Patterns and Sequences

Students learn how to recognise and describe a number and picture sequence using a term-to-term and position-to-term rule.  As learning progresses they find the nth term of a sequence and begin to plot sequences on a grid.

This unit takes place in Term 4 of Year 7 and is followed by Functions, Graphs and Equations.


Patterns and Sequences Lessons

 



Prerequisite Knowledge
  • Use simple formulae
  • Generate and describe linear number sequences
  • Express missing number problems algebraically
  • Find pairs of numbers that satisfy an equation with two unknowns

Key Concepts
  • A sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
  • A term is a number or diagram in a sequence.
  • A sequence can be described on a term-to-term basis or position to term.
  • A formula can be used to calculate the term of a sequence when given its position number.  n is often used to represent the position number for any term of the sequence.
  • Linear sequences will appear as straight lines when drawn as a graph.


Working mathematically

Develop fluency

  • Select and use appropriate calculation strategies to solve increasingly complex problems
  • Develop algebraic and graphical fluency, including understanding linear functions

Reason mathematically

  • Identify variables and express relations between variables algebraically and graphically

Solve problems

  • Begin to model situations mathematically and express the results using a range of formal mathematical representations
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Algebra

  • Substitute numerical values into formulae and expressions, including scientific formulae
  • Understand and use standard mathematical formulae
  • Recognise, sketch and produce graphs of linear functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
  • Generate terms of a sequence from either a term-to-term or a position-to-term rule
  • Recognise arithmetic sequences and find the nth term
  • Recognise geometric sequences and appreciate other sequences that arise.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]