Course Description

This course provides teachers with a comprehensive guide to the knowledge and techniques required to teach Mathematics Advanced 11-12 Syllabus (2024). It covers all of the dot points in the two focus areas Permutations and combinations & The binomial theorem.


The course goes into greater detail than the textbooks, so that teachers become more comfortable in their ability to deliver the content. All 90 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.


The course includes:

•90 recorded examples
•A total of 40 quiz questions at the end of each lesson
•A 146 page course handout in two formats – one with blank space for you to complete the examples and a second with completed solutions to the examples.
•A 23 page exercise booklet with 90 optional practice questions matching the examples from the course, with fully worked solutions.


The Mathematics Extension 1 11-12 Syllabus (2024) will be covered in seven courses. The courses are:

Extension 1 Course 1 - Year 11   Permutations and combinations

  The binomial theorem

Extension 1 Course 2 - Year 11   Polynomials

  Further work with functions

Extension 1 Course 3 - Year 11    Further trigonometry

Extension 1 Course 4 - Year 12    Proof by mathematical induction

  Inverse trigonometric functions

Extension 1 Course 5 - Year 12    Introduction to vectors

Extension 1 Course 6 - Year 12    Further calculus skills

  Further applications of calculus

Extension 1 Course 7 - Year 12    The binomial distribution and sampling
distribution of the mean


Audience

This course is suitable for teachers with any level of previous experience.


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

Course curriculum

  • 1

    Course information

    • Course information and introduction
  • 2

    Part 1a Preparing to teach the 2024 Mathematics syllabuses

    • 2024 Syllabuses

    • Extension 1 scopes and sequences
  • 3

    Part 1b How is teaching Extension 1 different to teaching Advanced?

    • How is teaching Extension 1 different to teaching Advanced?

    • General hints for student success in Extension 1
  • 4

    Part 2a Introduction to Permutations and combinations & The binomial theorem

    • Summary of the content in this course

    • What has changed from the 2017 syllabus?
  • 5

    Part 2b Lessons

    • List of lessons
  • 6

    Lesson 1 - Factorial notation and background information

    • Lesson introduction

    • Background information

    • The multiplication principle

    • Factorial notation

    • Practice exercises

    • Lesson 1 Quiz
  • 7

    Lesson 2 - Basic permutations

    • Lesson introduction

    • Arranging all the objects from a group in a line

    • Arranging all objects from a group in a line where some of the objects are identical

    • Arranging all objects from a group of distinct objects around a circle

    • Arranging some objects from a group in a line

    • Arranging some objects from a group of distinct objects around a circle

    • Practice exercises

    • Lesson 2 Quiz
  • 8

    Lesson 3 - Permutations with restrictions

    • Lesson introduction

    • Arranging objects in a line or circle where some objects must be together

    • Arranging objects in a line or circle where some objects must be apart

    • Arranging objects in a line or circle where some objects must alternate

    • Arranging groups of objects around a circle

    • Practice exercises

    • Lesson 3 Quiz
  • 9

    Lesson 4 - Combinations

    • Lesson introduction

    • Combinations

    • Selecting some or all of the objects in the set for multiple subsets

    • Placing all objects in subsets of variable size - stars and bars method

    • Triangles as combinations

    • Practice exercises

    • Lesson 4 Quiz
  • 10

    Lesson 5 - Harder permutations

    • Lesson introduction

    • Mixing permutations and combinations

    • Considering cases

    • Ascending or alphabetical order

    • Practice exercises

    • Lesson 5 Quiz
  • 11

    Lesson 6 - Probability

    • Lesson introduction

    • Probability

    • Practice exercises

    • Lesson 6 Quiz
  • 12

    Lesson 7 - Binomial theorem

    • Lesson introduction

    • Binomial expansions

    • Pascal’s triangle

    • Binomial theorem

    • Practice exercises

    • Lesson 7 Quiz
  • 13

    Lesson 8 - Identities involving binomial coefficients

    • Lesson introduction

    • Identities involving binomial coefficients

    • Practice exercises

    • Lesson 8 Quiz
  • 14

    Conclusion

    • Conclusion
  • 15

    Course Feedback

    • Course Feedback

Features of TTA Online PD

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