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 ).
solve money problems involving proportions
find equivalent proportions
find fractions of a whole number
find equivalent fractions
use proportions to solve problems
compare fractions to 0, 1/2 and 1 benchmarks
- Name the fraction for a given Cuisenaire rod with reference to one (whole).
- Give the relationship between one Cuisenaire Rod and another, especially when one rod is a fraction of the other.
- Add and subtract fractions by expressing fractions as equivalents with the same denominator.
- Order fractions300
calculate rates to solve problems
solve problems involving simple linear proportions
Find equivalent fractions and order fractions.
- Explore and know equivalent fractions including halves, thirds, quarters, fifths, tenths and hundredths.
- Use equivalent fractions to convert fractions to decimals and percentages.
- Use equivalent fractions to order fractions with different denominators.
solve problems using simple proportions
- Convert fractions to decimals
- Convert fractions to equivalent fractions
use proportions to solve problems (Problem 2)
find patterns in a series of equations (Problem 3)
solve problems using addition facts (Problem 4)
use addition, multiplication and systematic approach to solve problems (Problem 1)
interpret distance and direction information on a road map (Problem 2)
find fractions of whole number to solve problems (Problem 3)
use simple ratios to solve problems (Problem 4)
find a fraction between two fractions using equivalent fractions