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Unit 4 Five daily lessons Fractions, decimals and percentages Year 6 Autumn term This Unit Plan is designed to Unit Objectives guide your teaching. Year 6 Reduce a fraction to its simplest form by cancelling common factors. Page 23 You will need to adapt it to meet the needs of your class. Recognise the equivalence between the decimal and fraction forms. Page 31 Use decimal notation for tenths and hundredths; extend to thousandths for Page 29 measurements. Resources needed to teach this unit: Know what each digit represents. Page 29 Resource sheet 4.1 Understand percentage as the number of parts in every 100. Page 33 Resource sheet 4.2 Resource sheet 4.3 Page 33 Find simple percentages of small whole number quantities. Resource sheet 4.4 Resource sheet 4.5 Resource sheet 4.6 Resource sheet 4.7 Link Objectives Resource sheet 4.8 Year 5 Year 7 Resource sheet 4.9 Use decimal notation for tenths and Simplify fractions by cancelling all common Counting stick hundredths. factors and identify equivalent fractions. Related Key Stage 2 national test questions Relate fractions to their decimal Recognise the equivalence of percentages, representations. fractions and decimals. Use fraction notation, including mixed numbers, Calculate simple percentages. and the vocabulary numerator and denominator. Begin to understand percentage as the number of parts in every 100, and find simple percentages of small whole number quantities. (Key objectives in bold) NNS Unit Plans Planning Day One Unit 4 Fractions, decimals and percentages Term: Autumn Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Recognise equivalent Using a fraction wall Reduce a fraction to its Cutting up Resource sheet 4.2, order fractions by converting them Write the fraction 12/48 on the board; make sure fractions. (Resource sheet 4.1) on the simplest form by to fractions with a common denominator and position them on a the fraction family extends in both directions. OHP/wall chart to recap cancelling common number line. Lead on to questions such as: equivalent fractions, record factors in the numerator Q Can you tell me any other equivalent and denominator. Q How do you know that 2/5 is more than ¼? fractions? ½ = 2/4 = 4/8 Establish the need to change to a common denominator. Q Can you give me a fraction that is equivalent to Ask children to continue the 2 /3 but has a denominator of 18. Invite 1 7 sequence, repeating with Discuss other examples such as comparing ¼ and /3, ¾ and /10 individual children to explain their working. thirds, sixths and twelfths. etc. Q How do you know when you have the simplest Q Can you write four more Repeat with other examples if appropriate. form of a fraction? fractions equivalent to half? Repeat with ½, 1/3, ¾. Bring the class back together and discuss some of their examples. Encourage children to explain their reasoning. Revise the meanings of numerator and denominator. Show a fraction family such as: By the end of the lesson children should 3 /10 = 30/100 = 300/1000 recognise that: 300 Q How can we work backwards to reduce /1000 to a family of A fraction such as 5/20 can be reduced to an fractions with smaller numbers? equivalent fraction by dividing both numerator and denominator by a common Introduce harder examples e.g. 600/800 where different factors are factor; required and cancelling can be introduced. A fraction such as 3/10 can be changed to an equivalent fraction by multiplying both the Q Can you continue the fraction family? numerator and denominator by the same number; Q What is happening to the numerator/denominator? If the numerator and denominator have no common factors, the fraction is expressed Repeat with other fraction families. in its lowest terms. Children work independently on further examples. (Refer to supplement of examples, section 6, page 23.) VOCABULARY reduce to simplest form VOCABULARY cancel equivalent factors numerator denominator denominator numerator RESOURCES RESOURCES Resource sheet 4.1 Resource sheet 4.2 NNS Unit Plans Planning Day Two Unit 4 Fractions, decimals and percentages Term: Autumn Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Vocabulary Vocabulary Questions Change an improper Write 25/20 on the board. Recognise the Write the following fractions on the board: Write on the board or use on OHT: fraction to a mixed equivalence between the 3 2 4 number and vice Q Can you think of a decimal and fraction /10 ¼ /25 /5 0.5 = ½ versa. different way to write forms. 0.25 = □ this fraction? Q Can you put these fractions in order? □=¾ If necessary, suggest Discuss how it can be done, leading to converting to hundredths. □ = 1/10 writing a mixed number. 0.01 = □ Q Would it have been easier if the numbers had already been written in hundredths or □ = 1/1000 Practise converting from as decimal fractions? mixed numbers to Discuss what goes in the boxes and improper fractions and Discuss how they can be converted to decimal form (i.e. 0.3, 0.25, 0.08, 0.8) and use ask children to write out their own back. the discussion to assess children’s previous knowledge of decimal notation in copy. hundredths. HOMEWORK – Learn the common Repeat with other examples. fraction and decimal equivalences by heart. Draw a number line on the board. Q What other equivalences can I work Give out the cards on Resource sheets 4.3 and 4.4. out? Q Can you place your cards in the correct place on the number line? Encourage children to justify why they choose a particular place on the number line. By the end of the lesson the Draw children’s attention to the fact that some children will want to put two or more children should be able to: cards in the same place. For example ¾, 75/100 and 0.75. Convert an improper fraction to a Provide differentiated examples for pupils to practise ordering fractions, decimals, mixed number, such as 33/8 to 41/8 then a mixture of both on a number line. and 57/12 to 4¾; Recognise the equivalence between decimals and fractions. (Refer to supplement of examples, section 6, pages 23 and 31.) VOCABULARY decimal fractions VOCABULARY proper fraction improper fraction RESOURCES mixed number Resource sheets 4.3, 4.4 NNS Unit Plans Planning Day Three Unit 4 Fractions, decimals and percentages Term: Autumn Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Consolidate knowing Play a ‘loop’ or ‘follow me’ Use decimal notation for Ask questions like: Write on the board and discuss: by heart up to 10 x 10. card game (Resource sheets tenths and hundredths; 4.5 and 4.6). Set a time. Try extend to thousandths for Q When do we meet decimals in real life? Q If the running track is 500m how many laps Derive quickly division to beat your own record. measurements. are needed to run 2.5km? facts corresponding to Q What in this room would measure 0.5m, 0.08m, 15.7cm etc? tables up to 10 x 10. Know what each digit Establish that conversion to the same unit of represents. Q What in this room holds 0.27 litres? measurement is necessary to solve the problem. Explore metric units and the relationship between them. Q There are 2.54cm to 1 inch. 1 yard is 36 Pupils begin to convert larger metric units to smaller and convert inches. About how many centimetres are halves, quarters, tenths and hundredths to larger units. there in a yard? e.g. ¾ kg = ? grams (Other problems from supplement of 3.5m = ? cm examples, section 6, page 87.) 1.25km = ? metres 2 litres = ? ml 500ml = ? litres 6000cm =?m By the end of the lesson children should 100mm = ? cm be able to: Some children might be limited to one decimal place whilst others can Convert, for example, 3.125km to metres; be introduced to thousandths and associated word problems. 300ml to 0.3 litres. (Refer to supplement of examples, section 6, page 29.) VOCABULARY multiple VOCABULARY RESOURCES double Resource sheets 4.5, factors 4.6 multiple NNS Unit Plans Planning Day Four Unit 4 Fractions, decimals and percentages Term: Autumn Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Recognise the Use questions to recall the Understand percentage Using a 100 square, shade all the even numbers. (Teacher Allow children to report back their findings. equivalence between homework from day 2. as the number of parts in could do this using an OHT of Resource sheet 4.7, or children the decimal and every 100. could do this on their own copy). Draw out the connections between fraction, fraction forms. Q What other equivalences can you decimal and percentage notation. work out? Find simple percentages Q What percentage of the square is shaded? of small whole number For example: 15/100 = 15% = 0.15 Extend children’s understanding by quantities. Q What percentage of the square is not shaded? asking questions about other Q Which would you rather have? fractions and decimals using an Now shade all the multiples of 5. a) 50% of £90 equivalence table for example: b) 25% of £200 Q What percentage of the square is/is not shaded? 0.1 =□ Children work in pairs and feed back their answers and methods. Repeat with other 0.2 =□ Repeat with other examples. examples if appropriate. 0.7 =□ Stressing appropriate vocabulary, remind the children that 0.04 =□ percentage means the number of parts in every 100. 0.09 =□ □ = 3/100 Using the multiples of 5 example, point out that: 20/100 = 20% = 0.2. By the end of the lesson children should 0.006 = □ be able to: □ = 9/1000 Repeat with other examples. Answer questions such as which of Children work in pairs to make up some of their own. these percentages is equivalent to 0.26? 0.26%, 2.6%, 26%, 260%; Make sure that they can make connections between the fraction Know that 13 and percentage notation. /100 = 13% = 0.13 For example: digits whose sum is 10 is: 9/100 = 9% = 0.09. (Refer to supplement of examples, section 6, page 33.) VOCABULARY percentage per cent % in every VOCABULARY equivalent RESOURCES equivalence Resource sheet 4.7 NNS Unit Plans Planning Day Five Unit 4 Fractions, decimals and percentages Term: Autumn Year Group: 6 sheet Oral and Mental Main Teaching Plenary Objectives and Teaching Activities Objectives and Teaching Activities Teaching Activities/ Focus Questions Vocabulary Vocabulary Count on in steps of Using a counting stick, count on Find simple percentages Remind children of the previous lesson’s question: 0.1, 0.2, 0.25, 0.5… and back in steps of 01, 0.2, 0.25, of small whole number Q What is wrong with this statement? and then back. 0.5 from different start points. quantities. Q Which is bigger: 50% of £90 or To calculate 10% of a quantity you divide it Pointing to various places, ask 25% of £200? by 10. So to find 20% you must divide it by 20. Q If this is 0.2, what will this be? Encourage children to discuss their methods of finding these percentages. Take feedback on responses. Q Will 0.35 (for example) be in this sequence? Use two sets of cards Emphasise that in some cases, calculations – three cards selected from Resource sheet 4.8 (to suit the can be done in a single step. Often two or ability range of the pupils) more steps may be more appropriate. Show examples. – all the cards from Resource sheet 4.9 placed face down on a table. By the end of the lesson children should Ask a child to choose at random one card from each set to understand: create a problem such as 20% of 240m. How to find simple percentages of small Ask everyone to calculate the percentage of the measurements whole number quantities, without a and discuss methods used. Repeat with different combinations. calculator e.g. find 60% of £40, 40% of 3m. Ask questions like: (Refer to supplement of examples, section 6, Q If I know 10% of £40 is £4 what other percentages do I know? page 33.) Q What are the most useful percentages to find? Children work in pairs to calculate other percentages. VOCABULARY percentage per cent % VOCABULARY tenth twentieth hundredth RESOURCES Percentage cards Measurement cards RESOURCES Resource sheet 4.8 Counting stick Resource sheet 4.9 NNS Unit Plans