Ratio and Proportion Questions - 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

• Use of ratios to describe relative sizes
• Multiplication of fractions by fractions through use of the rectangle area model (grid)

3.5

• Representation of simple ratios as percentages, fractions and decimals

3.75

• Recognition of equivalent rates expressed as percentages, fractions and decimals
• Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)

4.0 Standard

... Students use decimals, ratios and percentages to find equivalent representations of common fractions (for example, ³ / ₄ = ⁹ / ₁₂ = 0.75 = 75% = 3 : 4 = 6 : 8).

4.25

• Knowledge of decimal and percentage equivalents or ¹ / ₂ , ¹ / ₄ , ³ / ₄ , ¹ / ₃ , ² / ₃
• Expression of single digit decimals as fractions in simplest form and conversion between ratio, fraction, decimal and percentage forms
• Division of fractions using multiplication by the inverse

4.0 Standard

... Students know the decimal equivalents for the unit fractions ¹ / ₂ , ¹ / ₃ , ¹ / ₄ , ¹ / ₅ , ¹ / ₈ , ¹ / ₉ and find equivalent representations of fractions as decimals, ratios and percentages (for example, a subset: set ratio of 4:9 can be expressed equivalently as 4 / 9 = 0. 4 ≈ 44.44%).

Students understand ratio as both set: set comparison (for example, number of boys : number of girls) and subset: set comparison (for example, number of girls : number of students), and find integer proportions of these, including percentages (for example, the ratio number of girls: the number of boys is 2 : 3 = 4 : 6 = 40% : 60%).

5.25

• Solution of problems involving ratio and proportion

5.5

• Solution of proportion problems using real numbers