# 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

The purpose of this activity is to engage students in solving a financial problem using decimal arithmetic techniques.

Rich learning activities

Number and Algebra

Level Four

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

solve money problems involving proportions

Figure It Out activities

Number and Algebra

Level Four

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

find equivalent proportions

Figure It Out activities

Number and Algebra

Level Four

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.

find fractions of a whole number find equivalent fractions

Figure It Out activities

Number and Algebra

Level Four

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.

Rich learning activities

Number and Algebra

Level Four

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

Figure It Out activities

Number and Algebra

Level Four

use proportions to solve problems

Figure It Out activities

Number and Algebra

Level Four

compare fractions to 0, 1/2 and 1 benchmarks

Figure It Out activities

Number and Algebra

Level Four

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.

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 fractions...

Units of Work

Number and Algebra

Level Four

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.

calculate rates to solve problems

Figure It Out activities

Number and Algebra

Level Four

solve problems involving simple linear proportions

Figure It Out activities

Number and Algebra

Level Four

Find equivalent fractions and order fractions.

Numeracy activities

Number and Algebra

Level Four

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...

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.

Units of Work

Number and Algebra

Level Four

solve problems using simple proportions

Figure It Out activities

Number and Algebra

Level Four

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.

Rich learning activities

Number and Algebra

Level Four

These exercises and activities are for students to use independently of the teacher to practice number properties.

convert fractions to decimals convert fractions to equivalent fractions

Secondary activities

Number and Algebra

Level Four

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.

use proportions to solve problems (Problem 2) find patterns in a series of equations (Problem 3) solve problems using addition facts (Problem 4)

Figure It Out activities

Number and Algebra

Level Four

These are level 4 number, and geometry problems from the Figure It Out series. A PDF of the student activity is included.

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)

Figure It Out activities

Number and Algebra

Level Four

The purpose of this activity is to engage students in a practical investigation that leads to comparing fractions and/or decimals quantitatively.

Rich learning activities

Number and Algebra

Level Four

find a fraction between two fractions using equivalent fractions

Figure It Out activities

Number and Algebra

Level Four

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.

use doubles and simple proportions to solve problems

Figure It Out activities

Number and Algebra

Level Four

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.

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....

Figure It Out activities

Geometry and Measurement

Level Four

These exercises and activities are for students to use independently of the teacher to practice number properties.

Ordering unit fractions (exercises 1 and 2) Ordering non-unit fractions (exercises 3 to 5)

Secondary activities

Number and Algebra

Level Three

order fractions convert improper fractions to mixed fractions find equivalent fractions

Figure It Out activities

Number and Algebra

Level Four

Find equivalent fractions and order fractions.

Numeracy activities

Number and Algebra

Level Four