# 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 ).

## Mixing Paint and Other Problems

- Units of Work
- Number and Algebra
- Level Four

In this unit we look at ratio in the context of objects, physical space, geometric quantities and mixable things such as paint.

## Scaling Our School

- Units of Work
- Number and Algebra
- Level Four

In this unit we look at estimating the length and height of buildings at your school. We then compare these estimates with the actual heights or lengths. Students will then build scale models selecting appropriate scales using ratio to translate the "real" dimensions into the dimensions for the scale model.

## Equivalent Fractions

- Units of Work
- 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 use equivalent fractions to compare fractions.

## Equivalent Fractions

- Numeracy activities
- Number and Algebra
- Level Four

Find equivalent fractions and order fractions.

## Fractions

- Numeracy activities
- Number and Algebra
- Level Four

Find equivalent fractions and order fractions.

## The Same but Different

- Numeracy activities
- Number and Algebra
- Level Four

Find equivalent fractions and order fractions.

## Fraction Number Lines

- Numeracy activities
- Number and Algebra
- Level Four

Find equivalent fractions and order fractions.

## Simplifying fractions

- Secondary activities
- Number and Algebra
- Level Four

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

## Feeding pets

- Secondary activities
- Number and Algebra
- Level Four

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

## Flying-fish Soup

- 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.

## Fun with 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.

## Numbers on the Line

- 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.

## Marble Marvels

- Figure It Out activities
- Number and Algebra
- Level Four

A PDF of the student activity is included.

## Stretch and Grow

- 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.

## Bean Brains

- 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.

## Hot Shots

- 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.

## Sandwich Survey

- Figure It Out activities
- Number and Algebra
- Level Four

## Measuring Up

- Figure It Out activities
- Number and Algebra
- Level Four

## Large or Huge?

- Figure It Out activities
- Number and Algebra
- Level Four

## How Slow Can You Go?

- Figure It Out activities
- Number and Algebra
- Level Four

## Challenge Time

- Figure It Out activities
- Number and Algebra
- Level Four

## Choosing Fruit

- Figure It Out activities
- Number and Algebra
- Level Four

## Sporting Fractions

- Figure It Out activities
- Number and Algebra
- Level Four

## Boxed Bisuits

- 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.

## Kapa Haka Hāngi

- 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.

## Saving and Spending

- 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.

## Bargain Packs

- Figure It Out activities
- Number and Algebra
- Level Four

## Hypertufa Tiles

- Figure It Out activities
- Number and Algebra
- Level Four

## Pulley Power

- Figure It Out activities
- Number and Algebra
- Level Four

## What You See...

- Figure It Out activities
- Number and Algebra
- Level Four

## The Fish Hooks of Ngāke

- Figure It Out activities
- Number and Algebra
- Level Four

## Seeing Double

- Figure It Out activities
- Number and Algebra
- Level Four

## Unusual Rulers

- Figure It Out activities
- Number and Algebra
- Level Four

## Worm Wipe-out

- Figure It Out activities
- Number and Algebra
- Level Four

## Slip-sliding Away

- Figure It Out activities
- Number and Algebra
- Level Four

## Ewe Scan

- Figure It Out activities
- Number and Algebra
- Level Four

## Megabytes of Memory

- Figure It Out activities
- Number and Algebra
- Level Four

## Run like the Wind

- Figure It Out activities
- Number and Algebra
- Level Four

## Taking Turns

- Figure It Out activities
- Number and Algebra
- Level Four

## Enough Rice?

- Figure It Out activities
- Number and Algebra
- Level Four

## Close Ties

- Figure It Out activities
- Number and Algebra
- Level Four

## Fishy Fractions

- Figure It Out activities
- Number and Algebra
- Level Four

## Growing Avocados

- Figure It Out activities
- Number and Algebra
- Level Four

## Size-wise

- Figure It Out activities
- Number and Algebra
- Level Four

These are level 4 number problems from the Figure It Out series.

A PDF of the student activity is included.

## Ps for Ever

- Figure It Out activities
- Geometry and Measurement
- Level Four

These are level 4 measurement, number and algebra problems from the Figure It Out series.

A PDF of the student activity is included.

## Thirsty Work

- Figure It Out activities
- Number and Algebra
- Level Four

These are level 4 number, algebra and statistics problems from the Figure It Out series.

A PDF of the student activity is included.

## Finding a Way

- 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.

## Lining Up

- Figure It Out activities
- Number and Algebra
- Level Four

These are level 4 number and statistics problems from the Figure It Out series.

A PDF of the student activity is included.

## Filling the Gaps

- Figure It Out 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.

## Waste Not ...

- Figure It Out activities
- Statistics
- Level Three

These are level 3 probability and level 4 number problems from the Figure It Out series.

A PDF of the student activity is included.

## Munching Monachs

- Figure It Out activities
- Number and Algebra
- Level Four

A PDF of the student activity is included.

## Rolling Up!

- Figure It Out activities
- Number and Algebra
- Level Four

A PDF of the student activity is included.

## Speed Read

- Figure It Out activities
- Number and Algebra
- Level Four

## Small Business

- Figure It Out activities
- Number and Algebra
- Level Four

A PDF of the student activity is included.

## Demolition Dollars

- Figure It Out activities
- Number and Algebra
- Level Four

A PDF of the student activity is included.

## Fraction Line-up

- Figure It Out activities
- Number and Algebra
- Level Four

## Paper Partitions

- Figure It Out activities
- Number and Algebra
- Level Four

A PDF of the student activity is included.

## Guess the Mass

- Figure It Out activities
- Statistics
- Level Five

This is a level 5 statistics and level 4 number activity from the Figure It Out series.

A PDF of the student activity is included.

## Fraction circles

- Secondary activities
- Number and Algebra
- Level Three

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

## Food Energy

- Figure It Out activities
- Geometry and Measurement
- 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.

## Paralympic Power

- Figure It Out activities
- Number and Algebra
- Level Four

This is a level 4 activity from the Figure It Out series.

A PDF of the student activity is included.

## Share the Profit

- Rich learning activities
- Number and Algebra
- Level Four

The purpose of this activity is to engage students in solving a problem involving fractions and proportional reasoning.

## Running Rates

- Rich learning activities
- Number and Algebra
- Level Four

The purpose of this activity is to engage students in solving a problem involving fractions (time in hours, minutes and seconds) and decimals (distance in km) to find a rate.

## Pasta bundles

- Rich learning activities
- Number and Algebra
- Level Four

The purpose of this activity is to engage students in using volume/capacity calculations to solve a problem.

## Tennis costs

- Rich learning activities
- Number and Algebra
- Level Four

The purpose of this activity is to engage students in using arithmetic and pre-algebra techniques to solve a financial problem.

## Cats and bods

- Rich learning 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.

## A fair dip

- Rich learning activities
- Number and Algebra
- Level Four

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

## Find Your Hero Rating

- Rich learning 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.

## Cuisenaire Rod Fractions: Level 4

- Units of Work
- 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.