Differentiated plans for Years 5 & 6. Fractions, decimals, percentages & ratios

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1 Differentiated plans for Years 5 & 6 Fractions, decimals, percentages & ratios Ian Lowe, MAV Professional Officer, 2006 IF YOU USE ANY OF THIS PLEASE PROVIDE FEEDBACK TO IAN AT THIS WILL QUALIFY YOU FOR AN IMPROVED VERSION WHEN AVAILABLE Materials are recommendations only; suitable substitutions may be made. MAV materials may be bought from Download the Curriculum Corporation catalogue from and look at pages 48 and 49. For Learning Federation materials (Learning Objects), check out Digital Learning Resources on your laptop, or download them from the new education website 1

2 Differentiated plans for Years 5 & 6 Fractions, decimals, percentages and ratios Ian Lowe, MAV Professional Officer, 2006 What do we have here? Fractions and its associated ideas are difficult for children. But they are a major focus for VELS Standard 4 Years 5 and 6 for the average child. So extra effort is required to create a rich learning environment that can help children to understand and to achieve at their own level. This combined topic is given 4 to 5 weeks, depending on interruptions. This set of units one per semester for Years 5 & 6 could achieve this goal. It matches the specifications for VELS, but recognises that there will be a wide spread of achievement in each class. So children are differentiated into working groups by need, for some of the time only. There may be more than one group at any Standard, or some Standards may need to be combined. Plan a stimulating set of activities for homework review, such as spreadsheets. It also balances the toolbox requirements concepts and skills with the need to learn to apply those tools in problem solving situations. Hence there are whole class lessons (often from Maths300 or RIME) punctuating the toolbox development, at regular intervals. These are on the same topic, but do not attempt to mesh with the work done by each standard group. They ensure that Working Mathematically is always part of the learning process, integrated into each dimension. The mix of activities will provide a stimulating and rich learning environment, with students learning from and helping one another. Connections between topics will be made and reinforced, and the variety of learning styles will accommodate learners with different needs. How does it work? In Years 5 and 6 it is assumed that children will be working anywhere from Standard 2 to Standard 5. Probably most will be working on Standards 3 or 4. At regular intervals whole class lessons are taught to mixed ability groups. Around these are cycles of a fixed pattern of lessons. In Years 5 and 6, the cycle has three parts: teaching, worksheet or games, computer use. On any day all are taking place in the same classroom, so only a fraction of the resources are needed. But the cycle also works for the students: they follow the pattern teaching, worksheet, (problem solving) and computer. As a consequence, teaching is to a different group each day in a regular pattern. ing will be for a concentrated 20 minutes or so, and then the teacher will supervise the rest of the class. Instructions on the board will inform the other groups of what they are to do. Encourage students to help each other. What resources are needed? Access to 4 or 5 computers daily is expected. pods or laptop trolleys might be the best solution. Membership of Maths300 is a requirement; many schools have membership here is how to use it. The pages in the resources are listed for each day s lesson, but are summarised here. Sources are: MAV (Mathematical Association of Victoria), CC (Curriculum Corporation), LF (Learning Federation). ing: Guidelines in Number (MAV), Maths Continuum (DE&T), People count (MAV) Worksheets:, (MAV), No textbooks are listed, but use them as required if you wish. : (MAV), Learning Objects (LF) Problem solving: Problem Solving Task Centre (CC), RIME (MAV), Maths300 (CC), RIME 5&6 (MAV) How could it be adapted to different situations? There is no expectation that lessons are sequential. Blocks of time without follow up lead to memory loss. If your class does not have the range predicted, or you cannot manage three or four groups, you should adapt by ignoring columns. You may substitute other learning tasks at any time. If you run out of time, leave stuff out. In this rich environment you will be surprised how much is learned outside the planned activities. How do I assess the learning? Your observations, digital photographs and copies of children s work will be more useful than any external test. Above all, if children have not all learned the same things, they should not attempt the same test. 2

3 Year 5 Semester 1 Fractions, decimals, percentages, ratios Day Yr 5 sem 1: Towards Std 3 Towards Std 4 group Towards Std 5 group 1 Maths300 #33 Fraction Estimation 2 Basic ideas of denominator and numerator Guidelines in Number p37-39, 59 Continuum 3.25 Fraction wall People count #18 F1 Fraction circles 3 F2 Fractions of things, F1 Fraction circles N5 Fractions Fraction bars and pies, Fractions up to 1, Fractions of an amount, Rod fractions, Mixed numbers, Improper fractions, Skip count fractions, Missing fractions Dynamic tools Fraction bars and pies, Fractions up to 1, Fractions of an amount, Rod fractions, Mixed numbers, Improper fractions, Skip count fractions, Missing fractions, Skip count decimals, Spending money, Subtracting money Dynamic tools, Fraction fiddle, Cassowary fractions Review basics and fraction equivalence People count #18 20, 23 F1 Fraction circles, F2 Fractions of things, 4 RIME #19 Clock fractions 5 Fraction bars and pies, Fractions up to 1, Dynamic tools, Fraction fiddle, Cassowary fractions Basic fractions denominator, numerator, mixed & improper Guidelines in Number p Continuum 3.25 Fraction wall People count #18, 19 N14 Using fractions F2 Fractions of things, F3 Fraction rally N9 Fraction applications 6 RIME #20 Compass fractions 7 Mixed numbers & improper fractions Guidelines in Number p60 People count #19 8 Mixed/improper N14 Using fractions F3 Fraction rally Fractions of dollars, Fractions of time, Fractions of numbers, Fractions of money Dynamic tools, Cassowary fractions Estimating decimals, Ordering decimals, Reading a scale Dynamic tools Review fraction operations People count #26, 27 F4 Fractions on a graph 9 RIME #22 Fractions of whole numbers 3

4 Day Yr 5 sem 1: Towards Std 3 Towards Std 4 group Towards Std 5 group 10 Fractions of an amount, Rod fractions Cassowary fractions, Dynamic tools Whole number of fractions, Fractions of whole numbers Guidelines in Number p121 Continuum 3.5 Activities 1, 2 People count #20 F5 Fraction magic squares and unit fractions N14 Using fractions 11 RIME #23 Fractions by comparing lengths 12 Fractions of whole numbers Guidelines in Number p59, 60 Continuum 3.25 Fraction wall People count #20 F2 Fractions of things Powers of 10(x), Powers of 10 ( ), 13 Equal circle fractions, Equal square fractions, Equal line fractions, Equal block fractions, Clock fractions, Graph fractions, Missing fractions Cassowary fractions, Dynamic tools Review decimals place value, order & operations People count #13, 16 F7 Counter abacus, 14 RIME #24 Order of fractions 15 Mixed numbers, Improper fractions Cassowary fractions, Dynamic tools Equivalent fractions Continuum 3.5 Activity 3 People count #23 F8 Order of operations, 16 RIME #25 Equal fractions 17 Mixed numbers Guidelines in Number p121 People count #19 18 N14 Using fractions F3 Fraction rally Skip count fractions Cassowary fractions, Dynamic tools Fractions of dollars, Fractions of time, Fractions of numbers, Fractions of money Review decimal operations F9 Mentally adding and subtracting, 4

5 Year 5 Semester 2 Fractions, decimals, percentages, ratios Day Yr 5 sem 2: Towards Std 3 Towards Std 4 group(s) Towards Std 5 group(s) 1 Maths300 #99 What s it worth? 2 Tenths, hundredths, order Guidelines in Number p61, 73, 83, 103 People count #13 Add & subtract fractions Worksheet / games Estimating decimals, Fractions of a dollar, Guitar fractions 3 Skip count decimals, Spending money, Subtracting money, Estimating decimals, Ordering decimals, Reading a scale Dynamic tools Fractions to percentages, percents of whole numbers Guidelines in Number p Maths300 #99 What s it worth? 5 Money by 10 or 100, 10 or 100 times what? Dynamic tools Order of decimals, simple fractions to decimal conversions Guidelines in Number p108, 112, 113, 118 Continuum 4.0 Activities 1, 2, 3 People count #24 F10 Number hunt and build-aproblem 6 Maths300 #99 What s it worth? 7 Quantities of fractions Guidelines in Number p121 Fractions of quantities People count #20 Percentage square, Percentage pie, Percentage line, Percentage fraction, Percentage full, Percentage rectangle 8 Powers of 10(x), Powers of 10 ( ), Estimating decimals, Fractions of a dollar, Guitar fractions Equivalent decimals, fractions and percentages and Dividing with remainders as fractions & decimals 9 Maths300 #99 What s it worth? 10 Fractions of dollars, Fractions of time Dynamic tools Add and subtract decimals Guidelines in Number p176, 177 Continuum 4.0 Activity 4 People count #13 F12 Dividing by decimals in your head, 5

6 Day Yr 5 sem 2: Towards Std 3 Towards Std 4 group(s) Towards Std 5 group(s) 11 Maths300 #144 Rod mats 12 Add decimals Guidelines in Number p108, 109, , People count #13 Percentage square, Percentage pie, Percentage line, Percentage fraction, Percentage full, Percentage rectangle Design briefs 13 Fractions of dollars, Fractions of time, Fractions of numbers, Fractions of money Equivalences of fractions, decimals and percentages People count #14, 21, Maths300 #72 Fraction magic square 15 Fractions of money, Fractions of a dollar, Guitar fractions Fraction fiddle, Dynamic tools Whole numbers of decimals Guidelines in Number p , People count #15 F10 Number hunt & Build-aproblem, F11 Converting decimals to fractions 16 RIME #26 Card thickness 17 Subtract decimals Guidelines in Number p126 (rounding), People count #13 Fraction to percentage, Decimal to fraction Squirt, Scale matters 18 Comparing fractions, Fraction triangles, Ones times tenths, Remainders, Dividing with remainders Equivalence with calculator & order on number line People count #24 19 RIME #27 Add and subtract fractions 20 Skip count decimals, Spending money, Subtracting money Rounding, estimation Guidelines in Number p94, 140, 174 People count #13 F13 Estimating percentages N13 Converting forms of fractions 6

7 Year 6 Semester 1 Fractions, decimals, percentages, ratios Day Yr 6 sem 1: Towards Std 3 Towards Std 4 group(s) Towards Std 5 group(s) 1 Maths300 #11 This goes with this 2 dividing by whole numbers dealing with remainders Guidelines in Number p66, People count #15 F13 Estimating percentages, Ones times tenths, Tenths times tenths 3 Percentage square, Percentage pie, Percentage line, Percentage fraction, Percentage full, Percentage rectangle, Review of all ideas and operations with fractions & decimals (except dividing) People count #13 to 24 4 Maths300 #11 This goes with this 5 Dividing strips, Sharing dampers, Dividing money, Steps The divider Dividing by whole numbers dealing with remainders Guidelines in Number p People count #15 F5 Fraction magic squares and unit fractions, F8 Order of operations N13 Converting forms of fractions 6 RIME5/6 Newspaper fractions 7 Equivalent fractions Continuum 3.25 Fraction wall People count #23 Add circle fractions, Add strip fractions, Add fractions, Subtract fractions, Fractions of (circles), Fractions of (strips), Fractions of (rectangle) The multiplier, The divider, Design briefs 8 Dividing strips, Sharing dampers, Dividing money, Steps, Remainders, Dividing with remainders conversions between fractions, decimals and percentages Guidelines in Number p159 People count #14, 21, 24 9 RIME #28 Multiplying fractions 10 Equal circle fractions, Equal square fractions Conversions: fractions, decimals and percentages Guidelines in Number p159 People count #14, 21, 24 F11 Converting decimals to fractions N13 Converting forms of fractions 11 Maths300 #135 Chocolate cake 7

8 Day Yr 6 sem 1: Towards Std 3 Towards Std 4 group(s) Towards Std 5 group(s) 12 Equivalent fractions and simple conversions to decimals and percentages Guidelines in Number p118 People count #14, 21, 24 F11 Converting decimals to fractions N13 Converting forms of fractions Tenths times tenths, Multiply by tenths, Estimate to multiply 13 Equal circle fractions, Equal square fractions, Equal line fractions, Equal block fractions, Clock fractions, Percentage square, Percentage pie, Percentage line, Percentage fraction, Percentage full, Percentage rectangle Decimals multiplied or divided by decimals Continuum 4.75 Activities 1 to 4 People count #16, RIME #27 Add and subtract fractions 15 Equal line fractions, Equal block fractions, Clock fractions Adding and subtracting fractions, with different denominators Guidelines in Number p , People count #26 F12 Dividing by decimals in your head, 16 Maths300 #201 Rectangle fractions 17 Order of fractions, decimals, percentages on a number line Estimate to divide by whole numbers, Missing decimals, Wage sheet 18 Add circle fractions, Add strip fractions, Add fractions, Subtract fractions F14 Percentage in your head, 19 Chance and Data Investigations vol 1 Horse races 20 Comparing fractions, Fraction triangles Chance as a fraction RIME #32 Equally likely - experiments F15 Percentage circles 8

9 Year 6 Semester 2 Fractions, decimals, percentages, ratios Day Yr 6 sem 2: Towards Std 3 Towards Std 4 group(s) Towards Std 5 group(s) 1 RIME #29 Sharing by ratio 2 Equivalent fractions People count #23 Sharing by ratio 3 Sharing by ratio Equivalent ratios and proportion Guidelines in Number p163 People count #18, 22 4 RIME #30 Estimating scale factors 5 Equal circle fractions, Equal square fractions, Equal line fractions, Equal block fractions Decimals divided by whole numbers Guidelines in Number p People count #15 N33 Proportion concept test N16 who uses proportion? N17 Understanding proportions 6 RIME #31 Same shape rectangles 7 Adding fractions with different denominators Guidelines in Number p People count #26 N20 Dividing by whole numbers in your head, Orange cordial, Proportional cordial 8 Estimate to divide (by whole numbers) Squares and cubes of fractions and decimals 9 Maths300 #9 First principles percent 10 Add circle fractions, Add strip fractions Design briefs Decimals multiplied by decimals People count #16 11 Maths300 #9 First principles percent 12 Subtracting fractions with F7 Counter abacus, 9 Tenths times tenths, Multiply by

10 Day Yr 6 sem 2: Towards Std 3 Towards Std 4 group(s) Towards Std 5 group(s) different denominators Guidelines in Number p People count #26 tenths, Estimate to multiply, Estimate to divide (by whole numbers), Missing decimals 13 Tenths times tenths, Multiply by tenths, Estimate to multiply, Estimate to divide (by whole numbers), Missing decimals Rounding, estimation and use of calculators 14 Maths300 #9 First principles percent 15 Add circle fractions, Add strip fractions, Add fractions, Subtract fractions Ratio and equivalent ratios Guidelines in Number p163 People count #18, 22, 28 N34 Finding the whole thing, 16 RIME #32 Enlarging cartoons 17 Fractions of whole numbers, simple fractions of fractions People count #20, 27 N16 who uses proportion? N17 Understanding proportions N33 Proportion concept test Multiply with powers of 10, Divide with powers of 10, Multiply & divide by decimals, Decimal dividing 18 Orange cordial, Proportional cordial Calculator use for roots and reciprocals 19 RIME #34 Garbage bag kite (make it) 20 Go fly a kite 10

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