### Course Description

This course covers every dot point of ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions  (F1.1: Graphical Relationships) from the new NSW Year 11 Mathematics Extension 1 syllabus (both new and old content). Please note that only Extension 1 content is covered, not Mathematics Advanced. These are 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.

The course goes into greater detail than the textbooks, so that teachers become 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.

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

• 139 page course handout

• 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.

The remainder of the Mathematics Extension 1 syllabus, is covered in four other courses:

EXT1#2 of the series covers the remainder of ME-F1 Further Work with Functions plus ME-F2 Polynomials.

Ext1#3 covers ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities & ME-C1 Rates of Change.

Ext1#4 (Year 12) covers ME-P1 Proof by Mathematical Induction and ME-V1 Introduction to Vectors.

Ext1#5 (Year 12) covers ME-T3 Trigonometric Equations, ME-C2 Further Calculus Skills, ME-C3 Applications of Calculus and ME-S1 The Binomial Distribution.

### Audience

Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.

### Teaching Standards

2.1.2 Proficient Level - Know the content and how to teach it - Content and teaching strategies of the teaching area:  Apply knowledge of the content and teaching strategies of the teaching area to develop engaging teaching activities

### This Course:

Combinatorics & Further Work with Functions Part A - EXT1#1

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### Complete Subject:

Extension 1 Mathematics (5 courses)

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#### Do you teach in NSW? If so, this is relevant to you:

Completing Mathematics Extension 1 Year 11: Combinatorics and Futher Work with Functions Part A - EXT1#1 will contribute 10 hours of NSW Education Standards Authority (NESA) Accredited PD in the priority area of Delivery and Assessment of NSW Curriculum/Early Years Learning Framework, addressing Standard Descriptor 2.1.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher in NSW.

## Course curriculum

• 1

### Introduction (5 mins)

• Introduction to the Mathematics Extension 1 In Depth Year 11 Series

• Introduction to Part I

• 2

### Combinatorics (5 mins)

• Introduction to Combinatorics

• Relevant Parts of the Syllabus

• 3

### Combinatorics 1: Fundamental Counting Principle and Background Information (15 mins)

• 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

• 4

### Combinatorics 2: Basic Permutations (25 mins)

• 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

• 5

### Combinatorics 3: Permutations with Restrictions (20 mins)

• 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

• 6

### Combinatorics 4: Combinations (20 mins)

• Lesson 4 Overview

• Combinations

• Groups

• Stars and Bars

• Combinatorics 4 Quiz

• 7

### Combinatorics 5: Harder Permutations (20 mins)

• Lesson 5 Overview

• Mixing Permutations and Combinations

• Arranging some items in a line with some identical

• Ascending/ Alphabetical order

• Combinatorics 5 Quiz

• 8

### Combinatorics 6: Probability (20 mins)

• Lesson 6 Overview

• Probability Theory

• Probability with Combinatorics

• Combinatorics 6 Quiz

• 9

### Combinatorics 7: Pigeonhole Principle (30 mins)

• Lesson 7 Overview

• Pigeonhole Principle

• Pigeonhole Principle - Generalised Form

• Combinatorics 7 Quiz

• 10

### Combinatorics 8: Binomial Expansion and Pascal’s Triangle (30 mins)

• Lesson 8 Overview

• Binomial Expansions for small numbers

• Pascal’s Triangle

• Patterns in Pascal's Triangle

• Binomial Theorem

• Combinatorics 8 Quiz

• 11

### Combinatorics 9 (Optional): Beyond the Syllabus (35 mins)

• 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

• 12

### Graphical Relationships (5 mins)

• Introduction to Graphical Relationships

• Relevant Part of the Syllabus

• Vertical versus Horizontal Changes

• 13

### Graphical Relationships 1: Reciprocal Functions (15 mins)

• Lesson 1 Overview

• Reciprocal of a Function

• Graphical Relationships 1 Quiz

• 14

### Graphical Relationships 2: Square Roots of Functions (15 mins)

• Lesson 2 Overview

• Square Roots of a Function

• Y Squared Equals a Function

• Graphical Relationships 2 Quiz

• 15

### Graphical Relationships 3: Absolute Values of Functions (10 mins)

• Lesson 3 Overview

• Absolute Value of a Function

• Function of the Absolute Value of x

• Graphical Relationships 3 Quiz

• 16

### Graphical Relationships 4: Sums and Products of Functions (30 mins)

• Lesson 4 Overview

• Addition of Ordinates

• Multiplication of Ordinates

• Graphical Relationships 4 Quiz

• 17

### Graphical Relationships 5 (Optional): Beyond the Syllabus (15 mins)

• Lesson 5 Overview

• Square of a Function

• Function of a Square

• Cube of a Function

• Higher Powers of a Function

• 18

### Conclusion

• Highlights of Combinatorics and Further Work with Functions Part A

• Conclusion to Part I (1 min)

• 19

### Course Feedback

• Course Feedback

## Presenter

Steve Howard

Steve Howard has inspired and equipped hundreds of Maths teachers with his In-Depth Senior Mathematics courses, providing all the tips, examples and resources to teach the HSC syllabus with confidence. He loves to discover the most efficient techniques for solving mathematical problems, by analysing other experts' solutions or by developing his own approaches when he finds a better way. As a student, Steve did Unit 4 Mathematics, gaining a mark of 198/200, before training as an actuary. After retraining as a teacher, Steve has taught Maths at Cowra High School, NSW, for 28 years. He has also taught gifted and talented students online through Xsel and Aurora College, and developed all student course material for TTA's Year 12 Extension Maths Portal.

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