# Teaching Units

Presented in the table below are suggested teaching units for both Maths SL and Maths HL. These do not correspond exactly with the six topics into which the syllabus is divided (core syllabus for HL) - but it is not recommended that a teacher use the structure of the syllabus as a plan for teaching. So, to devise a plan for organizing the teaching of the syllabus content it is helpful to divide the material into parts, or units, that are suitable for teaching as a 'whole' and then assessing the students' understanding of the concepts and skills in that unit - i.e. having the students sit a unit test.

I must stress that the teaching units displayed below are just a suggestion although one based on a substantial amount of teaching experience and from writing textbooks for IB Maths HL and IB Maths SL. You may certainly decide to organize the syllabus content for either Maths HL or Maths SL differently than I have but the following units have worked well for me with my students. Using these teaching units also aid in organizing the material for this site in a more coherent manner.

Each of the unit titles in the table below is an active link that when clicked will open a new window showing content details for all of the teaching units. You can click here to navigate directly to the top of this page with content details for all of my suggested teaching units.

### Suggested Teaching Units for SL and HL

Maths SL Maths HL (core)
0. Fundamentals 0. Fundamentals
1. Functions & Equations 1. Functions - Basics
2. Sequences & Series; Binomial Theorem 2. Functions, Equations & Inequalities
3. Exponential & Logarithmic Functions 3. Sequences & Series
[ Matrices (optional) ] 4. Counting Principles; Binomial Theorem; Induction
4. Trigonometric Functions & Equations 5. Exponential & Logarithmic Functions
5. Triangle Trigonometry [ Matrices (optional) ]
6. Vectors 6. Trigonometric Functions & Equations
7. Differential Calculus I 7. Triangle Trigonometry
8. Differential Calculus II 8. Vectors
9. Integral Calculus 9. Complex Numbers
10. Statistics 10. Differential Calculus I
11. Probability 11. Differential Calculus II
12. Probability Distributions 12. Integral Calculus
13. Statistics
14. Probability
15. Probability Distributions

Of course, a teacher could decide on a different set of teaching units and/or a different sequence than what is presented in the table above. There are several factors that could have a significant influence over the organization of teaching units and may vary considerably from one school to another - and from one teacher to another. These factors may include: teaching materials (e.g. textbook), time for each class meeting, whether students are preparing for other external exam(s) in addition to the IB, and if the class group consists of only HL students, or only SL students, or a combination of HL and SL students.

There are some key practical questions that I think need to be answered when devising how to teach either Maths HL or Maths SL. There are no necessarily 'right' or 'wrong' answers to these questions. What is important is that these questions/issues need to be considered and some thought put into coming up with an answer that fits the circumstances of the school and the teaching approach of the teacher.

#### Important questions concerning the organization of teaching units:

1. Should calculus be primarily taught in the first year or in the second year? Or should it be split with differential calculus in the first year and integral calculus in the second year?

2. Will the schedule for completing the internal assessment (Exploration) have an affect on when a certain topic is taught?

3. Will it be beneficial (and is there enough time) to have students briefly review some of the knowledge and skills in the Prior Learning Topics (previously Presumed Knowledge) at the start of the course (e.g. the first unit in the list above is a Fundamentals unit)?

4. Should all the material in the Statistics and Probability topic be taught consecutively - or is it better, or more manageable, to teach the syllabus content on statistics and probability in 2 or 3 separate units - and not necessarily consecutively? [in the set of units above, statistics and probability is divided into 3 teaching units]

5. What syllabus content requires other syllabus content to be covered before it (i.e. prerequisites)? For example, trigonometry needs to be done before vectors or complex numbers (HL only) is covered.

6. Is some of the syllabus content which only appears on the HL syllabus sufficiently robust so that it can make up one whole teaching unit on its own? For example, it may work to have a separate Complex Numbers unit in HL, but not a separate Proof by Induction unit in HL. Induction would have to 'fit' into another unit because there is not sufficient quantity of material on induction to be one teaching unit on its own.

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