One Pathway for Teaching Percentages

Where do Percentages sit in NZC? 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 on the Number Framework? 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 = = 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 = 15.6) partitioning %

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

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 = % of $20 = 40

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

This is a simple version Students draw up a 3 x 3 grid and pick 9 of these Call 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%)

Teaching % Where do we start?

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

Activities to build knowledge

2/ /10020% 3/10 3/10 + 5/100 40% 65/ /100 Use a bead string to fill in the gaps

1/1010%1/20 1/51/25 1/42/10 1/83/5 3/41/100

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

Teaching progression 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

Percentages What type of problem do we expect to meet in years 9/10 ? 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

Using double number lines to solve % problems

20% of 150 is 30 20% of 150 is 20% of is 30 % of 150 is 30

0% 20% 100%  20% of 150 is  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 150

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

0% 20% 100%  x x x 2 15 x 2

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? There are 30 students in 9CT and 40% are girls. How many girls are there in the class? 40% of 30 is  30% of 500gm is 

Abigail is working on a set of 50 number problems and she has just finished question 28. What % of the questions has she finished. 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? 28 is  % of 50 8 is  % of 20

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

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

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

Revision of % knowledge Starter pack

Increasing/decreasing by a %

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 0% 80%100% $350

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  Or divide 400 by 10 (to get 10%) and multiply by 12. X 4 0%120%100% $400 

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

Activity 5 Dominoes - using number properties

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 0% 100%120% $480 

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