NA4-4: Apply simple linear proportions, including ordering fractions.

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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

Across Lake Taupō

Level Four

Integrated

Rich learning activities

The purpose of this activity is to engage students in using multiplicative and/or additive strategies to solve a measurement problem.

A fair dip

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.

Applying multiplication and division to rates

Level Four

Number and Algebra

The purpose of this activity is to support students in finding the multiplicative ‘operator’ that connects the numbers in two rates to find an unknown value. The operator may apply within measures or between measures strategies.

Bargain Packs

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.

Bean Brains

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.

Boxed Bisuits

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.

Cats and bods

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.

Challenge Time

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.

Choosing Fruit

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.

Close Ties

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.

Comparing ratios

Level Four

Number and Algebra

The purpose of this activity is to support students in comparing ratios that do not have a common part or whole. They do so by using their knowledge of fractions, and by expressing the part-whole relationships as fractions.

Comparing ratios with a common part

Level Four

Number and Algebra

The purpose of this activity is to support students in comparing ratios with a common part but different whole. They do so by creating and comparing fractions.

Cuisenaire Rod Fractions: Level 4

Level Four

Number and Algebra

Units of Work

This unit introduces the fact that fractions come from equi-partitioning of one whole. Therefore, the size of a given length can only be determined with reference to the size of one whole. Usually the one must be defined in context.

Demolition Dollars

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.

Enough Rice?

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.

Equivalent Fractions

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...

Equivalent Fractions

Level Four

Number and Algebra

Numeracy activities

Ewe Scan

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.

Face fractions

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.

Feeding pets

Level Four

Number and Algebra

Secondary activities

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

Filling the Gaps

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.

Finding a Way

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.

Finding unit rates

Level Four

Number and Algebra

The purpose of this activity is to support students in finding the unit rate in context. Students come to know the meaning of “per” as "for every", whilst connecting the concept of rate with everyday contexts.

Find Your Hero Rating

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.

Fishy Fractions

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.