NA5-4: Use rates and ratios.

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Elaboration on this Achievement Objective

This means students will solve problems involving rates and ratios. In this curriculum rates are defined as a multiplicative relationship between different measures, for example, 24 litres per 60 minutes, while ratios are defined as a multiplicative relationship between identical measures, for example, 30 litres: 40 litres. This distinction is blurred where the measures are of the same attribute, for example, 10mL per 1 Litre, but problems involving unit conversion are delayed until Level Six. In terms of their behaviour problems involving both rates and ratios can be modelled by the equation a/b = c/d where one of the values, a, b, c, or d is unknown or as a situation where a/b and c/d must be compared. Rate and ratios can also be represented by ratio tables or double number lines. For example:

A wallpaper hanger mixes 300 grams of glue powder to every 4 litres of water. She wants to make up 25 litres of paste. How many grams of powder will she need?

ratios.

At Level Five students are expected to solve problems of this type in which the unknown can be in any of the four positions on the table and in which the scalar within (for example 4 x = 25) or between (for example 4 x = 300) operators are positive integers or fractions. Students should be able to use equivalent rates to compare two given rates and express the part-whole relationships in ratios as equivalent fractions to compare given ratios. For example, 3 litre orange: 5 litres apple has a stronger orange flavour than 4:6 because the part-whole fractions are 3/8 and 4/10 respectively which have equivalent forms of 15/40 and 16/40.

Teaching resources for this Achievement Objective

Ancient Architecture

Level Five

Integrated

Figure It Out activities

This is a level 5 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.

A neutral solution

Level Five

Number and Algebra

This unit provides an opportunity for students to explore an integrated mathematics and science context: chemical reactions involving acids and bases. Within this, students develop their use of rates and ratios through exploration of linear relationships using tables and graphs. Students also...

Animal Antics

Level Five

Number and Algebra

Figure It Out activities

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

A Sizeable Problem

Level Five

Number and Algebra

Figure It Out activities

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

Astronomical Proportions

Level Five

Number and Algebra

Figure It Out activities

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

Body Ratios

Level Five

Number and Algebra

Secondary activities

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

Cereal Calculations

Level Five

Number and Algebra

Figure It Out activities

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

Chocolate choices

Level Five

Number and Algebra

Figure It Out activities

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

Circuit Problems

Level Five

Number and Algebra

The purpose of this unit is to engage students in applying their understanding of algebra to solve problems within the science - physical world context of electrical circuits. Subsequently, students develop their skills and knowledge on the following mathematics learning progression: Using Symbols...

Coast to Coast

Level Five

Number and Algebra

Figure It Out activities

This is a level 5 number activity from the Figure It Out theme series. A PDF of the student activity is included.

Combining Proportions

Level Five

Number and Algebra

Numeracy activities

Comparing by Finding Rates

Level Five

Number and Algebra

Numeracy activities

Cuisenaire Rod Fractions: Level 5

Level Five

Number and Algebra

Units of Work

This unit explores how the properties, that hold for multiplication and division of whole numbers, also apply to fractions (commutative, associative, distributive, and inverse). The operations of multiplication and division can be developed using a length model (Cuisenaire rods). While the size of...

da Vinci's Ratio

Level Five

Number and Algebra

Figure It Out activities

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

Deb the Driver

Level Five

Number and Algebra

Figure It Out activities

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

Dog Torque

Level Five

Number and Algebra

Figure It Out activities

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

Doing Time

Level Three

Level Four

Level Five

Integrated

Secondary activities

In this activity students will explore activities relating to time.

Dreaming of Millions

Level Five

Number and Algebra

Figure It Out activities

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

Drink Stall

Level Five

Number and Algebra

Figure It Out activities

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

Energy Levels

Level Five

Number and Algebra

Figure It Out activities

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

Extending Hotshots

Level Five

Number and Algebra

Numeracy activities

Extending Mixing Colours

Level Five

Number and Algebra

Numeracy activities

Fair Exchanges

Level Five

Number and Algebra

Figure It Out activities

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

Fat in Foods

Level Five

Integrated

Figure It Out activities

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. A PDF of the student activity is included.

Feel the Beat

Level Five

Number and Algebra

Figure It Out activities

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