Drawing
of diagrams to show sharing of up to 20 items

Counting
by 2s, 5s and 10s from 0 to a given target.

Students describe and calculate simple
multiplication as repeated addition, such as
3 × 20
as 20 + 20 + 20; and division as sharing,
such as 60 shared between 3.
They use commutative and associative
properties of addition and multiplication in mental computation (for example,
40 + 20
= 20 + 40
and
30 + 20 + 10
can be done as
30 + 30.

Use of money as a model for grouping and
unpacking lots of 10s.
Use of written number sentences such as
60 ÷ 3 = 20 to summarise sharing (partition) and
‘how many?’ (quotition) processes

Automatic
recall of number facts from 2, 5
and 10 multiplication tables. (6 tens is 60)

Representation of multiplication as a rectangular
array and as the area of a rectangle
Use of fact families to solve division problems,
for example
3 × 20 = 60,
60 ÷ 3 = 20

Students compute with numbers up to 30
using all four operations.
They provide automatic recall of
multiplication facts up to 10 × 10.
They devise and use written methods for whole number problems of addition and subtraction involving numbers up to
999; multiplication by single digits (using recall of multiplication tables)
and multiples and powers of ten (for example,
5 × 100, 5 × 70 );
division by a singledigit divisor (based
on inverse relations in multiplication tables).

Appropriate selection and use of mental and
written algorithms to add, subtract, multiply and divide (by single digits)
natural numbers
Multiplication of fractions by fractions through
use of the rectangle area model diagrams.

Multiplication by increasing and decreasing by a
factor of two; for example,
60 × 1
= 30 × 2
= 15 × 4 and 20 x 3 = 10 x 6 = 5 x 12.
Recognition that multiplication can either
enlarge or reduce the magnitude of a number (multiplication by fractions or
decimals) 60 x 35 cents will be less than $60.
Use of inverse relationship between
multiplication and division to validate calculations

Students explain and use mental and written algorithms for the addition,
subtraction, multiplication and division of natural numbers (positive whole
numbers).
They add,
subtract and multiply fractions and decimals (to two decimal places).Therefore calculate total cost 60 x $1.35 = $81 with working out shown.
