Download Fractions policy March 17

Cirencester Primary School
Fractions Policy
Updated March 2017
“Fair’s Fair!” – Whatever you do to the top, you do to the
bottom.
-ELG: Solve problems including doubling, halving & sharing practically using objects
-Exceeding: Solve problems including doubling, halving & sharing using actual numbers.
6 objects
...
6
YR
Half of 6 = 3
...
-Recognise, find and name a half as one of two equal parts of an object, shape or quantity
-Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity
Give shapes and chn find half
Half & half again
Fractions are fair
Y1
Chn to chop shapes in half Link to concrete that ½ is also ÷ 2
8÷2=4
¼ of 8 =
½ of 8 = 4
½ of 4 = 2
Therefore ¼ of 8 = 2
-Recognise, find, name and write fractions ⅓, ¼, ²⁄₄, ¾ of a length, shape, set of objects or
quantity
-Write simple fractions eg ½ of 6 = 3 and recognise the equivalence of two quarters and one half
Shape
½ of 12 = Shade in half of the grid
6 parts of the grid are shaded, so ½ of 12 = 6
Quantity
¼ of 12: Divide by denominator. So 12 ÷ 4 = 3
Use a fraction wall to show the equivalence of two quarters and one half
1 Whole
Y2
½
¼
Length
Use string, fold in half to find half and again to find quarter
Partition number. Eg ½ of 48cm
Half of 40 = 20
Half of 8 = 4
20 + 4 = 24cm
Chn can find ¼ and use repeated addition to find 2 , 3 and 4
4
4
4
½
¼
¼
¼
-Count up and down in tenths; recognise
that tenths arise from dividing an object
into 10 equal parts and in dividing onedigit numbers or quantities by 10
U
Y3
1
DP
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Tnths
1
2
3
4
-Recognise, find and
write fractions of a
discrete set of objects:
unit fractions and nonunit fractions with small
denominators
-Recognise and use
fractions as
numbers: unit
fractions and nonunit fractions with
small denominators
-Recognise and show, using diagrams, equivalent fractions with small
denominators
See Y2 quantity
¼ of 12
Shade in ¼
Shade in ½
Divide by the D
Multiply by the N
-Add and subtract
fractions with the same
denominator within one
whole (eg ⅗ + ⅕ = ⅘)
-Compare and
order unit
fractions with the
same denominator
Add N’s together
1 + 2
As D is the same,
chn need to look
at N only and
order depending
on size.
4
4
1+2=3
See Y5 smaller equivalent fractions
Leave denominator as it
is. Therefore
4
3
6
4
7
8
9
1.0 ÷ 10 = 0.1
Relate to money: £ and p
£1.10 = 1 and 1
= 110p
10
Do the same for
subtraction but take
away N’s instead, leaving
the D as it is!
2
3 4
4
4 4
-Solve problems
that involve all
of the above
-
-
-
-
Recognise and sf how, using diagrams,
families of common equivalent fractions
Count up and down in hundredths; recognise
that hundredths arise when dividing an object
by a hundred and dividing tenths by ten
Recognise and write decimal
equivalents to ¼, ½, ¾
Recognise and write decimal
equivalents of any number of
tenths or hundredths
1 =
=
2
x5
x5
5
10
1 is shaded
10
Y4
5 is shaded
10
Ensure pupils are shown a wide range of
shapes and visual ways to represent
fractions
U
DP
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Tenths
0
Hundredths
1
0
2
0
0
3
4
0
5
0
6
0
7
0
8
0
9
1
0
N ÷ D will give you fraction
to decimal
DP
1
4
1.00 ÷ 4 = 0.25
.
.
.
Tnths
7
Hths
Tenths
7
7
Thths
Adding Subtracting decimals to
1/100
0.02 + 3. 5 =
¼ of 8 =
¾ of 8 =
1
Hundredths
1
7
Thousandth
1.0 ÷ 100= 0.01
Relate to money: £ and p
£1.01 = 1 and 1
= 110p
100
Fractions of
quantities
Therefore 0.7 = 7 tenths
= 7
10
If you have a digit in the
100th column that is not a 0
then it represents 100ths
e.g.
in
0.71,
the
7
represents tenths and the
1 represents hundredths
Mixed Numbers
13 / 15 + 9 / 15 =
Adding and
subtracting
fractions, where
the denominator
is the same
-Solve simple
measure and
money problems
involving
fractions/decima
-Solve problems
involving
increasingly
harder fractions
to calculate
quantities, and
fractions to
divide quantities,
including non-unit
fractions where
the answer is a
whole number
Finding a
fraction of a
number
÷ by D
X answer by N
5
7
+ 2
7
3 12
1
12
2
8
of 72
72 ÷ 8 = 9
9 X 2 = 18
Therefore
2
of 72 = 18
8
-Read and write decimal numbers as
fractions [eg 0.71 = 71/100]
Recognise the value of the digits: tenths,
hundredths or thousandths
Place over appropriate denominator [D
for down, D being the bottom of the
fraction]
DP
.
.
.
Tnths
7
Hths
Tenths
7
7
Thths
N
Numerator
D
Denominator
3X½
Multiply whole number by numerator
3X1=3
Leave denominator as it is = 2
3
Therefore ____
2
1
Hundredths
1
-Multiply proper fractions and mixed numbers
by whole numbers, supported by materials and
diagrams
7
Thousandth
7 tenths therefore 7/10
71 hundredths therefore 71/100
717 thousandths therefore 717/10002
7X4¼
Multiply the two whole numbers
7 X 4 = 28
Multiply whole number by numerator
7X¼= #
7
=
4
Therefore 28
Y5
1¾
+ 1 ¾ = 29 ¾
-Identify, name and write
equivalent fractions of a given
fraction, represented visually,
including tenths and hundredths
‘Fairs Fair’: whatever you do to
D you must do to N
Smaller equivalent fractions
Find a number you could divide
both the N and D of the fraction
by.
8
____
80
÷ by 8
÷ by 8
1
Therefore
10
Larger equivalent fractions
Multiply both the N and D by the
same number
X by 2
6
____
18
X by 2
-Recognise mixed numbers and
improper fractions and convert
from one form to the other and
write mathematical statements >1
as a mixed number [eg ⅖ + ⅘ =
1⅕]
-Add and subtract
fractions
If both denominators in
the fraction are the
same:
-Compare and
order fractions
whose
denominators are
all multiples of the
same number
Improper fraction to mixed
number
Add N’s together
Find LCD
12
____
8
0 1 r4
8 1 12
12 ÷ 8 = 1 r 4
The remainder is recorded as a
fraction
4
Therefore 1 ___
8
Mixed number to improper
fraction
4
5 ___
2/5 of 25
8
Multiply whole number by D
5 X 8 = 40
Add on your numerator
40 + 4 = 44
Leave denominator as it is
2/3 of 66
Therefore
Fractions of Quantities
1/5 of 20
Therefore
12
36
44
_____
8
1
2
____ + ____
4
4
1+2=3
Leave denominator as it
is
3
Therefore ____
4
If both denominators in
the fraction are
ifferent:
d
Find a LCD [lowest
common denominator: a
number that will appear
in both the D times
table]
1
2
____ + ____
4
8
LCD = 8
Leave a fraction alone if
it already has the LCD
X by 2
1
____
4
2
____
8
X by 2
‘Fairs fair’ whatever you
do to D you must do to N
Now add N
Therefore
2
4
2
____ + ____ = ____
8
8
8
‘Fairs fair’
whatever you do
to D you must do
to N
Once D is the
same for all
fractions, use the
value of the N to
compare and order
the size
Which is larger?
1
2
____ or ____
4
8
LCD = 8
Leave a fraction
alone if it already
has the LCD
X by 2
1
____
4
2
____
8
X by 2
‘Fairs fair’
whatever you do
to D you must do
to N
They are
therefore equal.
-Solve problems
which require
knowing
percentage and
decimal
equivalents of ½,
¼, ⅕, ⅖, ⅘ and
those fractions
with a
denominator of a
multiple of 10 or
25
-Associate a
fraction with
division to calculate
decimal fraction
equivalents (eg
0.375) for a simple
fraction [eg ⅜]
3
8
3÷8
0. 3 7 5
Y6
.30
Find LCD
‘Fairs fair’
whatever you do
to D you must do
to N
N÷D
8 3
-Compare and
order fractions,
including
fractions >1
6
0 40
Therefore
3
= 0.375
8
Once D is the
same for all
fractions, use the
value of the N to
compare and
order the size
Which is larger?
1
2
____ or ____
4
8
LCD = 8
Leave a fraction
alone if it already
has the LCD
X by 2
1
____
4
2
___
8
X by 2
‘Fairs fair’
whatever you do
to D you must do
to N
They are
therefore equal.
-Multiply simple pairs of
proper fractions, writing
the answer in its simplest
form [eg ¼ x ½ = ⅛]
-Divide proper
fractions by whole
numbers [eg ⅓ ÷
2 = ⅙ ]
-Use common factors to simplify fractions; use common multiples to
express fractions in the same denomination ½ 4/8
NXN
Multiply the
denominator by
the whole number
To simplify: Find LCD = 4
DXD
2X3=6
Numerator stays
the same
¼x½
1X1=1
4X2=8
1
Therefore = 1
8
6
-Add and subtract fractions with different
denominators and mixed numbers, using the
concept of equivalent fractions
Fairs Fair! Whatever you do to D you must do to N
4
÷4
1
12
÷4
3
To express fraction in same denomination multiply both D and N by a
whole number
1
X4
4
2
X4
8
Add and subtract fractions with different
denominators and mixed numbers: See Y5
Add and subtract mixed numbers,
34
8
- 1
2
4
1.
Change both fractions into improper
fractions
2.
Make denominator the same by finding
LCD
3.
Simply add/subtract numerators and
denominators
4.
Change back to mixed fraction if
appropriate
-Recall and use
equivalences
between simple
fractions,
decimals and
percentages,
including in
different
contexts
F
1
_
10
D
0.1
%
10
F to D you do
N÷D
% to D you ÷10
D to % you X10
Chn must know
1
3
2
3
0.33 33%
0.66 66%