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
ilowe@mav.vic.edu.au
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 www.mav.vic.edu.au/shop
Download the Curriculum Corporation catalogue from
http://www.curriculum.edu.au/catalogue/downloads/pc2007_pages39-54.pdf
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
www.education.vic.gov.au/studentlearning/teachingresources/elearning/digilearn.htm.
1
Differentiated plans for Years 5 & 6
Fractions, decimals, percentages and ratios
Ian Lowe, MAV Professional Officer, 2006
ilowe@mav.vic.edu.au
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
Interactive Learning 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. Teaching 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. Computer 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).
• Teaching: Guidelines in Number (MAV), Maths Continuum (DE&T), People count (MAV)
• Worksheets: Active Learning 1 (Number), Active Learning 2 (Number) (MAV),
No textbooks are listed, but use them as required if you wish.
• Computer: Interactive Learning (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
Year 5 Semester 1
Day
Yr 5 sem 1: Towards Std 3
1
2
Fractions, decimals, percentages, ratios
‘Towards Std 4’ group
Maths300 #33 Fraction Estimation
Teach
Worksheet / hands-on
Computer
Basic ideas of denominator
and numerator
Active Learning 1 (Number)
F1 Fraction circles
Interactive Learning
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
Guidelines in Number p37-39, 59
Continuum 3.25 Fraction wall
Active Learning 2 (Number)
N5 Fractions
People count #18
Active Learning 1 (Number)
F1 Fraction circles
3
Learning objects
Dynamic tools, Fraction fiddle,
Cassowary fractions
Worksheet / hands-on
Computer
Teach
Active Learning 1 (Number)
F2 Fractions of things,
Interactive Learning
Fraction bars and pies, Fractions up
to 1, Fractions of an amount, Rod
fractions, Mixed numbers, Improper
fractions, Skip count fractions,
Missing fractions
Review basics and fraction
equivalence
Learning objects
Design briefs, Fraction fiddle,
Dynamic tools
4
5
‘Towards Std 5’ group
People count #18 – 20, 23
Active Learning 1 (Number)
F1 Fraction circles,
F2 Fractions of things,
RIME #19 Clock fractions
Computer
Teach
Worksheet / hands-on
Interactive Learning
Fraction bars and pies,
Fractions up to 1,
Basic fractions –
denominator, numerator,
mixed & improper
Active Learning 1 (Number)
F2 Fractions of things,
F3 Fraction rally
Learning objects
Dynamic tools, Fraction fiddle,
Cassowary fractions
Guidelines in Number p
Active Learning 2 (Number)
N9 Fraction applications
Continuum 3.25 Fraction wall
People count #18, 19
Active Learning 2 (Number)
N14 Maths@work: Using fractions
6
7
RIME #20 Compass fractions
Teach
Worksheet / hands-on
Computer
Mixed numbers &
improper fractions
Active Learning 1 (Number)
F3 Fraction rally
Interactive Learning
Estimating decimals, Ordering
decimals, Reading a scale
Guidelines in Number p60
Learning objects
Design briefs, Fraction fiddle,
Dynamic tools
People count #19
8
Mixed/improper
Worksheet/games
Active Learning 2 (Number)
N14 Maths@work: Using fractions
Computer
Teach
Interactive Learning
Fractions of dollars, Fractions of
time, Fractions of numbers,
Fractions of money
Review fraction operations
Learning objects
Design briefs, Fraction fiddle,
Dynamic tools, Cassowary fractions
9
People count #26, 27
Active Learning 1 (Number)
F4 Fractions on a graph
RIME #22 Fractions of whole numbers
3
Day
Yr 5 sem 1: Towards Std 3
‘Towards Std 4’ group
‘Towards Std 5’ group
10
Computer
Teach
Worksheet / hands-on
Interactive Learning
Fractions of an amount,
Rod fractions
Whole number of fractions,
Fractions of whole numbers
Active Learning 1 (Number)
F5 Fraction magic squares and unit
fractions
Learning objects
Design briefs, Fraction fiddle,
Cassowary fractions, Dynamic tools
Guidelines in Number p121
Continuum 3.5 Activities 1, 2
Active Learning 2 (Number)
N14 Maths@work: Using fractions
11
12
People count #20
RIME #23 Fractions by comparing lengths
Teach
Worksheet / hands-on
Computer
Fractions of whole numbers
Active Learning 1 (Number)
F2 Fractions of things
Interactive Learning
Powers of 10(x), Powers of 10 (÷),
Guidelines in Number p59, 60
Learning objects
Decimaster
Continuum 3.25 Fraction wall
People count #20
13
Worksheet/games
Computer
Teach
Interactive Learning
Equal circle fractions, Equal square
fractions, Equal line fractions, Equal
block fractions, Clock fractions,
Graph fractions, Missing fractions
Review decimals place
value, order & operations
Learning objects
Design briefs, Fraction fiddle,
Cassowary fractions, Dynamic tools
14
15
Active Learning 1 (Number)
F7 Counter abacus,
RIME #24 Order of fractions
Computer
Teach
Worksheet / hands-on
Interactive Learning
Mixed numbers, Improper fractions
Equivalent fractions
Active Learning 1 (Number)
F8 Order of operations,
Learning objects
Design briefs, Fraction fiddle,
Cassowary fractions, Dynamic tools
People count #23
16
17
People count #13, 16
Continuum 3.5 Activity 3
RIME #25 Equal fractions
Teach
Worksheet / hands-on
Computer
Mixed numbers
Active Learning 1 (Number)
F3 Fraction rally
Interactive Learning
Fractions of dollars, Fractions of
time, Fractions of numbers,
Fractions of money
Guidelines in Number p121
People count #19
Learning objects
Measures, Squirt, Foul Foodmaker
18
Worksheet/games
Computer
Review decimal operations
Learning objects
N14 Maths@work: Using fractions
Interactive Learning
Skip count fractions
Active Learning 1 (Number)
F9 Mentally adding and subtracting,
Learning objects
Design briefs, Fraction fiddle,
Cassowary fractions, Dynamic tools
4
Year 5 Semester 2
Day
Yr 5 sem 2: Towards Std 3
1
2
Fractions, decimals, percentages, ratios
Towards Std 4 group(s)
Maths300 #99 What’s it worth?
Teach
Add & subtract fractions
Computer
Tenths, hundredths, order
Worksheet / games
Interactive Learning
Estimating decimals, Fractions of a
dollar, Guitar fractions
Guidelines in Number
p61, 73, 83, 103
Learning objects
Decimaster
People count #13
3
Towards Std 5 group(s)
Worksheet/games
Computer
Teach
Interactive Learning
Skip count decimals, Spending
money, Subtracting money,
Estimating decimals, Ordering
decimals, Reading a scale
Fractions to percentages,
percents of whole numbers
Guidelines in Number p165-167
Learning objects
Design briefs, Fraction fiddle,
Dynamic tools
4
5
Maths300 #99 What’s it worth?
Computer
Teach
Worksheet / hands-on
Interactive Learning
Money by 10 or 100,
10 or 100 times what?
Order of decimals, simple
fractions to decimal
conversions
Active Learning 1 (Number)
F10 Number hunt and build-aproblem
Learning objects
Design briefs, Fraction fiddle,
Dynamic tools
Guidelines in Number
p108, 112, 113, 118
Continuum 4.0 Activities 1, 2, 3
People count #24
6
7
Maths300 #99 What’s it worth?
Teach
Worksheet/games
Quantities of fractions
Computer
Interactive Learning
Percentage square, Percentage pie,
Percentage line, Percentage
fraction, Percentage full,
Percentage rectangle
Guidelines in Number p121
Fractions of quantities
People count #20
8
Worksheet/games
Computer
Teach
Interactive Learning
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
Learning objects
Decimaster
9
10
Maths300 #99 What’s it worth?
Computer
Teach
Worksheet / hands-on
Interactive Learning
Fractions of dollars,
Fractions of time
Add and subtract decimals
Active Learning 1 (Number)
F12 Dividing by decimals in your
head,
Learning objects
Design briefs, Fraction fiddle,
Dynamic tools
Continuum 4.0 Activity 4
Guidelines in Number p176, 177
People count #13
5
Day
Yr 5 sem 2: Towards Std 3
11
12
Towards Std 4 group(s)
Towards Std 5 group(s)
Maths300 #144 Rod mats
Teach
Worksheet/games
Add decimals
Computer
Interactive Learning
Percentage square, Percentage pie,
Percentage line, Percentage
fraction, Percentage full,
Percentage rectangle
Guidelines in Number p108,
109,112-114, 127-128
People count #13
Learning objects
Design briefs
13
Worksheet/games
Computer
Teach
Interactive Learning
Fractions of dollars, Fractions of
time, Fractions of numbers,
Fractions of money
Equivalences of fractions,
decimals and percentages
People count #14, 21, 24
Learning objects
Decimaster
14
15
Maths300 #72 Fraction magic square
Computer
Teach
Worksheet / hands-on
Interactive Learning
Fractions of money, Fractions of a
dollar, Guitar fractions
Whole numbers of decimals
Active Learning 1 (Number)
F10 Number hunt & Build-aproblem,
F11 Converting decimals to
fractions
Learning objects
Fraction fiddle, Dynamic tools
16
17
Guidelines in Number p133-134,
178-180
People count #15
RIME #26 Card thickness
Teach
Worksheet/games
Computer
Subtract decimals
Interactive Learning
Fraction to percentage,
Decimal to fraction
Guidelines in Number p126
(rounding), 129-131
Learning objects
Squirt, Scale matters
People count #13
18
Worksheet/games
Computer
Teach
Interactive Learning
Comparing fractions, Fraction
triangles, Ones times tenths, Remainders, Dividing with remainders
Equivalence with calculator
& order on number line
People count #24
Learning objects
Decimaster
19
20
RIME #27 Add and subtract fractions
Computer
Teach
Worksheet / hands-on
Interactive Learning
Skip count decimals, Spending
money, Subtracting money
Rounding, estimation
Active Learning 1 (Number)
F13 Estimating percentages
Learning objects
Decimaster
Guidelines in Number
p94, 140, 174
People count #13
6
Active Learning 2 (Number)
N13 Converting forms of fractions
Year 6 Semester 1
Day
Yr 6 sem 1: Towards Std 3
1
2
Fractions, decimals, percentages, ratios
Towards Std 4 group(s)
Maths300 #11 This goes with this
Teach dividing by whole
numbers – dealing with
remainders
Worksheet / hands-on
Computer
Active Learning 1 (Number)
F13 Estimating percentages,
Interactive Learning
Ones times tenths, Tenths times
tenths
Guidelines in Number
p66, 135-137
Learning objects
Decimaster
People count #15
3
Worksheet/games
Computer
Interactive Learning
Percentage square, Percentage pie,
Percentage line, Percentage
fraction, Percentage full,
Percentage rectangle,
4
5
Review of all ideas and
operations with fractions &
decimals (except dividing)
People count #13 to 24
Maths300 #11 This goes with this
Computer
Teach
Worksheet / hands-on
Interactive Learning
Dividing strips, Sharing dampers,
Dividing money, Steps
Dividing by whole numbers
– dealing with remainders
Learning objects
The divider
Guidelines in Number p134-137
Active Learning 1 (Number)
F5 Fraction magic squares and unit
fractions,
F8 Order of operations
6
7
Towards Std 5 group(s)
People count #15
Active Learning 2 (Number)
N13 Converting forms of fractions
RIME5/6 Newspaper fractions
Teach
Worksheet/games
Equivalent fractions
Computer
Interactive Learning
Add circle fractions, Add strip
fractions, Add fractions, Subtract
fractions, Fractions of (circles),
Fractions of (strips),
Fractions of (rectangle)
Continuum 3.25 Fraction wall
People count #23
Learning objects
The multiplier, The divider,
Design briefs
8
Worksheet/games
Computer
Interactive Learning
Dividing strips, Sharing dampers,
Dividing money, Steps,
Remainders, Dividing with
remainders
9
10
Guidelines in Number p159
People count #14, 21, 24
RIME #28 Multiplying fractions
Computer
Teach
Worksheet / hands-on
Interactive Learning
Equal circle fractions,
Equal square fractions
Conversions: fractions,
decimals and percentages
Active Learning 1 (Number)
F11 Converting decimals to
fractions
Guidelines in Number p159
Active Learning 2 (Number)
N13 Converting forms of fractions
People count #14, 21, 24
11
Teach conversions between
fractions, decimals and
percentages
Maths300 #135 Chocolate cake
7
Day
Yr 6 sem 1: Towards Std 3
Towards Std 4 group(s)
Towards Std 5 group(s)
12
Teach
Worksheet / hands-on
Computer
Equivalent fractions and
simple conversions to
decimals and percentages
Active Learning 1 (Number)
F11 Converting decimals to
fractions
Interactive Learning
Tenths times tenths, Multiply by
tenths, Estimate to multiply
Active Learning 2 (Number)
N13 Converting forms of fractions
Learning objects
Decimaster
Computer
Teach
Interactive Learning
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
Guidelines in Number p118
People count #14, 21, 24
13
Worksheet/games
Continuum 4.75 Activities 1 to 4
People count #16, 17
Learning objects
Measures, Squirt, Foul Foodmaker
14
15
RIME #27 Add and subtract fractions
Computer
Teach
Worksheet / hands-on
Interactive Learning
Equal line fractions, Equal block
fractions, Clock fractions
Adding and subtracting
fractions, with different
denominators
Active Learning 1 (Number)
F12 Dividing by decimals in your
head,
Learning objects
Measures, Squirt, Foul Foodmaker
Guidelines in Number
p119-120, 160-162
People count #26
16
17
Maths300 #201 Rectangle fractions
Teach
Worksheet/games
Order of fractions,
decimals, percentages on a
number line
Computer
Interactive Learning
Estimate to divide by whole
numbers, Missing decimals,
Wage sheet
Learning objects
Decimaster
18
Worksheet/games
19
20
Computer
Worksheet / hands-on
Interactive Learning
Add circle fractions, Add strip
fractions, Add fractions,
Subtract fractions
Active Learning 1 (Number)
F14 Percentage in your head,
Chance and Data Investigations vol 1 Horse races
Computer
Teach
Worksheet / hands-on
Interactive Learning
Comparing fractions,
Fraction triangles
Chance as a fraction
Active Learning 1 (Number)
F15 Percentage circles
RIME #32
Equally likely - experiments
8
Year 6 Semester 2
Day
Yr 6 sem 2: Towards Std 3
Towards Std 4 group(s)
1
2
Fractions, decimals, percentages, ratios
Towards Std 5 group(s)
RIME #29 Sharing by ratio
Teach
Worksheet/games
Computer
Equivalent fractions
Interactive Learning
Sharing by ratio
People count #23
3
Learning objects
Measures, Squirt, Foul Foodmaker
Worksheet/games
Computer
Teach
Interactive Learning
Sharing by ratio
Equivalent ratios and
proportion
Learning objects
Measures, Squirt, Foul Foodmaker
Guidelines in Number p163
People count #18, 22
4
5
RIME #30 Estimating scale factors
Computer
Teach
Worksheet / hands-on
Interactive Learning
Equal circle fractions, Equal square
fractions, Equal line fractions,
Equal block fractions
Decimals divided by whole
numbers
Active Learning 1 (Number)
N33 Proportion concept test
Guidelines in Number p134-137
People count #15
6
7
RIME #31 Same shape rectangles
Teach
Worksheet / hands-on
Computer
Adding fractions with
different denominators
Active Learning 1 (Number)
N20 Dividing by whole numbers in
your head,
Interactive Learning
Orange cordial,
Proportional cordial
Guidelines in Number p119-120
Learning objects
Measures, Squirt, Foul Foodmaker
People count #26
8
Active Learning 2 (Number)
N16 Maths@work: who uses
proportion?
N17 Understanding proportions
Worksheet/games
Computer
Teach
Interactive Learning
Estimate to divide (by whole
numbers)
Squares and cubes of
fractions and decimals
Learning objects
Decimaster
9
10
Maths300 #9 First principles percent
Computer
Teach
Interactive Learning
Add circle fractions,
Add strip fractions
Decimals multiplied by
decimals
Learning objects
Design briefs
People count #16
11
12
Worksheet/games
Maths300 #9 First principles percent
Teach
Worksheet / hands-on
Computer
Subtracting fractions with
Active Learning 1 (Number)
F7 Counter abacus,
Interactive Learning
Tenths times tenths, Multiply by
9
Day
Yr 6 sem 2: Towards Std 3
Towards Std 4 group(s)
Towards Std 5 group(s)
different denominators
tenths, Estimate to multiply,
Estimate to divide (by whole
numbers), Missing decimals
Guidelines in Number p119-120
People count #26
13
Worksheet/games
14
15
18
Computer
Teach
Interactive Learning
Tenths times tenths, Multiply by
tenths, Estimate to multiply,
Estimate to divide (by whole
numbers), Missing decimals
Rounding, estimation and
use of calculators
Maths300 #9 First principles percent
Computer
Teach
Worksheet / hands-on
Interactive Learning
Add circle fractions, Add strip
fractions, Add fractions,
Subtract fractions
Ratio and equivalent ratios
Active Learning 1 (Number)
N34 Finding the whole thing,
16
17
Learning objects
Decimaster
Guidelines in Number p163
People count #18, 22, 28
RIME #32 Enlarging cartoons
Teach
Worksheet / hands-on
Computer
Fractions of whole
numbers, simple
fractions of fractions
Active Learning 2 (Number)
N16 Maths@work: who uses
proportion?
N17 Understanding proportions
Interactive Learning
Multiply with powers of 10, Divide
with powers of 10, Multiply & divide
by decimals, Decimal dividing
People count #20, 27
Active Learning 1 (Number)
N33 Proportion concept test
Worksheet/games
Computer
Teach
Interactive Learning
Orange cordial, Proportional cordial
Calculator use for roots and
reciprocals
Learning objects
Measures, Squirt, Foul Foodmaker
19
RIME #34 Garbage bag kite (make it)
20
Go fly a kite
10