Partial Products in Multiplication - Progression Points

Dimension

Level

Progression Point

Number

3.0 Standard

… Students devise and use written methods for:

• multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten (for example, 5 × 100, 5 × 70 )

3.25

• Multiplication of fractions by fractions through use of the rectangle area model (grid)

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.

Structure

2.25

• Knowledge of the effect of multiplying by ten on the location of the decimal point in a number

2.75

• Use of distributive property in calculations; for example, 6 × 37
  = 6 × 30 + 6 × 7

3.0 Standard

… Students investigate sequences of decimal numbers generated using multiplication or division by 10.

They multiply using the distributive property of multiplication over addition (for example, 13 × 5 = (10 + 3) × 5 = 10 × 5 + 3 × 5).

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).