Flexible Addition and Subtraction - Progression Points

Number

1.0 Standard

… They use materials to model addition and subtraction of subtraction by the aggregation (grouping together) and disaggregation (moving apart) of objects. They add and subtract by counting forward and backward using the numbers from 0 to 20.

1.25

• counting forwards and backwards by 1 from starting points between 1 and 100
• calculation of the next number when asked to add 1 or 2 to any natural number from 0 to 10
• drawing of diagrams to show subtraction activities

1.5

• addition and subtraction of two-digit multiples of ten by counting on and counting back
• counting on from the larger of two collections to find their total
• use of the number properties (commutative and associative) of addition in mental computation, and recognition of complements to ten; for example, 3 + 4 + 7 + 6 = 3 + 7 + 4 + 6 = 10 + 10 = 20

2.0 Standard

… They add and subtract one- and two-digit numbers by counting on and counting back. They mentally compute simple addition and subtraction calculations involving one- or two-digit natural numbers, using number facts such as complement to 10, doubles and near doubles. 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).

2.5

• addition and subtraction of amounts of money including calculation of change from $10
• use of strategies such as ‘near doubles’, ‘adding 9’ and ‘build to next 10’ to solve addition and subtraction problems
• use of written methods for whole number problems of addition and subtraction involving numbers up to 99

3.0 Standard

… They estimate the results of computations and recognise whether these are likely to be over-estimates or under-estimates. They compute with numbers up to 30 using all four operations. They devise and use written methods for:

• whole number problems of addition and subtraction involving numbers up to 999

They devise and use algorithms for the addition and subtraction of numbers to two decimal places, including situations involving money. They add and subtract simple common fractions with the assistance of physical models.

4.0 Standard

Students explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers).

Structure

2.5

o        variation of order and grouping of addition (commutative and associative property) to facilitate computations; for example, 3 + 5 + 7 + 5 = 3 + 7 + 5 + 5 = 10 +10 = 20

3.0

They use number properties in combination to facilitate computations (for example, 7 + 10 + 13 = 10 + 7 + 13 = 10 + 20).

4.0

Students recognise that addition and subtraction…are inverse operations.