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Level Five > Number and Algebra

# AO4: Use rates and ratios.

Children
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## Introducing Trig

In this unit students will explore the importance of triangles, particularly right angled triangles, in the real world. Students will use practical measuring skills and calculations to find a pattern linking the ratio of the sides of a triangle with the angles.
This unit may take longer than one week, but introducing trigonometry using scale diagrams and practical measuring tasks allows for improved understanding of the concepts and how they apply to real life situations.

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## Scale Factors for Areas and Volumes

This unit provides students with the opportunity to discover the effect of a change of length by a given factor on area and volume.

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## Ratios

In this unit we use the theme of drinks to develop an understanding of ratios. It is suitable for students working at Level 5 of the curriculum or Stage 8 of the Number Framework. The unit provides a sequence of demonstrations and questions to help guide students' learning. It includes activities that require students to convert between the metric units for capacity, and to use their knowledge of fraction, decimal and percentage conversions. Students use proportional thinking to explore, compare and combine ratios. The unit concludes with a session on rates (a subset of ratios).

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## Olympic Training

Form and solve linear equations

Use ratios

Devise and use problem solving strategies to explore situations mathematically (draw a diagram).

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## Cart Before The Horse

Use their mathematical knowledge to invent problems

Devise and use problem solving strategiesto explore situations mathematically.

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## Working Backwards

Use their mathematical knowledge to invent problems

Devise and use problem solving strategiesto explore situations mathematically.

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## Ratios

In this unit we use the theme of drinks to develop an understanding of ratios. It is suitable for students working at Level 5 of the curriculum or Stage 8 of the Number Framework. The unit provides a sequence of demonstrations and questions to help guide students' learning. It includes activities that require students to convert between the metric units for capacity, and to use their knowledge of fraction, decimal and percentage conversions. Students use proportional thinking to explore, compare and combine ratios. The unit concludes with a session on rates (a subset of ratios).

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## Playing with Money (From the New Zealand Point of View)

In this unit we look at exchange rates for five countries. We see (i) how much various New Zealand dollar amounts are worth in these other currencies; (ii) how to make a currency converter; (iii) how to approximate these conversions; (iv) how currencies’ values change; and (v) how to use the exchange rates to find foreign currency values in New Zealand dollars.

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## Playing with Money (From the Other Point of View)

In this unit we look at exchange rates for five countries. We see (i) how much various foreign currency amounts are worth in New Zealand dollars; (ii) how to make a currency converter; (iii) how to approximate these conversions; and (v) how to use the exchange rates to find foreign currency values in other foreign currencies.

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## Mixing Colours

Solve problems involving ratios.

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## Inverse Ratios

Solve problems involving ratios.

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## Ratios with Whole Numbers

Solve problems involving ratios.

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## Sharing in Ratios

Solve problems involving ratios.

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## Comparing by Finding Rates

Solve problems involving rates.

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## Combining Proportions

Solve problems involving ratios.

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## Extending Hotshots

Solve problems involving ratios.

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## Extending Mixing Colours

Solve problems involving ratios.

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## Rates of Change

Solve problems involving rates.

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## Tree-mendous Measuring

Solve problems involving ratios.

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## Mixing Colours

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

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## Body Ratios

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

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## Proportional Problems 1

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties and problem solving. They may also be useful as training problems for teachers. Some involve investigation. These can be written up formally an investigation write up (see Related Resouces) so may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity. Allow students time to problem solve and discuss solutions.

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## Seed packets

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

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## Ratios with Whole Numbers

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

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## Inverse Ratios

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

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## Ancient Architecture

This is a level 5 geometry strand activity from the Figure It Out series.

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## Plentiful Plankton

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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## Fat in Foods

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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## Television Views

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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## Hot Dogs

This is a level 5 measurement strand activity from the Figure It Out series. It also has an achievement objective from the Level 5 Number strategies and knowledge substrand.

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## Gumboot Games

This is a level 5 measurement strand activity from the Figure It Out series.

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## More Thinking

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Dreaming of Millions

This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Feel the Beat

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Animal Antics

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Lunchtime Mardi Gras

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Drink Stall

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Fair Exchanges

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Energy Levels

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Astronomical Proportions

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## No Space to Spare

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Locomotive Magic

These are level 4 and 5 number problems from the Figure It Out series.

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## Chocolate choices

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Cereal Calculations

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Painting by Numbers

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Pop Star Pics

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Tiring Teamwork

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## The Great Race

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Magnificent Models

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Planet Peewee

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Skilful Skaters

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Fruit Proportions

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Smart Sizes

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## The Right Mix

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Top Shoot

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Deb the Driver

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Dog Torque

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Flavoursome

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Just Right

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## Ratio Rip

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## A Sizeable Problem

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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## da Vinci's Ratio

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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