Number and Algebra: Number strategies, Level 3
AO1: Use a range of additive and simple multiplicative strategies with whole
numbers, fractions, decimals, and percentages.
This means students will use a range of mental strategies based on partitioning and
combining to solve addition and subtraction problems with multi-digit whole numbers
and simple decimals (tenths). These strategies include, standard place value, e.g.
603 – 384 = 
as 60 – 38 tens less one (219), rounding and compensating,
e.g. 923 – 587 = as 923 – 600 + 13 = ,
and reversing (applying inverse), e.g. 923 – 587 = as 587 +
= 923. Students should also connect known multiplication facts to solve
multiplication and division problems, e.g.
13 x 6 = as 10 x 6 + 3 x 6 =
(distributive property), 14 x 9 = as 2 x (7 x 9) =
(associative property)
and 36 ÷ 9 =
using 4 x 9 = 36 (inverse). This multiplicative understanding allows students at Level Three to
find fractions of quantities, e.g. two-thirds of 24 as 24 ÷ 3 x 2 = 16, find simple equivalent fractions
related to doubling and halving, e.g. 3/4 = 6/8 , to add and subtract fractions with the same denominators, e.g. 3/4 + 3/4 = 6/4 = 1 2/4,
and to convert improper fractions to mixed numbers, e.g. 17/3 = 5 2/3. Students should know the decimals and percentage
conversions of simple fractions (halves, quarters, fifths, tenths) and use these to solve simple percentage of
amount problems, e.g. 50% is fifty out of one hundred. 50% is one half so 50% of 18 is 9 or five is half of ten so = 0.5 and = 0.5.
Level Three corresponds to the Advanced Additive stage of the number framework.
