Numerical Solutions of equations
The activities in this list of resources is designed to enable students explore strategies to find approximate solutions to equations using the numerical method of iteration.
Visit the secondary mathematics webpage to access all lists.
Average Limits
Average Limits is an investigation in which students explore limiting values of an iterative process, using arithmetic, algebra or spreadsheets. Students move from identifying patterns to forming, verifying and proving conjectures.
This resource can also be used to develop the key processes of moving from generation of a few results to systematic exploration of the relationship between starting numbers and limit, working systematically and controlling variables to identify patterns leading to generalisations. Students also have the opportunity to explore and verify generalisations about the limit with a view to expressing patterns algebraically, justifying their results and generalisations and explaining the approach taken, thus describing the outcomes and conclusions.
Resources include students’ stimulus sheet and spreadsheet, teachers’ notes which include suggestions for teaching strategies support and extension and probing questions and feedback. There is also included a progression table supported by examples of pupils work at different levels.
Focus Year 10/11 Algebra Extension
This book focuses on using calculators, spreadsheets and graphs to solve equations and explore the behaviour of functions. There is significant development of the use of algebra but this is spread in small sections amongst different units.
Chapter 7 is concentrates upon iterations using a scientific calculator or spreadsheet, graphing an iteration, convergence and divergence; more on factorising quadratics, and algebraic fractions.
Fractals
This National Strategies Study Plus unit has been designed to cover a number of areas of mathematics, particularly work with number and algebra. It also addresses a range of learning styles along with links to literacy and ICT through the use of spreadsheets.
The unit on fractals explores the patterns and sequences generated from the perimeters and areas of the von Koch Snowflake. The unit includes work on adding and multiplying fractions. The iterative sequence for the areas involves proportional change and students are guided towards using multiplicative relationships with a single multiplier. This work is then extended into looking at other sequences, functions and graphs. It meets the criteria of a rich task that encourages easy access and high exit. The resource includes all pupil resources as well as teachers notes. The notes provide guidance on how it fits into the curriculum as well as teaching strategies and probing questions to support and challenge learners.
Numerical Methods
This Virtual Textbook resource contains two excel programs with interactive spreadsheets dealing with linear inequalities in one or two variables.
Trial and Improvement
This excel workbook starts with finding square roots then cube roots by trial and improvement. Similar methods are used to solve problems related to areas and volumes. The workbook contains a further four printable worksheets providing further questions for use in the classroom.
Iterative Solutions of Quadratic Equations
This interactive spreadsheet shows calculations and graphs for the iterative method of solving quadratic equations. The graphs can show the stages of the iterations for both of the solutions. There is also a sheet of questions which may be suitable for use in the classroom.
