Download CURRICULUM SUMMARY * September to October 2008

CURRICULUM SUMMARY – September to December 2016
SUBJECT: Mathematical Studies
YEAR GROUP: IB1
TEACHER: Agata Piskorz
Week Date
Learning objectives
Activities (in brief)
1
SEQUENCES AND SERIES
Students will understand and use:
 definition of a sequence, the general term ( n-th term ) of a
sequence,
 definition of arithmetic and geometric sequences, the
formula for the n-th term of an arithmetic sequence,
 the formula for the n-th term of a geometric sequence
 the sum of an arithmetic sequence -arithmetic series, the
formula for the sum of the first n terms,
Generating terms of a sequence using term-to-term and position-toterm definitions of the sequence.
Specifying sequences by using words, using an explicit formula (general
term – n-th term formula).
Showing that a sequence is arithmetic.
Finding sums of the arithmetic and geometric series.
Using sequences to solve word problems.
Revision – solving problems at class and at home.
Writing a test;
Discussing results of the test.
2
5-9 Sep
12 -16
Sep
3
19-23
Sep

4
26-30
Sep
DESCRIPTIVE STATISTICS
Students will understand and use:
 concept of population and sample; classification of data as
discrete or continuous;
 mean, mode, median for discrete data;
 quartiles; Box and Whisker Plots (boxplots); parallel
boxplots;
 grouped discrete or continuous data – organization and
display;
 mean, mode, median for grouped discrete or continuous
data;
 cumulative frequency
 cumulative frequency tables for grouped discrete data and
grouped continuous data; cumulative frequency curves
percentiles from the cumulative frequency curves;
 measures of dispersion; range, interquartile range,
standard deviation;
5
3-7 Oct
the sum of an geometric sequence, geometric series,
Showing that a sequence is geometric.
Finding the formula for the general term of an arithmetic or geometric
sequence. Deriving the formula for the sum of an arithmetic series.
What is statistics, its methods and purposes – discussion.
Finding examples of different types of data.
Using the GDC to present data: tables; frequency tables (lists); graphs,
diagrams, boxplots.
Summarizing data – calculations with and without the GDC;
Drawing and interpreting cumulative frequency diagrams.
Presenting situations where percentiles are used.
Calculating dispersion of the data.
Calculating variance and standard deviation.
6
10-14
Oct

7
17-21
Oct
NUMBERS
Students will understand and use:
 the exponential expression: a b , b  Q; rules of indices;
 the index notation (scientific notation): a  10n , where
1  a  10 and a Z; very large and very small numbers in
scientific, economic and other applications; awareness and
use of scientific mode on the GDC;
 operations with numbers expressed in the form: a  10n ,
where 1  a  10 and a Z;
 decimals; decimal places; approximations; rounding off to a
given number of decimal places or significant figures;
 the absolute errors; percentage errors;
 System International (SI); other basic units of
measurements;
 conversion between different units.
8
9
24-28
Oct
31 Oct –
4 Nov
7 -11
Nov
10
14 – 18
Nov
11
21 – 25
Nov
significance of the numerical value of standard deviation.
Finding out the significance of standard deviation – examples from real
world.
Revision – solving problems at class and at home.
Writing a test;
Discussing results of the test.
Revising rules of indices and scientific notation.
Using GDC (Graphic Display Calculator) for conversion between scientific
and standard notation.
Rounding and estimating numbers.
Calculating errors.
Estimating and accuracy –homework investigation.
Converting between different units .
Revision – solving problems at class and at home.
Writing a test.
Discussing results of the test.
Mid-Term Break
SETS
Students will understand and use:
 the concept of a set; members (elements) of a set, the
empty set; equal sets; subsets; appropriate notation;
 Venn diagrams; union; intersection;
 the universal set; complement of a set;
 the relationship between the set of natural numbers; the
set of integers; the set of rational numbers and the set of
real numbers; sets of prime numbers, multiples and
factors;
 Venn diagrams to illustrate set operations; regions on a
Venn diagram;
 set operations with three sets;
 numerical problems on three sets.
Elements of a lecture – introducing new symbols, definitions and
algorithms ;
Solving problems at class– individual or group work.
Shading regions in Venn diagrams – Interactive White Board activity.
Solving problems at class– individual or group work;
Students’ homework.
Shading regions in Venn diagrams – three sets.
Solving real word problems – numbers in regions of Venn diagrams.
Students’ homework.
Revision – solving problems at class and at home.
Writing a test. Discussing results of the test.
12
13
14
28 Nov – PROBABILITY
2 Dec
 Basic concepts of probability: outcome, event, sample
space.
 Theoretical probability of an event
 Compound events. Independent events.
5 Dec –
 Probabilities from Venn diagrams.
9 Dec
 Conditional probability
12 Dec –
16 Dec

Complementary events and their probabilities.
Probability from tree diagrams.
Chance investigation. Estimating probability from data.
Using tables of outcomes, grids, tree diagrams to represent a
sample space and calculate probability.
Students’ homework.
Solving problems at class– individual or group work.
Using Venn diagrams to calculate probability of events.
Calculating conditional probability with Venn diagrams.
Students’ homework.
Solving problems at class– individual or group work.
Using tree diagrams to calculate probability of events.
Students’ homework.