How can you use numbers and symbols to represent mathematical ideas?

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Presentation transcript:

How can you use numbers and symbols to represent mathematical ideas? Rational Numbers and Exponents How can you use numbers and symbols to represent mathematical ideas? Lesson 1-4

Identify and use properties of addition and multiplication Rational Numbers and Exponents Identify and use properties of addition and multiplication Use properties to simplify algebraic expressions Lesson 1-4

Counterexample – an example that shows the conjecture is not true. Rational Numbers and Exponents Counterexample – an example that shows the conjecture is not true. Deductive reasoning – the process of using facts, properties, or rules to justify reasoning. Simplify – to write an expression in simpler form. Properties – statements that are true for any number. Lesson 1-4

Commutative Properties Rational Numbers and Exponents Commutative Properties Words The order in which numbers are added or multiplied does not change the sum or product. Symbols For any numbers a and b, a + b = b + a. For any numbers a and b, a · b = b · a. Examples 6 + 9 = 9 + 6 4 · 7 = 7 · 4 15 = 15 28 = 28 Lesson 1-4

Associative Properties Rational Numbers and Exponents Associative Properties Words The order in which numbers are grouped when added or multiplied does not change the sum or product. Symbols For any numbers a, b, and c, (a + b) + c = a + (b + c). For any numbers a, b, and c, (a · b) · c = a · (b · c). Examples (3 + 6) + 1 = 3 + (6 + 1) (5 · 9) · 2 = 5 · (9 · 2) 9 + 1 = 3 + 7 45 · 2 = 5 · 18 10 = 10 90 = 90 Lesson 1-4

Number Properties Property Words Symbols Examples Additive Identity Rational Numbers and Exponents Number Properties Property Words Symbols Examples Additive Identity When 0 is added to any number, the sum is the number For any number a, a + 0 = 0 + a = a 5 + 0 = 5 0 + 5 = 5 Multiplicative Identity When any number is multiplied by 1, the product is the number. For any number a, a · 1 = 1 · a = a. 8 · 1 = 8 1 · 8 = 8 Multiplicative Property of Zero When any number is multiplied by 0, the product is 0. For any number a, a · 0 = 0 · a = 0 3 · 0 = 0 0 · 3 = 0 Lesson 1-4

How did what you learned today help you answer the Rational Numbers and Exponents How did what you learned today help you answer the How can you use numbers and symbols to represent mathematical ideas? Lesson 1-4

Rational Numbers and Exponents Ratios and Proportional Relationships Name two properties and explain how the properties help you in mathematics. Your explanations should include examples of the properties. Lesson 1-4

Mathematical Practices Rational Numbers and Exponents 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 7 Look for and make use of structure. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Lesson 1-4