Percentage of a Quantity – Non-Calculator – Complete Lesson Preview the presentation to check ability-level, AFL questions, and the animations during demonstrations. It is recommended to delete slides/sections not needed for your class.

Starter A task at the beginning of the lesson that reviews a skill required for the learning. Knowledge Check Questions to assess students’ current understanding and to consequently show progress. Real-Life Example A ‘hook’ to raise interest and provide a concrete example. Demonstration Slides for a teacher to lead students – didactically or via questioning – through a mathematical method. AFL Questions Assessment For Learning Questions, used to assess students’ competency for independent tasks/activities. Plenary An opportunity for students to prove/evaluate their learning.

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25 -5 ÷4 x10 ÷10 +30 ÷10 x2 4 x3 +8 ÷5 ??

STARTER 30% = 70% = 40% = 25% = 34% = 240 ÷ 2 = 500 ÷ 10 = 460 ÷ 10 = Change these percentages to fractions. (The first one has been done for you) 240 ÷ 2 = 30% = 30 100 = 3 10 500 ÷ 10 = 460 ÷ 10 = 70% = 220 ÷ 10 = 40% = 160 ÷ 4 = 25% = 60 ÷ 4 = 34% = 70 ÷ 4 =

STARTER 30% = 70% = 40% = 25% = 34% = 240 ÷ 2 = 120 500 ÷ 10 = 50 Change these percentages to fractions. (The first one has been done for you) 240 ÷ 2 = 120 30% = 30 100 = 3 10 500 ÷ 10 = 50 460 ÷ 10 = 46 70% = 70 100 = 7 10 220 ÷ 10 = 22 40% = 40 100 = 4 10 = 2 5 160 ÷ 4 = 40 25% = 25 100 = 5 20 = 1 4 60 ÷ 4 = 15 34% = 34 100 = 17 50 70 ÷ 4 = 17.5

Percentage of a Quantity 27 August 2019 Percentage of a Quantity

£500 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75 = £150 KNOWLEDGE CHECK David went on holiday with his family. He took £500 to pay for everything. Calculate how the money was divided. £500 Transport: 25% = £125 Food: 15% = £75 Accommodation: 30% = £150 Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson. Ice Cream: 3% = £15 Drinks: 7% = £35 How much was he left with?

£500 £100 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75 KNOWLEDGE CHECK David went on holiday with his family. He took £500 to pay for everything. Calculate how the money was divided. £500 Transport: 25% = £125 Food: 15% = £75 Accommodation: 30% = £150 Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson. Ice Cream: 3% = £15 Drinks: 7% = £35 How much was he left with? £100

Mortgage: Pension: 20% 10% Tax: Charity: 15% 5% Kids: Car Expenses: Jenny earns £2000 every month. She is trying to save for a holiday but she has lots of expenses! Mortgage: 20% Pension: 10% Tax: 15% Charity: 5% How much can she save each month? Kids: 20% Car Expenses: 20% She has 10% leftover to save. 10% = £200

Jenny earns £2000 every month. She is trying to save for a holiday but she has lots of expenses! The total is 100% How much can she save each month? A percent is a proportion of a whole. 20% = 20 out of 100 pieces = 20 100 Percentages are very useful in real-life: business, bills, shopping, taxes… She has 10% leftover to save. 10% = £200

1 2 of 20 = 10 Jenny gives 50% of her chocolate bar to Anna. There are 20 squares, how many does Anna get? 50% = 50 out of 100 = 50 100 = 5 10 = 1 2 1 2 of 20 = 10

1 4 of 20 = 5 Joe gives 25% of his chocolate bar to Pete. There are 20 squares, how many does Pete get? 25% = 25 out of 100 = 25 100 = 5 20 = 1 4 1 4 of 20 = 5

1 10 of 20 = 2 Sheila gives 25% of his chocolate bar to James. There are 20 squares, how many does James get? 10% = 10 out of 100 = 10 100 = 1 10 1 10 of 20 = 2

£8 £4 £4 Josh has £8. He gives 50% to Tom How much does Tom get? 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Josh has £8. He gives 50% to Tom How much does Tom get? £8 £4 £4 Tom gets £4

£3 £12 £3 £3 £3 Sally has £12. She gives 25% to Anna 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Sally has £12. She gives 25% to Anna How much does Anna get? £3 £12 £3 £3 £3 Anna gets £3

5 50 Jane had £50. She gave 10% to Joe. How much does Joe get? 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Jane had £50. She gave 10% to Joe. How much does Joe get? 50 5 Joe gets £5

120 12 Sarah had £120. She gave 10% to Sam. How much does Sam get? 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Sarah had £120. She gave 10% to Sam. How much does Sam get? 120 12 Sam gets £12

40 4 Polly had £40. She gave 20% to Mark. How much does Mark get? 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Polly had £40. She gave 20% to Mark. How much does Mark get? 40 4 Mark gets £8

60 6 Anna had £60. She gave 30% to Polly. How much does Polly get? 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Anna had £60. She gave 30% to Polly. How much does Polly get? 60 6 Polly gets £18

20 2 Mary had £20. She gave 60% to Tim. How much does Tim get? 50% = 1 2 25% = 1 4 10% = 1 10 Remember! Mary had £20. She gave 60% to Tim. How much does Tim get? 20 2 Tim gets £12

40 4 Jane had £40. 10% How much is…. How much is…. How can we find 5%? 10%? 50%? How much is…. 20%? 25%? 15%? 40%? 75%? 95%? 60%? 35%? 85%? 70%? 45%? How can we find 1%?

40 4 Jane had £40. 10% How much is…. How much is…. How can we find 5%? 10%? £4 50%? £20 How much is…. 20%? £8 25%? £10 15%? £6 40%? £16 75%? £30 95%? £38 60%? £24 35%? £14 85%? £34 70%? £28 45%? £18 How can we find 1%?

Percentage of a Quantity Alice had £80. Complete the boxes showing 50%, 25% and 10%. Use the bar models to help you answer the questions. a) 20% = £ 100% = £80 b) 30% = £ 50% = £40 c) 60% = 25% £20 d) 40% = 10% £8 e) 75% = f) 65% = 100% = £140 50% = £70 £35 Tom had £140. Complete the bar models and use them to answer the questions. a) 20% = d) 30% = g) 5% = b) 40% = e) 75% = h) 15% = c) 70% = f) 35% = i) 35% = Tim had £120. He gave 30% to Sally, 25% of Tom, 15% to David and £20 to John. How much did he have left?

Percentage of a Quantity Alice had £80. Complete the boxes showing 50%, 25% and 10%. Use the bar models to help you answer the questions. a) 20% = £16 100% = £80 b) 30% = £24 50% = £40 c) 60% = £48 25% £20 d) 40% = £32 10% £8 e) 75% = £60 f) 65% = £52 100% = £140 50% = £70 £70 £35 Tom had £140. Complete the bar models and use them to answer the questions. 35 14 7 a) 20% = £28 d) 30% = £42 g) 5% = £7 b) 40% = £56 e) 75% = £105 h) 15% = £21 c) 70% = £98 f) 35% = £49 i) 35% = £49 Tim had £120. He gave 30% to Sally, 25% of Tom, 15% to David and £20 to John. How much did he have left? 30% = £36 25% = £30 15% = £18 £20 = £104 Answers He had £16 left.

Percentage of a Quantity Percentage of a Quantity Alice had £80. Complete the boxes showing 50%, 25% and 10%. Use the bar models to help you answer the questions. Alice had £80. Complete the boxes showing 50%, 25% and 10%. Use the bar models to help you answer the questions. a) 20% = £ a) 20% = £ 100% = £80 100% = £80 b) 30% = £ b) 30% = £ 50% = £40 50% = £40 c) 60% = c) 60% = 25% £20 25% £20 d) 40% = d) 40% = 10% £8 e) 75% = 10% £8 e) 75% = f) 65% = f) 65% = 100% = £140 100% = £140 50% = £70 50% = £70 £35 Tom had £140. Complete the bar models and use them to answer the questions. £35 Tom had £140. Complete the bar models and use them to answer the questions. a) 20% = d) 30% = g) 5% = a) 20% = d) 30% = g) 5% = b) 40% = e) 75% = h) 15% = b) 40% = e) 75% = h) 15% = c) 70% = f) 35% = i) 35% = c) 70% = f) 35% = i) 35% = Tim had £120. He gave 30% to Sally, 25% of Tom, 15% to David and £20 to John. How much did he have left? Tim had £120. He gave 30% to Sally, 25% of Tom, 15% to David and £20 to John. How much did he have left?

How can we quickly find 25%? 100% ÷ 2 50% 50% ÷ 2 25% 25%

How can we quickly find 5%? 100% ÷ 10 10% ÷ 2 5%

How can we quickly find 1%? 100% ÷ 10 10% ÷ 10 1%

Sam stole 60% of the money from the safe! $400 How can we calculate how much that is? Addition Multiplication 50% = $200 10% = $440 + 10% = $240 × 6 × 6 60% = $240 60% = $240 Which method do you prefer?

Sam stole 70% of the money from the safe! $500 Addition Multiplication 50% = $250 10% = $450 + 10% = $250 × 7 × 7 + 10% = $250 70% = $350 70% = $350

Multiplication & Addition Sam stole 35% of the money from the safe! $300 Addition Multiplication & Addition 25% = $275 10% = $430 + 10% = $230 × 3 × 3 30% = $090 35% = $105 + 5% = $215 35% = $105

Multiplication & Addition Sam stole 13% of the money from the safe! $600 Multiplication & Addition 10% = $460 31% = $436 × 3 × 3 43% = $018 13% = $078

Multiplication & Addition Sam stole 28% of the money from the safe! $800 Multiplication & Addition 10% = $480 × 2 × 2 20% = $160 31% = $438 × 8 × 8 48% = $064 28% = $224

Use combinations of bags to find: ÷ 2 ÷ 2 100% 50% 25% $800 $400 $200 ÷ 2 ÷ 10 Use combinations of bags to find: ÷ 2 40% 60% 55% 35% 46% 18% 77% 34.5% 10% 5% $80 $40 ÷ 10 1% $8

Use combinations of bags to find: ÷ 2 ÷ 2 100% 50% 25% $800 $400 $200 ÷ 2 ÷ 10 Use combinations of bags to find: ÷ 2 40% $320 60% $480 55% $440 35% $280 46% $368 18% $144 77% $616 34.5% $276 10% 5% $80 $40 ÷ 10 1% $8 Answers

How would you calculate the answer? Find 27% of $400. How would you calculate the answer?

Find 27% of $400. Todd Anne May Tim Jim Find 25% 1% × 2 = 2% Add them together! 10% × 2 = 20% Find 5% 1% × 2 = 2% Add them together! Anne May Find 27% of $400. Find 1% and multiply by 27! 10% × 2 = 20% 1% × 7 = 7% Add them together! Tim Jim 10% × 3 = 30% 1% × 3 = 3% Subtract 3% from 30%!

Use the common percentages to help. 100% = 400 20% = 40% = 55% = 15% = 35% = 11% = 21% = 61% = 50% = 200 10% = 40 5% = ? 1% = ? 100% = 600 100% = 150 30% = 21% = 95% = 938% = 70% = 94% = 35% = 994% = 95% = 99% = 97% = 965% = 15% = 53% = 23% = 123% = 35% = 74% = 66% = 43.5% =

Use the common percentages to help. 100% = 400 20% = 80 40% = 160 55% = 220 15% = 60 35% = 140 11% = 44 21% = 84 61% = 244 50% = 200 10% = 40 5% = ? 1% = ? 100% = 600 100% = 150 30% = 180 21% = 126 95% = 7.5 938% = 57 70% = 420 94% = 24 35% = 52.5 994% = 141 95% = 30 99% = 54 97% = 10.5 965% = 97.5 15% = 90 53% = 318 23% = 34.5 123% = 184.5 35% = 210 74% = 444 66% = 99 43.5% = 65.25

Use the common percentages to help. 100% = 160 30% = 60% = 65% = 25% = 85% = 12% = 23% = 47% = 50% = 80 10% = 16 5% = ? 1% = ? 100% = 80 100% = 150 40% = 31% = 97% = 138% = 60% = 97% = 38% = 171% = 95% = 19% = 79% = 10.5% = 15% = 58% = 94% = 24.5% = 35% = 67% = 63% = 17.4% =

Use the common percentages to help. 100% = 160 30% = 48 60% = 96 65% = 104 25% = 40 85% = 136 12% = 19.2 23% = 36.8 47% = 75.2 50% = 80 10% = 16 5% = ? 1% = ? 100% = 80 100% = 150 40% = 32 31% = 24.8 97% = 10.5 138% = 207 60% = 48 97% = 5.6 38% = 57 171% = 256.5 95% = 4 19% = 15.2 79% = 118.5 10.5% = 15.75 15% = 12 58% = 46.4 94% = 141 24.5% = 36.75 35% = 28 67% = 53.6 63% = 94.5 17.4% = 26.1

Percentage of a Quantity A) Calculate the value of each size bag (the first has been done for you). Use these percentages to calculate your answers. $150 $300 50% 10% 5% 1% How much is… 40%? 25%? 15%? 60%? 8%? 19%? 43%? 6%? 82%? 79%? 5.5%? 57%? B) Complete the table. Calculate common percentages (10%, 5%, 1%) first. 20% 45% 11% 53% 79% 0.5% 300 4000 160 60 C) All these clothes are on sale. What is their new price? Jeans Were: £60 3% off! Now: Hoodie Was: £76 84% off! Now: Shirt Was: £60 40% off! Now: £ T-Shirt Was: £30 15% off! Now: £ Dress Was: £55 24% off! Now: Underpants Were: £4.50 37% off! Now:

Percentage of a Quantity A) Calculate the value of each size bag (the first has been done for you). Use these percentages to calculate your answers. $150 $30 $15 $3 $300 50% 10% 5% 1% $180 How much is… $18 $171 40%? 25%? 15%? 60%? 8%? 19%? 43%? 6%? 82%? 79%? 5.5%? 57%? $120 $24 $246 $75 $57 $237 $45 $129 $16.50 B) Complete the table. Calculate common percentages (10%, 5%, 1%) first. 20% 45% 11% 53% 79% 0.5% 300 60 135 33 159 237 1.5 4000 800 1800 440 2120 3160 20 160 32 72 17.6 84.8 126.4 0.8 12 27 6.6 31.8 47.4 0.3 C) All these clothes are on sale. What is their new price? Jeans Were: £60 3% off! Now: Hoodie Was: £76 84% off! Now: £58.20 £12.16 Shirt Was: £60 40% off! Now: £ T-Shirt Was: £30 15% off! Now: £ Dress Was: £55 24% off! Now: Underpants Were: £4.50 37% off! Now: Answers £36 £25.50 £41.80 £2.84

Percentage of a Quantity Percentage of a Quantity A) Calculate the value of each size bag (the first has been done for you). Use these percentages to calculate your answers. A) Calculate the value of each size bag (the first has been done for you). Use these percentages to calculate your answers. $150 $150 $300 $300 50% 10% 5% 1% 50% 10% 5% 1% How much is… How much is… 40%? 25%? 15%? 60%? 8%? 19%? 43%? 6%? 82%? 79%? 5.5%? 57%? 40%? 25%? 15%? 60%? 8%? 19%? 43%? 6%? 82%? 79%? 5.5%? 57%? B) Complete the table. Calculate common percentages (10%, 5%, 1%) first. B) Complete the table. Calculate common percentages (10%, 5%, 1%) first. 20% 45% 11% 53% 79% 0.5% 300 4000 160 60 20% 45% 11% 53% 79% 0.5% 300 4000 160 60 C) All these clothes are on sale. What is their new price? Jeans Were: £60 3% off! Now: C) All these clothes are on sale. What is their new price? Hoodie Was: £76 84% off! Now: Jeans Were: £60 3% off! Now: Hoodie Was: £76 84% off! Now: Shirt Was: £60 40% off! Now: £ Shirt Was: £60 40% off! Now: £ T-Shirt Was: £30 15% off! Now: £ T-Shirt Was: £30 15% off! Now: £ Dress Was: £55 24% off! Now: Underpants Were: £4.50 37% off! Now: Dress Was: £55 24% off! Now: Underpants Were: £4.50 37% off! Now:

£500 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75 = £150 KNOWLEDGE CHECK David went on holiday with his family. He took £500 to pay for everything. Calculate how the money was divided. £500 Transport: 25% = £125 Food: 15% = £75 Accommodation: 30% = £150 Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson. Ice Cream: 3% = £15 Drinks: 7% = £35 How much was he left with?

£500 £100 Transport: 25% = £125 Food: 15% Accommodation: 30% = £75 KNOWLEDGE CHECK David went on holiday with his family. He took £500 to pay for everything. Calculate how the money was divided. £500 Transport: 25% = £125 Food: 15% = £75 Accommodation: 30% = £150 Previous knowledge check to see whether students can already complete the learning objective. If they can’t, this provides an excellent opportunity to show progress at the end of the lesson. Ice Cream: 3% = £15 Drinks: 7% = £35 How much was he left with? £100

£24 60 100 × 40 40 100 ×60 = What is 60% of £40? What is 40% of £60? What’s interesting about the answers? Can you explain why? 60 100 × 40 40 100 ×60 = It works for any percentage! Try these… 30% of £50 = £15 24% of £50 = £12 85% of £20 = £17 90% of £20 = £18 18% of £25 = £4.50 180% of £3 = £5.40

Check your success! I can calculate 10% and 5% of a quantity and use that to find other percentages. I can calculate whole number percentages (13%, 72%). I can calculate the cost of items on sale.

Check your success! I can calculate 10% and 5% of a quantity and use that to find other percentages. I can calculate whole number percentages (13%, 72%). I can calculate the cost of items on sale.

How to calculate 43% of a quantity. Write a text message to a friend describing… How to calculate 43% of a quantity.

tom@goteachmaths.co.uk Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths.co.uk