Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships

Steve Howard
Passionate about Mathematics
A comprehensive guide to the knowledge and techniques needed to teach Combinatorics and Graphical Relationships from the new Mathematics Extension 1 Year 11 syllabus.
Target Audience
Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.
54 reviews
237

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.

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- 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

Completing Mathematics Extension 1 Year 11: In Depth Part I – Combinatorics & Graphical Relationships before 31 July 2021 under NESA’s interim arrangements will contribute 5 hours and 0 minutes of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and assessment of NSW curriculum addressing standard descriptors 2.1.2, 6.2.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.


This course contributes to 5.0 professional development hours.

Occurrences

  Start Date Location Availability Price    
Enrol Now Now Online Places available $269 + GST Enrol Now

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

5.0

Latest 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)!!