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

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

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

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

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

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

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

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

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

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

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

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.

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.

Hierarchy of Number Systems Q 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}

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}

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

Rounding Numbers The surface area of the Dominican Republic is 48734 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 = 48734 km2 In 2006, the number of IB World Schools teaching the Diploma Programme was 1195. Round this number correct to the nearest 10. 1195  1200 Same rules apply when rounding decimals.  49000 km2. Thousands

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** 0.00200 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

Significant Figures Examples To enclose the irrigated area used for cultivation in a farm, 2306.51 m of wire is needed. Write this length correct to 1 s.f. Solution: 2306.51 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.

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 126.8 m and a width of 48.6 m. Solution: 126.8 x 48.6 m  100 m x 50 m = 5000 m2.

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)

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

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.

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: 24−24.6 24.6 𝑥100%  -0.02439 x 100% = -2.44 %

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%  0.05042 x 100% = 5.04 %