ࡱ> \( / 0DArialNew RomanppuF0DWingdingsRomanppuF0 DTimes New RomanppuF0@ .  @n?" dd@  @@`` ( Dm HH**>>  +, -./0123456789:<=?@ABC 0AA@T!"3ʚ;ʚ;g4ldldF0ppp@ <4dddd<@0pu 80___PPT10 pp?  %O  =Working Mathematically*Problem Solving Strategies What is Working Mathematically5 interrelated processes Integrated into the content of each of the content strands- Patterns & Algebra, Measurement, Space & Geometry, Data & Number Focused upon one at a time but also overlapping  The 5 ProcessesBQUESTIONING APPLYING STRATEGIES COMMUNICATING REASONING REFLECTING Questioning and ReflectingQuestioning- the questions that the student ask in mathematical situations Reflecting- it s the student thinking about their experiences and understandings and linking these to form generalisations Communicating and ReasoningCommunicating- use mathematical language to talk about concepts with a peer(s) and teachers Reasoning- students explains possible strategies and provide reasons for their choices and conclusionsGwApplying StrategiesStudents need to learn about and then select from 7 to 10 strategies to explore and solve problems These strategies begin with objects and move to written strategies that involve the use of technological languageRead, Plan, Work, Check,Read the question  look for the key words and what it is that has to be found out [questioning] Plan  which strategies could be used. What operations will be needed to solve the problem [Applying strategies] Work  do it and show how you solved it Check  use another strategyZ  Problem-RPWCErin began reading at 4 o clock. She stopped at 7 o clock. How long did she read? Liz has 16 pencils and Chris has 3 pencils. How many pencils altogether? How many more pencils has liz than Chris?  Draw a DiagramyDiagrams allow students to see the problem clearly Through Diagrams students show their understanding of the concepts Draw simple pictures, lines or shapes to represent the information in the problem & its solution Move onto number and time lines, Venn and tree diagrams 4 main skills- choose the diagram, convert data to visual format, check the solution and explain solutionzz Look For PatternsLays a foundation for teaching algebra Fun Leads to a strong understanding of mathematical thinking Key strategy-unlocking many solutions to problems Steps-recognise, describe, complete, name the rule and solve the problemZ : Make A ListMethodical Investigation Systematic method of organising information in rows and /or columns Allows for data to be examined and conclusions drawn more easily Links back to patterns/ }  Open Ended)Represent in as many ways as possible. )*  /    0` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> $(    6ɓ  `}  T Click to edit Master title style! !  0̓  `  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  0Pӓ ^ `  X*  0ؓ ^   Z*  0ݓ ^ `  Z*H  0޽h ? 3380___PPT10."px Default Design1 0` 3fffff3̙3f̙` ̙3f` ff3f` f33f3f` 3ffƍ` fff3` f33̙` 3f|>?" dZ@$?lKd@   l@  P`lA n?" dd@   @@``PT   @ ` `p>>N0    6 (  .T   "\\   "h  s *"   $0e0e BCDELF>5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?|b4"%>Ul @   `c"$  f\   "n"  0G"r B T??"  <؈GH "`<$0  T Click to edit Master title style! !V  6 "<$0  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S   ` ??"`>   ^*    ` ??"`@a   ^*    ` ??"\5  b* B  s *޽h ? 3fffff3̙3f̙  ___PPT10 .$@GDS+8D& ' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =A@BB3BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* )?D' =0l9 BB A AHCC*<3<* )?D' =0l9 BBHCCBB*<3<* %()?D' =1:B (0.5)*Y3>B ppt_x<* D' =+4 .? B (0.5)0B(#ppt_x)*Y3>B ppt_x<* %()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<* D#' =+4 .? B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<* %()?D~' =%(D&' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* !%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* !D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* !D' =-g6B fade*<3<* !DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* !.%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* !.D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* !.D' =-g6B fade*<3<* !.DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* .:%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* .:D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* .:D' =-g6B fade*<3<* .:DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* :G%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* :GD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* :GD' =-g6B fade*<3<* :GDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* GS%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* GSD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* GSD' =-g6B fade*<3<* GS+p+0+ 0 ++0+ 0 + Capsules !0N0    s (  T p  "p  6 "@  J 0 "  BG0* "pp  J 0 rZ    # "  n" B 0G" R r  T??"L    < "4 ` <$0  W#Click to edit Master subtitle style$ $   ` ??"`>   b*    `8† ??"`@a   ^*    `Ɔ ??"`0  b* <"   fɆG0* ??"p <$0  T Click to edit Master title style! !B  s *޽h ? 3fffff3̙3f̙rj___PPT10J.$@GDS+qD' ņ= @B Di' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =A@BB3BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* )?D' =0l9 BB A AHCC*<3<* )?D' =0l9 BBHCCBB*<3<* %()?D' =1:B (0.5)*Y3>B ppt_x<* D' =+4 .? B (0.5)0B(#ppt_x)*Y3>B ppt_x<* %()?D' =1:B(#ppt_y+0.4)*Y3>B ppt_y<* D#' =+4 .? B(#ppt_y+0.4)0B(#ppt_y)*Y3>B ppt_y<* %()?D' =%(D' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*$D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*$D' =-g6B fade*<3<*$+p+0+0 ++0+ 0 +0 zr@ (    0t  P    P*    0      R*  d  c $ ?    0  0  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S  6 _P   P*    6 _   R*  H  0޽h ? 3380___PPT10." (    0_ P    X*   0̲     Z*   6T _P   X*   6x _   Z* H  0޽h ? 3380___PPT10.0B"0N0  0(  x  c $4ن p   x  c $ن4 `   H  0޽h ? 33___PPT10i."px+D=' = @B + !0N0 $(  r"  S xk `   r  S 3   H  0޽h ? 3fffff3̙3f̙___PPT10i.$Yo+D=' = @B + !0N0 $(  r"  S P `   r  S (   H  0޽h ? 3fffff3̙3f̙___PPT10i.%ӹ+D=' = @B + !0N0 $(  r"  S   `   r  S    H  0޽h ? 3fffff3̙3f̙___PPT10i.&k!+D=' = @B + !0N0  $(  r"  S  `   r  S D   H  0޽h ? 3fffff3̙3f̙___PPT10i.+!S+D=' = @B + !0N0 @$(  r"  S  `   r  S P   H  0޽h ? 3fffff3̙3f̙___PPT10i.,+D=' = @B + !0N0 P$(  r"  S ԋ `   r  S ˋ   H  0޽h ? 3fffff3̙3f̙___PPT10i.-d+D=' = @B + !0N0 $(  r"  S ׋ `   r  S ,؋   H  0޽h ? 3fffff3̙3f̙___PPT10i./@G0+D=' = @B + !0N0 $(  r"  S  `   r  S H   H  0޽h ? 3fffff3̙3f̙___PPT10i.3+D=' = @B + !0N0 $(  r"  S  `   r  S    H  0޽h ? 3fffff3̙3f̙___PPT10i.3P+D=' = @B + !0N0 `$(  r"  S @ `   r  S    H  0޽h ? 3fffff3̙3f̙___PPT10i.- +D=' = @B + !0N0 $(  r"  S  `   r  S    H  0޽h ? 3fffff3̙3f̙___PPT10i.3m+D=' = @B +} 0  $(   r  S \ `}   r  S  `  H  0޽h ? 33___PPT10i.#0;'+D=' = @B +0 zr (  X  C    r  S : 0   You find WM on your child s report and you wonder what is it that the teachers are assessing. What do you understand by the term Working Mathematically? Your child does in Numeration but sometimes that working Mathematically grade is lower. Why is this? WM is mage up of 5 processes that are both part of learning new skills and concepts as well as when they are used to apply existing knowledge to solve problems, They assist the student to think about how to find the answer as much as help them to solve the posed problem. These processes can be applied to any area not just maths, however, that is our focus today.C$H  0޽h ? 3380___PPT10.%>Bg0 w(  X  C      S J 0   yeBoth are the same across all grades/stages. They are linked to the content being taught at the time. H  0޽h ? 3380___PPT10.'Y0 ME0(  X  C    E  S `4 0   Both of these are progressive in their expectations. The begin at an oral level and then as the students moves from stage to stage take on the formal conventions of symbols as well as mathematical terms H  0޽h ? 3380___PPT10.+QNp0 p(  X  C      S  R 0   LRead- underline the key words. What do you have to find out? What facts will help you answer the question? What words will help you solve the problem? Plan  what needs to be done to find the answer? Have they seen a similar problem? What is similar about it? What did you need to do? What operations do you need to use? Tell me how you plan to solve the problem. Work out the problem and show how it is solved. Write the answer clearly. Check the answer- discuss how this could be done find or make up similar problems to practise this strategy H  0޽h ? 3380___PPT10..0x 0 l d (  X  C    d  S 0+ 0   This is an area that we have been asked about and so today we will aim to explain the Outcomes of WM and its link with Problem Solving. We will also explain a number of Problem Solving Strategies and you will have the opportunity to became familiar with them through hands on activities. To assist you we have Jenny O Young, Sue Hurst, Michele Beach and myself. Today s presentation is an informal one so please stop and ask for clarification if you have any questions. I m sure between us we should be able to come up with an answer. Michele and I have presented together in the past and it is our habit to interject when one thinks of a pt not mentioned. We hope this is not to distracting for you. My experiences are predominately with K-3 and Michele will be able to add the 4-6 perspective. Therefore we will have covered K-6. We all teach from a Syllabus written by the Board of Studies. They determine what outcomes that student are to learn within each stage. You can view these on line.<H  0޽h ? 3380___PPT10.0PV~ 0 (  X  C      S c 0   >The first step with any problem is to read the question. What information do you have ? What do you need to find out? [QUESTIONING] We have just talked about this in RPWC. We now look at one way that could be used  the plan. Diagrams are powerful tools for setting out and showing clear understanding of various problems and for planning their solutions. Diagrams help in understanding the connections and interactions between parts of a problem. They are a concrete version of the data. What the problem is asking becomes clearer as does the solution. Diagrams allow students to work out complex/hard problems. It begins with ES1 being simple drawings or symbols/marking to stand in place of the data or numbers. As students move through school they met other types of Diagrams. The number line, [show] is often first. On this they can move forwards or backwards completing sums tat need addition/multiplication/subtraction. Timelines are another form of diagram  used when the history of events needs to be organised so relationships can be seen. Diagrams are excellent when solving problems involving fractions. You can use circles or bars. Tree diagrams are useful when you have a number of items. Family trees. Venn Diagrams are used when things need to be sorted or placed into groups and common items found. These last 2 are used more in 3-6. Step 1 which diagram is going to work best? [QUESTIONING, APPLY STRATEGIES, REFLECTING] Step 2 change the data or information known into a picture, plenty of space will be needed to draw and show the working out and recording of the answer Step 3 check the answer by re-reading the question and making sure the diagram is showing the information in the question. Is it valid. [COMMUNICATION] Step 4 Explain the solution- shows the level of understanding. Responding to questions like Why did you choose that diagram? How did& ? Looking for the use of mathematical language,[ communication/reasoning]  H  0޽h ? 3380___PPT10.ExX 0 h(  X  C      S  0   jMaths is about patterns. Recognise a pattern and you have the power to solve any type of question. Patterns may be in an arrangement of elements or in the form of a sequence. Both have rules that must be recognised. First  recognise that there are a range of patterns, shape, size, number, letters, position, colour, sound rhythm and determine what the pattern is Next describe the pattern  explain orally and in written form using positional and ordinal language 3rd- complete or continue the pattern - check that your rule works give it to someone else 4th state the rule for the pattern + 7 -2 Problem solved 5. Learning to look for patterns in the information given Stage 3 Sometimes diagrams help with patterning6YZ   MH  0޽h ? 3380___PPT10.P`G0 )! (  X  C    !  S  0   Methodical Investigation that allows all possibilities of a solution to be seen and set out. There is a need to decide where to start and then systematically work out all possibilities. Amazing race- name of Russian author Lists may be a table- working out is part of the process Picture the combinations and recognise patterns 3 4 5 6 How many numbers can be made using these 4 numerals. 5 HH  0޽h ? 3380___PPT10.[о2 0 0 B(   X   C       S  0   D0Participants to answer question and then discussH   0޽h ? 3380___PPT10.$x7Yrxpmd^"TWx{}D:FׂtsKP"|# 1Oh+'0H `h  Working MathematicallyJULIE PICKERING DET User4Microsoft Office PowerPoint@̞@[j"@`ZaB?G0g   ^ ^ &WMFCZlxI EMFx@F(GDICx!b $$==% % V0xx x % % $$AA" FGDICF(GDICgxF(GDICPx!b $$=='̙% % V0Pxxx% % $$AA" FGDICF(GDIC g3( !b $$=='%  ;X400##6X#X4#cccX=<> g3 % $$AA" FGDICFGDICF(GDIC?U\F(GDIC?U\( !b $$=='3f%  ; QX( Q Q Q6 X(   6X(6QX(QQQ=<>?U[ % $$AA" FGDICF(GDICU\!b $$==%  ;" QX46 QG eG ~G 6 " Y$Q=<>U[ % $$AA" FGDICFGDICF(GDIC*lQwFGDICF(GDICdlwFGDICF(GDIC 4FGDICRp@Arial_8Arial( @ArialZ 0 .O000(<eH0y0 dv%    ̙Tx&E%n۶An۶A&$L\Working % ( Rp@Arial_8@ArialZ 0 .4|A|H]| <e00(0y0  dvH(4^Zw%(4 X D?!dv%    ffTH%n۶An۶AH$LhMathematically % ( F(GDICQ2TFGDICRp@Arial/8pT,00$pH*0$0(p80@$ dv%    ffTSEJn۶An۶ASJLlProblem Solving  % ( Rp@Arial 8Arialކ( @ArialZ 0 . O000(<e 0y0hdv%    ffTSLoQn۶An۶ASQ LdStrategies  % (   x--$xx--'̙--$xPxP--'--+8  " (-12V2\1a-e(f"ea\V--'3f--8 UU[[?[?[?U?UU--'--8UVXZ[[UU--'@Arial_??-. ̙2 $&Working."System-@Arial_??-. ff2 $HMathematically.-@Arial/??-. ff2 JSProblem Solving .-@Arial ??-. ff2 QS Strategies v.-՜.+,0    On-screen ShowkJ  ' Arial WingdingsTimes New RomanDefault Design CapsulesWorking MathematicallyWhat is Working MathematicallyThe 5 ProcessesQuestioning and ReflectingCommunicating and ReasoningApplying StrategiesRead, Plan, Work, Check Problem-RPWCDraw a DiagramLook For Patterns Make A List Open Ended Slide 13  Fonts UsedDesign Template Slide Titles  _GDET UserDET User  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijkmnopqrstuvwxz{|}~Root EntrydO)Current UserSummaryInformation(lxPowerPoint Document(kDocumentSummaryInformation8y