Presentation by Marina Nazarova International Baccalaureate Diploma Programme Mathematics

1. Presentation by Marina Nazarova International Baccalaureate Diploma Programme Mathematics

2. Name - Marina Nazarova • I work at school № 9 • Study at Perm Teacher Training University • Work with DP Mathematics HL and SL • Sphere of interests – Computer in Mathematical Studies

3. Aims and Objectives: The main aim: • to study DP Mathematics guide, syllabus content, evaluation, portfolio management, diploma requirements Objectives: • to enrich our IB, general and special terminology; • to work with special literature; • to use different sources of information about different topics of the syllabus; work out lessons and lesson plans • to communicate with our foreign colleagues.

4. For this we studied IB documents : IB DP overview Command terms for lessons on mathematics Assessment system and terminology Presumed knowledge content Syllabus content Maths SL themes Maths HL themes

5. The guide “IB DP“ helped us to understand • - The concept and aims of IB DP • - “What the DP is” • - “What is special about DP” • The qualities which every IB student must possess • Difficulties we need to overcome

6. As a result: • - We understand that the core of the IB DP is the ToK, CAS and Extended essay. • - There are also 6 groups of subjects. • We know aims of Maths of HL and SL, assessment system and conditions of getting Diploma or certificate. • This is my presentation with IB DP Overview

7. Core syllabus content ( 190 hrs) Requirements All topics in the core are compulsory. Students must study all the sub-topics in each of the topics in the syllabus as listed in guide. Students are also required to be familiar with the topics listed as presumed knowledge (PK). Topic 1—Algebra 20 hrs Topic 2—Functions and equations 26 hrs Topic 3—Circular functions and trigonometry 22 hrs Topic 4—Matrices 12 hrs Topic 5—Vectors 22 hrs Topic 6—Statistics and probability 40 hrs Topic 7—Calculus

8. Assessment Internal A - Portfolio There are two types of tasks: • mathematical investigation • mathematical modelling. External assessment There are 3 examination papers, assest by external experts. Studentsneed to be familiar with notation the IBO uses and the command terms, as these will be used withoutexplanation in the examination papers

9. Let’s demonstrate the way we studied the topic “Arithmetic and geometric sequences and series”.

10. Arithmetic sequences An arithmetic sequence, sometimes known as an arithmetic progression, is one where the terms are separated by the same amount each time. This is known as the common difference and is denoted by d.Note that for a sequence to be arithmetic, a common difference must exist. Consider the sequence 5, 7, 9, 11, 13, ... The first term is 5 and the common difference is 2. So we can say a = 5 and d = 2. Sequences can be defined in two ways, explicitly or implicitly. An implicit expression gives the result in relation to the previous term, whereas an explicit expression gives the result in terms of n. Although it is very easy to express sequences implicitly, it is usually more useful to find an explicit expression in terms of n.

11. un = a + (n – 1) d

15. This is an example of command terms glossary

16. Write downObtain the answer(s), usually by extracting information. Little or no calculation isrequired. Working does not need to be shown. CalculateObtain the answer(s) showing all relevant working. “Find” and “determine” can alsobe used. Find Obtain the answer(s) showing all relevant working. “Calculate” and “determine” canalso be used. DetermineObtain the answer(s) showing all relevant working. “Find” and “calculate” can also beused. DifferentiateObtain the derivative of a function. Integrate Obtain the integral of a function. Solve Obtain the solution(s) or root(s) of an equation.

17. Draw Represent by means of a labelled, accurate diagram or graph, using a pencil. A ruler(straight edge) should be used for straight lines. Diagrams should be drawn to scale. Graphs should have points correctly plotted (if appropriate) and joined in a straightline or smooth curve. SketchRepresent by means of a diagram or graph, labelled if required. A sketch should givea general idea of the required shape of the diagram or graph. A sketch of a graph should include relevant features such as intercepts, maxima, minima, points ofinflexion and asymptotes. PlotMark the position of points on a diagram. CompareDescribe the similarities and differences between two or more items.

18. DeduceShow a result using known information. JustifyGive a valid reason for an answer or conclusion. ProveUse a sequence of logical steps to obtain the required result in a formal way. Show thatObtain the required result (possibly using information given) without the formality of proof. “Show that” questions should not generally be “analysed” using a calculator. Hence Use the preceding work to obtain the required result. Hence orotherwiseIt is suggested that the preceding work is used, but other methods could also receive credit.

20. We tried whole approach in teaching mathematics at IB conference Food Presentation

21. Prospective for our self training • Read more special literature • Create more detailed glossary list • Try modern techniques of teaching • Co-operate with IB teachers in Perm, Russia and abroad • Continue working with professional portfolio

22. Thank you for attention