SPRING UNIT 13. second half. Fractions of quantities. Fractions and percentages. Changing fractions to decimals. Ordering fractions and decimals
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1 PART SPRING second half FRACTIONS DECIMALS PERCENTAGES RATIO AND PROPORTION SECTION Fractions of quantities SECTION Fractions and percentages SECTION Changing fractions to decimals SECTION Ordering fractions and decimals SECTION Ratio and proportion Key Stage National Strategy CROWN COPYRIGHT 00
2 NOTES FOR THE TEACHER FRACTIONS, DECIMALS PERCENTAGES, RATIO AND PROPORTION SUGGESTED TIME hours TEACHING OBJECTIVES Relate fractions to division and find simple fractions and simple percentages of whole number quantities. Order a set of fractions and position them on a number line. Order a set of numbers or measurements with the same number of decimal places. Use a calculator effectively, for example, to convert fractions to decimals and find fractions of numbers. Solve simple problems involving ratio and proportion using informal strategies. SECTION Fractions of quantities SECTION Fractions and percentages SECTION Changing fractions to decimals SECTION Ordering fractions and decimals SECTION Ratio and proportion HOMEWORK Find fractions of quantities, using mental, written or calculator methods as appropriate. Find percentages of quantities. Learn equivalent fractions, decimals and percentages. Key Stage National Strategy CROWN COPYRIGHT 00 0
3 Key Stage National Strategy PART CHECKLIST Unit Checklist for pupils Fractions of quantities You will: work out fractions of amounts of money and other quantities Fractions and percentages You will: use the connection between fractions and percentages work out percentages of quantities Changing fractions to decimals You will: use decimal equivalents of simple fractions Ordering fractions and decimals You will: put fractions in order of size review place values for tenths and hundredths order decimals Ratio and proportion You will: solve simple problems involving ratio ( for every ) and proportion ( in every ) Key Stage National Strategy CROWN COPYRIGHT 00
4 SECTIONS AND : FRACTIONS OF QUANTITIES FRACTIONS AND PERCENTAGES DIRECT TEACHING POINTS Section exercises, and are opportunities to practise mental calculations. Pupils need to understand fractions as parts of a whole, positions on a number line and the links with division. Star Challenge introduces simple ideas of ratio and proportion (Section ). Revise units of measurement. Section exercise can form the basis of oral work to consolidate these ideas. Make sure pupils can recall simple fraction to percentage conversions of a half, quarter, three quarters, tenths, hundredths and then eighths. Section exercise are mental calculations. % 0% 0% % 0% 7% 00% 0 Demonstrate how to deduce percentages, for example, 0%, from 0%. Use exercise to consolidate this work. Illustrate and emphasise the links between fractions, decimals and percentages. Include some fraction calculations that involve the use of a calculator. KEY TO VOCABUL ARY LEAR USE AND fraction decimal percentage reduced reduction discount Key Stage National Strategy CROWN COPYRIGHT 00
5 Key Stage National Strategy PART SECTION Fractions of quantities Halves and quarters To find a quarter......find half of a half. IDEA of of 8 trees... of of kg... of of 7p... of of 80 m... of 0 cm... 0 of 6 m... Other fractions Example lots of so of... so of... 6 so of... 0 so of 0... Key Stage National Strategy CROWN COPYRIGHT of of 0... of... of... 0 of 0... of... of 0... of... of 0... of p... of of 0...
6 Key Stage National Strategy PART SECTION Fractions of quantities and its multiples IDEA To find seven tenths...find a tenth and multiply by 7. of 0... so of 0... of so of of 0... so of 0... of so of of 0... so of of of 0... of of of of of 0... of of Multiples of simple fractions of 6... so of 6... of 9... so of 9... of 0... so of 0... To find two thirds...find a third and double it. IDEA of 8... so of of... so of... of 0... so of 0... of so of of 0... so of 0... of so of IDEA To find three quarters...find a quarter and multiply by. Key Stage National Strategy CROWN COPYRIGHT 00
7 Key Stage National Strategy PART SECTION Fractions of quantities Fractions of time and length hour... minutes day... hours hour... minutes day... hours hour... minutes 6 day... hours foot inches 7 foot... inches 8 foot... inches 9 foot... inches More difficult fractions 6 of 0... so of 0... of... so of... of 0... so of 0... of of 0... of of 8... of of correct stars 7-8 correct star Key Stage National Strategy CROWN COPYRIGHT 00
8 Key Stage National Strategy PART SECTION Fractions of quantities Fractions in action 7-8 correct star How many centimetres are there in of a metre?... A full bottle of squash contains 70 millilitres. Two thirds of the squash has been drunk. How many millilitres are left?... Fred and Rashida painted the Youth Club. Fred did one third of the work. Rashida did the rest. They were paid 0. Fred got paid one third of the money. (a) How much did Fred get paid?... (b) What fraction of the work did Rashida do?... (c) How much did Rashida get paid?... Mary and Alison dug Mrs Brown s garden. Mary worked for hours. Alison worked for 6 hours. They got paid for the whole job. (a) What fraction of the work did Mary do?... (b) How much should she get paid?... (c) How much should Alison get?... Key Stage National Strategy CROWN COPYRIGHT 00 6
9 Key Stage National Strategy PART SECTION Fractions and percentages Example Using fractions to find percentages Fractions can also be expressed as percentages: % 0% 0% % 0% 7% 00% 0 GUESS WHAT? 0% of an amount is the same as half of that amount. Learn: % Complete these calculations: 0% of % of... 0% of... % of p... 6 % of % of % of % of 60p... 9 % of 0... Learn: 0% 0 0% of 0p... 0% of % of % of 0 m... 0% of 0 m % of 0... % of 0 m... 6 % of % and its multiples Key Stage National Strategy CROWN COPYRIGHT 00 0% of % of % of % of 0 kg... 0% of % of 00 m... 70% of % of 00 kg... 0% of % of 00 m... 7
10 Key Stage National Strategy PART SECTION Fractions and percentages Reducing prices - correct stars 9-0 correct star CD SALE PRICE % off How much is the price reduced by?... What is the sale price of the CD?... Trainers SALE PRICE 0% off What is the reduction?... What is the sale price?... TV 00 SALE PRICE 0% discount 6 How much is the discount?... What is the sale price?... Video tape 0 SALE PRICE Price reduced by 0% 7 8 How much is the reduction?... What is the sale price?... Shirt 0 SALE PRICE off 9 0 How much is the reduction?... What is the sale price?... Jacket 0 SALE PRICE 0% off How much is the price reduced by?... What is the sale price?... Percentages and fractions - correct stars 9-0 correct star of of 60 m... 0% of % of 80 g... of % of % of kg... of 0... of 700 km... of % of % of Key Stage National Strategy CROWN COPYRIGHT 00 8
11 SECTIONS AND : CHANGING FRACTIONS TO DECIMALS ORDERING FRACTIONS AND DECIMALS DIRECT TEACHING POINTS Consolidate pupils understanding of place value to include decimals. Simple fraction to decimal conversions half, quarter, three quarters, tenths, hundredths and eighths should be learnt. Consolidate through oral work. Change these fractions into decimals: Key Stage National Strategy CROWN COPYRIGHT Complete these statements by filling in the boxes: Demonstrate the relative sizes of,, and so on. Consolidate by asking pupils to identify fractions on a number line Place in order, with the smallest first: Oral work, involving counting forward or back in equal steps, can help consolidate ordering. Continue each sequence: Place in order, with the smallest first: Rounding is best related to placing a number on a number line and deciding which boundary is closest. Model this process You may choose to spread work from this section throughout the unit. KEY TO VOCABUL ARY LEAR USE AND fraction decimal percentage tenth hundredth order smallest largest halfway 9
12 Key Stage National Strategy PART SECTION Changing fractions to decimals Changing fractions into decimals Example Change into a decimal. Calculator display 0.8 press these keys Change these fractions into decimals. You should know some of them Now use a calculator to turn,,,, and into decimals, and list the answers below What pattern can you see in the answers?... Key Stage National Strategy CROWN COPYRIGHT
13 Key Stage National Strategy PART SECTION Changing fractions to decimals The first fraction-decimal challenge correct stars correct star Complete these tables: Fraction Decimal Each Fraction represents a whole number. Decimal The second fraction-decimal challenge Complete these tables: correct stars correct star Fraction Decimal Key Stage National Strategy CROWN COPYRIGHT 00 Each represents a whole number. Fraction Decimal
14 Key Stage National Strategy PART SECTION Ordering fractions and decimals Tenths and hundredths Example tens units tenths hundredths T U. t h. 7 In.7, the stands for tens or 0 the stands for units the 7 stands for 7 tenths the stands for one hundredth Complete these statements: In 6.7 (a) the 6 stands for... (b) the 7 stands for... In.08 (a) the 0 stands for... (b) the 8 stands for... In.70 the 7 stands for... In.07 the 7 stands for... Example tenths and no hundredths, so In fractions, Now complete these pairs of fractions: Key Stage National Strategy CROWN COPYRIGHT
15 Key Stage National Strategy PART SECTION Ordering fractions and decimals Ordering decimals Fill in the next four terms in each sequence: Place these numbers in order with the smallest first: Halfway between Write in a number that is halfway between each pair of numbers: Key Stage National Strategy CROWN COPYRIGHT
16 Key Stage National Strategy PART SECTION Ordering fractions and decimals 7 Decimal sequences Write in the next four terms in each sequence: correct stars 6-7 correct star Putting numbers in their 8 place All correct star Put these numbers in the correct places on the line above. Use arrows to mark their positions clearly Put these numbers in the correct places on the line above. Use arrows to mark their positions clearly. Key Stage National Strategy CROWN COPYRIGHT 00
17 SECTION : RATIO AND PROPORTION DIRECT TEACHING POINTS Explain ratio as for every and proportion as in every. Demonstrate these ideas using objects. Link this work to the examples on fractions in Section. EY VOCABUL ARY Kratio proportion TO LEAR USE AND Key Stage National Strategy CROWN COPYRIGHT 00
18 Key Stage National Strategy PART SECTION Ratio and proportion In every and for every in every squares is black. Fill in the gaps in this grid: Fill in the gaps below: (a)... in every 6 squares are black. (b)... in every squares are black. (c) in every... squares are black. (d) 0 in every... squares are black. Number of black squares Number of white squares in every squares is black. In Hope Badminton Club, there are girls for every boy. There are boys in the club. Fill in the gaps: How many girl members are there?... Number of black squares Number of white squares How many members are there altogether? In Hope Snooker Club, there are boys for every girls. There are 0 girl members. How many boy members are there?... Key Stage National Strategy CROWN COPYRIGHT 00 How many members are there altogether?... 6
19 Key Stage National Strategy PART SECTION Ratio and proportion Ratio and the words that go with it Example R B B R B B R B B R B B For every red bead, there are blue beads. The number of blue beads is twice the number of red beads. The number of red beads is half the number of blue beads. The ratio of red to blue is to or :. G Y Y Y G Y Y Y G Y Y Y Green beads Yellow beads Total number of beads For every green bead there are... yellow beads. Key Stage National Strategy CROWN COPYRIGHT 00 The number of green beads is... the number of yellow beads. The ratio of green beads to yellow beads is... to... 7
20 Key Stage National Strategy PART SECTION Ratio and proportion Proportion R B B R B B R B B R B B in every beads is red or are red. (a) Fill in the gaps below: Red beads Blue beads Total number of beads 6 The ratio of red to blue is to The proportion of red beads is The proportion of blue beads is R B B R B B R B B R B B (a) If you know the number of red beads, how do you work out the number of blue beads?... (b) If you know the number of blue beads, how do you work out the number of red beads?... R B B B R B B B R B B B In a necklace like this, in every beads is red or are red. (a) Fill in the gaps below: Red beads Blue beads Total number of beads Key Stage National Strategy CROWN COPYRIGHT (b) What proportion of the beads is blue?... 8
21 Key Stage National Strategy PART SECTION Ratio and proportion Ratio and proportion 9 problems All correct star Mike is saving up to go skiing. Mike s father gives him for every that Mike earns. Fill in the spaces in the grid. Mike s money Father s money Total money For every Mike earns, his father gives him... The amount his father gives Mike is... the amount Mike earns. The ratio of father s money to Mike s earnings is... to... Laura is mixing red and white paint to make pink. For every can of red paint, she needs three cans of white. With two cans of red paint, she needs... cans of white paint. Key Stage National Strategy CROWN COPYRIGHT 00 The number of cans of white paint is... times the number of cans of red paint. She needs cans of pink paint. How many cans of red paint should she start with?... 9
22 Key Stage National Strategy PART ANSWERS Unit Answers Section Fractions of quantities Halves and quarters 0 cm 7 kg 9 0 m 6 trees 8 8p 0 6 m Other fractions p 0 6 and its multiples, 6 0, 7 0 0, , , Multiples of simple fractions,, 6 7, 7, 6, 9 8 0, 00 0, 0 6, 8 9 0, 80 Fractions of time and length Key Stage National Strategy CROWN COPYRIGHT 00 0
23 Key Stage National Strategy PART ANSWERS Unit Answers Section Fractions and percentages Using fractions to find percentages p m p m 0 p m 0% and its multiples kg 9 0 kg m m Section Changing fractions to decimals Changing fractions into decimals , 0.87, 0.87, 0.78, 0.78, 0.87 They all have the same digits, in the same order, but starting with a different digit. Section Ordering fractions and decimals Key Stage National Strategy CROWN COPYRIGHT 00 Tenths and hundredths (a) sixty (b) seven tenths (a) zero tenths (b) eight hundredths seven tenths seven hundredths
24 Key Stage National Strategy PART ANSWERS Unit Answers Ordering fractions and decimals continued Ordering decimals Halfway between Section Ratio and proportion In every and for every (a) (b) (c) 9 (d) 0 Black White Black White Key Stage National Strategy CROWN COPYRIGHT
25 Key Stage National Strategy PART ANSWERS Unit Answers Ratio and proportion continued Ratio and the words that go with it Green Yellow Total For every green bead there are yellow beads. The number of green beads is one third the number of yellow beads. The ratio of green beads to yellow beads is :. Proportion Red Blue Total (a) Number of blue beads double the number of red beads. Key Stage National Strategy CROWN COPYRIGHT 00 (b) Number of red beads half the number of blue beads. (a) Red Blue Total (b)
26 Key Stage National Strategy PART ANSWERS Unit Answers Star Challenge answers More difficult fractions 9 correct stars 7-8 correct star, , , 6 9 Fractions in action 7 8 correct star 7 cm (a) 0 (b) (c) 0 0 ml (a) (b) 6 (c) 8 Reducing prices correct stars 9-0 correct star 6 Percentages and fractions km kg m g The first fraction-decimal challenge The second fraction-decimal challenge - correct stars 9-0 correct star correct stars correct star Decimal Fraction correct stars correct star Key Stage National Strategy CROWN COPYRIGHT 00 Decimal Fraction
27 Key Stage National Strategy PART ANSWERS Unit Answers Star Challenge answers continued 7 8 Decimal sequences Putting numbers in their place 8 correct stars 6-7 correct star All correct star Key Stage National Strategy CROWN COPYRIGHT 00 9 Ratio and proportion problems Mike s money Father s money Total money All correct star For every Mike earns, his father gives him. The amount his father gives Mike is four times the amount Mike earns. The ratio of father s money to Mike s earnings is to. With two cans of red paint, she needs 6 cans of white paint. The number of cans of white paint is times the number of cans of red paint. How many cans of red paint should she start with?
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