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Unit 5 Fractions, decimals and percentages, ratio and proportion Year 6 National Autumn term Numeracy Strategy Five daily lessons UNIT OBJECTIVES Read a number with two decimal Resources needed to teach this unit: places to the nearest tenth or to the nearest whole number. • 1-100 chart • 0.1-1 chart Recognise the equivalence between • counting stick the decimal and fractions. • calculators Solve simple problems involving ratio and proportion. Round a number with Recognise the one or two decimal equivalence of places to the nearest percentages, fractions integer. and decimals. Relate fractions to their decimal representations. NNS Pilot Unit Plans – 9/2001 Planning Sheet Day One Unit: 5 Fractions, decimals and Term: Autumn Year Group: 6 percentages, ratio and proportion Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/focus vocabulary Vocabulary questions Know simple • Write a selection of fractions and Find pairs with sum of • Explain that today’s work will focus on complements. Discuss Repeat chanting exercise with fractions as percentages on the board e.g. 100, multiples of 50 the meaning of this. individuals/ pairs of children for decimal percentages. with sum of 1000, complements to ten e.g.: 26% 3 decimals with sum of Use 1 – 100 chart on OHP. Cover up 33. Ask for complement to 4.6 5.4 5 Find simple 1, 10. 100. 4.7 5.3 percentages. 70% 0.8% 0.3 9.7 0.26% 1 4 • Show / discuss how they can use the grid to help their 0.6 74% calculations of completion. Repeat with different numbers. 25% 8 4 Repeat process with 0.1 – 1 grid, recording examples. By the end of the lesson, the 0.25 0.75 children should be able to: • Demonstrate, using the counting stick with questions like: Q: Find a fraction greater Range from 0 – 100, my finger marks 37, how much is left? • Mentally convert fractions to than… • Range 0 – 1, finger marks 0.6, how much is left? decimals and percentages to Between… Increase speed to improve speed of pupils’ oral responses. solve simple problems. Less than … e.g. Which fraction is equivalent to 36 64 • Find complements using … 92 8 decimals and percentages. Which two fractions total a 0.1 0.9 whole? A half? • Without the counting stick, practise multiples of 50 to give (Supplement of examples, Section totals of 1000, e.g. 6) Ask questions like: 350 and 650 150 and 850 Q: If I have £100 how much is Discuss strategies used. 3 ? 0.25? three fifths? 4 Q: 60% of the class were girls, what percentage were boys? Q: A garment was 30% wool, 20% mohair and the rest acrylic. What percentage was acrylic? VOCABULARY VOCABULARY Number pairs Ask children to work on similar word problems in pairs (use both Equivalent Complements fractions and percentages). Percentage Explain your reasoning Decimal fraction RESOURCES 1 – 100 chart 0.1 – 1 chart Counting stick NNS Pilot Unit Plans – 9/2001 Planning Sheet Day Two Unit: 5 Fractions, decimals and Term: Autumn Year Group: 6 percentages, ratio and proportion Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/focus vocabulary Vocabulary questions Round decimals to • Explain to the children that we Round a number with • Tell the children we are going to work on rounding decimal Write a set of statements on the board the nearest whole often round numbers to help two decimal places to numbers with more than one decimal place. where some are incorrect e.g. number or nearest mental calculation, for example the nearest tenth or tenth. when working out the area of the nearest whole Write 0.78 on the board. 0.45 ≈ 0.4 carpet for a room. Show an number. Establish that the number lies between 0.7 and 0.8. Which 6.9 ≈ 7 example e.g. 3.8m x 4.1m will number is it nearest to? We can record: 3.49 ≈3 give an area roughly 16 square Give a decimal fraction 32.01 ≈ 32.1 metres. lying between two 0.78 ≈ 0.8 (to the nearest tenth) 166.6 ≈ 16 others. Repeat for other examples 644 ≈ 650 • Discuss why we round one number up and the other down. • Explain that another way of expressing this is to round to one Ask children to find which are incorrect decimal place. and to explain why. • Explain that 0.5 is rounded up to the next whole number. Consolidate with examples using both terms for the children to Invite children to add more to the list – work on. some correct and some incorrect. • Practise some examples from the board, rounding to the nearest • Extend to numbers with whole numbers and decimals e.g.: Ask the class for comments. whole number e.g. 9.7, 25.6, 148.3 Round 365.49 to - the nearest tenth By the end of the lesson • Round to the nearest metre: - the nearest whole number children should understand: 1.5m, 6.7m, 4.1m, 8.9m - nearest ten - nearest hundred • How to round numbers with two or more decimal places to the nearest tenth. (Supplement of examples Section 6, page 29) NNS Pilot Unit Plans – 9/2001 Planning Sheet Day Three Unit: 5 Fractions, decimals and Term: Autumn Year Group: 6 percentages, ratio and proportion Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/focus vocabulary Vocabulary questions Begin to convert a Write a range of equivalent fractions Recognise the Ask the children in pairs to use a calculator to key in a set of fraction to a decimal on the board such as: equivalence between fractions and record the results to 2 decimal places. Q: Which of these decimals is using division. 3 , 4 , 1 , 5 , 6 , 7 , 10 , 100 . decimals and equivalent to 193 ? 15 20 5 25 30 35 50 500 fractions. Gather results from the class. Record on the board. 100 Choose 3 numbers and ask the children to order them from Q: Use a calculator to find the Develop calculator smallest to largest. 1.93, 10.193, 0.193, 19.13 decimal equivalents of these skills and use a fractions. What do you notice? calculator effectively. Extend to fractions with 3 decimal places Move on to use an OHP calculator to Ask the children to work in pairs to find and order decimals. find the decimal equivalents of: Discuss without using a calculator and 1 , 3 , 5 , 7 , 3 , 1, 2 Challenge some children by including 1 1, 2 in sets of numbers. then use the calculator to check result. 4 4 8 10 5 3 3 3 6 3 Discuss results. Remind children of work on rounding in the previous lesson. Repeat with other examples. By the end of the lesson the children should be able to: RESOURCES • Enter fractions into a Calculator calculator VOCABULARY Divide • Use a calculator to compare fractions. (Supplement of examples, Section 6) NNS Pilot Unit Plans – 9/2001 Planning Sheet Day Four Unit: 5 Fractions, decimals and Term: Autumn Year Group: 6 percentages, ratio and proportion Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/focus vocabulary Vocabulary questions Understand the • Assess (or recap) children’s Solve simple problems • Use Framework examples from Y6 (Section 6 Page 27) to • Say there are 20 boys and 10 girls in language associated previous knowledge by asking involving ratio and assess children’s confidence in solving problems of the kind: Class 6. with ratio and questions like: proportion. proportion. A mother seal is fed 5 fish for every 2 fish given to the baby. Ask the children to: John has one stamp for every two Alice fed the mother seal 15 fish. How many fish did its baby that Mark has. Ask children what this get? Q: Give me a sentence using the means, recording results on the word ‘ratio’ (or proportion). Ask for board. • Show the children a tower with 8 red and 2 yellow linking alternatives. cubes: John has half as many stamps as Mark Mark has twice as many stamps as Mark • Repeat for other numbers. Take Ask how many yellow cubes there are to each red. feedback and record results. If Mark has 4 stamps, John has 2 stamps. Write on board ‘1 to every 4’ So what proportion of the strip is • Encourage children to use yellow? ‘ 1 in every 5’. appropriate vocabulary. • Now extend the work by posing questions like: Explain that the first statement describes the ratio. Emphasise By the end of the unit children the language ‘to every’ If Mark has 400 stamps and John should understand: has 200. The second statement describes the proportion or fraction. • How to solve simple ration Set children another problem and proportion problems VOCABULARY VOCABULARY such as, at a gym club there For every Ratio Julie has 20 sweets. She gives Jim one sweet for every 3 sweets are 2 boys for every 3 girls. To every Proportion she eats. How many sweets does Jim get? There are 30 children at the In every club. How many boys are As many as Reinforce stages of problem solving and go through solution on there? board. Check using real sweets. (Supplement of examples Section 6, Page 27) • If children appear confident let them try 2 more questions in pairs. NNS Pilot Unit Plans – 9/2001 Planning Sheet Day Five Unit: 5 Fractions, decimals and Term: Autumn Year Group: 6 percentages, ratio and proportion Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/focus vocabulary Vocabulary questions Give a decimal lying Draw a number line on the board Extend knowledge of • Write the number 16 on the board and Ask a pair of children to record all their between two others. from 5 to 6. Ask questions such as: decimals to several stages on the board, explaining their decimal places. Target 100 reasons for choosing each number. Q: Give me a fraction that lies Comment on strategies used. between 5 and 6. Develop calculator skills and use a calculator at the side. Homework effectively. Play target 100 starting with 96, Ask the children to estimate what we must multiply 16 by to 36, 55. Take feedback and extend the Explain methods and produce exactly 100. Discuss suggestions. problem to’zoom in’ on the tenths reasoning, orally and in Ask children what they notice notice divisions. writing. Children can try the suggestions on their own calculators. Write children’s suggestions on the board e.g. By the end of the lesson the • Tell the children you now want VOCABULARY 8 x 16 = 128 (too large) children should be able to : them to find a number between 5 Ten thousandths 6 x 16 = 96 (almost there) VOCABULARY and 5.5. Hundred thousandths 7 x 16 = 112 (too large) • Give a decimal lying between 2 Thousandths Children respond using individual Recurring What numbers come between 6 and 7? others. white boards. Decimal places 6.4 x 16 = 102.4 (too big) • Explain their reasoning to • Repeat for different numbers 6.3 x 16 = 100.8 (still too big) others. ‘zooming in’ each time to reach 2 By trial and improvement reach the conclusion that the number decimal places. For example: lies between 6.2 and 6.3. Try 6.25. • Use a calculator and read the display in decimal notation. Find me a number between • Repeat with a different start number, say 23. Explain that we cannot always reach 100 exactly but we can (Supplement of examples, Section 5.1 and 5.3 getnearer and nearer. 6) 5.2 and 5.3 5.2 and 5.25 • Stress the importance of recording each estimate to guide us 5.25 and 5.26 etc. to the next move. Discuss what each stage means using the language on Q: Can I squeeze in another tenths and hundredths and questions like ‘ how far off a number? How do you know? hundred is this?’ Continue until you reach an agreed level of accuracy perhaps 4.349 x 23 = 100.027. • Children work in pairs using start numbers like 32, 48. Some could be challenged with starting numbers like 11, 22, 45 which lead to recurring decimals. Others should be given • Emphasise the language of numbers which only need to go to 1 or 2 decimal places, like fractions when describing decimal 40, 80. parts of a number. (i.e. 3.528 is three and five tenths, two hundredths and eight thousandths.) NNS Pilot Unit Plans – 9/2001