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 ).
Teaching resources for this Achievement Objective
Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a financial problem using decimal arithmetic techniques.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.
Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a problem involving the multiplicative strategies that form the basis of early algebraic investigation.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
Level Four
Number and Algebra
Units of Work
This unit introduces the fact that fractions come from equi-partitioning of one whole. So the size of a given length can only be determined with reference to one. Usually the one must be defined in context.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.A PDF of the student activity is included.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.
Level Four
Number and Algebra
Numeracy activities
Level Four
Number and Algebra
Units of Work
In this unit we are exploring ways to find equivalent fractions. We use the concept of equivalent fractions to convert fractions to the benchmark fractions of halves, quarters, thirds, fifths and tenths. From these benchmark fractions it is easier to convert fractions to decimals and percentages. We...
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is for students to apply equivalent fractions and fractions as operators. The context is about maintaining proportionality of features on a face with reference to the total length of the face.
Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practice number properties.
Level Three
Level Four
Number and Algebra
Figure It Out activities
These are level 3 number problems and level 4 number and algebra problems from the Figure It Out series.A PDF of the student activity is included.
Level Four
Integrated
Figure It Out activities
These are level 4 number, and geometry problems from the Figure It Out series.A PDF of the student activity is included.
Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in a practical investigation that leads to comparing fractions and/or decimals quantitatively.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.A PDF of the student activity is included.
Level Four
Integrated
Figure It Out activities
This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.A PDF of the student activity is included.
Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practice number properties.
Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
Level Four
Number and Algebra
Numeracy activities