Download Progression in Teaching and Learning Multiplying and Dividing

Progression in Teaching and Learning Multiplying and Dividing Fractions
Multiplying Fractions
Year Group and Notes
Written Calculations
Models and Images
Mental Calculations for
Known Facts for fluency
Reasoning and Problem Solving
fluency
Year 5/6
-multiply proper fractions and
mixed numbers by whole
numbers.
- solve problems which require
knowing percentage and
decimal equivalents of:
1 1 1 2 4
, , , ,
2 4 5 5 5
- connect multiplication by a
fraction to using fractions as
operators.
- use common factors to
simplify fractions; use common
multiples to express fractions in
the same denomination.
- multiply simple pairs of proper
fractions, writing the answer in
its simplest form
1
[for example, ¼ x ½ = 8 ]
Fraction x Whole Number
8
5 x
=
10
Convert whole number into a
fraction:
- recognise fractions as operators
(fractions of), as numbers, and as equal
parts of objects, for example as parts
of a rectangle.
5 8
x
=
1 10
The red rectangle is ½ of the whole
Multiply denominators and
numerators respectively
5 8
40
4
x
=
simplify = 4
1
1 10 10
50
0
100
50 is half of 100
Fraction x Fraction
3
4
x
2
5
=
Multiply the numerators:
3
4
x
2
5
=
6
Multiply the denominators:
3
4
2
x
5
6
=
20
- Work backwards from a unit fraction
to find the value of a whole. E.g.
¼ of the area of a rectangle is 16cm2
then the whole is 16 x 4 = 64cm2
Rectangle Model:
1
4
x
1
1
=
2
8
4
7
x
6
24
=
8
56
Simplify the answer:
6
3
=
20 10
Rectangle Model
Use the rectangle model to visualise
multiplying fractions.
- Practise calculations with simple
fractions and decimal fraction
equivalents to aid fluency,
-List equivalent fractions to
identify fractions with common
denominators.
- Quickly calculate simple fractions
of amounts,
E.g. ½ of 120, ¼ of 60, ¾ of 200
- recognise multiplication of
amounts by a number <1will
make the amount smaller.
- recognise that multiplication
of amounts by number >1 but
<2 will increase the amount,
but by less than double.
- times tables facts enable
quick understanding of finding
common factors allowing
pupils to simplify fractions.
Nrich
Rising Stars:
Year 4 – Would You Rather?
Year 4 – Fraction Strips
Year 5 – Tricky Triangles
Year 5 - Equivalence
Year 6 – Monsters
Year 6 – Raspberry Cupcakes
Reasoning (NCETM)
Dividing Fractions
Year Group and Notes
Written Calculations
Models and Images
Mental Calculations for
Known Facts for fluency
Reasoning and Problem Solving
fluency
Year 5/6
- divide proper fractions by
whole numbers
1
1
E.g. ÷ 2 =
3
6
- associate a fraction with
division and calculate decimal
fraction equivalents
E.g.
3
0.375 for a simple fraction
8
- Divide simple fractions
2
2
1 8
E.g. ÷ 4 = 3 or 2
3
3
Fraction ÷ Fraction
2
1
÷
=
4
6
- Transform the divisor fraction into
its reciprocal, then multiply the
dividend fraction by the reciprocal.
2
4
8
x 1 = 6
6
Simplify if possible
8
4
1
=
or
6
3
3
1
Fraction ÷ Whole Number
- Convert the whole number into a
fraction first, then proceed as
normal.
Rectangle Model
Use the rectangle model to visualise
Dividing fractions.
Rectangle Model
÷ by whole numbers
1
1
÷ 2=
2
4
3
3
÷ 3 =
7
21
- Calculate multiples of numbers
- Adding numbers
- recognise dividing an amount
by a number > 1 will make
the amount smaller, while
dividing an amount by a
number <1 will make the
amount bigger.
Nrich
Rising Stars:
Year 4 – Fraction Strips
Year 4 – Would You Rather?
Year 5 – Equivalence
Year 5 – Tricky Triangles
Year 6 – Juice for School
Year 6 - Monsters
Year 6 – Raspberry Cupcakes
Year 6 – Pies or Lines?
Reasoning (NCETM)