NumeracyPlanning Sequence (3 week block) |
Classes: |
Year Groups: 5 |
Teachers: MrsJames |
Week: |
Beginning: 21 April | |
Block E SecuringNumber Facts relationships and Calculating | ||||||
Curricular Targets Must: Know by heart allmultiplication facts up to 10 10; derive quickly correspondingdivision facts. Recognisemultiples of 6, 7, 8, 9, up to the 10th multiple.
Should: Multiply anddivide whole numbers by 10 and 100 and explain the effect. Use thisto be able to multiply by multiples of ten and 100 and explaintheir answers. Derive quickly doubles of two-digit decimals (e.g.3.8 2, 0.76 2), and the corresponding halves. Could: Multiply and dividewhole and decimal numbers by 10 and 100 and explain the effect. Usethis to be able to multiply by multiples of ten and 100 and explaintheir answers. Be able to explain the relationship between twonumbers eg 4.6 and 46. | ||||||
Learning Outcome Children double and halve decimalnumbers using their knowledge of doubling and halving wholenumbers and decimal place value. They find, for example, double0.47 and half of 7.2. They answer questions such as: Find a number whose double liesbetween 1.3 and 1.4. What number lies halfway between2.47 and 2.83 on a number line? Children count in fractions.For example, they count from 0 in steps of14 initially using improperfractions (0, 14,24,34,44,54, ) and then using mixednumbers (0, 14, 24,34, 1,114, ). They record the count ona number line to establish equivalent pairs, e.g.234 = 114. They discuss how to findequivalent pairs without a number line, establishing that 1 wholeis equivalent to 4 quarters, so 2 wholes is 8 quarters (4quarters 2), and 234 is equivalent to 8 quarters + 3quarters, or 11 quarters. They use diagrams where helpful toconfirm the equivalent improper fraction for a given mixed numberand vice versa. Children relate fractions to theirdecimal equivalents. They recognise that fractions with adenominator of 10 or 100 can be converted to their decimalequivalent by placing the digits of the numerator in theappropriate column, e.g.310 = 0.3,7100 = 0.07,13100 = 0.13. They use numberlines (or the ITP Fractions) to establish the decimal equivalentof fractions such as 25 or120.
For example, they use a 0 to 1 numberline marked in steps of 0.1, divide it into fifths and mark15, 25, on it. Theyuse this to establish that15 = 0.2,25 = 0.4, They use thepatterns in such sequences to predict other equivalents,predicting, for example, that 45 will be equivalent to 0.8.Children understand how to use a calculator to convert afraction to a decimal. They appreciate that45 is equivalent to4 5. They appreciate that when they key thiscalculation into a calculator it will give them the answer indecimal form. So one way to find the decimal equivalent of45 is to key 4 5 intoa calculator. Children solve problems involvingfractions, including some where the calculations merit use of acalculator. For example, they find 23 of150 ml by dividing 150 ml by 3 tofind 13, then multiplying the answerby 2 to find 23. They solve problems suchas: Jay buys a 2 litre bottle ofpop. He drinks 14 of the bottle and spills25 of the bottle. How manymillilitres are left? A mile is 1760 yards. I havewalked 511 of a mile. How many yards isthis? Children understand percentage asthe number of parts in every 100. They represent particularpercentages using practical resources such as money (1, 10p and 1pcoins) or images such as a 10 by 10 square grid, for exampleshading 35 squares in the grid to represent 35%. To find thepercentage equivalent for simple fractions such as34 they shade this fraction of a10 by 10 grid and consider what percentage this represents.Children appreciate that 10% is equivalent is110, so to find 10% of an amountthey can divide it by 10. They find 10% of numbers and measuressuch as 2.00, 150, 25, 700 ml,3 kg. They begin to use 10% of an amount to find5%, then 20%, 30%, They use this method to work out percentagesof quantities such as 20% of 1 kg, 30% of200 ml, 5% of 80. Children recognise and interpret thevocabulary of ratio and proportion, usingdiagrams or objects to represent the situation. Theyunderstand that scaling involves increasing a quantity by agiven factor. Multiplication by 5 means scaling a number orquantity by a factor of 5, and making it 5 times as big.
They use pairs of number lines toshow scaling, for example by a factor of 3:
They scale up a relationship such asThere are 3 red sweets in every pack of 10 to establishthat there would be 6 red sweets in every 20 sweets, 9 red sweetsin every 30 sweets, and so on. They solve problems suchas: At the gym club there are 2 boysfor every 3 girls. Suggest some numbers of boys and girls thatthere might be at the club. A mother seal is fed 5 fish forevery 2 fish for its baby. Alice fed the mother seal 15 fish. Howmany fish did she feed to the baby? Paul uses 3 tomatoes forevery 12 litre of sauce. How much saucecan he make from 15 tomatoes? How many tomatoes would he need for4l of sauce? | ||||||
Mental Oral Objective (at least 2to be related to CT) I can double and halve two-digitnumbers and explain how to use this to double and halve relateddecimals Use a calculator to solve problems,including those involving decimals or fractions (e.g. find34 of 150 g);interpret the display correctly in the context ofmeasurement I can use a calculator tofind the decimal equivalent of a fraction Double and halve 2 digit numbersincluding decimals
| Learning Objectives for directteaching I can explain how to turn a mixednumber such as 234 into an improperfraction. I can draw a diagram to support myexplanation Express asmaller whole number as a fraction of a larger one I can give the decimalequivalent of a simple fraction such as310 and explain how Iknow Understand percentage as the numberof parts in every 100 and express tenths and hundredths aspercentages I know that per cent meansparts in every 100, so1% = 1100 I cangive a simple fraction such as110 as apercentage Use sequences to scale numbers up ordown; solve problems involving proportions of quantities (e.g.decrease quantities in a recipe designed to feed sixpeople) I can continue a sequencesuch as: There are 3 red sweets in every 10, there are 6 redsweets in every 20 | |||||
Speaking and Listening (How canyou develop talk around maths in your class this?) | Vocabulary problem, solution, calculator,calculate, calculation, equation, operation, symbol, inverse,answer, method, explain, predict, reason, reasoning, pattern,relationship add, subtract, multiply, divide, sum,total, difference, plus, minus, product, quotient, remainder,multiple, common multiple, factor, divisor, divisible by decimal fraction, decimal place,decimal point, percentage, per cent (%) fraction, proper fraction, improperfraction, mixed number, numerator, denominator, unit fraction,equivalent, cancel proportion, in every, for every, toevery
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Prior learning use diagrams toidentify equivalent fractions, e.g. 68and34, or70100and710; interpretmixed numbers and position them on a number line, e.g.312NEEDSTEACHING use decimal notation for tenthsand hundredths and partition decimals; position one- and two-placedecimals on a number line know the equivalence betweendecimal and fraction forms of one half, one quarter, tenths andhundredths double and halve two-digit numbersCT use written methods to record,support and explain multiplication and division of two-digitnumbers by a one-digit number, including division with remainders,e.g. 15 9, 98 6 (morningactivity) use the vocabulary of ratio andproportion NEEDSTEACHING | ||||||
| DirectTeaching | GuidedWork with teacher | Independent Work or TA supportedgroups | Plenary/Probing Qs. | |
DAY1 | Consolidate priorlearning | Probing Question/Images Fractions ITP Fractions ppt
| SealsUse cubes to create improperfractions and mixed fractions Order on a numberline. How do I knowthis fraction is 3/4? How doI Know thisfraction is 1and 1/4 ? What is this as an improperfraction?
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Dolphins WhalesIdentify improper andmixed fractions, place on a number line wsheet Anna, Hugh &Travis extension forimproper and mixed fractions | What mixed number is equivalent to134? How do you know? How many sevenths are there in threewholes? What calculation does this involve? Find an improper fraction that liesbetween 3 and 4. Sam says that235 is equivalent to135. Explain how he found thenumerator 13. |
M.O. use a calculator tofind fractions of a number L.O. I can convertimproper and mixed fractions Revise vocab for fractionsLW Identify simple fractions usingcubes/ folded paper Show fractions Itp what fractionis this? What is this fraction as adecimal? Next show improper fractions as 11/6 & 7/6 Repeat with 13/5. Why do we callthis an improper fraction? Show number line and count out1/5ths as marked on. Count on as 6/5ths; 7/5thsetc Repeat as mixed fractions, 1 1/5;1 2/5 Using number line what is the sameas 1 and 2/5?
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DAY2 | M.O. I can doublenumbers play doubling around the room use language twice; 2x;double L.O. I canorder mixed numbers Show http://www.primaryresources.co.uk /maths/powerpoint/mixed_fractions.swf
On a no. line where would I place21/2? 31/2?; 11/4? Explain that markers are needed start with whole numbers and then mark in divisions explain equalparts for a fraction. Repeat with no. loine 10 20 andask children to mark in 131/4, 151/2, 173/4
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DolphinsDraw number line 10cm longwith divisions every 2cm Label 0-5 Label with mixedfractions How do you know where toposition the fractio? What part of the number doyou need to lookat first?
Extend with1/3rds |
Whales Repeat for Dolphins but use1/3rds and 1/8ths
Seals Position 1/2s and 1/4s on anumber line | On a number line0-1 where would you place 1/3? How would you divide up the line?Why? How would youknow where to place 1/8th? 1/16th?
Where could weplace 3/4? 3/8? 2 and3/16? | |
Probing Question/Images Which part of the number do youlook at first for ordering on a number line? | |||||
DAY 3
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Probing Question/Images If I know 1/3rd of 9 is3 how can I work out 2/3rds of 9 http://www.freewebtown.com/weddell/mw/decimals/fraction%20of%20amount.swf
| Whales Start with finding eg 3/8of 64; 4/9 of 63; 1/5 of 45
What calculation are youdoing? What skills do you need tobe successful with this?
Tgt maths pg 27 sectionC | Dolphins Find simple and multiple fractionsof numbers eg 1/4 of 32; 3/4 of 24. Moveonto Tgt maths pg 27 B1 B12Seals Tgtmaths pg 27 section A | 13 of 75 is 25. Write this as adivision statement. What operation would you key into acalculator to find 18 of 256? One seventh of a number is 4. What isthe number?
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M.O. Pairs decimal number on the IWB show me what you need to add to this tomake 1.0 L.O. I can find afraction of a number Revise finding asimple fraction of a number eg 1/2 of 8 by2. 1/4 of 8. by 4 .What do I do to find 1/3rd of a number. Demo with 9children at front. If we can find1/3rd of 9, how can we find 2/3rds of 9? Using calculatorwhat is 2/3 of 15? 24? 36?
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DAY4 | Assess +review |
Probing Question/Images Fractions ITP |
Whales Dolphins andSeals Use a calculator to findequivalent decimal fractions. Highlight the fractions / decimalsthey think will be useful to learn
Ext: Tgt maths pg 22 sectionA
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Discuss findings did any of thefractions have the same decimal equivalents? Eg 1/5 = 2/10 = 0.2show using diagram on IWB What calculation would you key into acalculator to find 320 as a decimal? Use a calculator to establish whether2740 is bigger or smaller than0.75.
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M.O. I can add decimals to make10 L.O. Iknowthe equivalence between decimal and fraction forms of one half, onequarter, tenths and hundredths Write 2/10 on the board how can I express this as a decimal. Explain that calculators areuseful for converting fractions to a decimal equivalent. Reinforcepart of 1 Eg 1/2 of 1 is o.50. Explain fraction is the numeratordivided by the denominator. Key in 1 2. On f/c show 1/2 =0.5 Repeat for 1/10 and 1/4 Then show for 1/3 and discussrepeating decimals need to round to 2 dp What would 1/7 be as a decimalfraction?
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DAY5 | Directteaching |
Probing Question/Images http://www.freewebtown.com/weddell/mw/decimals/tenths-hundredths.swf
| Whales Dolphins andSeals
Play http://www.freewebtown.com/weddell/mw/decimals/tenths-hundredths.swfin mixed ability pairs
Workalongside seals
Also challenge maths pg 18HOMEWORK | What are the fraction equivalentsfor 0.7; 0.4; 0.6; 0.65; 0.25 Why cant 0.65 be represented astenths?
Using calculator does 2/5 have atenths equivalent? 6/20? | |
M.O. Double decimalnumbers L.O. I can recognise equivalentdecimals and fractions 7/10 on the board what doesthis mean? Is it greater orlass thn 1/ How do you know? Repeat for70/100. How would I write70/100 as a decimal? If I had a cakewould you like to eat 7/10ths or 70/100ths? Use calculators todemo =. Show 70/100 =7/10 as each number can be divided by 10
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DAY6 | Probing Question/Images Ppt equivalentfractions | Seals
Find simple fractions for tenthsand fifths | DolphinsFind simplefractions for tenths and fifths
Whales Convert fractions for sixthsninths etc
Cteaching | Write 1/4; 1/2;3/4 on the board.
How manyequivalent fractions can you find? What did you doto the numerator and denominator each time? | |
M.O. doubledecimals eg 2.5, 11.5; 2.25, 0.25 Whathappens when we double a number with 0.5; 0.25? L.O. I canconvert fractions Run through ppt Explain they need to know x tables and recognise a commondenominator
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DAY7 | Practice,investigate and apply | Probing Question/Images
Ppt fractions of 100 Fractions ITP show dec &% | Whales Tgtmaths pg 29 B | Dolphins &seals Calculator and fraction cards and100 squares Find fraction as a decimal andshade on 100 square | What is 0.15 as %? Otgher examples, mixture offractions and decimals to convert into %
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M.O. double decimalnumbers A number when doubled gives 9.2,what was the number? Same for 4.8; 6.4; 11.6? L.O. I canunderstand percentages as a fraction of 100 Introduce percentages as part of100. Show ppt Show equivalents Revise tenthsand hundredths as fractions and decimals. Use blank 100 square toshade in 10/100 as 10%. So 1/10 = 0.1=10% Learning Wall chart | |||||
DAY8 | Probing Question/Images
Fractions ITp | Dolphins Tgt maths pg 30 B Work together | Seals Challenge pg 54
Whales Tgt maths pg 30 B
| Find 75% of 200 ml.How did you do this? What percentages can you easily workout in your head? Talk me through a couple of examples. | |
M.O. halve 2 digitnumbers and decimals show on wbs L.O. I can find asimple percentage (50%, 25%, 75%, 10%) of aquantity 75 is the same as 75/100 or0.75. 25% is the samew as 25/100 or 0.25. refer back to yesterday to makelink that 75% = 3/4; 50%=1/2; 25%=1/4;10%=1/10. This means we can find 50% of anumber using these facts ie 50% = 1/2, so 50% of 30 is 50 2 =15. What is 10%0f 60? 25% of60? | |||||
DAY9 | Probing Question/Images
| Shade 10% of this grid.
Which is bigger: 65% or34? How do you know? What percentage is the same as710? Explain how youknow. What is31100 as a percentage? Which is a better markin a test: 61%, or 30 out of 50? How do you know? |
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M.O. Ican findequivalent fractions, decimals and % L.O. REPEATYESTERDAY
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DAY10 | Assess +Review | Probing Question/Images
| Whales, Seals &Dolphins
Differentiated word problems fromP& E, CgfL Eg Here is a chocolatebar.
Bill eats 3 pieces and Ann eats 2pieces. Mark 13 and56 on this number line.
Tell me two fractions that are thesame as 0.2. How would you write37100 as a decimal? Tell me a fraction that is equivalentto 23but has adenominator of 9. How did you do it?
| Discuss any difficulties,strategies used to solve the problems | |
L.O. I can solve problemsinvolving fractions Jay buys a 2 litre bottle of pop. Hedrinks 14 of the bottle and spills25 of the bottle. How manymillilitres are left? A mile is 1760 yards. Ihave walked 511 of a mile. How many yards isthis? CALCULATOR
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DAY11 | Consolidate learning | Probing Question/Images Fractions itp show rppart | Seals Use cubes to makepatterns and isentify the ratio and proportion for eachone Write onWB PHOTO | Dolphins Prepared multilink copy andco;our on book Write ratio and proportion for each tower Whales R & P wshhet | 4boys, 3 girls What is the ratio of boys togirls? What is the proportion of boys? Add one more boy, one more girland repeat. |
M.O. I can explain how to turn a mixed number such as234into an improper fraction and viceversa L.O. I can use thevocabulary of ratio and proportion Introduce ratio as onefor every If I have one blue cubefor every 3 then the ratio is 1:3 m show with cubes Show differentmultilinks. What fraction of thestick is blue? 1/4 what fraction is red? 3/4 This is the proportionie 1/4 of my stick is blue; 3/4 is red Demo with cubes and IWB
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DAY12 | Securingand extending understanding | Probing Question/Images | Dolphins Colour in sweet bags showingratios Discuss solving ratioproblems Ct sweets | Whales Colour sweet ratios; solveproblems Ct
Seals Colour sweet ratios; | There afre 30 children in a claswith a ratio of 2:1 girls to boys. How many girls and how manyboys are there?
What strategies would we use tosolve this? |
M.O. I cancalculate a fraction of a number L.O.I can continue asequence such as: There are 3 red sweets in every 10, there are 6red sweets in every 20
Bag of sweets 2 maltesers forevery 3 minstrels. Ratio of 2:3 (5sweets in total) New sweet productis always produced in this ratio. Double size ossweet packet. How many maltesers? Minstrels? (10 sweets intotal) I now have 10maltesers, how many minstrels would I have?
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DAY13 | Probing Question/Images | Whales, dolphins,seals
Smartie game! | Play human ratios | ||
M.O. I can identify the ratio andproportion of a coloured tower L.O. I can usethe vocabulary of ratio and proportion In a tea shop there are 7 cakesor biscuits on each plate. They are in a ratio of 3:4 biscuits tocakes. Draw thia plateto show this. What is thefraction or proportion of the cakes? | |||||
DAY14 | Assess +Review | Probing Question/Images | Whales, dolphins,seals
Differentiated word problems Schand PR Support as necessary Draw a diagram that shows thisstatement: My necklace has 2 yellow beads for every 3 greenbeads. There are 20 girls and 10 boys in aclass. Describe this with a sentence that uses the words forevery. You earn one voucher for every 20you spend at a shop. How much must you spend to get 4 vouchers?Tell me how you worked this out. One orange costs 15 pence. How muchwould five oranges cost? | What is the definition for ratio?Proportion?
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M.O. Ican double numbers L.O. I can solveproblems involving R & P I have 20 cakes on a plate and1/5 of them are chocolate. The rest are plain. How many cakes areplain? Discuss
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DAY15 | Probing Question/Images | Continue fromyesterday |
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Repeat as yesterday
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PROGRESSION FOR NEXTTERM
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