Teaching percent, rates and ratio
percent, ratio and rates topic covered on the CD-ROM is fairly comprehensive
and provides a general sequential approach which could be used to
teach percent, ratio and rates mainly in the secondary classroom.
Children are introduced to the common language usage of percent in the early to middle years of primary. Around Years 3 to 4 they understand 100% as being a 'full thing' and 50% as a 'half. At this stage children may also be familiar with ratio terms such as '50 : 50' and understand that this conveys the idea of balance. They may also have meaning for 10 to 1, 100 to 1 and 2 to 1. Children would also have some knowledge of commonly used rates, such as 'kilometres per hour' - 'how fast are we going?' and 'cents per litre' - 'how much does petrol cost?', although they would not necessarily have an understanding how they are made up of two separate measurements.
In later primary school the precise notion of percent is developed. Children learn the simple relationship between some fractions and their percent equivalents, such as 1/2, 1/3, 1/4, 1/5, 1/8, 1/10.
this stage children should be able to find simple percentages where
the percent acts as an operator, such as 25% of .., 10% of .., 5%
of .., 75% of .. 250% of ..
They may break up the percents into more manageable pieces,
75% of 60 apples = 50% of 60 apples + 25% of 60 apples = 1/2 x 60 apples + 1/4 of 60 apples.
Another example, 250% of the current airfare is 2 1/2 times the current airfare.
Before calculators, percent problems were generally worked out using fractions. Today, however, they can also be readily worked out using decimals. The method you use depends on the numbers involved and personal preference.
For example, 75% of 60 apples = 0.75 x 60 apples = 45 apples
It is important that children see the link between the percent representation, the fraction representation and the decimal representation. By early secondary school, children should be able to work with all percents in decimal or fraction form.
Elastic tape measure model
We have included an example of the elastic tape measure model on this CD-ROM. This is a good linear model of percent which teachers can easily make and which can be adapted for a number of examples. For more information about this model, see Meaning and Models.
Dual-scale number line
We have used the dual-scale number line as an aid to organising information when solving percent problems throughout the topic on the CD-ROM. By showing the number scale and percent scale on the one number line and representing the information we are given and the information we need to find out, we can write a proportion equation directly from the number line. See the CD-ROM content for more description and movies on how we use this model.
In late primary school children should be introduced to ratio as a part : part relationship with activities such as making up cordial.
For example, one part cordial mixed with 4 parts of water makes 5 parts of normal strength drink.
Children need to appreciate that the size of the part chosen does not affect the strength of the drink.
Ratio is a major topic in secondary school. Difficulties arise when the numbers are not simple whole numbers. The difficulties are not only computational, but conceptual.
We use rates when we are measuring one quantity or amount in relation to another quantity or amount. Children will meet many rates in everyday life but they need to learn how the rate is related to the measurable quantities.
For example, children will have a feeling of speed but need to learn how it relates the distance covered to a given time.
The calculation of rates again relies on thorough understanding of multiplication and division and the use of decimals and fractions in calculation.
Percent, ratio and rates is conceptually a very difficult area, and given that it is a significant component of the secondary school curriculum up to Year 10, care must be taken to help children to consolidate their understanding. In many applications of the topic there are potentially many right and wrong ways to get the answer. Teachers need to be aware of the fact that there are a range of methods to solve most problems and need to have the flexibility to adapt these methods to suit each child's needs.
University of Melbourne