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St Patrick’s Primary School

St Patrick’s Primary School. Mathematics Learning in Stage 3. What issues/concerns do you have about mathematics learning in Stage 3?. How do you plan for learning in mathematics?. The Australian Curriculum: Some of the key decisions.

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St Patrick’s Primary School

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  1. St Patrick’s Primary School Mathematics Learning in Stage 3 Judy Anderson The University of Sydney judy.anderson@sydney.edu.au

  2. What issues/concerns do you have about mathematics learning in Stage 3?

  3. How do you plan for learning in mathematics?

  4. The Australian Curriculum:Some of the key decisions • Mathematics success creates opportunities and all should have access to those opportunities • The curriculum should prioritise teacher decision making • The curriculum should foster depth and important ideas rather than breadth • Students can be challenged within basic topics, including the advanced students

  5. There are 3 content strands • Number and algebra • Measurement and geometry • Statistics and probability

  6. … and 4 proficiency strands • Understanding • Fluency • Problem solving • Reasoning

  7. Our Plan(September/November) • Review rich tasks • Link to the curriculum (Australian/NSW) – content AND proficiences • Consider the Six Key Principles for Effective Teaching of Mathematics • Design ‘good lessons’ • Trial/refine/retrial our ideas • Share/collaborate with colleagues

  8. What are rich tasks? foster engagement

  9. Some Rich Tasks Number and Algebra: Multi lotto Licorice factory Colour-in-fractions Calendar patterns Measurement and geometry: Building Views Money Measurement Statistics and Probability What’s in the bag? Dice Differences Finally: If Australia were a village of 100 people

  10. Number and Algebra

  11. Multi Lotto (Downton et al.) 5 x 6 On the grid, record 16 different numbers which are all answers to the multiplication facts. 9 x 1 8 x 4 10 x 2

  12. How many different numbers can you choose?Which are the best numbers to choose and why?Investigate, record and represent

  13. An Investigation: Which of the following game boards would you choose to use and why? Now create the ‘ideal’ game board.

  14. practice Six Key Principles for Effective Teaching of Mathematics set goals make connections Collaborative teacher learning foster engagement structure lessons differentiate

  15. Some questions • What is the mathematical purpose of that task? • What is the pedagogical purpose of that task? • How can this be communicated to students? • What mathematical proficiencies (actions) can be addressed by working on that task? set goals

  16. A counting chart

  17. A multiplication chart.

  18. Licorice Factory (MCTP, 1988) differentiate

  19. Colour in Fractions1. each player has a game board2. in turns, throw the dice to make a fraction3. colour in that fraction, or its equivalent on your board4. the first person to colour the entire board wins.

  20. 1 */2

  21. Recording = + +

  22. Challenge?? • Suppose the game looks like this, and you roll ½. • How could you colour ½.

  23. How many different ways can you make ½?

  24. Students’ Posing Problems:Mathematics from Photographs Look at the photographs and • What do you notice? • Write down some mathematical problems that occur to you. • Now do some mathematics based on the photograph. make connections

  25. Calendar PatternsJuly 2012

  26. Calendar PatternsJuly 2012

  27. Calendar PatternsJuly 2012

  28. Calendar PatternsJuly 2012

  29. Calendar PatternsJuly 2012

  30. Measurement and Geometry

  31. Cubed Houses • A block of city buildings is 3 cubes wide and 3 cubes long • It looks like this from the front What might the building look like? structure lessons

  32. The task • A block of city buildings looks like this from the side • And like this from the front • What might the set of buildings might look like?

  33. “Enabling prompts”

  34. A different destination • A block of city buildings looks like this from the side • What might the set of buildings might look like?

  35. Extension? • How many different designs that fit the directions can you make? • Draw a set of buildings on the isometric paper, and draw the front and side view as well.

  36. 1 3 1 2 3 3 1 1 2 • Draw what this representation might mean

  37. Building Views – A challenge • A block of city buildings looks like this from the FRONT • And like this from the SIDE • Build on a 4x4 grid to find the maximum number of cubes possible and the minimum number of cubes possible

  38. Money Trails • If I made a trail of 20 cent coins from the classroom door to the school gate, how much money would I need? • How far can $10 really stretch?

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