Conceptual Obstacles with Numbers Less Than 1 - Progression Points

Dimension

Level

Progression Point

Number

2.0 Standard

... 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.

2.75

• Representation of multiplication as a rectangular array and as the area of a rectangle

3.25

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

3.75

• Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)

4.0 Standard

... Students add, subtract and multiply fractions and decimals (to two decimal places) …

4.25

• Use of index notation to represent repeated multiplication
• Division of fractions using multiplication by the inverse

4.75

• Addition, multiplication and division of integers