Andy Clark Andy.clark@hmhpub Andyclark@qwest
2012NCTMRegionalConferenceAndy aicThinkingWednesday, October 31, 12
Top Scoring Nationfor 15 years!Wednesday, October 31, 12
67778992Low9390959898% of students whoreached at least thislevelSample problemsTIMSS–4thGradeProblemTrends in International Math and Science StudyWednesday, October 31, 12
Example of 8th Grade TIMSSProblemJoe knows that a pen costs 1 zed %Receivedfullmore than a pencil. His friendcreditbought 2 pens and 3 pencils for17 zeds. How many zeds will Joe Singapore:need to buy 1 pen and 2 pencils?59%UnitedStates37%Wednesday, October 31, 12
Example of 8th Grade TIMSSAdvanced ProblemJoe knows that a pen costs 1 zed more than apencil. His friend bought 2 pens and 3 pencils for17 zeds. How many zeds will Joe need to buy 1 penand 2 pencils?Pencil 3 zedsPen115Wednesday, October 31, 121 pen and 2 pencils 4 6 10 4 zeds1 15} 17
Example of 8th Grade TIMSSProblemThe length of a rectangle is 6 cm, and itsperimeter is 16 cm. What is the area of therectangle in square centimeters?AnswerMeasurement: Singapore, 86%; Korea, 66%; Japan,65%;Canada, 41%; France, 36%;U.S., 22%Wednesday, October 31, 12
hina(600)US487 Singapore Math, A World LeaderPedagogy based upon 20 yearsof research and successWednesday, October 31, 12
Teach to Mastery“ mathematics curriculum in the United Statesmust address the problem of a curriculum thatis a “mile wide and an inch deep.”Common Core State StandardsWhat can we learn?Wednesday, October 31, 12
Singapore: The Model for CCSSWhat can we learn?Wednesday, October 31, 12
Mathematics Standardsfor Mathematical Practice Able:– tomakesenseofproblemsandpersevere– toreasonabstractlyandquanVtaVvely– toconstructviablearguments– tomodelwithmathemaVcs– tousetoolsappropriately– toaXendtoprecision– tolooksforandmakeuseofstructure– tolookforregularityWednesday, October 31, 12
PreparingforCommonCoreWednesday, October 31, 12
PreparingforSBAC7th GradeWednesday, October 31, 12
PreparingforCommonCoreWednesday, October 31, 12
PARCCAssessmentWednesday, October 31, 12
PreparingforCommonCoreWednesday, October 31, 12
PreparingforCCSSAssessmentsWednesday, October 31, 12
Wednesday, October 31, 12
CommonCoreInstrucVonalemphases Focus:PrioriVzetopicsandfocusonthem ldsonthepreviousones derstandhow,why,andwhentheywork withproceduresandfactsWednesday, October 31, 12
What can we learn from Singapore? Teach math as a vehicle for teaching thinking Use an effective pedagogy – concrete to pictorial toabstract - that develops understanding and fluency Recognize the importance of visualization Teach fewer topics to mastery and greaterproficiency in each gradeWednesday, October 31, 12
Teach math as a vehicle forteaching thinkingMake sense of problems and persevere insolving them.Mathematically proficient students start by explaining tothemselves the meaning of a problem and looking forentry points to its solution. They analyze givens,constraints, relationships, and goals.Wednesday, October 31, 12
Mathematics Frameworkcreated by the SingaporeMinistry of EducationWednesday, October 31, 12
e sense of problems and persevereReason abstractly and quantitativelyConstruct viable argumentsCCSSWednesday, October 31, 12
Math As ThinkingWednesday, October 31, 12
MathSyllabusWednesday, October 31, 12
UseaneffecHveinstrucHonalstrategy:Concrete- ‐Pictorial- ay, October 31, 12
UseaneffecHveinstrucHonalstrategy:Concrete- ‐Pictorial- ‐AbstractHow many fourths in 1 whole? In 2How many fourths in 6 wholes? In 20?If you know one whole, how can you find the numberin any number of wholes#wholesx4 numberoffourthsWednesday, October 31, 12
Concrete- ‐Pictorial- yin1,howcanwefindhowmany2/3in5wholes?5x3/2 5 2/37x3/2 7 2/3Wednesday, October 31, 12
Mine is notto reasonwhy Wednesday, October 31, 12
Concrete- ‐Pictorial- ‐AbstractPlank1/10Wednesday, October 31, 12Tententhsin5/5,so4/5x10in4/5ofayard
Concrete- ‐Pictorial- ‐AbstractBook A Pg. 70Wednesday, October 31, 12
Concrete- ‐Pictorial- ‐Abstract1/2 1/41/2Wednesday, October 31, 124fourthsin1,so1/2x4in1/2ofawhole
Concrete- ‐Pictorial- ‐Abstract1/4 1/21/2Wednesday, October 31, 12Twohalvesin1,so1/4Vmes2 1/2inaquarter
Why visualization? Lilian’spresentageis2/3VmesMay’sage. a)FindtheraVoofMaysagetoLilian’sage. ge? y5Wednesday, October 31, 12 25 Lilian is 10 and May is 15
nesday, October 31, 12
Multiplicative ll?32AhmadJustin25Wednesday, October 31, 124units 321unit 8(32 4 8)Justinequals8
GRADE 5: Try This¡ Ben took a test with 3 sections A,B,and C. Ben spent 1/5 of his time onSection A and 1/3 of the remainingtime on Section B. He spent 48minutes on section C. How muchtime did Ben take to complete thewhole test.Wednesday, October 31, 12
GRADE 5: Fifth GradeFraction Model Ben took a test with 3 sections A,B, and C. Ben spent 1/5 ofhis time on Section A and 1/3 of the remaining time onSection B. He spent 48 minutes on section C. How muchtime did Ben take to complete the whole test.A1/5BC1/31/3241/324482472 4/5, so 72 4 1/51/5 18, 5/5 90 He spent 90 minutes on testWednesday, October 31, 12
GRADE 5: Fifth Grade Ben took a test with 3 sections A,B, and C. Ben spent 1/5 ofhis time on Section A and 1/3 of the remaining time onSection B. He spent 48 minutes on section C. How muchtime did Ben take to complete the whole test.A1/51- 1/5 4/5 12/151/3 of 12/15 4/1512/15 - 4/15 8/15Wednesday, October 31, 12B1/3 rest? what fraction?488/15 48 so1/15 6 minutes15/15 90 minutes
Ricardo spends 8/9 hour reading the newspaper. He spends1/4 of the time reading the world news and splits the remainingtime equally between the sports and the comics.How much time does he spend reading the Wednesday, October 31, 12
Grade 6: From fractions to ratio15Elinor is 15Mother will be 5515Wednesday, October 31, 12
Grade 6: ratio problems enPat75Karen 60Patricia had 150Wednesday, October 31, 1275 5 15 15
Grade 6: From ratios to rates“Solve unit rates problems includingthose involving unit pricing andconstant speed.”Wednesday, October 31, 12
Grade 6: From ratios to farcantheracingcartravelin3hours?1751h3hWednesday, October 31, 12unitrate3x175 525km
Grade 6: From ratios to ratesormethod2:Distance RatexTimeDistance 175km/hourx3hours 525kmWednesday, October 31, 12
Grade 6: From ratios to ratesWednesday, October 31, 12
Grade 6: Variable sday, October 31, 12
Grade 7: Variable expressionsWednesday, October 31, 12
Grade 7: Variable expressionsWednesday, October 31, 12
Grade 7: Solving woposiVvenumbersormethod2Large#x- ‐1/3x 483/3x- ‐1/3x 48Small#2/3x 4848x 72,otheris24Wednesday, October 31, 12
Two apples and a mango cost 4.Two apples and three mangos cost 9.Find the cost of a mango. 4? 9Wednesday, October 31, 12
x y 8x 2y 108XY10XY Y(x 2 y) - (x y) 10 -8 2Wednesday, October 31, 12Solve algebraically,first with elimination,then withsubstitution
TrajectoryAlgebra8thGrade7XX2x 3y 7x 6y 8Y Y Y8X Y Y Y Y Y ract? 16 - 7 9y 1, x 2XXY Y YXXY Y Y Y Y Y Y Y Y Y Y Y16Wednesday, October 31, 12
Grade 8: Systems of equationsThengraphicalsoluVonsforproblemsWhatdoesd 60tmean?Whatdoesd 50t 20mean?Wednesday, October 31, 12
NAEP 2011 8th GradeWednesday, October 31, 12
Teach fewer topics to masteryand greater proficiency in each grade§ Concepts covered in one grade arecovered in later grades, but only at amore advanced level§ Concepts are covered thoroughly whenintroduced and each grade builds on theprevious gradeWednesday, October 31, 12
Teach to mastery and proficiencyWednesday, October 31, 12
Teach to mastery and proficiency- ‐35Wednesday, October 31, 12
Teach to mastery and proficiencyx 2/5x - ‐357/5x - ‐35dividebothsidesby7/5x - ‐25Wednesday, October 31, 12
What can we learn from Singapore? Teach math as a vehicle for teaching thinking Use an effective pedagogy – concrete to pictorial toabstract - that develops understanding and fluency Recognize the importance of visualization Teach fewer topics to mastery and greaterproficiency in each gradeWednesday, October 31, 12
Singapore*MOE*Math*Syllabus Wednesday, October 31, 12. w Grade 6 Concrete Pictorial . ms& and&numberrelationships&that&is& inning& insecondgrade andextendingallthe way&to&algebra& . Grade 6: ratio problems
The Journals of Lewis and Clark. By Meriwether Lewis and and William Clark, 1804-1806. Note: These Journals are from May 14, 1804, the day the expedition left the Mississippi River, to September 26, 1806, a day or two after they arrived back in St. Louis. It includes all possible Journal entries of Lewis and Clark. Most of the "courses andFile Size: 4MBPage Count: 1023Explore furtherJournal Entries from the Lewis and Clark Expeditionwww.lewisandclarkexhibit.orgThe Journals of Lewis and Clark, by Meriwether Lewis and .www.gutenberg.orgThe Journals of the Lewis & Clark Expedition Center for .www.unl.eduHome Journals of the Lewis and Clark Expeditionlewisandclarkjournals.unl.eduJournal Excerpts Discovering Lewis & Clarklewis-clark.orgRecommended to you b
Chisholm, Paul & Michelle 72 Christie, Russell J. 114 Clanton, David 19 Clark, Eddie And Linda 19 Clark, Ernie 27 Clark, Fredrick 30 Clark, Geoffrey 29 Clark, Geoffrey 33 Clark, Jeff and Angie 15 Clark, Jonathan 76 Clark, Nick 16 Clay, Dixie H. 87 Clegg, Larry 61 Coghlan, Sr., F. H. 98 Coker, Randall 17 Cole, Bobby 106 Cole, Bobby 123 Cole .
al herrin advertising co. albers fred albers george. albert donald albertson george. aldrich dennis . clanton richard clanton wesley. clark anna clark frederick. clark charles clark cloes. clark joyce clark robert. . ford estate frieda ford susan. ford walter forsythe atwood. foster steven fowler james . fowler malcolm fox jason.
initial efforts end in failure so he drafts in Shaun and the gang to help out. 6:40pm Andy's Aquatic Adventures: Andy and the Tusk Fish (CC,Repeat,G) Andy boards his safari-sub to search for some tusk fish. Suddenly, a tusk fish appears amongst the coral, and on seeing its enormous teeth, Andy knows instantly how they got their name!
25 BOOGIE WOOGIE BUGLE BOY Andrews Sisters, 927 Boogie Woogie Bugle Boy Andrews Sisters, 1287 I Just Want To Be Your Everyth ing Andy Gibb 928 Love Is Thicker Than Water Andy Gibb 1288 Shadow Dancing Andy Gibb 1400 Rock Me Gently Andy Kim 26 CAN'T GET USED TO LOSIN G YOU AndyWilliams 882 MOON RIVER AndyWilliams
Andy Warhol. In 1965, curator Sam Green of the ICA at the University of Pennsylvania held Warhol's first retrospective. When over 2,000 people showed up, Green was forced to remove the artwork from the walls fearing mob damage. When Warhol and his muse Edie Sedgwick arrived, the crowd chanted, "Andy and Edie! Andy and Edie!"
Andy Warhol: By Hand, Drawings from the 1950s -1980s will be on display at the New York Academy of Art from 22 January until 10 March 2019. Featured image: Andy Warhol - Two Male Heads Face to Face, Outline, 1952. Ink and graphite on paper, 5 x 5.625 inches, 8.125 x 8.75 inches framed. Courtesy Anton Kern. Courtesy The Andy Warhol Foundation .
wesley long hospital . womack army medical center . 3 overview of goals the student should spend the majority of their time in the inpatient pharmacy learning the roles and responsibilities of every staff member. this is a medication use process and systems based experience, not a clinical experience. students should be encouraged to work with pharmacy technicians, including those .
