NA4-4: Apply simple linear proportions, including ordering fractions.

Elaboration on this Achievement Objective

This means students will solve problems involving linear proportions. “Linear proportion” is a term used to generalise situations that involve equivalent fractions. At Level Four students should be able to solve the following types of problems:

• Comparing the size of two fractions, by converting them to equivalent fractions with a common denominator, or with reference to benchmark fractions, for example 2/3 > 4/9 because 2/3 is greater than one half while 4/9 is less, or because 2/3 = 6/9.
• Finding equivalent ratios by either scaling up or down by a whole number multiplier, for example 2:5 is the same ratio as 8:20 (scaling up) or 12:18 is the same ratio as 2:3 (scaling down).
• Finding equivalent rates by either scaling up or down with the same measurement units, for example 18km in 15mins is the same speed as 72km in 60mins.
• Recognising when two “fraction of an amount” situations give equal or unequal answers, e.g 75% of \$12 is the same as 25% of \$36.
• Recognising when sharing division situations give equal or unequal shares, for example three pizzas shared between five people is a smaller share than two pizzas shared between three people.
• Finding how many measures of a fraction fit into one, for example A trip uses 2/5 of a tank of petrol. How many trips can be made on a full tank? (1 ÷ 2/5 = 5/2 = 2 1/2 ).