Learning Areas
Teaching Standards
General Description
The course covers every dot point from the new NSW Year 11 Mathematics Extension 1 syllabus, both old and new content. Please note that only Extension 1 content is covered, not Mathematics Advanced.
The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 127 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.
Part I covers ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (Part A) F1.1: Graphical relationships, two topics that can be taught without prerequisites from the Advanced course. Teachers of classes that include Extension and Advanced students may choose to start their Extension students with one of these topics.
New and existing content is explored in detail, including interesting and more efficient techniques that experienced teachers may not have seen before. Important points to be covered with students are noted, and the limits of the syllabus are discussed. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.
The course includes 127 recorded examples, with a 139 page course handout. There are also 127 optional practice questions matching the examples from the course, with fully worked solutions. A suggested scope and sequence for Year 11 Advanced and Extension 1 for combined classes is provided, plus a lesson by lesson breakdown of the Advanced, Extension 1 and Extension 2 courses for Year 11 and 12 to help you create your own scope and sequences.
Part II of the series will cover the remainder of ME-F1 Further Work with Functions plus ME-F2 Polynomials.
Part III of the series will cover ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities & ME-C1 Rates of Change.
Audience
Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.
Available Delivery Formats
Format Description
24/7 course access
IMPORTANT INFORMATION:
- If you have a TTA subscription or membership please ignore the pricing when enrolling. Rest assured if your school has a subscription you will not be charged and for Memberships, your invoice will be adjusted accordingly to reflect your discount.
- If you have no subscription or membership but you are interested in placing a bulk discounted order for a team of teachers see the ONLINE TEAM tab above.
- For more details on our Unlimited Online Subscription packages Click here .
- Money-Back Guarantee – If you complete less than 25% of an online course and aren’t impressed, simply visit tta.edu/go/refund to let us know what happened, and we will cancel your enrolment and provide a full refund.
Teaching Standards
2.1.2 Proficient Level – Content and teaching strategies of the teaching area
6.2.2 Proficient Level – Engage in professional learning and improve practice
Are you in NSW? If so, this is relevant for you
This course contributes to 5.0 professional development hours.
Occurrences
Sessions
Introduction
5 minutes
• Course Administration
• Introduction to the Mathematics Extension 1 In Depth Year 11 Series
• Introduction to Part I
Combinatorics
5 minutes
• Introduction to Combinatorics
• Syllabus
Combinatorics 1: Fundamental Counting Principle and Background Information
15 minutes
• Lesson 1 Overview
• Listing and Counting the Ways an Event can Occur
• Fundamental Counting Principle (multiplication principle)
• Factorial Notation
• Distinct or Identical?
• Choosing Between Methods
• Combinatorics 1 Quiz
Combinatorics Lesson 2 - Basic Permutations
25 minutes
• Lesson 2 Overview
• All items arranged in a line
• All items arranged in a line (identical ends)
• All items arranged in a line (some items identical)
• All items arranged around a circle
• All items arranged around a bangle
• All items arranged around a circle (some items identical) - outside syllabus
• Some items in a Line
• Some items in a Circle
• Combinatorics 2 Quiz
Combinatorics Lesson 3 - Permutations with Restrictions
20 minutes
• Lesson 3 Overview
• Some items must be together – Bubble Method
• Some items must be apart – Gap Method
• Groups of items must alternate
• Groups around a Circle
• Combinatorics 3 Quiz
Combinatorics Lesson 4 - Combinations
20 minutes
• Lesson 4 Overview
• Combinations
• Groups
• Stars and Bars
• Combinatorics 4 Quiz
Combinatorics Lesson 5 - Harder Permutations
20 minutes
• Lesson 5 Overview
• Mixing Permutations and Combinations
• Arranging some items in a line with some identical
• Ascending/ Alphabetical order
• Combinatorics 5 Quiz
Combinatorics Lesson 6 - Probability
20 minutes
• Lesson 6 Overview
• Probability Theory
• Probability with Combinatorics
• Combinatorics 6 Quiz
Combinatorics Lesson 7 - Pigeonhole Principle
30 minutes
• Lesson 7 Overview
• Pigeonhole Principle
• Pigeonhole Principle – Generalised Form
• Combinatorics 7 Quiz
Combinatorics Lesson 8 - Binomial Expansion and Pascal's Triangle
30 minutes
• Lesson 8 Overview
• Binomial Expansions for small numbers
• Pascal’s Triangle
• Patterns in Pascal’s Triangle
• Relationships in Pascal’s Triangle
• Binomial Theorem
• Combinatorics 8 Quiz
Combinatorics 9 (Optional): Beyond the Syllabus
35 minutes
• Lesson 9 Overview
• Numbering Faces on 3D solids
• Negative Conditions
• Derangements
• Paths on a grid
• Triangles formed between points
• Diagonals of a convex polygon
• Probability that an event first occurs on the kth trial
• Miscellaneous
Graphical Relationships
5 minutes
• Introduction to Graphical Relationships
• Vertical versus Horizontal Changes
• Syllabus
Graphical Relationships 1: Reciprocal Functions
15 minutes
• Lesson 1 Overview
• Reciprocal of a Function
• Graphical Relationships 1 Quiz
Graphical Relationships 2: Square Roots of Functions
15 minutes
• Lesson 2 Overview
• Square Roots of a Function
• Y Squared Equals a Function
• Graphical Relationships 2 Quiz
Graphical Relationships 3: Absolute Values of Functions
10 minutes
• Lesson 3 Overview
• Absolute Value of a Function
• Function of the Absolute Value of x
• Graphical Relationships 3 Quiz
Graphical Relationships 4: Sums and Products of Functions
30 minutes
• Lesson 4 Overview
• Addition of Ordinates
• Multiplication of Ordinates
• Graphical Relationships 4 Quiz
Graphical Relationships 5 (Optional): Beyond the Syllabus
15 minutes
• Lesson 5 Overview
• Square of a Function
• Function of a Square
• Cube of a Function
• Higher Powers of a Function
Conclusion
1 minute
• Conclusion to Part I
User Rating
5.0Latest Reviews
Please note the feedback listed here is unfiltered, and includes all comments and ratings collected.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
The course was entirely relevant and of high quality. Steve presented the concepts of combinatorics in a clear and concise way enabling me to improve my understanding of this topic. His approach to transforming graphs in a structured way was useful to me in my presentation of this topic to my students. His videos are very easy to follow.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
GOOD
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Excellent
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
High quality and very relevant
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Excellent quality and depth of content covered
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
The quality of the questions was excellent and the content was entirely relevant. It was good to include higher level problems as well that went beyond the syllabus. This course is extremely useful for teachers of Extension 1 Mathematics. My advice is to complete this course before beginning to teach the course as the graphing component is completed early in the course. The graphing explanations are excellent and would have assisted me in my teaching if I had completed this course earlier.
Joanne Allen
Blakehurst High School
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Great information. Different process than I usually use so all good
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Well-explained, easy to understand, very relevant. I found the course to be well-explained, easy to understand, relevant, enjoyable, challenging and engaging. I liked the evaluation of the changes to the course and expected ways that questions might be approached in the new HSC examinations.
James Loder Narrabri High School
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Excellent
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Great setup
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Excellent Very useful and timely.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Was very relevant and a good quality presentation.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
The resources and video explanations are great. I also like how you also show alternative pathways to get the same answer (especially in Combinatorics). Content beyond the syllabus are also clearly labelled.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/10/2020
Excellent quality and directly relevant to the current syllabus
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/07/2020
Very relevant to my teaching.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/07/2020
This course was fantastic having never taught Extension 2. I especially liked the graphing explanations.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/07/2020
As an experienced Maths teacher I greatly appreciated this review. It helped me crystallize my thinking around some of the new and old concepts
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/07/2020
The course was fantastic and addressed all the syllabus dot points extensively. A Great range of questions varying in levels of difficulty. The quality was good – I did struggle with getting a good volume from the clips even with my laptop volume up to 100%
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/07/2020
This is the first time in a really long time that I have been teaching extension students at the year 11 level. It is excellent as a refresher and have found my ability to explain concepts to my students is greatly improved because of the videos and techniques used.
Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard
08/07/2020
Very useful notes and lesson videos provided.
About the team
Steve Howard
Creator
Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for over 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the new syllabus, which you can access from any of his courses. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn’t for him, so he went back to uni to retrain as a maths teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!