NA4-4: Apply simple linear proportions, including ordering fractions.
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 ).
apply linear proportions
order fractions using benchmarks
find equivalent fractions
solve problems involving simple proportions
find equivalent fractions
find a fraction of a whole number
- Calculate measurements for simple scale models.
- Determine measures of height indirectly.
- Apply ratio knowledge to a measurement context.
- Make reasonable estimates of the height and length of a building.
- Measure length accurately to produce simple scale models.
convert fractions to decimals
- Simplify fractions using a range of strategies
- Deciding whether or not it is between to simplify or convert to a mixed number first
- Find unknowns in box equations
use place value knowledge and addition and subtraction to solve problems (Problems 1 and 2)
use simple proportions to solve problems (Problems 3 and 4)
solve multiplication problems
find fractions of a number
use simple proportions to solve problems
compare proportions
use multiplication to solve simple rate problems
order fractions
mark a fraction on a length
investigate proportions on a double number line
solve problems involving simple proportions
solve multiplication problems
Find equivalent fractions and order fractions.
use ratios to solve problems (Problem 1)
use diagrams to find and continue a sequential pattern (Problems 2 and 3)
use a tree diagram to find outcomes (Problem 4)
use linear proportions to solve problems
find outcomes using diagrams (Problem 1)
solve problems involving simple proportions (Problem 2 and 3)
apply simple proportions