Master: Number Theory

Master: Number Theory

Course Modules

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1. Distinguish among sets of numbers; Set of numbers: natural numbers {1, 2, 3, ...}, whole numbers {0, 1, 2, 3, ...}, integers {...-2, -1, 0, 1, 2, ...}, rational numbers (qp:p and q are integers, q ≠ 0), irrational numbers (numbers that cannot be expressed as terminating or recurring decimals, for example, numbers such as π and √2), the real numbers (the union of rational and irrational numbers); sequences of numbers that have a recognisable pattern; factors and multiples; square numbers; even numbers; odd numbers; prime numbers; composite numbers.
 
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Move done incomplete Classify and order real numbers (CK-12) Classify and order real numbers (CK-12)
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Move done incomplete Find factor pairs of given numbers (Open High School) Find factor pairs of given numbers (Open High School)
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Move done incomplete Real numbers and the number line (OpenAlgebra.com) Real numbers and the number line (OpenAlgebra.com)
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Move done incomplete Subsets of real numbers (CK-12) Subsets of real numbers (CK-12)
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Move done incomplete Classifying real numbers (Open High School) Classifying real numbers (Open High School)
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2. Order a set of real numbers.
 
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Move done incomplete Classify and order real numbers (CK-12) Classify and order real numbers (CK-12)
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Move done incomplete Compare decimals (Open High School) Compare decimals (Open High School)
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Move done incomplete Order decimals (Open High School) Order decimals (Open High School)
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Move done incomplete Order decimals from least to greatest (Open High School) Order decimals from least to greatest (Open High School)
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Move done incomplete Practice Number Theory Practice Number Theory
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3. Generate a term of a sequence given a rule; sequences of numbers that have a recognisable pattern.
 
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Move done incomplete Number patterns (Everything Maths) Number patterns (Everything Maths)
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Move done incomplete Number patterns (CNX) Number patterns (CNX)
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Move done incomplete Generate a sequence given a rule (millaismaths12 on YouTube) Generate a sequence given a rule (millaismaths12 on YouTube)
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4. Derive an appropriate rule given the terms of a sequence; sequences of numbers that have a recognisable pattern.
 
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Move done incomplete Number patterns (Everything Maths) Number patterns (Everything Maths)
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Move done incomplete Number patterns (CNX) Number patterns (CNX)
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Move done incomplete Number Series Tricks, Reasoning, Problems and Puzzles (unacademy on YouTube) Number Series Tricks, Reasoning, Problems and Puzzles (unacademy on YouTube)
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Move done incomplete Find a rule given a pattern (LearnZillion on YouTube) Find a rule given a pattern (LearnZillion on YouTube)
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5. Identify a given set of numbers as a subset of another set; Inclusion relations, for example, N ⊂ W ⊂ Z ⊂ Q ⊂ R.
 
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Move done incomplete Types of numbers (Wikipedia) Types of numbers (Wikipedia)
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Move done incomplete Real numbers and subsets (RSCSMATH on YouTube) Real numbers and subsets (RSCSMATH on YouTube)
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6. List the set of factors or a set of multiples of a given positive integer.
 
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Move done incomplete Factors (Wikibooks) Factors (Wikibooks)
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Move done incomplete Multiples, factors and primes (Teachertubemath on YouTube) Multiples, factors and primes (Teachertubemath on YouTube)
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7. Compute the H.C.F. or L.C.M. of two or more positive integers.
 
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Move done incomplete Find the LCM - book extract (Open High School) Find the LCM - book extract (Open High School)
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Move done incomplete Find the HCF or greatest common factor - book extract (Open High School) Find the HCF or greatest common factor - book extract (Open High School)
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Move done incomplete Find the lowest common multiple (Wikibooks) Find the lowest common multiple (Wikibooks)
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Move done incomplete Find the highest common factor (Wikibooks) Find the highest common factor (Wikibooks)
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Move done incomplete Find the GCF (HCF) and LCM (mathwithmrhunt.wikispaces.com) Find the GCF (HCF) and LCM (mathwithmrhunt.wikispaces.com)
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8. State the value of a digit in a numeral in base n, where n≤10; Place value and face value of numbers 2, 3, 4, 5, 6, 7, 8, 9 and 10 in base.
 
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Move done incomplete Express Decimals in Expanded Form - book extract (Open High School) Express Decimals in Expanded Form - book extract (Open High School)
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Move done incomplete Decimal place value (Open High School) Decimal place value (Open High School)
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Move done incomplete Number Theory Part 1 (Mastering Mathematics on YouTube) Number Theory Part 1 (Mastering Mathematics on YouTube)
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Move done incomplete Number Theory Part 2 (Mastering Mathematics on YouTube) Number Theory Part 2 (Mastering Mathematics on YouTube)
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9. Use properties of numbers and operations in computational tasks; Additive and multipicative identities and inverses, concept of closure, properties of operations such as commutativity, distributivity and associativity, order of operations in problems with mixed operations.
 
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Move done incomplete Number Operations - book extract The Next Step (New Brunswick Community College) Number Operations - book extract The Next Step (New Brunswick Community College)
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Move done incomplete Properties of real numbers (Rio Salado College OER) Properties of real numbers (Rio Salado College OER)
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Move done incomplete Associative and commutative properties (CK-12) Associative and commutative properties (CK-12)
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Move done incomplete Using the commutative and associative properties (Open High School) Using the commutative and associative properties (Open High School)
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Move done incomplete Using the distributive property (Open High School) Using the distributive property (Open High School)
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Move done incomplete Order of operations (Open High School) Order of operations (Open High School)
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Move done incomplete Number Theory Part 3 (Mastering Mathematics on YouTube) Number Theory Part 3 (Mastering Mathematics on YouTube)
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Move done incomplete Number Theory Part 4 (Mastering Mathematics on YouTube) Number Theory Part 4 (Mastering Mathematics on YouTube)
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10. Solve problems involving concepts in number theory.
 
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Move done incomplete Word problems - book extract The Next Step (New Brunswick Community College) Word problems - book extract The Next Step (New Brunswick Community College)
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Move done incomplete Problem solving using whole number operations (mkyou2tube on YouTube) Problem solving using whole number operations (mkyou2tube on YouTube)
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Move done incomplete Solving Math Word Problems (expertvillage on YouTube) Solving Math Word Problems (expertvillage on YouTube)
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Move done incomplete Problem Solving Using Whole Number Operations (mathispower4u on YouTube) Problem Solving Using Whole Number Operations (mathispower4u on YouTube)
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Self Assessment Activities
 
Move done incomplete Number Theory Self Assessment Quiz Number Theory Self Assessment Quiz
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