Drawing of diagrams to show sharing of
up to 20 items

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

.. Students skip count by 2s, 4s and 5s
from 0 to 100 starting from any natural number.
Students describe and calculate simple
multiplication as repeated addition, such as 3 × 5 = 5 + 5 + 5; and division
as sharing, such as 8 shared between 4.
They use commutative and associative
properties of addition and multiplication in mental computation (for example,
3 + 4 = 4 + 3 and 3 + 4 + 5 can be done as 7 + 5 or 3 + 9).

Use of
money as a model for grouping and unpacking lots of 10s
Use of
written number sentences such as 20 ÷ 4 = 5 to summarise sharing (partition)
and ‘how many?’ (quotition) processes

Automatic recall of number facts from
2, 5 and 10 multiplication tables

Representation
of multiplication as a rectangular array and as the area of a rectangle
Use of
fact families to solve division problems, for example 5 × 7 = 35, 35 ÷ 7 = 5

... 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 (grid)

Multiplication
by increasing and decreasing by a factor of two; for example, 24 × 16 = 48 ×
8 = 96 × 4 = 192 × 2 = 384 × 1 = 384
Recognition
that multiplication can either enlarge or reduce the magnitude of a number
(multiplication by fractions or decimals)
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) …
