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KS4/KS5 maths convergence investigation

KS4/KS5 maths convergence investigation

This investigation (includes teacher notes and worksheets) is suited to very able KS4 groups and those in KS5 studying Maths. It covers the topics of convergence, subject of a formula and even can be expanded to iteration for more advanced learners. Pupils are given a starting value of a sequence, which they multiply by 3, add 10 to then and finally divide by 4 to generate the next term in the sequence. They then multiply this value by 3, add ten to it and divide by 4 to get the next term and so forth, generating the sequence in an iterative manner until the sequence converges. The goal of this investigation is to find a relationship between the initial starting value of the sequence and that which it converges to. This can be explained in a satisfying algebraic way using subject of the formula although pupils may offer other alternative explanations.
samcurran1
Algebra: Sequences Bundle (6 Lessons - perfect for GCSE / IGCSE)

Algebra: Sequences Bundle (6 Lessons - perfect for GCSE / IGCSE)

All lessons come with a starter, learning objectives, key words, plenty of teaching slides/examples, questions or worksheets with answers and plenary. This is part of a bigger bundle on sequences / series, that can be purchased with additional A-Level lessons. The bundle contains the following: 1. Introduction to Linear Sequences 2. Linear Sequences in Diagrams 3. Quadratic Sequences 4. Other Sequences and Problems 5. Fibonacci Sequence, Golden Ratio and Spiral (one of the reasons I become passionate about mathematics!!) 6. Arithmetic Sequences or Series NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thanks.
ajf43
Algebra: Sequences 7 - Sum of Arithmetic Series (A-level)

Algebra: Sequences 7 - Sum of Arithmetic Series (A-level)

This lesson builds on the previous lesson introducing arithmetic sequences and series. This lesson focuses on where and how to use the formula for finding the sum of a series. It does look at some more challenging questions and when to use one formula as opposed to another, i.e. looking at efficiency. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Algebra: Sequences 6 - Arithmetic Sequences or Series (+ worksheet)

Algebra: Sequences 6 - Arithmetic Sequences or Series (+ worksheet)

This is an excellent first lesson introducing arithmetic sequences and series and is now included material for the new GCSE syllabus as well as for C1 at A-Level. This is an essential lesson to build understanding and become familiar with notation before moving onto more challenging A-Level content. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Algebra: Sequences 5 - Fibonacci Sequence, Golden Number, Ratio & Golden Spiral (2 lessons)

Algebra: Sequences 5 - Fibonacci Sequence, Golden Number, Ratio & Golden Spiral (2 lessons)

This lesson / revelation was one of the cornerstones of why I became passionate personally with mathematics. I have used various slides from this PowerPoint to do maths assemblies as well. Pupils love this lesson and some of the slides are mind blowing. Love it !!! This builds on pupils understanding of sequences and does lend well to looking at series (different ways of writing rules or describing sequences). What I am saying is this lesson is brilliant in terms of adding the WOW factor as well as leading nicely into part 6 of the bundle/ series on sequences. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Algebra: Sequences 4 - Cubic, Exponential and Other Sequences / Problems

Algebra: Sequences 4 - Cubic, Exponential and Other Sequences / Problems

This is the fourth lesson in the series. It looks at other sequences that are not linear or quadratic. These are becoming increasingly popular in GCSE exams as it stretches pupils understanding and not just their ability to pass exams. It also includes other sequences problems that don't neatly fit into the previous lessons. This is one of my favourite lessons to teach, because there are so many different types of sequences and it does make you think. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Algebra: Sequences 3 - Quadratic Sequences (+ worksheet)

Algebra: Sequences 3 - Quadratic Sequences (+ worksheet)

This lesson is on quadratic sequences and goes through two methods to solve quadratic sequences. One method builds on their understanding of linear sequences as well, which is helpful. The other builds on their understanding of substitution and simultaneous equations. I teach both methods even though the majority of pupils will adopt the first method. I have found that giving pupils more understanding and methods, does pay dividend in the long run. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Algebra: Sequences 2 - Linear Sequences in Diagrams / Patterns (+ resources)

Algebra: Sequences 2 - Linear Sequences in Diagrams / Patterns (+ resources)

This lesson builds on an excellent first lesson on linear sequences to build in linear sequences within patterns/diagrams and more real life contexts around linear sequences. The goal here is to get pupils to build on their understanding from lesson one and to become more familiar with exam style questions. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43
Algebra: Sequences 1 - Introduction to Linear Sequences (+ resources)

Algebra: Sequences 1 - Introduction to Linear Sequences (+ resources)

This is an excellent first lesson introducing linear sequences. Starting off with looking at the term to term rule and then quickly building into looking at the position to term rule or the nth term rule. This is a tricky topic for pupils and so there are quite a few teaching slides/ examples explaining what it is and why it is important. It goes onto looking at using the rule to work out another term further along in the sequence. The lesson comes with a starter, learning objectives, key words, plenty of teaching slides/examples, questions with answers and plenary. This is part of a bigger bundle on sequences / series, which can either be purchased with or without the additional A-Level lessons. NOTE: Feel free to browse my shop for more excellent free and premium resources and as always please rate and feedback, thank you.
ajf43