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Planning engaging and inclusive mathematics lessons

Planning engaging and inclusive mathematics lessons. Peter Sullivan. Planning engaging and inclusive mathematics lessons.

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Planning engaging and inclusive mathematics lessons

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  1. Planning engaging and inclusive mathematics lessons Peter Sullivan mtant 2013

  2. Planning engaging and inclusive mathematics lessons • This presentation will focus on structuring lessons that engage students by allowing them to build connections between ideas for themselves, which also extend student who are ready and support students who need it. Using content and proficiencies from the Australian Curriculum: Mathematics, examples from both primary and secondary level lessons will be presented, and processes for assessing the learning discussed. mtant 2013

  3. Why challenge? • Learning will be more robust if students connect ideas together for themselves, and determine their own strategies for solving problems, rather than following instructions they have been given. • Both connecting ideas together and formulating their own strategies is more complex than other approaches and is therefore more challenging. • It is potentially productive if students are willing to take up such challenges. mtant 2013

  4. Getting started “zone of confusion” “four before me” • representing what the task is asking in a different way such as drawing a cartoon or a diagram, rewriting the question … • choosing a different approach to the task, which includes rereading the question, making a guess at the answer, working backwards … • asking a peer for a hint on how to get started • looking at the recent pages in the workbook or textbook for examples. mtant 2013

  5. This week • Yesterday, on the literacy and numeracy panel • 47% of NT students are Indigenous • 29% do not have English as their first language • If you could say one thing to the chief minister (about numeracy teaching), what would it be? (do not ask for anything that will cost extra money) mtant 2013

  6. This week • On one hand … mtant 2013

  7. mtant 2013

  8. On the other hand … mtant 2013

  9. mtant 2013

  10. How might we write it … • 70 = 50 + 20 mtant 2013

  11. I have 50c in my hand … • What might it look like … mtant 2013

  12. Football scores How much are the Saints winning by? (Work out the answer in two different ways) mtant 2013

  13. Elizabeth is 202 years old • Debbie is 97 years old • How much older is Elizabeth? mtant 2013

  14. 97 202 mtant 2013

  15. 100 3 2 97 100 200 202 mtant 2013

  16. Enabling prompt mtant 2013

  17. Football scores How much are the Saints winning by? (Work out the answer in two different ways) mtant 2013

  18. Football scores How much are the Saints winning by? (Work out the answer in two different ways) mtant 2013

  19. Basketball scores How much did the Cats win by? (Work out the answer in two different ways) mtant 2013

  20. Darts scores How much did the Parrots win by? (Work out the answer in two different ways) mtant 2013

  21. Race to 10 • Start at 0 • You can add either 1 or 2 • Person who says 10 is the winner mtant 2013

  22. Race to $1 • Start at 0 • You can add either 1 or 2 • Person who says 10 is the winner mtant 2013

  23. mtant 2013

  24. mtant 2013

  25. Which ones are wrong? mtant 2013

  26. What might be the numbers on the L shaped piece that has been turned over? (I know that one of the numbers is 65) mtant 2013

  27. An enabling prompt • What might be the missing numbers on this piece? 65 mtant 2013

  28. As a consolidating task • The numbers 62 and 84 are on the same jigsaw piece. • Draw what might that piece look like? mtant 2013

  29. mtant 2013

  30. What might be the missing numbers on this piece? 650 mtant 2013

  31. First do this task • On a train, the probability that a passenger has a backpack is 0.6, and the probability that a passenger as an MP3 player is 0.7. • How many passengers might be on the train? • How many passengers might have both a backpack and an MP3 player? • What is the range of possible answers for this? • Represent each of your solutions in two different ways. mtant 2013

  32. Starting from the content descriptions mtant 2013

  33. Reading the content description(s) to identify the key ideas • Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) mtant 2013

  34. Reading the content description(s) to identify the key ideas • Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) mtant 2013

  35. Reading the content description(s) to identify the key ideas • Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) mtant 2013

  36. Reading the content description(s) to identify the key ideas • Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) mtant 2013

  37. Reading the content description(s) to identify the key ideas • Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) mtant 2013

  38. What would we say to the students are the learning goals/intentions? • Devising for ourselves different ways of representing categorical data mtant 2013

  39. Assume we have 10 people mtant 2013

  40. Assume we have 10 people mtant 2013

  41. Assume we have 10 people mtant 2013

  42. Assume we have 10 people mtant 2013

  43. mtant 2013

  44. Two way tables mtant 2013

  45. Venn diagrams Back pack MP3 player 0 3 4 3 Back pack MP3 player 3 6 1 0 mtant 2013

  46. What about the students who cannot get started?An enabling prompt • On a train, there are 10 people. • Six of the people have a backpack, and 7 of the people have an MP3 player. • How many people might have both a backpack and an MP3 player? • What is the smallest possible answer for this? • What is the largest possible answer? mtant 2013

  47. An extending prompt • On a train, the probability that a passenger has a backpack is 2/3, and the probability that a passenger has an MP3 player is 2/7.How many passengers might be on the train? How many passengers might have both a backpack and an MP3 player? What is the range of possible answers for this? • Represent each of your solutions in two different ways. mtant 2013

  48. A consolidating task • On a train, the probability that a passenger has a backpack is 0.65, and the probability that a passenger as an MP3 player is 0.57. • How many passengers might be on the train? • What is the maximum and minimum number of possibilities for people who have both a backpack and an MP3 player? • Represent each of your solutions in two different ways. mtant 2013

  49. (relevant) Year 8 Proficiencies • Understanding includes … • Fluency includes … • Problem Solving includes … using two-way tables and Venn diagrams to calculate probabilities • Reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, … mtant 2013

  50. Year 8 Achievement Standard • By the end of Year 8, students solve everyday problems …. Students model authentic situations with two-way tables and Venn diagrams. They choose appropriate language to describe events and experiments. … • Students determine complementary events and calculate the sum of probabilities. mtant 2013

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