NA5-4: Use rates and ratios.
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?
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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
This is a level 5 geometry strand activity from the Figure It Out series. A PDF of the student activity is included.
investigate ratios when enlarging
Figure It Out activities
Geometry and Measurement
Level Five
This unit integrates student learning in the mathematics and science learning areas. Students will be developing their use of rates and ratios, exploring linear relationships using tables and graphs, in the context of chemical reactions involving acids and bases. SI units of measure are used to...
Students develop their skills and knowledge on the mathematics learning progressions; Multiplicative Thinking, and Patterns and Relationships, in the context of science, understanding the material world; investigating the chemical properties of acids and bases.
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
sovle problems involving rates and ratios
Figure It Out activities
Number and Algebra
Level Five
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.
solve inverse ratio problems
Figure It Out activities
Number and Algebra
Level Five
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.
solve problems involving ratios use rounding to solve proportion problems
Figure It Out activities
Number and Algebra
Level Five
This is a level 4 number, algebra, statistics activity and level 5 number activity from the Figure It Out series. It relates to Stage 7 and 8 of the Number Framework. A PDF of the student activity is included.
use addition to sovle money problems use multiplication and division to solve problems find percentage of a number solve problems involving ratios find fraction of a number
Figure It Out activities
Number and Algebra
Level Four
These exercises and activities are for students to use independently of the teacher to practice number properties.
write a ratio use ratios to solve problems
Secondary activities
Number and Algebra
Level Five
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.
use ratio information to calculate amounts
Figure It Out activities
Number and Algebra
Level Five
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.
solve ratio problems compare ratios
Figure It Out activities
Number and Algebra
Level Five
The purpose of this unit is to engage the student in applying their knowledge and skills of algebra to solve problems within the context of electrical circuits.
Students develop their skills and knowledge on the mathematics learning progression Using Symbols and Expressions to Think Mathematically, in the science learning area, the physical world.
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out theme series.
calculate the average speed (involving decimals) using speeds calculate distances and times
Figure It Out activities
Number and Algebra
Level Five
Solve problems involving ratios.
Numeracy activities
Number and Algebra
Level Five
Solve problems involving rates.
Numeracy activities
Number and Algebra
Level Five
This unit explores the fact that 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 are developed using a length model (Cuisenaire rods). While the size...
Name the fraction for a given Cuisenaire rod with reference to one (whole) and with reference to another rod. Fluently multiply two or more fractions. Divide a fraction by another fraction, including when the divisor is greater than the dividend.
Units of Work
Number and Algebra
Level Five
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.
convert ratios to decimals to make comparisons
Figure It Out activities
Number and Algebra
Level Five
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.
calculate rates of km/litre calculate rates of km/hour
Figure It Out activities
Number and Algebra
Level Five
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.
use proportions to solve seesaw weight distance- relationships
Figure It Out activities
Number and Algebra
Level Five
In this activity students will explore activities relating to time.
finding time before and after a given time writing times in different ways working with 12 and 24 hour clocks find fractions and decimals of an hour solve problems involving time zones
Secondary activities
Geometry and Measurement
Level Four
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
multiply and divide decimals solve currency exchange rate problems
Figure It Out activities
Number and Algebra
Level Five
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.
solve ratio problems using multiplication and division
Figure It Out activities
Number and Algebra
Level Five
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.
solve problems involving rates and ratios
Figure It Out activities
Number and Algebra
Level Five
Solve problems involving ratios.
Numeracy activities
Number and Algebra
Level Five
Solve problems involving ratios.
Numeracy activities
Number and Algebra
Level Five
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.
solve problems involving currency exhange rates
Figure It Out activities
Number and Algebra
Level Five
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.
solve problems using ratios and units of mass
Figure It Out activities
Geometry and Measurement
Level Five