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.

 

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,

6.2.2 Proficient Level - Engage in Professional Learning - Engage in professional learning and improve practice:   Participate in learning to update knowledge and practice targeted to professional needs and school and/or system priorities

 

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 4th February 2022 under NESA’s interim arrangements will contribute 5 hours 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.

 

Course curriculum

  • 1

    Introduction (5 mins)

    • Course Administration

    • 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

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