Teaching for Conceptual Understanding:

Transcription

1 Cmmn Cre State Standards Prfessinal Develpment 2011 Teaching fr Cnceptual Understanding: Base Ten, Fractins, Ratis and Prprtinal Relatinships, and Functins Prfessinal Develpment Facilitatr Handbk

2 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Pearsn Schl Achievement Services Cmmn Cre State Standards Prfessinal Develpment 2011 Teaching fr Cnceptual Understanding Facilitatr Handbk Published by Pearsn Schl Achievement Services, a divisin f Pearsn, Inc E. Lake Ave., Glenview, IL Pearsn, Inc. r its affiliate(s). All rights reserved. Printed in the United States f America. ISBN 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 2

3 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Cntents Materials Checklist...Errr! Bkmark nt defined. Facilitatr Agenda... 4 Preparatin and Backgrund...Errr! Bkmark nt defined. Sectin 1: CCSSM Learning Prgressins (Slides 1 37)...Errr! Bkmark nt defined. Sectin 2: Teaching fr Understanding (Slides 38 84)... 9 Sectin 3: Assessing Students Understanding and Identifying Strategies fr Instructing Cncepts (Slides )...Errr! Bkmark nt defined. References...Errr! Bkmark nt defined Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 3

4 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Facilitatr Agenda Teaching fr Cnceptual Understanding: Base Ten, Fractins, Ratis and Prprtinal Relatinships, and Functins Sectin Time Agenda Items 1: CCSSM Learning Prgressins 80 minutes Slides 1 37 Welcme and Intrductin Outcmes Agenda Sectin Intrductin Big Questins Learning Objectives Brief Intrductin t the CCSSM CCSSM Critical Areas Activity: Anntating Grade Intrductin Grade-Level Standards Activity: Clarifying Standards Terminlgy Learning Prgressins Activity: Fllwing the Learning Prgressin Reflectin: Things t Cntinue and Things t Change Break 15 minutes 2: Teaching fr Understanding 90 minutes Slides Sectin Intrductin Big Questin Learning Objectives Critical Prir Knwledge Ratis Activity: Rati Tables Mini-Lessn Functins Activity: Srting Functins Mini-Lessn Mdel Wrkshp Base-Ten Activity: Place Value Tables and Patterns Fractins Activity Optin 1: Cmparing Fractins Fractins Activity Optin 2: Multiplying Fractins Ratis Activity: Graphing Prprtinal Relatinships Functins Activity: Rate f Change Cnnecting the Wrkshp t the Learning Prgressin Reflectin: Sentence Cmpletin 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 4

5 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Lunch 3: Assessing Students Understanding and Identifying Strategies fr Instructing Cncepts Ttal 60 minutes 115 minutes Slides Sectin Intrductin Big Questins Learning Objectives Math Prblems Base-Ten Activity: Math Prblems Fractins Activity: Math Prblems Ratis Activity: Math Prblems Functins Activity: Math Prblems Reviewing Student Wrk Activity: Evaluating Student Understanding Brainstrming Instructinal Strategies Activity: Brainstrming Appraches Instructinal Strategies Carusel Activity: Carusel Reflectin: Planning Instructinal Changes Wrkshp Clsing 6 hurs 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 5

6 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Wrkshp Infrmatin This ne-day wrkshp examines the cntent shifts by grade level fr the Cmmn Cre State Standards fr Mathematics (CCSSM) with an emphasis n either 1) the dmain f peratins in base ten, 2) the dmain f fractins, 3) the dmain f ratis and prprtinal relatinships, r 4) functins. Participants explre the changes in the language and the fcus f the new standards. They examine hw t use existing resurces t help students meet the expectatins fr the cntent dmains f the Cmmn Cre. Big Ideas The prgressin f a dmain acrss grades builds n prir learning tward future cncepts. Understanding hw dmains prgress is critical t building prficiency in mathematics and shuld guide instructin. The prgressins can help with the transitin t CCSSM because they identify the gaps that need t be filled in rder t prepare students fr success. Students need pprtunities t engage with relevant mathematics in rder t develp their mathematical expertise. Well-chsen, thughtful lessns are a critical element f this prcess. Strategies fr addressing the needs f special ppulatins need t be intentinal and planned. Assessing student wrk is abut much mre than lking fr right r wrng answers. Student wrk can prvide evidence f what students knw and understand abut the mathematics we are teaching. Well-chsen prblems prvide the best pprtunities fr such evidence t emerge. Instructin is mst effective when it directly addresses students miscnceptins, and student wrk can prvide evidence f thse miscnceptins. Enabling students t meet the CCSSM means implementing effective instructinal strategies t develp students mathematical expertise thrugh daily classrm interactins. Essential Questins Hw des the CCSSM impact instructin f base ten, fractins, ratis and prprtinal relatinships, and functins? What is the learning prgressin fr these tpics and hw shuld ur instructinal strategies change t reflect the learning prgressin? Activities within the Wrkshp Read abut the critical areas fr their grade level Review their grades standards related t either base ten, fractins, ratis and Prprtinal Relatinships, r functins, and clarify terms and phrases Discuss the learning prgressins with the whle grup and cnsider hw they are different frm current practices Reflectin n which current practices shuld cntinue and which new appraches shuld be added Participate in a mini-lessn and mdel wrkshp fr their tpic (base ten, fractins, ratis, and functins) Discuss the cnnectins between the wrkshp and the learning prgressin Discuss in the large grup the standards fr the dmain fcus Wrk n relevant mathematics prblems 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 6

7 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Review individually and in grups the student wrk fr the related math prblem t determine what students knw (and what the evidence is) and implicatins fr further instructin Identify strategies that shuld becme part f their regular teaching rutine Reflect n the next steps fr tmrrw, next week, next grading perid, and next schl year Assessment f Participants Learning during the Wrkshp Engage with the critical areas frm wn grade and build links t adjacent grade levels Discuss CCSSM terminlgy accurately (aviding miscnceptins) Identify instructinal changes needed t meet the CCSSM Engage in the prblems during the wrkshp Cnsider the kinds f instructinal strategies that mst supprt all students (including ELLs, SpEd) in building mathematical expertise Make cnnectins between the prblems and the standards, including hw the cncepts fit within the learning prgressin Discuss the evidence fund in the student wrk Assessment back in the Schl/Classrm Discuss with clleagues frm different grade levels the imprtance f the prgressin f mathematical cncepts Implement the identified instructinal changes in the classrm Share the differences in the CCSSM apprach t the specific tpic with clleagues and discuss changes in instructin that are needed t supprt students Evidence that apprpriate strategies are being implemented in the classrm and that students are engaging in apprpriate tasks that align t the CCSSM Review student wrk t find ut what students knw Use instructinal appraches that are infrmed by students wrk Incrprate effective instructinal strategies int their classrm practices Evidence f students wh are using apprpriate tls and exhibiting the practices as they wrk in class Outcmes Articulate the learning prgressins necessary fr students t cnceptually understand either 1) base-ten peratins, 2) fractins, 3) ratis and prprtinal relatinships, r 4) functins Identify strategies fr helping students build their mathematical understanding f either 1) base-ten peratins, 2) fractins, 3) ratis and prprtinal relatinships, r 4) functins Identify strategies that supprt simultaneus develpment f cnceptual understanding and prblem-slving skills with the intentinal use f purpseful student struggle, flexible gruping, and nging assessments Articulate cmmn miscnceptins as pprtunities fr develping students cnceptual understanding f either 1) base-ten peratins, 2) fractins, 3) ratis and prprtinal relatinships, r 4) functins Facilitatr Gals Intrduce the learning prgressin fr the dmain f fcus 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 7

8 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Prvide participants with specific suggestins f appraches that will increase students understanding f the imprtant CCSSM tpics Encurage participants t mdel the learning and practices they want their students t exhibit Supprt participants skills in frmatively assessing students understanding and implementing targeted instructin Guide participants in encuraging all students (including ELL, special educatin, and ther ppulatins) t understand the dmain 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 8

9 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Sectin 2: Teaching fr Understanding (Slides 38 84) Time: 90 minutes Big Questin What d the CCSSM lk like in practice? Learning Objectives Explain hw well-chsen, thughtful tasks help students meet the CCSSM Describe key differences in hw the CCSSM address the grade level tpic and hw these differences will affect instructin and student learning Identify instructinal strategies that will supprt all students in building their mathematical expertise Materials per Sectin Cmputer, Prjectr, Speakers, and PwerPint file (Slides are nly needed fr the Base Ten wrkshp, Slides are nly needed fr the Fractins wrkshp, Slides are nly needed fr the Ratis and Prprtinal Relatinships wrkshp, and Slides are nly needed fr the Functins wrkshp) Base Ten Wrkshp Participant Wrkbk: Pages 15 22, 55 Handut: Tens and Ones Place-Value Table Wrkspace (page 5) Backgrund Materials: Pages 7 10 Base-10 blcks r ther manipulatives Chart Paper Markers Fractins Wrkshp Participant Wrkbk: Pages 15 23, 55 Handut: Cmparing Fractins (pages 5 9) Handut: Multiplying Fractins (pages 11 15) Backgrund Materials: Pages 7 16 Scissrs Tape Blank Paper Ratis and Prprtinal Relatinships Wrkshp Participant Wrkbk: Pages 13 21, 58 Backgrund Materials: Pages 7 12 Chart Paper Markers Sticky Ntes 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 9

10 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Functins Wrkshp Participant Wrkbk: Pages 13 26, 56 Backgrund Materials: Pages 7 14 Handut: Types f Functins (pages 5 9) Scissrs Tape Blank Paper Chart Paper Markers * Reminder: Verify that unneeded slides are hidden befre beginning this sectin f the PwerPint presentatin. If facilitating the Fractins dmain versin, yu will need t hide additinal slides depending n which ptin f the mdel wrkshp yu select. If yu are facilitating Optin 1 (Cmparing Fractins) hide Slides If yu are facilitating Optin 2 (Multiplying Fractins), hide Slides If yu are facilitating either the Ratis and Prprtinal Relatinships r the Functins dmain, yu likely will als want t hide either Slides r Slides 81 83, which nly need t be shwn n an as-needed basis depending n the wrk created by participants. Tpic Presentatin Pints Presentatin Preview Sectin Intrductin Display Slide 38. Intrduce Sectin 2 by making the pints n the slide. Big Questin Display Slide 39. Explain t participants that in the secnd sectin f the wrkshp, they will discver the answers t the questins n this slide Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 10

11 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Tpic Presentatin Pints Presentatin Preview Learning Objectives Display Slide 40. Read the learning bjectives fr Sectin 2. Mdel Wrkshp Base Ten Activity: Place-Value Tables and Patterns Fractins Activity Optin 1: Cmparing Fractins Fractins Activity Optin 2: Multiplying Fractins Ratis Activity: Graphing Prprtinal Relatinships Functins Activity: Rate f Change Set the Stage: Tell participants that they will nw wrk thrugh a sample lessn that yu will present in the frmat f a mdel wrkshp. Explain that the purpse f using the mdel wrkshp is t shw teachers hw they can address a tpic in a manner that fits the CCSSM. They will be ding the math that they read abut in the standards. Tell participants that the purpse f the lessn is t give participants an pprtunity t experience a lessn as students d althugh participants will prbably mve thrugh the lessn in a mre prductive manner than their students wuld. Explain t participants that they will have a chance at the end f the wrkshp t discuss the lessn frm a teacher perspective. Select frm the lessns belw based n the wrkshp yu are presenting (Base Ten, Fractins, Ratis and Prprtinal Relatinships, r Functins). NOTE: Befre yu cnduct the lessn, wrk thrugh all f the prblems. Try t use as many methds as yu can think f t slve each prblem, in anticipatin f the appraches that participants might use. Base Ten Opening Base Ten: Display Slide Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 11

12 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Tpic Presentatin Pints Presentatin Preview Have participants turn t page 17 f the Participant Wrkbk. Ask a vlunteer t read the questin in the example alud. Ask participants what the arrw means in this example. [Answer: It means add ne 10] Refer participants t the slide and ask: Hw culd yu use an arrw t shw 10 less than a number? [Answer: Reverse the arrw s that it pints ut] What if yu want 1 mre r 1 less than a number? What wuld the diagram lk like? [Answer: The arrws will pint t the nes r t a 1 that is being remved.] PW: Pages 17 21, 55 Explain that this lessn fcuses n prblems that ask participants t find 1 mre, 1 less, 10 mre, and 10 less using varius tls. Participants might use place-value tables, number lines, base-10 blcks, and hundreds charts. Mdel the use f the phrases mre than and less than. Cnsider displaying them s that participants can see them as they wrk. Display Slides Read the prblems t participants and have them read alng n pages f the Participant Wrkbk. Tell participants that prblems 1 5 are very similar even thugh they may lk different at first. Distribute cpies f the Tens and Ones Place-Value Table Wrkspace handut and base-10 blcks r ther manipulatives fr participants t use as they slve the prblems. Explain that prblems 6 7 are a little different. They are place value riddles. Suggest that participants cnsider using base-10 blcks t help them with these prblems. Tell participants that in prblems 8 10 they will lk fr patterns in the ne-hundreds chart and then use these patterns t find the missing values in ther hundreds charts. Explain that in the ne-hundreds chart, as yu mve t the right thrugh the chart, yu are basically cunting by nes. Remind participants that they shuld fill in the missing numbers withut lking at the cmpleted chart. Have participants take the time t think abut the strategies they are 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 12

13 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Tpic Presentatin Pints Presentatin Preview using t slve each f the prblems, and t cnsider what difficulties they wuld expect their students t have. Wrk Time Clsing Have participants begin wrking n the prblems independently. After a few minutes, tell them that they can mve between sl wrk and partner wrk at their wn pace. Tell them they will have abut 20 minutes t wrk n the prblems. While yu circulate, use a cpy f the Mnitring Tl: Place-Value Tables and Patterns n page 9 f the Backgrund Materials t recrd: participants' respnses as they wrk; yu will use this infrmatin t decide which participants will present during the clsing evidence f wrk that is related t the Base Ten learning prgressin r that uses the mathematical practices; yu will discuss this wrk during the debrief Handut: Tens and Ones Place-Value Table Wrkspace (page 5) Base-10 blcks r ther manipulatives Chart Paper Markers Bkgd Materials: Pages 7 10 (facilitatr nly) Have participants present their wrk. Encurage presenting participants t explain hw they apprached the prblem, as well as any struggles they experienced thrughut the prcess. Depending n time cnstraints, yu might need t review nly ne f each type f prblem (such as prblems 2, 4, 6, 8, and 10). Finish the lessn by restating the imprtant mathematics f the lessn. Debrief structins alud. Grup participants int pairs and distribute the Multiplying Fractins handut, scissrs, and tape t each pair Wrk Time Have participants wrk in pairs t the match the cards. Mentin t participants that all fractin answers have been reduced t their simplest frm. Encurage participants t write r draw n blank paper as needed. Circulate amng the pairs t check fr understanding. While yu 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 13

14 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Tpic Presentatin Pints Presentatin Preview Clsing circulate, use a cpy f the Mnitring Tl: Multiplying Fractins frm page 13 f the Backgrund Materials t recrd: participants' respnses as they wrk; yu will use this infrmatin t decide which participants will present during the clsing evidence f wrk that is related t the Fractins learning prgressin r that uses the mathematical practices; yu will discuss this wrk during the debrief Have the participants yu selected present their wrk. Encurage presenting participants t explain hw they apprached the prblem, as well as any struggles they experienced thrughut the prcess. Finish the lessn by restating the imprtant mathematics f the lessn. Debrief Discuss which standard(s) this lessn addresses (CCSSM) and directly cnnect the standards t the larger learning prgressin. Ask participants hw the Standards fr Mathematical Practices were evident in the wrk tday. Have participants describe any elements f the lessn that were different frm a typical lessn (such as an emphasis n justificatin, r n making cnnectins between representatins). Take a minute t talk abut the preparatin that went int this lessn. Shw participants that yu wrked thrugh the card srt ahead f time. Pint ut that yu used multiple appraches t making the matches and rdering the cards in anticipatin f what participants might d. Make explicit any decisins yu made in planning fr the clsing. In particular, refer participants t the Mnitring Tl n page 55 f the Participant Wrkbk and explain hw yu used the tl t keep track f the different appraches that participants used t match and srt the cards. If yu have time, describe the five practices fr rchestrating prductive mathematical discussins 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 14

15 Cmmn Cre State Standards Prfessinal Develpment 2011, Teaching fr Cnceptual Understanding, Facilitatr Handbk Tpic Presentatin Pints Presentatin Preview (see page 7 f the Backgrund Materials fr mre infrmatin). : 2011 Pearsn, Inc. r its affiliate(s). All rights reserved. Revised 7/10/13 15