1 / 46

ced-mxteachers-news-site.wikispaces/

CENTRE FOR EDUCATIONAL DEVELOPMENT Developing practice around the realigned Level 2 Mathematics and Statistics standards Workshop Four Anne Lawrence, Alison Fagan , Cami Sawyer Advisers in Secondary Numeracy & Mathematics. http://ced-mxteachers-news-site.wikispaces.com/. Level 3 Consultation.

shoshana-herrera
Download Presentation

ced-mxteachers-news-site.wikispaces/

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CENTRE FOR EDUCATIONAL DEVELOPMENTDeveloping practice around the realigned Level 2 Mathematics and Statistics standardsWorkshop FourAnne Lawrence, Alison Fagan , Cami SawyerAdvisers in Secondary Numeracy & Mathematics • http://ced-mxteachers-news-site.wikispaces.com/

  2. Level 3 Consultation In small groups pick 2-3 standards and discuss what has changed • Think about the pathways from last time • Changes made to level 1 & 2 Resources • Draft level 3 standards • Draft Matrix • Summary of what has changed • http://ced-mxteachers-news-site.wikispaces.com/

  3. Level 3 Consultation Manawatu: 3.6 too much in it 3.8 evaluation – concern at higher literacy needed 3.8 Using existing data sets – but this seems to conflict with using each component of PPDAC ie posing problem, collecting data? 3.9 assume that making a prediction • http://ced-mxteachers-news-site.wikispaces.com/

  4. Level 3 Consultation Hawkes Bay feedback: • http://ced-mxteachers-news-site.wikispaces.com/

  5. TKI Senior Secondary Teaching and Learning Guides AO M 8-7 (trigonometric, polynomial, and other non-linear equations) What is new/changed? * Manipulating logs will be new AO M 8-11(differentiation, integration, and anti-differentiation techniques) What is new/changed? * There is no integration at level 7 * This does not include related rates of change, integration of relations, or volume of revolution. What will happen to Simultaneous Equations and Linear Programming? • http://ced-mxteachers-news-site.wikispaces.com/

  6. Achievement Objective M7- 5 In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to: Choose appropriate networks to find optimal solutions. Indicators • Solves problems that can be modelled by networks • Uses trial-and-improve methods to develop algorithms for solving network problems • http://ced-mxteachers-news-site.wikispaces.com/

  7. Network Definitions • http://ced-mxteachers-news-site.wikispaces.com/

  8. Becks Caps Freddy David Ace Gum Eddy Happy Spot the Features Identify the features or terminology from the last activity that are shown in this tramping network of huts linked by tracks. Do the US 5249 Tasks • http://ced-mxteachers-news-site.wikispaces.com/

  9. Networks AS2.5 –Use networks in solving problems Look at the standard: • What are the understandings required? • What do you think should be the step up from achieve to merit? merit to excellence? • http://ced-mxteachers-news-site.wikispaces.com/

  10. TKI Senior Secondary Teaching and Learning Guides • http://ced-mxteachers-news-site.wikispaces.com/

  11. TKI Senior Secondary Teaching and Learning Guides • http://ced-mxteachers-news-site.wikispaces.com/

  12. Minimum Spanning Tree Kruskal’s algorithm Select the shortest edge in a network Select the next shortest edge which does not create a cycle Repeat step 2 until all vertices have been connected Prim’s algorithm Select any vertex Select the shortest edge connected to that vertex Select the shortest edge connected to any vertex already connected Repeat step 3 until all vertices have been connected • http://ced-mxteachers-news-site.wikispaces.com/

  13. 5 Brinleigh Cornwell 3 4 6 8 8 Avonford Donster Fingley 7 5 4 2 Edan A cable company want to connect five villagesto their network which currently extends to the market town of Avonford.What is the minimum length of cable needed? • http://ced-mxteachers-news-site.wikispaces.com/

  14. 5 B C 3 4 6 8 8 A D F 7 5 4 2 E First model the situation as a network, then the problem is to find the minimum connector for the network • http://ced-mxteachers-news-site.wikispaces.com/

  15. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm ED 2 AB 3 AE 4 CD 4 BC 5 EF 5 CF 6 AF 7 BF 8 CF 8 List the edges in order of size: • http://ced-mxteachers-news-site.wikispaces.com/

  16. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm Select the shortest edge in the network ED 2 • http://ced-mxteachers-news-site.wikispaces.com/

  17. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm Select the next shortest edge which does not create a cycle ED 2 AB 3 • http://ced-mxteachers-news-site.wikispaces.com/

  18. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm Select the next shortest edge which does not create a cycle ED 2 AB 3 CD 4 (or AE 4) • http://ced-mxteachers-news-site.wikispaces.com/

  19. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm Select the next shortestedge which does not create a cycle • ED 2 • AB 3 • CD 4 • AE 4

  20. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm Select the next shortest edge which does not create a cycle ED 2 AB 3 CD 4 AE 4 BC 5forms a cycle EF 5 • http://ced-mxteachers-news-site.wikispaces.com/

  21. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Kruskal’s Algorithm All vertices have been connected. The solution is ED 2 AB 3 CD 4 AE 4 EF 5 Total weight of tree: 18 • http://ced-mxteachers-news-site.wikispaces.com/

  22. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Prim’s Algorithm Select any vertex A Select the shortest edge connected to that vertex AB 3 • http://ced-mxteachers-news-site.wikispaces.com/

  23. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Prim’s Algorithm Select the shortest edge connected to any vertex already connected. AE 4 • http://ced-mxteachers-news-site.wikispaces.com/

  24. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Prim’s Algorithm Select the shortest edge connected to any vertex already connected. ED 2 • http://ced-mxteachers-news-site.wikispaces.com/

  25. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Prim’s Algorithm Select the shortest edge connected to any vertex already connected. DC 4 • http://ced-mxteachers-news-site.wikispaces.com/

  26. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Prim’s Algorithm Select the shortest edge connected to any vertex already connected. CB 5forms a cycle EF 5 • http://ced-mxteachers-news-site.wikispaces.com/

  27. B 5 C 3 4 6 8 8 A D F 7 5 4 2 E Prim’s Algorithm All vertices have been connected. The solution is ED 2 AB 3 CD 4 AE 4 EF 5 Total weight of tree: 18 • http://ced-mxteachers-news-site.wikispaces.com/

  28. Prim’s and Kruskal’s Algorithms • Both algorithms will always give solutions with the same length. • They will usually select edges in a different order – students need to show this in their working. • Occasionally these algorithms will use different edges – this may happen when you have to choose between edges with the same length. In this case there is more than one minimum connector for the network. • http://ced-mxteachers-news-site.wikispaces.com/

  29. 4 4 1 2 4 7 7 3 2 3 2 5 Dijkstra’s Algorithmfinds the shortest path from the start vertex to every other vertex in the network. We will find the shortest path from A to G B F D A G E C • http://ced-mxteachers-news-site.wikispaces.com/

  30. Orderin which vertices are labelled. Permanent label = Distance from A to vertex Working label 4 B F 4 1 1st0 2 4 7 D A 7 Label vertex A 1stas it is the first vertex labelled 3 2 3 G 2 E 5 C Dijkstra’s Algorithm

  31. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C We update each vertex adjacent to A with a ‘working value’ for its distance from A. Dijkstra’s Algorithm 4 1st0 7 3 • http://ced-mxteachers-news-site.wikispaces.com/

  32. Orderin which vertices are labelled. Look at ALL the working labels (no ordinal yet). Which is smallest? Permanent label = Distance from A to vertex Working label 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm 4 1st0 7 Vertex C is closest to A so we give it a permanent label 3. C is the 2nd vertex to be permanently labelled. 2nd3 3 • http://ced-mxteachers-news-site.wikispaces.com/

  33. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C We update each vertex adjacent to C with a ‘working value’ for its total distance from A, by adding its distance from C to C’s permanent label of 3. Dijkstra’s Algorithm 4 6 < 7 so replace the t-label here 1st0 7 6 2nd 3 8 3 • http://ced-mxteachers-news-site.wikispaces.com/

  34. Look at ALL the working labels (no ordinal yet). Which is smallest? 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm The vertex with the smallest temporary label is B, so make this label permanent. B is the 3rd vertex to be permanently labelled. 3rd4 4 1st0 6 7 2nd3 8 3 • http://ced-mxteachers-news-site.wikispaces.com/

  35. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C We update each vertex adjacent to B with a ‘working value’ for its total distance from A, by adding its distance from B to B’s permanent label of 4. Dijkstra’s Algorithm 3rd4 4 5 < 6 so replace the t-label here 8 1st0 7 6 5 2nd3 8 3 • http://ced-mxteachers-news-site.wikispaces.com/

  36. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm The vertex with the smallest temporary label is D, so make this label permanent. D is the 4th vertex to be permanently labelled. 3rd4 4 8 4th5 1st0 7 6 5 2nd3 8 3 • http://ced-mxteachers-news-site.wikispaces.com/

  37. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C We update each vertex adjacent to D with a ‘working value’ for its total distance from A, by adding its distance from D to D’s permanent label of 5. Dijkstra’s Algorithm 3rd4 4 8 7 7 < 8 so replace the t-label here 4th5 1st0 7 6 5 7 < 8 so replace the t-label here 12 2nd3 8 7 3 • http://ced-mxteachers-news-site.wikispaces.com/

  38. Look at ALL the working labels (no ordinal yet). Which is smallest? 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm 3rd4 4 8 7 4th5 1st0 7 6 5 12 The vertices with the smallest temporary labels are E and F, so choose one and make the label permanent. E is chosen - the 5th vertex to be permanently labelled. 5th7 2nd3 8 7 3 • http://ced-mxteachers-news-site.wikispaces.com/

  39. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C We update each vertex adjacent to E with a ‘working value’ for its total distance from A, by adding its distance from E to E’s permanent label of 7. Dijkstra’s Algorithm 3rd4 4 8 7 4th5 1st0 7 6 5 12 9 5th7 2nd3 8 7 3 9 < 12 so replace the t-label here • http://ced-mxteachers-news-site.wikispaces.com/

  40. Look at ALL the working labels (no ordinal yet). Which is smallest? 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm The vertex with the smallest temporary label is F, so make this label permanent.F is the 6th vertex to be permanently labelled. 3rd4 4 6th7 8 7 4th5 1st0 7 6 5 12 9 5th7 2nd3 8 7 3 • http://ced-mxteachers-news-site.wikispaces.com/

  41. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C We update each vertex adjacent to F with a ‘working value’ for its total distance from A, by adding its distance from F to F’s permanent label of 7. Dijkstra’s Algorithm 3rd4 4 6th7 8 7 4th5 1st0 7 6 5 12 9 5th7 2nd3 8 11 > 9 so do not replace the t-label here 7 3 • http://ced-mxteachers-news-site.wikispaces.com/

  42. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm Can you SEE the shortest path from A to G? 3rd4 4 6th7 8 7 4th5 1st0 7 6 5 7th9 12 9 5th7 2nd3 8 7 G is the final vertex to be permanently labelled. 3 • http://ced-mxteachers-news-site.wikispaces.com/

  43. To find the shortest path from A to G, start from G and work backwards, choosing arcs for which the difference between the permanent labels is equal to the arc length. 4 B F 4 1 2 4 7 D A 7 3 2 3 G 2 E 5 C Dijkstra’s Algorithm 3rd4 4 6th7 8 7 4th5 1st0 7 6 5 7th9 12 9 5th7 2nd3 8 7 3 The shortest path is ABDEG, with length 9. • http://ced-mxteachers-news-site.wikispaces.com/

  44. Assessment Judgements Using the assessment activity 2.5A • Complete the task • Examine the Assessment Schedule • Compare with your own solution • http://ced-mxteachers-news-site.wikispaces.com/

  45. Discussion • Where will this learning fit in your curriculum level 7 (NCEA level 2) courses? • What prior knowledge will students need to access this AO and standard? • What are some of the new ideas in this standard that you think are important? • Where will it lead – careers and pathways? • http://ced-mxteachers-news-site.wikispaces.com/

  46. Where does this go? http://www.newton.ac.uk/wmy2kposters/june/ • http://ced-mxteachers-news-site.wikispaces.com/

More Related