# NA5-4: Use rates and ratios.

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?

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.

investigate ratios when enlarging

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.

sovle problems involving rates and ratios

solve inverse ratio problems

solve problems involving ratios

use rounding to solve proportion problems

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

write a ratio

use ratios to solve problems

use ratio information to calculate amounts

solve ratio problems

compare ratios

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.

calculate the average speed (involving decimals)

using speeds calculate distances and times

Solve problems involving ratios.

Solve problems involving rates.

- 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.

convert ratios to decimals to make comparisons

calculate rates of km/litre

calculate rates of km/hour

use proportions to solve seesaw weight distance- relationships

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

multiply and divide decimals

solve currency exchange rate problems

solve ratio problems using multiplication and division

solve problems involving rates and ratios

Solve problems involving ratios.

Solve problems involving ratios.

solve problems involving currency exhange rates

solve problems using ratios and units of mass