Number+9

** Number Systems of the World ** Image: '[|Happy Pi Day (to the 36th digit)!] ' www.flickr.com/photos/64419960@N00/2332789392
 * Unit Questions || Significant Concepts  || Area of Interaction  ||
 * # How have different civilizations symbolized amounts and performed calculations?
 * 1) Why were negative numbers, rational numbers and irrational numbers created?
 * 2) How can very large and very small numbers be represented? || Civilizations represented numbers using a variety of symbols || Human Ingenuity - develop an awareness and understanding of why humans created different number systems ||

==** Vocabulary ** ==
 * === English === || === Bahasa  === ||
 * prime, composite, rational, irrational, natural, integer, real, exponent || eksponen, rasional, prima, irasional, integer, asli ||

** Key Links **
===**Content and skills ** ===
 * [|Purple Math] || Lowest common multiple and greatest common factor ||
 * [|Purple Math] || Converting between fractions, decimals and percents ||
 * [|Purple Math] || Operations with fractions ||
 * [|Rational vs. Irrational] || Nice explanation of the difference between rational and irrational numbers with an emphasis on surds ||
 * **Content**: || **Extended Content**: ||
 * * real number system with emphasis on irrational numbers
 * operations with real numbers
 * order of operations
 * number systems in other bases
 * rounding and significant figures
 * square root radicals
 * scientific notation || * cube root and fourth root radical expressions
 * rational exponents ||
 * **Outcomes/Skills**: || **Extended outcomes/skills**: ||
 * # classify numbers as natural, integer, rational, irrational
 * 1) investigate the meaning and development of irrational numbers
 * 2) understand the relationship between irrational numbers and radicals
 * 3) locate real numbers on a number line with emphasis on locating irrational and rational numbers.
 * 4) change recurring decimals to fractions
 * 5) compare and order real numbers written in any form
 * 6) express real numbers in a variety of equivalent forms
 * 7) understand the difference between exact and approximate values of numbers
 * 8) perform, with confidence, operations on whole numbers, integers, fractions and decimals.
 * 9) use the order of operations and understand how the calculator uses the order of operations
 * 10) express large and small numbers in scientific notation
 * 11) perform operations with numbers written in scientific notation
 * 12) simplify square root radicals
 * 13) add, subtract and multiply square root radical expressions
 * 14) rationalize denominators for monomial and binomial square root radicals
 * 15) convert numbers into different base systems and perform simple addition and multiplication in different base systems || # prove that the square root of 2 is irrational
 * 16) simplify cube root and fourth root radical expressions
 * 17) investigate the relationship between rational exponents and radicals
 * 18) convert easily between radical and exponential forms
 * 19) evaluate powers with rational exponents and assess the reasonableness of answers
 * 20) rationalize denominators for cube root and fourth root monomial radicals ||

 Standards and Benchmarks
<span style="cursor: pointer; font-family: Verdana,Geneva,sans-serif; margin: 0px; padding: 0px;">[|Math 08 - Number Systems - Real Number System Venn.doc] || <span style="cursor: pointer; font-family: Verdana,Geneva,sans-serif; margin: 0px; padding: 0px;">[|Math 08 - Number Systems - Classifying Numbers Practice.docx] || <span style="font-family: Verdana,Geneva,sans-serif; margin: 0px; padding: 0px;">** Develop understanding of the relationship between irrational numbers and radicals. ** || <span style="font-family: arial,helvetica,sans-serif; font-weight: normal;">**<span style="font-family: Verdana,Geneva,sans-serif;">Develop and use strategies to make reasonable estimates when finding sums, differences, products and quotients of real numbers written in any form. ** || Simplifying radicals Adding and subtracting radicals Expanding with radicals || Review methods of lattice multiplication, partial product multiplication || Operations with fractions, decimals and natural numbers || <span style="font-family: Verdana,Geneva,sans-serif;">** <span style="font-family: arial,helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">**<span style="font-family: Verdana,Geneva,sans-serif;">Write real numbers in a variety of equivalent forms and develop understanding of the difference between exact and approximate values of equivalent forms of numbers. ** ** || ||   ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of positive integers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’) and real numbers (R) and understand the relationships amongst the different sets ** ||
 * <span style="cursor: pointer; font-family: Verdana,Geneva,sans-serif; margin: 0px; padding: 0px;">[|Math 08 - Number Systems - Number Definitions] || <span style="font-family: Verdana,Geneva,sans-serif; margin: 0px; padding: 0px;">Students should know the following terms: odd, even, prime, composite, positive and negative. Use a Venn diagram to show the relationships between the different types of numbers and be able to classify numbers.
 * <span style="font-family: Verdana,Geneva,sans-serif; margin: 0px; padding: 0px;">** Investigate and demonstrate understanding of the meaning and development of irrational numbers. **
 * [|Math 09 - Number - Rational and Irrational Numbers.ppt] || What is the difference between a rational and and irrational number? All real numbers can be place exactly on a number line. Can you try and find the exact location of the square root of 2? || [|Math 09 - Number - The Real Number System practice.docx] ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Simplify, add, subtract, multiply and divide real numbers written in any form with emphasis on square root radicals and numbers written in scientific notation form. **
 * Operations with radicals || Task: How does a calculator calculate a radical? Page 99 MYP4 || Multiplying radicals
 * Review operations with real numbers || Review methods of multiplying and dividing decimals by finding reasonable estimates.
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Rationalize denominators for monomial and binomial square root radicals. ** ||
 * Rationalizing denominators ||  || Rationalizing denominators ||
 * <span style="font-family: Verdana,Geneva,sans-serif;">** Read, write, compare and order real numbers written in any form and find their approximate locations on a number line. **
 * Finding exact locations of rational and irrational numbers on a number line || Use a geometry set and Pythagoras to find irrationals on the number line - see Exercise 4A page 88
 * Review relationships between fractions, decimals and percents || Task: Egyptian fractions - representing fractions as the sum of unit fractions; using Egyptian fractions to compare and to divide up a whole into its parts. ||  ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Evaluate algebraic expressions which require the use of order of operations with real numbers written in any form with emphasis on radicals. ** ||
 * Order of operations || Evaluating expressions by substitution as well. ||  ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Master understanding and use of scientific notation and round numbers to a certain number of significant figures. ** ||
 * Significant figures || Significant figures, decimal places ||  ||
 * Scientific notation || Operations with numbers in scientific notation ||  ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Convert numbers into different base systems and perform simple addition and multiplication in different base systems ** ||
 * Understanding different base systems ||  ||   ||
 * Operations with numbers in different base systems ||  ||   ||