Starting on paper, this activity asks students to generate sequences using a 'first term' and 'common change' technique. Moving on to excel, students generate more sequences, and in doing so, become aware of both the power of excel as an investigative tool (and a a labour saver) and of the numerous possibilities that exist for different sequences. The aim is that by starting with the structure of the sequence, rather than the sequence itself, students get a feeling for how sequences are structured and what to sorts of things to look for when starting with a sequence. In the extension, students consider new possibilities involving two steps.
Why we like this activity ….
Using excel allows for much quicker investigation and as such encourages a focus on the relationship between structure and sequence. Students, particularly those new to using spreadsheets, are often amazed as the possibilities and power of the application become apparent. In the beginning there is the perception that the spreadsheet is doing the work, but that quickly shifts to the recognition that the spreadsheet is simply generating terms based on the programming students put in. The application and medium help to engage students and add a dimension to this stage of the topic of sequences.
How this activity can be used ….
We have used it with a lesson starter to be done on paper followed by an example or two done with the whole class - this has the advantage of allowing the teacher the chance to demonstrate some spreadsheet basics for everyones benefit. At this point the activity is most likely individual, with students comparing the results, depending on the availability of computers. The activity would probably sustain pairs. Variations are possible where students generate their own sequences and try to deduce from eachother the structures used.
What to expect when using this activity – from our experience
Students are quickly drawn to striking patterns and the teachers role at this point is careful questioning aimed at asking students to articulate the whats?, and whys? This is very approachable for new users to excel, but it is normal to expect technical questions. These often offer the opportunity to talk about the maths though - for example; when using the drag down feature, the effect is not always as desired at which point students can be asked to think about exactly what they have asked the program to do.
Extra Notes
There is a video demonstration of the first question for those who need some help with entering formulae in Excel.
Students need to know that on Excel multiple is "*" and divide is "/" and some discussion of the term "consecutive" may be needed.
