Physical World Sequences
'Sequences, graphs and equations allow you to predict what will happen and hence influence the world around you'
Anything that can be measured can be analysed using sequences. In this activity you have 5 sets of cards: (1) 'Physical World' things that can be measured, (2) number relations, (3) equations, (4) graphs and (5) formulae for generating each set of numbers (nth term rule). In groups or pairs you are going to decide which cards go together.
Almost everything can be measured and represented using numbers (even colours !). We can then use mathematics to analyse these numbers to see if there is a pattern. If we find a pattern, then it should help us to predict, and therefore influence/control, and discover what the relationship is between different factors e.g. CO2 emissions and global temperatures.
Matching cards - do the cards below go together? If not, why not?
This Physical World Sequences file can be used directly, with matching cards copied and pasted onto a new slide and then shared with other groups via the school's network. Alternatively, these slides can be printed off and cut out for groups to match as they see fit (cards can be laminated if prepared prior to the lesson).
A slight extension on the same activity is provided here that focuses further on function notation and range: Representing the Physical Universe
Teachers can read these notes which provide further information and what one might expect from students on this task Physical World Sequences.
- Match each graph with its corresponding equation, number relation, nth term rule and 'Physical World' statement.
- Make sure you have a reason why the equation matches the graph, the graph the sequence, the sequence the nth term rule etc.
- Students could use TiNspire, Geogebra, Autograph or any other graphing software to check their work, see the Matching Sequences activity for more information and technical help with how to do this. Students could try the Freundenthal Institute's virtual manipulative (only for the sequences where the 'n' terms increase by 1 each time) to check if their equation, graph and number relation are correct.