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One Pathway for Teaching Percentages

One Pathway for Teaching Percentages. Level three Number and Algebra Knowledge NA3-5 Know fractions and % in everyday use Strategies NA3-1 Use a range of additive and simple multiplicative strategies with whole numbers,fractions,decimals and %. Level four Number and Algebra Knowledge

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One Pathway for Teaching Percentages

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  1. One Pathway for Teaching Percentages

  2. Level three Number and Algebra Knowledge NA3-5 Know fractions and % in everyday use Strategies NA3-1 Use a range of additive and simple multiplicative strategies with whole numbers,fractions,decimals and % Level four Number and Algebra Knowledge NA4-5 Know the equivalent decimal and % for everyday fractions Strategies NA4-3Find fractions,decimals and % of amounts expressed as whole numbers, simple fractions and decimals Where do Percentages sit in NZC?

  3. Knowledge Stage 7 The student recalls fraction,decimal,% conversions for halves,thirds,quarters,fifths and tenths. Stage 8 The student recalls fraction, decimal,% conversions for given fractions and decimals, eg 9/8 = 1.125 = 112.5% Strategies Stage 7 The student can find simple equivalent fractions and rename common fractions as decimals and % Stage 8 The student chooses from a wide range of mental strategies to solve problems, Eg 65% of 24 (50% = 12, + 10% = 2.4 ,+ 5%= 1.2) so the answer is 12 + 2.4+ 1.2 = 15.6) partitioning % Where do Percentages sit on the Number Framework?

  4. What do we mean by % • Percentages are fractions with denominators hundredths

  5. Some starters Put an amount on the board eg $40 Students make that amount by as many different % as possible Eg • 100% of 40 = 40 • 50% of 80 = 40 • 25% of 160 = 40 • 200% of $20 = 40

  6. 100% $250 100% $250 100% 90kg 30% 24kg 20% $250 100% $60 10% 50% 10% 10% 25% 1% 5% 15% 80% 11% 2% 15% 75%  10  2 3 100% $2 25% 5% 30% 100% 10% 5.5kg 5% 1% 100% 10% 5% 9 2.5% Box trails

  7. This is a simple versionStudents draw up a 3 x 3 grid and pick 9 of these0.5 0.15 0.7 0.01 0.10.9 0.2 2.1 1.5 0.1251.3 0.175 0.03 0.25 0.40.6 0.75 0.3 0.37 0.8Call out % or the decimal and students pick the %0.5(50%) 0.15(15%) 0.7(70%) 0.01(1%) 0.1(10%)0.9(90%) 0.2(20%) 2.1(210%) 1.5(150%) 0.125(12.50%)1.3(130%) 0.175(17.50%) 0.03(3%) 0.25(25%) 0.4(40%)0.6(60%) 0.75(75%) 0.3(30%) 0.37(37%) 0.8(80%)

  8. Teaching % Where do we start?

  9. Knowledge is essential • Equipment very important at the start • Teach the strategy reasonably quickly and then……… • Application is crucial - students need lots of opportunities to make the strategies work for them. • Context • Revisit ideas frequently

  10. Activities to build knowledge

  11. Use a bead string to fill in the gaps

  12. What we going to look at to day? • How to use double number lines to answer % problems • Using the teaching model • What our students need to know to do this work? • Resources for practising and sustainability

  13. Materials Images Knowledge • Start by: • Using materials, diagrams to illustrate and solve the problem • Progress to: • Developing mental images to help solve the problem • Extend to: • Working abstractly with the number property Teaching progression

  14. What type of problem do we expect to meet in years 9/10 ? Percentages • Finding one number as a % of another • Finding a % of a quantity • Finding the total given a % of the total • Increase/decrease by a % • Finding the original after an increase/decrease • GST and other problems

  15. Using double number lines to solve % problems

  16. 20% of 150 is 30 • 20% of 150 is • 20% of is 30 • % of 150 is 30

  17. Question (in context) The local dairy farmer is selling 20% of his herd of 150 cows. How many is he selling? Rewrite in maths language 20% of 150 is   150 0% 20% 100%

  18. 150  150 0% 20% 100% 0% 20% 100% How do we use the lines to get the answer? 150 divided by 5 = 30 20 x 5 = 100 Find 10% : 150 divided by 10 So 10% = 15 So 20% =30

  19. 150 0% 20% 100% 15 x 10 15 x 2 10 x 2 10 x 10

  20. There are 30 students in 9CT and 40% are girls. How many girls are there in the class? • 40% of 30 is  • In a berry mix there are 30% strawberries and 20% raspberries and the rest are blackberries. In a 500gm punnet of berries what weight are the strawberries? • 30% of 500gm is 

  21. Abigail is working on a set of 50 number problems and she has just finished question 28. What % of the questions has she finished. 28 is  % of 50 • Mr Sharp spent the day at the races and his horses were placed in 8 out of 20 races. In what % of the races was he successful? 8 is  % of 20

  22. 30% of the swimming team are girls. If there are 18 girls . How many are in the team altogether? 18 is 30% of 

  23. Activities to practice these skills • Activity 1 • Activity 3 Note: these are not teaching activities FIO’s • Fully grown Page 9 • The Percentage Game page 14/1 • Laser Blazer page 12/13

  24. What do students need to be able to do before we use this? Have a sound knowledge of percentage • Recall of all multiplication and division facts Discounts, markups, inflation etc • To know answers must be in context with correctunits • Common factors and lowest common multiples • AM/AP

  25. Revision of % knowledge Starter pack

  26. Increasing/decreasing by a %

  27. Decreasing by a % Sarah went shopping for a new bike which cost $350 When she got to town there was a sale and she got 20% off the price, What did she pay? Did she pay more or less? How much less? So instead of paying 100% she only paid? Show all this on the number lines $350 0% 80% 100%

  28. X 4 X 4 Increasing by a percentage The value of a $400 antique vase has been increased by 20%. What is its value now? What questions do we ask? 120% of 400 is   $400 0% 100% 120% Or divide 400 by 10 (to get 10%) and multiply by 12.

  29. Moving to number properties 20% of 150 is ? Now is time to link what they know about % with decimal fractions. How else can we write this? What does 20% actually mean? How could we do this without the number line? For some students this stage will be a long time coming! For others they will tell you. Now might be the time to bring in a calculator and some more “awkward” q’s

  30. Activity 5 Dominoes - using number properties

  31. Finding the original amount after a % increase/decrease Example: After an increase in his weekly wage of 20% Joe has $480.What was his wage before the increase? Talk through and write the maths question $480 is 120% of  Complete a number line with this information  $480 0% 100% 120%

  32. Revision (maintenance) Some activities to use to give students constant revision. Activities 2, 4, 6, 7 and 8

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