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.
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
use doubles and simple proportions to solve problems
- measure and record data on temperature change
- convert between temperature change and food energy units
- calculate the total energy needs and intake for sample menus, using food energy unit values
- investigate the relative proportions of energy provided by different foods in their diet.
Ordering unit fractions (exercises 1 and 2)
Ordering non-unit fractions (exercises 3 to 5)