Multiplication and Division Strategies
Focus for Staff Meeting <ul><li>Revisiting Multiplication and Division Strategies </li></ul><ul><li>Identifying strategies...
Big Ideas Multiplication Division Symbols Language Special features Definitions
Initial strategy understanding <ul><li>Number Framework and scenario  </li></ul><ul><li>match-up. </li></ul><ul><li>Sort t...
Time  to Think!!! How might your students work these out?
Multiplication and Division Strategies for CA - EA Problem: A class of 28 students are going on a school trip. They are tr...
Where are these strategies on the Number Framework? 4 x   = 28 I got 28 counters and put them into groups of four. I foun...
Multiplication and Division Strategies for AA-AM <ul><li>Problem: If I planted 4 rows of strawberry plants and put 18 plan...
Where are these strategies on the Number Framework? 18 x 4 =   18 x 4 is the same as 10 x 4 = 40 and 8 x 4 = 32 so 40 + 3...
Multiplication and Division Strategies for AA-AM <ul><li>Problem:   If I wanted to buy 72 cans of soft drink how many 6 pa...
Where are these strategies on the Number Framework? 72  ÷ 6 =   Half of 72 is 36 and half of 6 is 3 so 36 ÷ 3 is 12. Can ...
Multiplication and Division Strategies for AM-AP <ul><li>Problem: I cut 24 metres of material into lengths of 0.75m how ma...
Where are these strategies on the Number Framework? What visual supports could you use to support these strategies? 24 ÷  ...
Multiplication and Division Strategies <ul><li>Grouping and sharing </li></ul><ul><li>Skip counting and skip sharing </li>...
Activity Sharing
<ul><li>CA - AC  page 7 - 8 </li></ul><ul><li>AC – EA  page 11 - 12 </li></ul><ul><li>EA – AA  page 24 - 25 </li></ul><ul>...
Making connections <ul><li>Consider where your students </li></ul><ul><li>are on the strategy framework.  </li></ul><ul><l...
Multiplication/Division Strategy Understanding <ul><li>Complete the ‘Multiplication/Division Strategy Understanding’ sheet...
Supporting Readings <ul><li>Multiplication and Division </li></ul><ul><li>Fuson, K. (2003). Toward computational fluency i...
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Mult Div Strategy Meeting[1]

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Mulplication and Division

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Mult Div Strategy Meeting[1]

  1. 1. Multiplication and Division Strategies
  2. 2. Focus for Staff Meeting <ul><li>Revisiting Multiplication and Division Strategies </li></ul><ul><li>Identifying strategies on Number Framework </li></ul><ul><li>Exploring key knowledge and mathematical ideas about Multiplication and Division </li></ul>
  3. 3. Big Ideas Multiplication Division Symbols Language Special features Definitions
  4. 4. Initial strategy understanding <ul><li>Number Framework and scenario </li></ul><ul><li>match-up. </li></ul><ul><li>Sort the scenarios against the strategy stages </li></ul><ul><li>(No peeking in Book 1 until all sorted!) </li></ul>
  5. 5. Time to Think!!! How might your students work these out?
  6. 6. Multiplication and Division Strategies for CA - EA Problem: A class of 28 students are going on a school trip. They are travelling by car. Each car can take 4 passengers. How many cars will be needed for the trip? How would you solve it if you were Counting All? What if you were an Advanced Counter? What about if you were Early Additive?
  7. 7. Where are these strategies on the Number Framework? 4 x  = 28 I got 28 counters and put them into groups of four. I found that we needed 7 cars. I counted using my fingers in groups of 4 and got to 7 fingers for 7 cars. I know 4 +4+4+4+4+4+4=28. 4 + 4 = 8 and 8 + 8 + 8 is 24 and + 4 is 28. So that’s 7 groups. I know that 4 x 10 = 40 so 4 x 9 = 36 and 4 x 8 = 32 and 4 x 7 = 28. I can skip count in 4’s so I went 4, 8, 12, 16, 20, 24, 28
  8. 8. Multiplication and Division Strategies for AA-AM <ul><li>Problem: If I planted 4 rows of strawberry plants and put 18 plants in each row how many plants would I have altogether? </li></ul>How would you solve it using doubling and halving? What about thirding and trebling? Could you solve it using Rounding and Compensating? If you used Place value partitioning what would it look like?
  9. 9. Where are these strategies on the Number Framework? 18 x 4 =  18 x 4 is the same as 10 x 4 = 40 and 8 x 4 = 32 so 40 + 32 = 72. Triple 4 is 12 and a third of 18 is 6 so 12 x 6 = 72 Can you name each strategy? Double 4 is 8 and half of 18 is 9, So 8 x 9 = 72. 20 x 4 = 80. But that’s two plants too many in each row so takeaway 4 x 2 which is 8, so 80 – 8 = 72.
  10. 10. Multiplication and Division Strategies for AA-AM <ul><li>Problem: If I wanted to buy 72 cans of soft drink how many 6 packs would I need to buy? </li></ul>How would you solve it using reversibility? What about proportional adjustment? (Make the same change to both numbers.) Could you use Divisibility? (Multiples, factors)
  11. 11. Where are these strategies on the Number Framework? 72 ÷ 6 =  Half of 72 is 36 and half of 6 is 3 so 36 ÷ 3 is 12. Can you name each strategy? 12 x 6 is 72 therefore 72 ÷ 6 = 12 Well 60 + 12 = 72. I know 60 is a multiple of 6 and so is 12 so 10 + 2 = 12 A third of 72 is 24 and a third of 6 is 2. 24 ÷ 2 = 12.
  12. 12. Multiplication and Division Strategies for AM-AP <ul><li>Problem: I cut 24 metres of material into lengths of 0.75m how many pieces do I have? </li></ul>Can you use Conversion? (Change the order and decimals to fractions) How could you use Doubling and Halving using place value?
  13. 13. Where are these strategies on the Number Framework? What visual supports could you use to support these strategies? 24 ÷ ¾ =  so I know that ¾ x  = 24? If 24 is ¾ then ¼ is 8. So 8 x 4 = 32 pieces. 24 ÷ 0.75 =  24 ÷ 0.75 is the same as 48 ÷ 1.5 which is the same as 96 ÷ 3 =32. I know that 0.75m is the same as ¾m so now I can use this to… 0.75 is 1 piece 1.5 is 2 pieces 3 is 4 pieces So 3 x 8 = 24, then 8 x 4 = 32 pieces. +20
  14. 14. Multiplication and Division Strategies <ul><li>Grouping and sharing </li></ul><ul><li>Skip counting and skip sharing </li></ul><ul><li>___________________________ </li></ul><ul><li>Repeated addition </li></ul><ul><li>Deriving from known facts </li></ul><ul><li>___________________________ </li></ul><ul><li>Rounding </li></ul><ul><li>Reversibility </li></ul><ul><li>Place value partitioning </li></ul><ul><li>Rounding and compensating </li></ul><ul><li>Proportional adjustment </li></ul><ul><li>Doubling and Halving </li></ul><ul><li>Trebling and Thirding </li></ul><ul><li>Rounding and divisibility </li></ul><ul><li>Doubling and halving with place value </li></ul>Counting Part-whole Early Additive Advanced Additive Advanced Multiplicative
  15. 15. Activity Sharing
  16. 16. <ul><li>CA - AC page 7 - 8 </li></ul><ul><li>AC – EA page 11 - 12 </li></ul><ul><li>EA – AA page 24 - 25 </li></ul><ul><li>AA – AM page 41 - 43 </li></ul>Key Knowledge and Ideas about Multiplication and Division
  17. 17. Making connections <ul><li>Consider where your students </li></ul><ul><li>are on the strategy framework. </li></ul><ul><li>Based on the discussions in this workshop… Are there any students you need to consider moving to another group or move a group on in their strategies ? </li></ul>
  18. 18. Multiplication/Division Strategy Understanding <ul><li>Complete the ‘Multiplication/Division Strategy Understanding’ sheet </li></ul><ul><ul><li>Name the strategy </li></ul></ul><ul><ul><li>Where on the Framework is the </li></ul></ul><ul><ul><li>student working at/working towards? </li></ul></ul>
  19. 19. Supporting Readings <ul><li>Multiplication and Division </li></ul><ul><li>Fuson, K. (2003). Toward computational fluency in multi-digit multiplication and division. Teaching Children Mathematics, 9 (6) , 300 – 305. </li></ul><ul><li>Young-Loveridge, J. (2005). A developmental perspective on mathematics teaching and learning: The case of multiplicative thinking. Teachers and Curriculum, 8, 49 – 58. </li></ul>

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