# SL & HL Core teaching sequence

The following is a **suggested teaching sequence (plan)** for the content in the Maths SL syllabus and the **Maths HL Core **syllabus. Of course, there is no single teaching sequence which is best for everyone - so it is certainly worth the effort to consider this *suggested *plan with a critical eye. Nevertheless, I have come up with this teaching sequence after quite a bit of experimentation and fine-tuning. There is one obvious change that many teachers will probably make to this plan - and that's teaching the content for Statistics & Probability (topic 5) earlier in the course - e.g. before Calculus (topic 6). I prefer to teach Calculus earlier because I find many students are interested in writing their Exploration (IA) on a topic that is directly or indirectly associated with Calculus. That's precisely the reason that some teachers will prefer teaching Statistics & Probability earlier - i.e. because they feel that many of their students may choose an Exploration topic from that area of the syllabus. Regardless of what plan you come up with, it will be important to include where in your teaching sequence it will be best for your students to be working on their Exploration (IA task).

I have included a total of 14 units - including a unit 0 that covers a range of material listed in the Prior Learning Topics, a review of important algebra skills and other skills and concepts that you might consider to be 'fundamental' for a Maths SL or Maths HL to know before teaching the syllabus content of either course. Of course, depending on the level of preparation of your students this unit 0 may be unnecessary and can be skipped. If so, then my plan contains 13 units. The content that makes up a 'unit' are syllabus items that I feel are sufficiently connected together and comprise a reasonable quantity of content which is suitable (not too much, not too little) for covering in a single unit test (and one or two quizzes before the test).

You will find a list of the** teaching units for Maths HL** and a list of the** teaching units for Maths SL** with an estimated number of teaching hours for each unit immediately after the teaching sequence below.

And below that (at bottom of this page) you will find **planning documents** (one each for HL and SL) that I made for myself which I find very useful. The documents have columns with boxes representing each week of the entire course. Before the start of the first year of a course, I use this document to make a plan for the sequence in which I will teach my units for each course - and indicate how much time (# of weeks) I intend to devote to each unit. I also write in when I think it will be best for my students to work on their Exploration (IA task). It helps me a great deal to see an **overall plan for an entire 2-year course on one sheet of paper.**

Ideally, I try to time it so that I finish teaching the 2nd differential calculus unit at the end of the first year, and then start the second year with the unit on integral calculus. I usually find it best to have students complete their Exploration during the 1st half of the second year after presenting information about the Exploration near the end of the first year. This allows students to do some thinking - maybe some reading or research - on a topic for their Exploration during the summer. However, I refrain from requiring any work on the Exploration to be completed during the summer between the 1st and 2nd year because that is when students should be focused on making as much progress as possible on their Extended Essay.

[__note__: information written in **bold **(except for unit titles) is relevant to **Maths HL**; and the symbol (**+HL**) written after a content item means that the topic includes some material only for **Maths HL**]

### Suggested Teaching Sequence for Maths SL and Maths HL Core

__Unit 0__: Prior Learning Topics / Fundamentals / Algebra Review **[? hours]**

**♦ Topic 2 – Functions & Equations** [SL: 17 hrs; **HL: 16 hrs**]

__Unit 1__: Functions

1.1 basics / composite & inverse functions

1.2 transformations of graphs

1.3 rational functions

1.4 quadratic functions & equations (**+ HL**)

1.5 solving other equations (+** HL**)

**1.6 polynomial functions & equations (HL only)**

**1.7 solving inequalities (HL only)**

**♦ Topic 1 – Algebra ** [SL: 9 hrs; **HL: 10 hrs**]

__Unit 2__: Sequences & Series and Binomial Theorem

2.1 sequences & series

2.2 exponents & logarithms - basics

2.3 arithmetic sequences & series

2.4 geometric sequences & series

2.5 counting principles & binomial theorem (**+ HL**)

**♦ Topic 2 – Functions & Equations** (continued) [SL: 7 hrs; **HL: 6 hrs**]

__Unit 3__: Exponential & Logarithmic Functions & Equations

3.1 exponential functions

3.2 logarithmic functions

3.3 exponential & logarithmic equations

**♦ Topic 3 – Trigonometry ** [SL: 16 hrs; **HL: 22 hrs**]

__Unit 4__: Trigonometric Functions & Equations

4.1 angles, circles, arcs & sectors

4.2 trigonometric functions (**+ HL**)

4.3 trigonometric equations & identities (**+ HL**)

**4.4 inverse trigonometric functions (HL only)**

__Unit 5__: Triangle Trigonometry

5.1 trigonometric functions and angles

5.2 law of sines

5.3 cosine rule

5.4 applications

**♦ Topic 4 – Vectors ** [SL: 22 hrs; **HL: 24 hrs**]

__Unit 6__: Vectors

6.1 vector basics & operations

6.2 scalar product & applications

6.3 equations of lines

**6.4 vector product & applications (HL only)**

**6.5 lines & planes in space (HL only)**

**♦ Topic 1 – Algebra** (continued **HL only**) [**HL: 20 hrs**]

__Unit 7__**: Systems of Equations, Complex Numbers & Proof by Induction (HL only)**

__Unit 7__

**7.1 systems of linear equations (HL only)**

**7.2 complex numbers - basics, notation, complex plane**

**7.3 imaginary roots of polynomial equations**

**7.4 powers & roots of complex numbers**

**7.5 proof by induction**

**♦ Topic 6 – Calculus** [SL: 40 hrs; **HL: 48 hrs**]

__Unit 8__: Differential Calculus I

8.1 differentiation basics

8.2 maxima & minima

8.3 tangents & normal

__Unit 9__: Differential Calculus II

9.1 trigonometric, exponential & logarithmic functions (**+ HL**)

9.2 further differentiation methods (**+ HL**)

9.3 optimization

**9.4 implicit differentiation & related rates (HL only**

__Unit 10__: Integral Calculus

10.1 integration basics

10.2 integration by substitution (**+ HL**)

**10.3 further integration methods (HL only)**

10.4 areas & volumes (**+ HL**)

10.5 modelling linear motion

**♦ Topic 5 – Statistics & Probability** [SL: 35 hrs; **HL: 36 hrs**]

__Unit 11__: Descriptive Statistics

11.1 basics & graphical tools

11.2 measures of central tendency & variability

11.3 linear regression (SL only*)

__Unit 12__: Probability

12.1 probability of events

12.2 operations with events & conditional probability

**12.3 Bayes’ theorem (HL only)**

__Unit 13__: Probability Distributions

13.1 discrete random variables

13.2 binomial distribution

**13.3 Poisson distribution (HL only)**

**13.4 continuous random variables (HL only)**

13.5 normal distribution

### Lists of units for HL and SL with estimated teaching hours

** HL teaching units** (230

**teaching**hours + 10 hours for Exploration-IA)

0: Fundamentals (?)

1: Functions (14)

2: Sequences, Series & Binomial Theorem (10)

3: Exponential & Logarithmic Functions (8)

4: Trigonometric Functions & Equations (13)

5: Triangle Trigonometry (9)

6: Vectors (24)

7: Systems of Equations, Complex Numbers & Proof by Induction (20)

8: Differential Calculus I (14)

9: Differential Calculus II (18)

10: Integral Calculus (16)

11: Descriptive Statistics (7)

12: Probability (14)

13: Probability Distributions (15)

Option Topic (48)

** SL teaching units** (140

**teaching**hours + 10 hours for Exploration-IA)

0: Fundamentals (?)

1: Functions (14)

2: Sequences, Series & Binomial Theorem (9)

3: Exponential & Logarithmic Functions (7)

4: Trigonometric Functions & Equations (9)

5: Triangle Trigonometry (7)

6: Vectors (16)

7: Review (?)

8: Differential Calculus I (13)

9: Differential Calculus II (13)

10: Integral Calculus (14)

11: Descriptive Statistics (8)

12: Probability (14)

13: Probability Distributions (13)

Below are blank schedules for Maths HL and Maths SL. They are useful for diagramming a teaching plan for each course indicating when a unit will be taught and for how long (# of weeks). The document shows weeks (estimated to be about 61) for the entire 2-year course. **Click on either document to view/download it.**