Quadratic sequences rich tasks

At least a lesson’s worth of activities on the theme of quadratic sequences.

Designed to come after pupils have learnt the basics (how to use and find an nth term rule of a quadratic sequence). Gives pupils a chance to create their own examples and think mathematically.

There are four activities included:

Activity 1 - given sets of four numbers, pupils have to order them so that they form quadratic sequences. Designed to deepen pupils understanding that the terms in a quadratic sequences don’t necessarily always go up or down.

Activities 2 and 3 - on the same theme of looking at the sequences you get when you pick and order three numbers of choice. Can you always create a quadratic sequence in this way? What if you had four numbers? Could be used to link to quadratic functions.

Activity 4 - inverting the last activity, can pupils find possible values for the first three terms and a rule, given the fourth term? A chance for pupils to generate their own examples and possibly do some solving of equations in more than one variable.

Where applicable, worked answers provided.