Number+8

** Number Sense **
 * = == Unit Questions == ||= == Significant Concepts == ||= == Area of Interaction == ||

Image: '[|Happy Pi Day (to the 36th digit)!] ' www.flickr.com/photos/64419960@N00/2332789392

Vocabulary

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

Key Links

 * [|Purple Math] || Lowest common multiple and greatest common factor ||
 * [|Purple Math] || Converting between fractions, decimals and percents ||
 * [|Purple Math] || Operations with fractions ||
 * AAA Math || Interactive activities for operations with rational numbers, ordering and comparing rational numbers ||

Content and skills

 * ===**Content** === || **Outcomes/Skills: ** ||
 * * real number system with emphasis on rational numbers
 * prime numbers
 * operations with real numbers
 * order of operations
 * absolute value
 * exponent laws
 * square and cube root radical expressions
 * scientific notation (standard form) || * define, the terms odd, even, prime, composite, positive and negative.
 * use a Venn diagram to show the relationships between the different types of numbers
 * classify a number as natural, integer, rational, irrational or real.
 * identify a prime number and use a test to determine whether or not a number is prime.
 * compare and order rational numbers and find their approximate location on the number line
 * master understanding of absolute value and simplify expressions containing absolute value
 * perform operations on real numbers.
 * use an estimation technique to judge the reasonable of results.
 * compute the square roots and cube roots of numbers which are perfect squares and cubes.
 * apply the laws of exponents to simplify expressions containing integer exponents.
 * understand and use the order of operations to simplify expressions.
 * write large and small numbers using scientific notation
 * perform simple operations on numbers written in scientific notation with an emphasis on using the exponent laws to simplify expressions. ||

Standards and Benchmarks
[|Math 08 - Number Systems - Real Number System Venn.doc] || [|Math 08 - Number Systems - Classifying Numbers Practice.docx] || [|Math 08 - Number - Prime Number Algorithm] [|PrimeAlgorithm.xlsx] [|Factors and Multiples Challenge_MS.docx] || [|Math 08 - Number - Factors and Multiples Practice] || [|Math 08 - Number - Operations with Decimals.docx] || You should be able to add, subtract, multiply and divide all types of numbers including natural numbers, integers, fractions and decimals || [|Math 08 - Number - Adding and Subtracting Fractions worksheet.pdf] [|Math 08 - Number - Fractions, decimals, percents worksheet.pdf] [|Math 08 - Number - Multiplying and Dividing Fractions worksheet.pdf] [|Math 08 - Number - Multiplying and Dividing Integers worksheet.pdf] [|Math 08 - Number - Operations with Decimals Worksheet.docx] || Investigate the converse of the rule of Pythagoras. Find missing sides in a right triangle. Find Pythagorean triples Solve problems involving the Pythagorean theorem || Ex. 9D Rule of Pythagoras Ex. 9E Converse of the rule of Pythagoras Ex. 9F Pythagorean triples Ex. 9G Using the rule of Pythagoras to solve problems ||
 * <span style="font-family: Verdana,Geneva,sans-serif;">**<span style="font-family: Verdana,Geneva,sans-serif;">Recognize and classify numbers in different number systems including the set of natural numbers and zero (N), integers (Z), rational numbers (Q), irrational numbers (Q’). **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Understand rational numbers as all numbers that can be expressed as a ratio of two integers and irrational numbers as numbers that cannot be expressed as a ratio of two integers. ** ||
 * <span style="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 define 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;">Primes, factors and multiples of natural numbers || <span style="font-family: Verdana,Geneva,sans-serif;">Do you know the difference between a factor and a multiple? How can we determine whether or not a number is a prime number? Use a spreadsheet to investigate the prime algorithm
 * <span style="font-family: Verdana,Geneva,sans-serif;">** Add, subtract, multiply, divide and carry out order of operations (including exponents) with rational numbers written in any form ** ||
 * [|Math 08 - Number - Operations with rational numbers.docx]
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Read, write, compare and order rational numbers written in any form and find their approximate locations on a number line ** ||
 * || Activities: Rational vs. Irrational skit, rational number bingo, ordering the class ||  ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Use square roots, cube roots, squares, and cubes of rational numbers in computation **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Begin to explore simplification of square root radicals by representing a number as a product of its prime factors ** ||
 * **<span style="font-family: Verdana,Geneva,sans-serif;">Investigate and develop understanding of the rule of Pythagoras and Pythagorean triples. **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Solve problems that require the use of the rule of Pythagoras. ** ||
 * [|Math 08 - Number - The Converse of the Pythagorean Theorem] || Use GSP to construct a tool for drawing squares. [|Pythagoras.gsp] Draw squares on the sides of a right triangle and investigate the relationship between the areas of the squares.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Solve problems that require the use of the rule of Pythagoras. ** ||
 * [|Math 08 - Number - The Converse of the Pythagorean Theorem] || Use GSP to construct a tool for drawing squares. [|Pythagoras.gsp] Draw squares on the sides of a right triangle and investigate the relationship between the areas of the squares.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Develop understanding of very large and very small numbers and recognize and use various representations of these numbers including exponential, scientific and calculator notation **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Write big and small numbers using scientific notation and convert from scientific form to standard form and vice versa **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Perform operations on numbers written in scientific notation **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Round numbers to a certain number of significant figures when using scientific notation **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Apply laws of exponents to numbers written in scientific notation **
 * operations/estimations on real numbers, comparing and ordering/locate on a number line, absolute value, square roots and cube roots, laws of exponents, order of operations, scientific notation and calculation ||
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use exponential notation (index notation) to express and simplify powers of rational numbers expressed in any form including squares, cubes, square roots and cube roots **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Investigate and develop conceptual understanding of negative and zero exponents and represent numbers using exponential form (index notation) **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Apply the laws of exponents (multiplication law, division law, power of a power, power of a product, power of a quotient) to simplify expressions containing integer exponents **
 * operations/estimations on real numbers, comparing and ordering/locate on a number line, absolute value, square roots and cube roots, laws of exponents, order of operations, scientific notation and calculation ||
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use exponential notation (index notation) to express and simplify powers of rational numbers expressed in any form including squares, cubes, square roots and cube roots **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Investigate and develop conceptual understanding of negative and zero exponents and represent numbers using exponential form (index notation) **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Apply the laws of exponents (multiplication law, division law, power of a power, power of a product, power of a quotient) to simplify expressions containing integer exponents **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Investigate and develop conceptual understanding of negative and zero exponents and represent numbers using exponential form (index notation) **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Apply the laws of exponents (multiplication law, division law, power of a power, power of a product, power of a quotient) to simplify expressions containing integer exponents **