 3x + 2x   ! 5x ! 2 $                      is  divided  by    (  x    +    2  )                             # 3 !2 &
  14. 14. Line-­‐Ups  «  Each  student  is  given  a  card  with  some  type  of   problem  on  it.  «  Students  evaluate  the  answer  to  their  problem   and  then  line  up  in  order  from  least  to  greatest.  «  Once  students  are  lined  up,  they  then  discuss   their  card  and  posi2on  with  a  nearby  partner.  «  Partners  may  be  formed  by  pairing  up  or  by   ‘folding’  the  line  in  half.  
  15. 15. Line-­‐Ups  «  Line  up  in  order  from  the  teacher  who  has  taught   the  most  years  to  the  teacher  who  has  taught  the   fewest.  «  Fold  the  line.  «  The  more  experienced  teacher  tells  the  less   experienced  about  their  most  embarrassing   teaching  moment.  «  The  less  experienced  teacher  then  shares  with  the   more  experienced  how  that  situa2on  could  have   been  avoided.  
  16. 16. Line-­‐Ups  «  Frac2ons,  Decimals,  &  Percents  «  Sta2s2cs  «  Order  of  Opera2ons  «  Algebraic  Expressions  «  Angle  Measures  «  Radian  and  Degree  Measures  «  Arithme2c  and  Geometric  Sequences  
  17. 17. Inside-­‐Outside  Circle  «  Students  form  two  concentric  circles,  with   equal  numbers  of  students  in  each  circle.   Students  stand  face-­‐to-­‐face  with  a  partner,  one   person  from  the  inside  circle  and  one  from  the   outside.  «  The  circles  rotate  according  to  the  teacher’s   instruc2ons.  «  Partners  take  turn  asking  each  other  ques2ons,   quizzing  each  other  with  flashcards,  sharing   some  informa2on,  or  answering  ques2ons.  
  18. 18. Inside-­‐Outside  Circle  «  Structure  works  best  when  the  problems  being   solved  do  not  require  lengthy  paper-­‐pencil   solu2ons.  «  Structure  is  more  conducive  to  short-­‐answer  or   higher  level  thinking  ques2ons  that  can  be   answered  verbally.  «  Any  ideas?  
  19. 19. Rally  Coach  «  Students  pair  up  and  decide  who  is  Person  A  and   who  is  Person  B.  There  is  only  one  sheet  of  paper   and  one  pencil  for  each  student  pair.  «  Teacher  poses  a  problem,  verbally  or  on  paper.  «  Person  A  begins  contribu2ng  to  the  solu2on  of  the   problem  in  wri2ng  and  states  aloud  what  (s)he  is   doing.  «  Meanwhile,  Person  B  watches,  listens,  and   coaches.  If  necessary,  Person  B  reteaches.  «  Reverse  roles.  
  20. 20. Rally  Coach  «  Mul2-­‐Step  problems  «  Comple2ng  worksheets  «  Genera2ng  lists  «  Constructed  response  items  
  21. 21. Round  Table  «  Similar  to  Rally  Coach  but  involves  four   students  instead  of  two.  «  Students  take  turns  passing  the  paper  and   pencil,  each  wri2ng  one  answer  or  making  a   contribu2on.  
  22. 22. Round  Table  «  Given  three  points,  A  (4,  -­‐7),  B  (3,  1),  and  C  (-­‐2,  0)…  «  Person  1  finds  the  slope  of  the  line  passing  through   A  and  B.  «  Person  2  writes  the  equa2on  of  line  AB.  «  Person  3  writes  the  equa2on  of  the  line  parallel  to   AB  and  passing  through  C.  «  Person  4  writes  the  equa2on  of  the  line   perpendicular  to  AB  and  passing  through  C.  
  23. 23. Mix  Pair  Rally  Coach  «  Each  student  is  given  a  card  containing  some   informa2on.  «  Students  ‘mix’  around  the  room  and  find  a  partner,   Person  A  and  Person  B.  «  Person  A  solves  the  problem  on  his/her  card  while   Person  B  watches,  checks,  and  praises.  «  Person  B  then  solve  the  problem  on  his/her  card   while  Person  A  watches,  checks,  and  praises.  «  Partners  reteach  as  necessary.  
  24. 24. Showdown  «  Teacher  selects  one  student  from  each  group  to   be  the  Showdown  Captain.  «  The  Showdown  Captain  draws  the  first  card,   reads  the  ques2on,  and  provides  think  2me.  «  Working  alone,  all  students,  including  the   Showdown  Captain,  write  their  answers.  «  ‘Showdown’  is  called  and  teammates  share  and   discuss  their  answers.  
  25. 25. Showdown  «  The  Showdown  Captain  leads  the  checking.  «  If  correct,  the  team  celebrates;  if  not,   teammates  tutor,  then  celebrate.  «  Repeat  with  a  new  captain.  «  Modifica2ons—oral  ques2ons,  ques2ons  from   a  handout,  or  ques2ons  displayed  by  a   projector  
  26. 26. Classroom  Setup  
  27. 27. Stations  «  Sta2on  1:  Students  will  be  given  eight  index  cards   with  func2ons  and  func2on  answers  on  them.   They  will  match  the  func2ons  with  the  appropriate   func2on  answers.  Then,  they  will  evaluate   func2ons.  «  Sta2on  2:  Students  will  use  a  ruler  to  perform  the   ver2cal  line  test  on  graphs  of  rela2ons.  They  will   determine  if  the  rela2on  is  a  func2on.  They  will   construct  a  graph  that  is  a  func2on.  Then,  they  will   determine  if  a  rela2on  is  a  func2on  by  analyzing   coordinate  points.  
  28. 28. Stations  «  Sta2on  3:  Students  will  be  given  a  calculator  to   help  them  solve  a  real-­‐world  linear  func2on.   They  will  write  and  solve  a  linear  func2on  based   on  two  data  points.  «  Sta2on  4:  Students  will  be  given  a  number   cube.  They  roll  the  number  cube  to  populate  a   rela2on.  They  find  the  domain  and  range  of  the   rela2on  and  determine  if  it  is  a  func2on.  Then   for  given  rela2ons,  they  determine  the  domain,   range,  and  whether  or  not  it  is  a  func2on.  
  29. 29. Questions  
  30. 30. References  «  Kushnir,  Dina.  (2001).  Coopera*ve  learning  and   mathema*cs:  High  school  ac*vi*es.  San   Clemente,  CA:  Kagan  Publishing.  «  The  Marshmallow  Challenge:   hLp://marshmallowchallenge.com  
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