Addition and Subtraction Algorithms - Progression Points

Dimension

Level

Progression Point

Number

2.5

• Addition and subtraction of amounts of money including calculation of change from $10

• Use of written methods for whole number problems of addition and subtraction involving numbers up to 99

2.75

• Use of algorithms for the addition and subtraction of numbers to two decimal places

3.0 Standard

… Students 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.

3.25

• Appropriate selection and use of mental and written algorithms to add, subtract, multiply and divide (by single digits) natural numbers

3.5

• Addition, subtraction and multiplication of fractions and decimals (to one decimal place) using approximations such as whole number estimates and technology to confirm accuracy.

4.0 Standard

… 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) and apply these operations in practical contexts, including the use of money.

They use estimates for computations and apply criteria to determine if estimates are reasonable or not.

4.5

• Use of calculations involving operations with mixed numbers

4.75

• Addition, multiplication and division of integers
• Representation of subtraction of integers through the use of a physical model, and of integer subtraction as an equivalent integer addition, and as the difference between integers

5.0 Standard

… Students use a range of strategies for approximating the results of computations, such as front-end estimation and rounding (for example, 925 ÷ 34 ≈ 900 ÷ 30 = 30).

They use efficient mental and/or written methods for arithmetic computation involving rational numbers, including division of integers by two-digit divisors.

5.5

• Computation involving natural numbers, integers, finite decimals and surds without the aid of technology, giving exact answers as applicable.

Structure

5.0 Standard

… Students apply the commutative, associative, and distributive properties in mental and written computation (for example, 24 × 60 can be calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10).