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A Guide to Advanced Number Patterns
Teaching Approach
The section number patterns is an incredibly important part of the current CAPS curriculum
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Learners should be taught how quadratic equations, factorizing and
simultaneous equations form part of this section
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The series begins by reviewing the basic knowledge that learners should know from
previous grades
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The first
lesson covers in depth all the knowledge that learners should have learnt in grade eleven
regarding linear or arithmetic number patterns as well as quadratic number patterns
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We begin with lesson two which
introduces learners to sigma notation and teaches learners how to use and work with this
very important notation
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Lessons 4, 5 and 6 focus on series where sigma
notation is covered in depth and the concepts of infinite series is introduced
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It is important to show learners the differences
so that they are not confused when using older resources such as study guides or past
papers
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So, when you preview the videos, think about how to introduce each lesson and
what follow up activities will be useful
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Video Summaries
Some videos have a ‘PAUSE’ moment, at which point the teacher or learner can choose to
pause the video and try to answer the question posed or calculate the answer to the problem
under discussion
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Mindset suggests a number of ways to use the video lessons
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Then ask learners to
watch a video related to the lesson and to complete the worksheet or questions, either in
groups or individually
 Worksheets and questions based on video lessons can be used as short assessments or
exercises
 Ask learners to watch a particular video lesson for homework (in the school library or on
the website, depending on how the material is available) as preparation for the next days
lesson; if desired, learners can be given specific questions to answer in preparation for
the next day’s lesson
1
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Learners are taught how to
identify arithmetic or linear sequences as well as quadratic sequences
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Using Sigma Notation
In this lesson we introduce the notation that denotes summation
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3
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Sigma notation is introduced and learners are
shown how to use this notation and more importantly how to interpret it
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Investigating Geometric Number Patterns
In this lesson the focus is on teaching learners what a geometric sequence is and how to
identify geometric or exponential number patterns
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5
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Sigma notation is once again used and learners are
shown how to use this notation and more importantly how to interpret it
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Infinite Geometric Series
In this lesson learners are guided through an investigation to help them understand the
concept of diverging and converging series
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Resource Material
Resource materials are a list of links available to teachers and learners to enhance their experience of
the subject matter
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1
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mathsisfun
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html

http://www
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gov
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aspx?fileticket=wZRXkSStB
0A%3D&tabid=621&mid=1735

http://m
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co
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cnxmlplus

http://www
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co
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htm

2
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youtube
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Arithmetic Series

http://mathworld
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com/Arit
hmeticSeries
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purplemath
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htm
http://www
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ac
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pdf
http://www
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ac
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pdf

4
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Geometric Series

http://www
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com/numb
erpatterns
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purplemath
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htm
https://people
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edu/james/
lecture/m116/sequences/geometri
c
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math
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edu/~vatter/te
aching/m8w10/m8l05
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This resource contains examples
and detailed solutions of linear
patterns and could be used by
learners who want more practice
or used by educators to develop
quick spot tests
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This website below could expose
learners to other patterns that
exist in the real world but are not
part of the curriculum
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This is a video clip note on how to
use sigma notation and how it
links to series
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This resource is best for
educators, it can be used to assist
educators when making notes for
their learners of for the educator
who wants to improve their
knowledge and understanding of
this exciting topic
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Theory notes that cover content
and practice examples that can
be used as a recap lesson
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Infinite Geometric Series

http://formulas
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com/mat
h/infinite-geometric-seriesformula
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ltcconline
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HTM
http://hotmath
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html

educators when making notes for
their learners of for the educator
who wants to improve their
knowledge and understanding of
this exciting topic
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Best used as a consolidation
lesson
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1 Determine the 15th term of the sequence: 5; 8; 11; …
1
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Calculate which term in the sequence is equal to

Question 2
2
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2 Calculate the value of
in the sequence
9; 3; 1; …
Question 3
The 1st term of an arithmetic sequence is 10 and the 6th term is 85
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Question 4
Evaluate

Question 5
Consider the pattern: 5; -2; -7;-10; …
5
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2 Determine an expression for the nth terms
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3 Show that the sequence will never have a term with a value less than -11
Question 6
A tunnel is built by digging 1km each day
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After how many days will the workers
have travelled a total of 1260km in the tunnel?
Question 7
The first term of an arithmetic sequence is 5 and the 6th term is ten times the 3rd term
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1 Calculate the common difference
7
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Question 8
The first three terms of a convergent geometric series are:
8
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2 Calculate the sum to infinity of the series

Task Answers
Question 1
1
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2

Question 2
2
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2

Question 3

Question 4

Question 5
5
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2

-11; -10

5
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1

7
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1

r

Therefore K = 3 as the ratio is half and will then converge

8
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This resource is licensed under a Attribution-Share Alike 2
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When using this
resource please attribute Mindset as indicated athttp://www
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co

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