There are many instances in every day life where students are confronted by compound measures. Speed, distance and time are met in mathematics and physics to calculate speeds using different units. This resource list is to support the teaching and learning of the use of compound units such as speed, flow rates, unit pricing and density to solve problems.
Visit the secondary mathematics webpage to access all lists.
Links and Resources
This video raises quick-fire starter questions. A question is posed for each topic, offering pause points while students discuss the question.
Boxes of Teabags is a starter about best buys. Two techniques are demonstrated, each of which can be used depending on the values provided. The first example shows how buying three small boxes of tea bags gives the same number of tea bags as one large box thus prices can be compared. The second example requires students to find the unit price in order to make a comparison.
Mobile Phone Tariffs: using graphs, a pay as you go tariff is compared to a monthly deal, plotting minutes against cost, to see which is the better option. This starter could be used as inspiration for looking at unusual rates such as the cost of calls per minute, the number of texts per day and the cost per text in different situations.
This resource covers the ideas of instantaneous speed and average speed, calculating speed, distance and time, problems involving mixed units, distance - time graphs and other compound measures.
The activities file contains the activity Speed to School in which students are required to collect information about how long it takes students to get to school and then calculate their average speed. Running Speeds asks students to analyse men’s running world records over different distances by calculating average speeds and then using the results to make predictions. Premiership Goal Rates asks students to explore the rates of goals per match and goals per match of different football teams.
The Shape, Space and Measures section of this text book contains Chapter 16 Compound Measures (page 135 of the pdf) which begins with a discussion of who ran the fastest and how speeds are calculated. This is a good opportunity to discuss what compound measures are, what they mean and why they are useful. The discussion continues to consider different compound measures such as grams per millilitre. The following section considers average speed, giving explanations, examples and exercises.
It is important that students feel confident when converting between units in order to compare rates. In the section entitled Different units, kilometres per hour and metres per second are compared and a number of practical tasks are described for students to undertake in order to explore the topic further.
It is useful to explore compound measures other than just speed. This resource is useful as it illustates a variety of different situations in which compound measures are used. The chapter Compound Measures (page 16 of the pdf) begins by considering the number of calories per serving given the number of calories per 100g. Other examples of rates include the number of litres of petrol per second that pass through the nozzle of a petrol pump and how long it takes to fill a bath with water. The final section explores the concept of density using multi-link cubes.