Designing	  Common	  Core	  State	  Standards	     Systemic	  Mathema4cs	  Curriculum	  	  	  	  	  	  	  	  	            ...
Architects   Contractors design.        build. LEARN         TEACH
Aspen Grove MentalitySystemic Design - Interdependent      1 Grove…1 Root System
Phase 1 Design / Phase 2 Design   Vertical Alignment                Horizontal Alignment Design units that represent      ...
Designing Systemic K-12CCSS Math Collaborative Maps              How long will it take for              the K-12 Task Forc...
Part 1: Laying a Solid Foundation•  Unit Names•  Enduring Understandings/  Essential Questions•  Standards forMathematical...
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe cod...
CCSS Mathematics – 3 Key Shifts                                 (www.achievethecore.org)1.  FOCUS  Focus Strongly Where th...
1.  FOCUS	   2.  COHERENCE	  Presenta)on	  Slide	  from	  CCSS	  for	  Mathema-cs:	  Key	  Shi4s	  -­‐Sandra	  Alber),	  S...
3.	  RIGOR	                                    Grade	  7	  	  (Content	  lis-ng	  in	  an	  Essen-al	  Map	  unit)	  	    ...
1.  Use	  mul)media.	                                                                        2.  Encourage	               ...
Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe cod...
Cognitive Complexity         New       BLOOM’S        DOK
The	  Three-­‐Story	  Intellect	    NewBloom’s               Duplicate   Identify   Paraphrase               Count       L...
The	  Three-­‐Story	  Intellect	                 Compare     Distinguish    Analyze  New          Contrast    Explain     ...
The	  Three-­‐Story	  Intellect	                 Evaluate   Predict        Hypothesize               Generate Speculate   ...
Cognitive Complexity          New        BLOOM’SR/U      A/A      E/CInput   Process   Output        DOK
Norman	  Webb’s	  	                                   Depths	  of	  Knowledge	    DOK	  Model	  (1997)	  created	  to	  an...
DOK	  	  Four	  Levels                                                                                                    ...
DOK	  	  Four	  Levels                                                                                                    ...
CAUTION!	  Bloom’s	  Verbs	  cannot	  be	  applied	  with	  the	  same	  mindset	       for	  what	  students	  must	  cog...
This	  cau4on	  influences	  wri4ng	  skills…	  	          Measurable	  Verb	  +	  Descriptor	  DOK	  1	  –	  Describe	  sh...
Cognitive Complexity                                                 New                                               BLO...
Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe cod...
walk	  C   ross                   Gap	  A                           nalys                                is	  
walk	               Most	  Beneficial	  Use	  of	  	  	  C   ross                     Crosswalk	  Documents	  	  	  	  	  	...
nalysis	  G ap	  AMost	  Beneficial	  Use	  of	  Gap	  Analysis	  Documents	  for	  Curriculum	  Design	  	               I...
walk	        ss                                                             Best	  to	  incorporate	  use	  of	  C   ro   ...
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Arizona                                                    http://www.azed.gov/standards-practices/                       ...
Math CCSS Courses                       UNIT NAME SIGNIFIERS: ____________Math (K-8)GEOMETRY (K-8)                        ...
Math CCSS Courses                     Progression of Systemic                          UNIT NAMES    once task-force teach...
Content = What Students Must KNOW                    Noun/Noun Phrase: Descriptor                     Think … Table of “Co...
Noun/Noun Phrase: DescriptorLength/Height/Width: ½ Inch, Inch, Foot, Yard / Centimeter,MeterFractions/Equal Shares: 2 Shar...
Use of Intra-Alignment Coding for Internal Alignment    The	  legers’	  job	  is	  to	  align	  Content	  to	  Skills	  
Skills = What students must cognitively be able to     DO in relationship to the intra-aligned KNOWingThere are technicall...
1.  Measurable Verb    Not Measurable Verbs = Demonstrate,    Understand, Know, Show, Use   Use appropriate tools to measu...
2.	  Target	  	  	  	  	  The	  measurement	  mode(s)	  …	  In	  other	  words,	  “how”	               learning	  is	  for...
2.	  Target	     	  Important	  Note:	  Some4mes	  a	  measureable	  verb	  does	    not	  need	  a	  target.	            ...
Classify          Differentiate      JustifyCompare           Discriminate       OrganizeCommunicate       Distinguish    ...
Design	  Note	  …	  Use	  of	  parentheses	  in	  skill	  statements	  	  	    	  Reduce	  complex	  frac)on	  (frac)on	  ...
3.	  Descriptors	  add	  clarity/details	  to	  the	  aligned	     content	  lis4ng,	  not	  duplicate	  it.          	  N...
Math	  CCSS	  Glossary,	  Page	  88	  
Quality	  Content	  C.	  Addi)on/Subtrac)on:	  1-­‐Step/2-­‐Step	  Word	  Problems	  	  Skills	  Ca.	  Solve	  5	  types	 ...
Decided	  to	  create	  an	  agachment	  associated	  with	  the	  Skill	  /	  Table	  1,	  but	  “more	  teacher	  friend...
ContentG.	  Scale	  Drawings:	  	  Square,	  Right	  Triangle,	  Rectangle	  /	  Unique	  FiguresSkillsG.	  Reduce	  large...
A bit of “fine tuning” is     oftentimes needed when  first writing skill statements.Sometimes difficult for task-forcemem...
Wearing	  the	  right	  design	  “gear”	  …	  Dive	  on	  in!	  	  	  	  	  	  	  	  	   (Even	  though	  it	  may	  feel	...
While	  breaking	  apart	  standards	  and	                     determining	  content,	  and	  especially	  skills,	      ...
www.LiveBinders.comSearch for: Janet Hale > Select Author > Click Search
www.azed.gov/standards-practices/mathematics-standards/
http://www.azed.gov/standards-practices/mathematics-standards/
www.illustrativemathematics.org
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group  Compariso...
Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group  Compariso...
 1.	  Collec4ng	  the	  Data	  
 2.	  First	  Read-­‐Through	  
 3.	  Small	  Group	  Review	  
 4.	  Large	  Group	        Comparisons	  
 5.	  Determine	  Immediate	  Revision	  Points	     Modify	  exis4ng	  and/or	  	  	  	  	    add	  new	  skill	  stateme...
 6.	  Determine	  Points	  Requiring	        Research	  and	  Development	  (?)	  	  
 7.	  Plan	  For	  Next	  Review	  
Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group  Compariso...
Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Developmen...
Phase 1 Design / Phase 2 Design   Vertical Alignment                Horizontal Alignment Design units that represent      ...
Janet	  Hale	    www.CurriculumMapping101.com	  teachtucson@aol.com	  	  	  520-­‐241-­‐8797	  
Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2
Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2
Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2
Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2
Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2
Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2
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Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2

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This slideshare represents the visuals used in a Webinar I presented highlighting critical considerations for designing systemic curriculum based on the CCSS. To listen to the archived podcast, please visit my Web site: www.CurriculumMapping101.com.

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Designing Common Core State Standards Systemic Mathematics Curriculum: Part 2

  1. 1. Designing  Common  Core  State  Standards   Systemic  Mathema4cs  Curriculum                   Part  2   Presented  By  Janet  Hale        www.CurriculumMapping101.com  
  2. 2. Architects Contractors design. build. LEARN TEACH
  3. 3. Aspen Grove MentalitySystemic Design - Interdependent 1 Grove…1 Root System
  4. 4. Phase 1 Design / Phase 2 Design Vertical Alignment Horizontal Alignment Design units that represent Design units of study that K-12 learning continuum integrate learning among(e.g., Geometry, Measurement/Data) strands in one grade level by domains (e.g., intradisciplinary, with cross-connections program-based, interdisciplinary)
  5. 5. Designing Systemic K-12CCSS Math Collaborative Maps How long will it take for the K-12 Task Force to complete Phase 1?
  6. 6. Part 1: Laying a Solid Foundation•  Unit Names•  Enduring Understandings/ Essential Questions•  Standards forMathematical Practice•  Vocabulary
  7. 7. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  8. 8. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  9. 9. Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe codes, but need to first consider design influences.•  Math CCSS - The 3 Key Shifts•  Depth of Knowledge•  When to incorporate the use ofstate-provided Crosswalk andGap Analysis documents.
  10. 10. CCSS Mathematics – 3 Key Shifts (www.achievethecore.org)1.  FOCUS Focus Strongly Where the Standards Focus (narrow scope of content to allow in-depth learning; no “but we have so much to cover”; “inch wide, mile deep” mindset to ensure time necessary for students to have time to explore, test, and reach conceptual understanding)2. COHERENCE Think across grade levels (systemic design) (each new standard is not a “new event” … each new standard is an extension of previous distinct or linked learning) Link learning among domains within one grade level (leverage) (conceptual relationships across and among standards to aid in conceptual understanding and reasoning)3. RIGOR Equitable, balanced curriculum (learning/teaching): –Conceptual Understanding –Procedural Skills and Fluencies –Application of Math Process using real-world/authentic problems/tasks (within/across disciplines)
  11. 11. 1.  FOCUS   2.  COHERENCE  Presenta)on  Slide  from  CCSS  for  Mathema-cs:  Key  Shi4s  -­‐Sandra  Alber),  Student  Achievement  Partners  
  12. 12. 3.  RIGOR   Grade  7    (Content  lis-ng  in  an  Essen-al  Map  unit)     --Conceptual Understanding Algebraic  Representa)ons:                                         --Procedural Skills and Fluencies --Application of Math Process   Equa)on  Fluency  Involving  4  Opera)ons   Mul)-­‐Step  Word  Problems  (Posi)ve/Nega)ve   Ra)onal  Numbers,  Inequali)es,  Complex   www.achievethecore.org   Frac)ons)   CCSS  Fluency  ≠  Rote  Memoriza4on   CCSS  Fluency    =    Speed  and  Accuracy         using  self-­‐selected  strategies     High  School  Fluencies:  Algebra,  Func4ons,   Geometry,  Sta4s4cs  &  Probability,  and  Modeling  
  13. 13. 1.  Use  mul)media.   2.  Encourage   student   intui)on.   3.  Ask  the  shortest   ques)on  you   can.   4.  Let  students   build  the   problem.   5.  Be  less  helpful.  hMp://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_makeover.html  
  14. 14. Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe codes, but need to first consider design influences.•  Math CCSS - The 3 Key Shifts•  Depth of Knowledge•  When to incorporate the use ofstate-provided Crosswalk andGap Analysis documents.
  15. 15. Cognitive Complexity New BLOOM’S DOK
  16. 16. The  Three-­‐Story  Intellect   NewBloom’s Duplicate Identify Paraphrase Count List Recite Input Understanding/Bena Kallick Define Memorize Locate R/U RememberingCCSSPresentation Describe Name Reproduce
  17. 17. The  Three-­‐Story  Intellect   Compare Distinguish Analyze New Contrast Explain Synthesize ProcessBloom’s Classify Discriminate Reason A/A Analyzing/ Applying Infer Sequence Interpret Duplicate Identify Paraphrase Count List Recite Input Understanding/Bena Kallick Define Memorize Locate R/U RememberingCCSSPresentation Describe Name Reproduce
  18. 18. The  Three-­‐Story  Intellect   Evaluate Predict Hypothesize Generate Speculate Forecast Output Creating/ Imagine If/then Create E/C Evaluating Judge Apply Speculate Compare Distinguish Analyze New Contrast Explain Synthesize Process Analyzing/Bloom’s Classify Discriminate Reason A/A Applying Infer Sequence Interpret Duplicate Identify Paraphrase Count List Recite Input Understanding/Bena Kallick Define Memorize Locate R/U RememberingCCSSPresentation Describe Name Reproduce
  19. 19. Cognitive Complexity New BLOOM’SR/U A/A E/CInput Process Output DOK
  20. 20. Norman  Webb’s     Depths  of  Knowledge   DOK  Model  (1997)  created  to  analyze  the  cogni)ve  expecta)on  demanded  by  standards,  curricular  ac4vi4es,  and  assessment  tasks.     redesign.rcu.msstate.edu       Several  things  are  involved,   including  the  content,  the  ac4vity   and/or  thinking  processes,  and  the   complexity  of  both  the  content  and   ac4vity/thinking  processes.     -­‐-­‐Debbie  Baughman,     The  Standards  Company  
  21. 21. DOK    Four  Levels  Level  1  Recall/Reproduc4on              Recall  facts,  informa)on,  procedures,                              basic  concept  founda)ons                                                                                            (minor  comprehension  involved  at  this  level,                                                                                                  no  depth,  no  complexity)  Level  2  Skill/Concept                                      Apply/process  facts,  informa)on,  procedures,  conceptual  understanding  involving  at  least  two  steps  that  require  reasoning                                                                                      (a  need  to  interpret  material  and  make  simple  decisions  about  how  to  approach  a  problem,  but  does  not  yet  have  a  deep  complexity)  
  22. 22. DOK    Four  Levels  Level  3  Strategic  Thinking                    Requires  deeper  reasoning,  developing  a                                                        plan  or  sequence  of  steps  to  complete  a  task;                    more  than  one  possible  solu)on/answer                                                          (deal  with  abstrac-ons  and  open-­‐ended  conclusions  and  able  to      support  one’s  reasoning;  wrestle  with  complex  concepts,  tasks,  material)  Level  4  Extended  Thinking  Process  mul)ple  condi)ons  and  solu)ons  for  the  problem;  extend  thinking  by  comple)ng  much  deeper  and  complex  tasks                                                                                                          (according  to  Webb,  higher-­‐level  thinking  is  absolutely  central;  interac-on  with  concepts,  tasks,  material  is  in-­‐depth  and  purposeful)  
  23. 23. CAUTION!  Bloom’s  Verbs  cannot  be  applied  with  the  same  mindset   for  what  students  must  cogni0vely  do  when                             applying  Webb’s  Depth  Of  Knowledge  (DOK)  to                  student  learning,  teaching,  and  assessment  items/tasks.  
  24. 24. This  cau4on  influences  wri4ng  skills…     Measurable  Verb  +  Descriptor  DOK  1  –  Describe  shape-­‐paMern  term/number-­‐paMern  rule  using  real-­‐world  examples  (e.g.,  Pretend  you  are  walking  outside.  Draw  and  explain  a  natural  or  man-­‐made  paJern’s  term.)  DOK  2  –  Describe  number/shape  paMerns  that  follow  determined  term/rule  and  jus)fy  reasoning  (e.g.,  Look  at  the  bowling  pins  paJern.  What  will  the  next  two  rows  look  like  in  this  paJern?  Explain  the  increase  using  textual,  visual,  and  number  representa-ons.  Without  drawing,  what  would  be  the  number  of  pins  in  the  15th  row?  Explain  your  reasoning.  )  
  25. 25. Cognitive Complexity New BLOOM’S R/U A/A E/C Input Process Output 1 2 3 4 Recall/ Skill/ Strategic ExtendedReproduction Concept Thinking Thinking DOKPARCC Smarter Balanced www.smarterbalanced.org/wordpress/wp-content/uploads/2012/03/www.parcconline.org/parcc-content-frameworks DRAFTMathItemSpecsShowcase2.pdf
  26. 26. Implicit Influences•  Breaking Apart (Unpacking) StandardsTeachers as designers will spend time explicitly studyingthe codes, but need to first consider design influences.•  Math CCSS - The 3 Key Shifts•  Depth of Knowledge•  When to incorporate the use ofstate-provided Crosswalk andGap Analysis documents.
  27. 27. walk  C ross Gap  A nalys is  
  28. 28. walk   Most  Beneficial  Use  of      C ross Crosswalk  Documents                                   for  Curriculum  Design     Verifies  what  task-­‐force  members     discover  acer  first                                                           studying  and  analyzing                                         ver)cal/horizontal  Math  CCSS.  
  29. 29. nalysis  G ap  AMost  Beneficial  Use  of  Gap  Analysis  Documents  for  Curriculum  Design     Indicates  to  task-­‐force  members  who  may  be  called  upon  to  be                                                                 resident  experts  for  fellow  task-­‐force  members  who                                                                                       may  need  some  or  a  lot  of  aid  in  designing  unfamiliar  learning  (content  –  skills).  
  30. 30. walk   ss Best  to  incorporate  use  of  C ro Crosswalk  and  Gap  Analysis   documents  AFTER  task-­‐force   teachers  have  systemically   studied  and  discussed                 the  Math  CCSS  Domain(s).   Gap  A nalys www.LiveBinders.com   Search  for:  Curriculum  21   is  
  31. 31. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  32. 32. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  33. 33. Arizona http://www.azed.gov/standards-practices/ mathematics-standards/ Ohiohttp://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspxPage=3&TopicRelationID=1704&Content=123507 (Transitional Tools)
  34. 34. Math CCSS Courses UNIT NAME SIGNIFIERS: ____________Math (K-8)GEOMETRY (K-8) = Suggested Starting Point K-8DATA: MEASUREMENT/DATA (K-5)DATA: STATISTICS/PROBABILITY (6-8)NUMBER/QUANTITATIVE: COUNTING/CARDINALITY (K)NUMBER/ALGEBRAIC: NUMBER BASE 10/OPERATIONS (K-5)NUMBER: NUMBER SYSTEM/EXPRESSIONS/EQUATIONS (6-8)QUANTITATIVE: RATIOS/PROPORTIONAL RELATIONSHIPS (6-8)Coordinate Algebra (9) (Integrated Pathway)EXPRESSIONS/EQUATIONSLINEAR FUNCTIONS Determine DesiredEXPOTENTIAL FUNCTIONS PathwayDATA ANALYSISCOORDINATE PLANE Math CCSSINEQUALITIES Appendix AAnalytic Geometry (10) Advanced Algebra (11)(Above examples based on work in Muscogee CSD, Columbus, GA)
  35. 35. Math CCSS Courses Progression of Systemic UNIT NAMES once task-force teachers began studying the architectural codes (clusters/standards) while considering influences and beginning to determine potential content listings.GEOMETRY (Grades K-2)GEOMETRY/MEASUREMENT (Grades 3-5)GEOMETRY (Grade 6)Phase 2 … GEOMETRY: AREA AND VOLUMEGEOMETRY (Grade 7)Phase 2 … GEOMETRY: GEOMETRYGEOMETRY (Grade 8)Phase 2 … GEOMETRY: GEOMETRIC APPLICATIONSOF EXPONENTS(Above examples based on work in Muscogee CSD, Columbus, GA)
  36. 36. Content = What Students Must KNOW Noun/Noun Phrase: Descriptor Think … Table of “Contents” 3-Dimensional Shapes : Needs A Descriptor 3-Dimensional Shapes: Sphere, Cone, Cylinder 3-Dimensional Shapes: Sphere  Time: Analog Face (Hour Hand, Minute Hand), Digital Face (Hour Digits,Colon, Minute Digits) / O-clock, ThirtyTime: Nearest Minute, ElapsedTime: Comparison (Second, Minute, Hour, Day, Week, Months, Year,Decade, Century, Millennium) / Conversion Of Units (Within SingleSystem)Distance/Weight/Mass/Capacity/Time/Money: Conversion Of Unlike Units- Same System (Smaller to Larger/Larger to Smaller) / 2-Step & Multi-Step Word Problems
  37. 37. Noun/Noun Phrase: DescriptorLength/Height/Width: ½ Inch, Inch, Foot, Yard / Centimeter,MeterFractions/Equal Shares: 2 Shares, 3 Shares, 4 Shares(Circle, Rectangle)Quadratic Polynomials: Fundamental Theorem of AlgebraMeasures Of Central Tendency: Mean, Median, Mode,Range, Outlier Whenever possible (in any element field), use numeral instead of number word for 0-9. It is easier on the eye/mind to locate information quickly.  
  38. 38. Use of Intra-Alignment Coding for Internal Alignment The  legers’  job  is  to  align  Content  to  Skills  
  39. 39. Skills = What students must cognitively be able to DO in relationship to the intra-aligned KNOWingThere are technically three parts to a quality written skill statement:1.  Measurable Verb (can “see” the thinking)2.  Target (how learning is measured - assessments)3.  Descriptor (provides clarity/detail related to the intra- aligned Content)Do not begin skill statements with:The student will…A skill statement startswith a capital letter,but needs no periodat end of statement
  40. 40. 1.  Measurable Verb Not Measurable Verbs = Demonstrate, Understand, Know, Show, Use Use appropriate tools to measure and record to nearest abbreviated unit (½ in., 1 in., 1 ft. / 1 cm, 1 m, 1 yd) ☺Measure manipulatively and record in writing to nearest unit nearest abbreviated unit (½ in., 1 in., 1 ft. / 1 cm, 1 m, 1 yd) using appropriate tools Use number line to order up to 5 rational numbers (based on place value of each number) ☺Order up to 5 rational numbers (based on place value of each number) using number lineIf using Apply… Apply to what? Apply in writing self-selected strategies to solve real-world 2-step word problems and justify reasoning
  41. 41. 2.  Target          The  measurement  mode(s)  …  In  other  words,  “how”   learning  is  formally  assessed.        -­‐-­‐in  wri4ng,  orally      /  -­‐-­‐manipula4vely,  visually        Note:  in  wri4ng  =  not  orally    •  (Gr.  3)  Iden)fy  in  wri)ng  value  of  given  digit  based  on  base-­‐ten   placement  (e.g.,  3,491  …  What  does  the  digit  3  represent  in  3,491?  Student   writes:  The  digit  3  represents  3  thousands.)  •  (Gr.  K  –  Qtr  1.)  Correlate  manipula)vely,  visually,  and  orally   concept  of  “1  real/illustrated  object  in  pictograph  represents                         1  unit  in  bar  graph”  using  labeled  graph  paper/adult  support  •  (FUNCTIONS)  Iden)fy  in  wri)ng  center  and                                                                     radius  of  circle  by  comple)ng  the  square  
  42. 42. 2.  Target    Important  Note:  Some4mes  a  measureable  verb  does   not  need  a  target.    Obvious:  Recite…    Write…  Mathema4cs/Science:  Solve…  Find…  Calculate…   Construct…  and  other  math-­‐specific  cogni4ons         are  considered  to  be  in  wri4ng  unless  otherwise   noted.  Ba.  Solve  for  unknown  to  make  equa)on  true   (e.g.,  53  +  □  =  73  …  53  +  20  =  73)    Universal  Verbs:  Such  as  Iden4fy…  Compare  and   contrast…  do  need  a  target/targets    
  43. 43. Classify Differentiate JustifyCompare Discriminate OrganizeCommunicate Distinguish PredictContrast Estimate PrioritizeConvert Evaluate ProveCorrelate Explain RankCriticize Generalize RecognizeCritique Identify SequenceDefine Infer SummarizeDescribe Interpret TransferDetermine Invent*This is a sample list and therefore not comprehensive.
  44. 44. Design  Note  …  Use  of  parentheses  in  skill  statements        Reduce  complex  frac)on  (frac)on  over  frac)on)  by  mul)plying   by  common  denominator  (e.g.,  see  complex  frac-on  example)      Describe  orally  and  in  wri)ng  par))oned  shares  using                                         6  terms  (halves,  half  of,  thirds,  third  of,  quarters,  quarter  of)             (e.g.,  Ali  par--ons  a  circle  into  2  shares.  She  writes:  The  circle  has  2  equal   shares  or  2  halves.)  (e.g.,  _____________  )  =   for  example  (i.e.,  ______________)  =   that  is  (______________)    =   that  is    
  45. 45. 3.  Descriptors  add  clarity/details  to  the  aligned   content  lis4ng,  not  duplicate  it.  Not  Yet  Quality  Content    C.  Addi)on/Subtrac)on:  1-­‐Step/2-­‐Step  Word  Problems    Skills  C.  Solve  word  problems   If  you  were  the  Assessment  Fairy,   could  you  design  a  quality   assessment  to  measure  the   required  skill  learning?  
  46. 46. Math  CCSS  Glossary,  Page  88  
  47. 47. Quality  Content  C.  Addi)on/Subtrac)on:  1-­‐Step/2-­‐Step  Word  Problems    Skills  Ca.  Solve  5  types  (adding  to,  taking  from,  puing  together,  taking  apart,   comparing  (more  /  less))  of  1-­‐step  word  problems  (compose/ decompose/  regroup  with  minuend  up  to  100,  sum  up  to  100)  using   self-­‐selected  strategies  and  jus)fy  reasoning:  -­‐-­‐Adding  to  (Result  Unknown)  (e.g.,  Twenty  bunnies  sat  on  the  grass.  Thirty-­‐ three  more  bunnies  hopped  there.  How  many  bunnies  are  on  the  grass  now?)    -­‐-­‐Adding  to  (Change  Unknown)  (e.g.,  Twelve  bunnies  were  si]ng  on  the  grass.   Some  more  bunnies  hopped  there.  Then  there  were  thirty-­‐seven.  How  many   bunnies  hopped  over  to  the  twelve?)  -­‐-­‐Adding  to  (Start  Unknown)  (e.g.,  Some  bunnies  were  si]ng...)     Could  the  skill  statement                                                               s4ll  be  improved  design-­‐wise?  
  48. 48. Decided  to  create  an  agachment  associated  with  the  Skill  /  Table  1,  but  “more  teacher  friendly.”     Addition and Subtraction Word Problem Types Add To (addition) – Involve physical action, Take From (subtraction) – Involve physical change in quantity over a period of time action, change in quantity over a period of time Result Change Start Result Change Start Unknown Unknown Unknown Unknown Unknown Unknown Lela had four dolls. Lela had four dolls. Lela had some dolls. Luke had ten Luke had ten Luke had some She bought two She bought some She bought two more cookies. He ate cookies. He ate cookies. He ate more. How many more dolls. Now, she dolls. Now she has six three cookies. How some of the cookies. three cookies. Now dolls does she have has six dolls. How dolls. How many dolls many cookies does Now he has seven he has seven now? many dolls did Lela did Lela have before Luke have left? cookies. How many cookies left. How buy? she bought some cookies did Luke many cookies did more? _____ + 2 = 6 eat? Luke have to start 4 + 2 = ______ 4 + _____ = 6 10 - 3 = ______ 10 - _____ = 7 with? _____ - 3 = 7 4 + 2 = ______ 4 + 2 = ______ Put Together/Take Apart – A visual relationship 10 - 3 = ______ representation between whole and its two separate Compare – A visual comparison of two parts unconnected sets Total Addend Both Addends Difference Bigger Smaller Unknown Unknown Unknown Unknown Unknown Unknown Zach has two brothers. Cam has one more Luke had ten cookies. Luke has five cookies Zach has two brothers. Cam has three brother than Zach. Luke had ten cookies. He ate some of the and two plates. How Cam has one more brothers. Cam has how Cam has three He ate three cookies. cookies. Now he has many different brother than Zach. many more brothers brothers. How many How many cookies seven cookies. How combinations of How many brothers than Zach? brothers does Zach does Luke have left? many cookies did Luke cookies can he make? does Cam have? have? eat? 3 – 2 = _____ _____ + 1 = 3 10 - 3 = ______ 10 - _____ = 7 5=5+0 5=0+5 2 + 1 = _____ 10 - 3 = _____ 5=1+4 5=4+1 2 + _____ = 3 3 – 1 = _____ 5=2+3 5=3+2 Pendergast  Elementary  School  District    Phoenix,  AZ    
  49. 49. ContentG.  Scale  Drawings:    Square,  Right  Triangle,  Rectangle  /  Unique  FiguresSkillsG.  Reduce  larger  image  using  graph  paper  to  reproduce  larger  image  as  a  similar  figure  (e.g.,  see  Edwins  Reduc-on  example)  G.  Enlarge  smaller  image  using  graph  paper  to  reproduce  smaller  image  as  a  similar  figure  G.  Iden)fy  in  wri)ng  scale  key  in  scale  drawings  (e.g.,  city  maps,  architect  blueprints,  landscape  plans,  engineering  blueprint  /  e.g.,  see  Scale  Keys  example)  G.  Correlate  in  wri)ng  scale  key  to  drawing  representa)on(s)  (e.g.,  Michael  is  looking  at  a  scale  drawing.  The  scale  key  reads:    1"  =  1  Foot      Michael  writes:  In  this  scale  drawing,  1  inch  represents  1  foot  of  the  actual  boat.)  G.  Reduce  larger  image  (2-­‐dimensional  quadrilaterals)  based  on  given  scale  using  graph  paper  (e.g.,  see  Campbelles  Parallelogram  example)  G.  Enlarge  smaller  image  (2-­‐dimensional  quadrilaterals)  based  on  given  scale  using  graph  paper  (e.g.,  see  Harpers  Rectangles  example)  Ga.  Determine  dimensions  of  figures  when  given  scale  and  iden)fy  impact  of  scale  on  actual  length  (1-­‐dimension),  area  (2-­‐dimension)  and  jus)fy  reasoning  (e.g.,  see  Coach  Cleggs  Problems  example)  
  50. 50. A bit of “fine tuning” is oftentimes needed when first writing skill statements.Sometimes difficult for task-forcemembers to differentiate betweena SKILL/STRATEGY or ACTIVITY. A skill is focused on what students must cognitively be able to do. An activity is focused on providing practice concerning a particular skill’s or skills’ development or reinforcement. No: Practice orally addition facts No: Review steps to solve … No: Walk around room to measure…
  51. 51. Wearing  the  right  design  “gear”  …  Dive  on  in!                   (Even  though  it  may  feel  a  ligle  unnerving  at  first…)  
  52. 52. While  breaking  apart  standards  and   determining  content,  and  especially  skills,   task-­‐force  members  are  always  ques4oning   and  inquiring  using  on-­‐line  resources  as   well  as  each  another’s  exper4se.    Researchers  
  53. 53. www.LiveBinders.comSearch for: Janet Hale > Select Author > Click Search
  54. 54. www.azed.gov/standards-practices/mathematics-standards/
  55. 55. http://www.azed.gov/standards-practices/mathematics-standards/
  56. 56. www.illustrativemathematics.org
  57. 57. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  58. 58. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  59. 59. Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group Comparisons 5. Determine Immediate Revision Points 6. Determine Points Requiring Research and Planning 7. Plan for Next ReviewHeidi  Hayes  Jacobs,  Mapping  The  Big  Picture  (1997)  
  60. 60. Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group Comparisons 5. Determine Immediate Revision Points 6. Determine Points Requiring Research and Planning 7. Plan for Next Review
  61. 61.  1.  Collec4ng  the  Data  
  62. 62.  2.  First  Read-­‐Through  
  63. 63.  3.  Small  Group  Review  
  64. 64.  4.  Large  Group   Comparisons  
  65. 65.  5.  Determine  Immediate  Revision  Points   Modify  exis4ng  and/or           add  new  skill  statements  ,   examples,  and  agachments.  
  66. 66.  6.  Determine  Points  Requiring   Research  and  Development  (?)    
  67. 67.  7.  Plan  For  Next  Review  
  68. 68. Seven-Step Review Process 1. Collecting the Data 2. First Read-Through 3. Small Group Review 4. Large Group Comparisons 5. Determine Immediate Revision Points 6. Determine Points Requiring Research and Planning 7. Plan for Next Review
  69. 69. Part 2•  Breaking Apart (Unpacking)Standards(Explicit Process, Implicit Influences)•  Systemic Content / Skills Development(Process: Format … Collaborative Agreement on Tight and Loose)•  PreK-12 Vertical Reviews(Internal Alignment – Content/Skills &External Alignment to Standards; if using, EUs/EQs)
  70. 70. Phase 1 Design / Phase 2 Design Vertical Alignment Horizontal Alignment Design units that represent Design units of study that K-12 learning continuum integrate learning among(e.g., Geometry, Measurement/Data) strands in one grade level by domains (e.g., intradisciplinary, with cross-connections program-based, interdisciplinary)
  71. 71. Janet  Hale   www.CurriculumMapping101.com  teachtucson@aol.com      520-­‐241-­‐8797  

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