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 ).
use doubles and simple proportions to solve problems
Students will:
- 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.
Stude300
- Ordering unit fractions (exercises 1 and 2)
- Ordering non-unit fractions (exercises 3 to 5)
order fractions
convert improper fractions to mixed fractions
find equivalent fractions
Find equivalent fractions and order fractions.
Find equivalent fractions and order fractions.
use fraction circles to find equivalent fractions
use linear proportions to solve problems
construct a line graph
describe the data
construct a box and whisker graph
find quartiles and median of data set
simplify a fraction
convert a fracion to a percentage
calculate speeds
solve problems involving linear proportions
solve proportion problems
simplify fractions
explore number puzzles using addition (Problem 1)
find outcomes by using diagrams (Problem 2)
find a fraction of a number
take measurements and find an approximate fraction
solve problems involving simple proportions
- Find relative numbers of objects, and the lengths of sides, with a given ratio.
- Find relevant fractions using given ratios.
- Find relevant rations using given fractions.
- Find ratios between three objects.
use multiplication to solve simple ratio problems
use double number lines to solve problems involving proportions
use paper folding to find equivalent fractions
investigate the relationship between area and perimeter (Problem 1)
solve problems involving proportions (Problem 2)
investigate a sequential pattern (Problem 3)
use multiplication and addition to solve money problems (Problem 4)