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G ood S olid T eaching of Percentages

G ood S olid T eaching of Percentages. Vince Wright The University of Waikato. Intended outcomes of the webinar: Identify similarity of structure in percentage problems Consider how numbers and co-ordination of steps make a difference Use some useful representations

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G ood S olid T eaching of Percentages

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  1. Good Solid Teaching of Percentages Vince Wright The University of Waikato

  2. Intended outcomes of the webinar: • Identify similarity of structure in percentage problems • Consider how numbers and co-ordination of steps make a difference • Use some useful representations • Relate these ideas to GST

  3. 10% 50% 100% 0% 0 10 40 20 30 50 An item costs $50.00 usually. It is on sale at 25% discount. What is the sale price? 75 100 ? 50

  4. Part Whole 50 ½ x ½ x 75% 100

  5. 10% 20% 50% 80% 100% 0% 0 10 40 20 30 50 60 http://www.nzmaths.co.nz/sites/default/files/Numeracy/2007matmas/Bk7/MM%207_4.pdf An item costs $60.00 usually. It is on sale at 20% discount. What is the sale price? 80 100 ? 60

  6. Part Whole 60 x 6 x 6 10 8 ÷ 10 ÷ 10 80 100

  7. 240 cows give birth to 180 calves. What is the calving percentage? ? 100 240 180 calves cows

  8. calves cows 240 180 ÷ 10 ÷ 10 24 18 ÷ 6 ÷ 6 4 3 x 25 x 25 100

  9. 140 ewes give birth to 245 lambs. What is the lambing percentage? 100% 140

  10. 245 140 ÷ 5 ÷ 5 49 28 ÷ 7 ÷ 7 7 4 x 25 x 25 ewes lambs 100

  11. 27 out of 45 kiwi chicks survive. What is the survival rate as a percentage? 45 27 x 3/5 ÷ 9 ÷ 9 5 3 x 3/5 X 20 X 20 100 60 survivors chicks

  12. Goods and Services Tax GST exclusive price GST inclusive price GST

  13. GST exclusive price 10 % GST inclusive price 0% 100% 110%

  14. GST exclusive price 12.5 % GST inclusive price 0% 100% 112.5%

  15. GST exclusive price 15 % GST inclusive price 115% 0% 100%

  16. The GST exclusive price of an item is $86.00 Work out the GST inclusive price. 5% 10% 15 % GST inclusive price

  17. Percentage Amount $86.00 100% $8.60 10% $4.30 5% $98.90 115%

  18. The GST inclusive price of an item is $345.00 Work out the GST inclusive price. 15 % GST inclusive price

  19. Percentage Amount 115% $345 ÷ 115 ÷ 115 1% $3 x 15 x 15 15% $45 x 100 x 100 100% $450

  20. Where does the multiply by 3 then divide by 23 rule come from? Take any multiple of 4. Divide by 4. Now multiply the number by 3. What fraction of the number did you find? Take any multiple of 4. Multiply the number by 3. Now divide by 4. What fraction of the number did you find?

  21. Multiplying by 3 then dividing by 23 is finding 3/23 of the amount. You need to know this GST inclusive price 15 % You know this

  22. 3 lots of 5% 20 lots of 5% GST inclusive price 15 % 23 lots of 5%

  23. Good Solid Teaching of percentages means: • Using representations to show learners how the part-whole or whole-whole relationships work • Connecting understanding with calculation proficiency vince@waikato.ac.nz

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