1. THE I.B. LEARNER PROFILE
The aim is to develop internationally minded people who help to create a better and more peaceful world.

2. INQUIRERS Develop natural curiosity
Acquire skills necessary to conduct research
Show independence in learning
Actively enjoy learning
The love of learning will be with them all their life

3. KNOWLEDGEABLE
Explore concepts, ideas and issues that have local and global significance
Acquire in-depth knowledge across a range of disciplines
Develop understanding across a range of disciplines

4. THINKERS
Apply thinking skills critically
Recognise complex problems
Make reasoned, ethical decisions

5. COMMUNICATORS
Understand and express ideas and information confidently and creatively in more than one language
Use a variety of modes of communication
Collaborate with others effectively

6. PRICIPLED Act with integrity and honesty
Have a strong sense of fairness, justice and respect
Take responsibility for their actions and accept the consequences that accompany them

7. OPEN-MINDED Understand and appreciate their own cultures
Are open to the perspectives, values and traditions of others
Accustomed to seeking and evaluating a range of points of view
Are willing to grow from their experiences

8. CARING
Show empathy, compassion and respect towards the needs and feelings of others
Have a personal commitment to service
Act to make a positive difference to the lives of others and the environment

9. RISK-TAKERS
Approach unfamiliar situations with courage and forethought
Have the independence of spirit to explore new roles, ideas and strategies
Are brave and articulate in defending their beliefs

10. BALANCED
Understand the importance of intellectual, physical and emotional balance to achieve personal well-being

11. REFLECTIVE
Give thoughtful consideration to their own learning and experience
Able to assess their strengths and limitations

12. Special Number Sets & Percentage Errors, Significant Figures, Estimation
2.1 - The sets of natural numbers, N ; integers, Z ; rational numbers, Q; and real numbers, R .
2.2 - Approximation: decimal places; significant figures. Percentage errors. Estimation.

13. Objectives/Aims for 8/12/2013
2.1 - The sets of natural numbers, N ; integers, Z ; rational numbers, Q; and real numbers, R .
2.2 - Approximation: decimal places; significant figures. Percentage errors. Estimation.

14. Hierarchy of Number SystemsQ Z N
Where number systems abbreviations are:
N = {0, 1, 2, 3, …}
Z = {…-2, -1, 0, 1, 2, …}
Q = {N + Z + fractions}
Where fractions = a/b & b≠0
R = {N + Z + Q + irrational numbers}

15. Rational vs. Irrational #’s
Rational numbers:
Q: { 𝑎 𝑏 where a & b are integers and b ≠ 0}
Can be written as a fraction or a decimal
Examples: {3/4, 8, 81/5, 4.125, …}
Why does b ≠ 0?
All numbers are rational, unless they are irrational
Irrational numbers:
Can be written as a decimal, but not a fraction
Has endless non-repeating decimals to the right of the decimal
Examples: {∏, √2}

16. Having a Solution…
Solve for x & tell what number system the answer falls into:
2x – 1 = 7
x = 4, so N
-x + 6x + 3 = 2
x = -(1/5), so Q

17. Rounding Numbers
The surface area of the Dominican Republic is km2. Round this figure correct to the nearest 1000 km2.
We round when…the number directly to the right of our number of interest is ≥5.
So, our solution is = km2
In 2006, the number of IB World Schools teaching the Diploma Programme was Round this number correct to the nearest 10.
1195  1200
Same rules apply when rounding decimals.
 km2.
Thousands

18. Significant Figures Rules regarding significant figures are:
All non-zero digits are significant
1.235 g  has 4 significant figures
Zero between non-zero digits are significant
1.02 ml  has 3 significant figures
Zeros to the left of the first non-zero digit are not significant; such zeros merely indicate the position of the decimal point.
0.05 cm  only has 1 significant figure
Zeros placed after other digits but to the right of the decimal point are significant. **most confusing**
ml  has 3 significant figures
For non-decimal numbers, zeros after the last non-zero digit are not significant.
345,700 m  has 4 significant figures

19. Significant Figures Examples
To enclose the irrigated area used for cultivation in a farm, m of wire is needed. Write this length correct to 1 s.f.
Solution: m
The Museo del Prado exposition held in Tokyo in July 2006 had 501,932 visitors. Write down this number correct to 3 s.f.
Solution: 501,932  502,000 visitors
 2000 m is correct to 1 s.f.
1st s.f.

20. Estimation
An estimate of a quantity is an approximation that is usually used to check the reasonableness of an answer. When we estimate a quantity we try to gain an idea of the size of that quantity. This is done by rounding the numbers involved in the calculations to make them more straightforward.
Estimate the area of a rectangular piece of land which has a length of m and a width of 48.6 m.
Solution: x 48.6 m
 100 m x 50 m = 5000 m2.

21. Errors
When we estimate or measure a quantity, it is important to consider the difference between any of these values and the exact value of the quantity. This difference is called the error.
The error in a measurement is the difference between the value found by measurement or estimation and the exact value of the quantity.
Error = Va – Ve (Approximate Value – Exact Value)

22. Errors Examples
Paula estimates that the weight of a herring is 250 g. The exact weight of the herring is 246 g. Find the error that Paula made in her estimation.
Error = 250 – 246 = 4 g
Zhou estimates that the weight of four herrings is 1000 g. The exact weight of the herrrings is 996 g. Find the error in Zhou’s estimation.
Error = 1000 – 992 = 4 g

23. Percentage Error Percentage Error = (VA – VE / VE) x 100%
Looking at the last two problems from the previous slide, both of the errors were the same.
Let’s see if the same holds true for the percentage error.
(4/246) x 100% =
(4/996) x 100% =
Error
1.63% correct to 3 s.f.
0.402% correct to 3 s.f.

24. Percentage Error Examples
The size of angle A is 24.6º. Isabella measured A with her protractor and found that its size was 24º. Find the percentage error made by Isabella when measuring A.
Solution: 24− 𝑥100% 
x 100% = %

25. Student Percentage Error Example
Akio estimated that the wall was 2.50 m high when in fact it was 2.38 m. Find the percentage error he made in his estimate.
Solution:
2.50 – 2.38
2.38
x 100% 
x 100% = 5.04 %