Lesson Menu Main Idea and New Vocabulary Key Concept:Commutative Properties Key Concept:Associative Properties Key Concept:Number Properties Example 1:Identify.

Slides:

Advertisements

Similar presentations

Welcome to Interactive Chalkboard

Advertisements

Commutative and Associative Properties

Chapter 3 Math Vocabulary

Transparency 2 Click the mouse button or press the Space Bar to display the answers.

Vocabulary Section 1-2 Power: has two parts a base and an exponent.

PO D basicadvanced 4b + 6 b= 5, c= 3, d=7 (10c ÷b) 2 + d 4(5) (10(3) ÷5) (30 ÷5) (6)

Algebra 1 Chapter 1 Section Properties of Real Numbers The commutative and associate properties of addition and multiplication allow you to rearrange.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–2) Then/Now Key Concept: Product Powers of Property Example 1:Multiply Powers Example 2:Multiply.

Chapter 1-4: Properties Commutative Property: the order in which you add or multiply numbers does not change the sum or product Ex = * 8.

Algebra Properties of Real Numbers

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 3) Then/Now New Vocabulary Key Concept: Distributive Property Example 1: Evaluate Numerical.

Properties and Numbers 1.4. Deductive Reasoning Using facts, properties or rules to reach a valid conclusion Conjecture: statement that could be true.

Course Properties Learn how to identify properties of rational numbers and use them to simplify numerical expressions.

1-6 Properties of Real Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Splash Screen. Lesson Menu Main Idea and Vocabulary Key Concept: Distributive Property Example 1:Write Sentences as Equations Example 2:Write Sentences.

Properties of Real Numbers The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

1-3 Properties of Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

1-8 Simplifying Expressions Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation.

Holt McDougal Algebra Simplifying Expressions Warm Up Add Multiply (8) (22)

Holt Algebra Simplifying Expressions Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. Objectives.

Over Lesson 1–2 A.A B.B C.C D.D 5-Minute Check 1 A.15 B.11 C.7 D.6 Evaluate the expression c + 8 – a if a = 4 and c = 3. Evaluate the expression 7a –

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 1–7) Main Idea and Vocabulary Key Concept: Distributive Property Example 1:Write Sentences as.

PROPERTIES OF OPERATIONS Section 5.3. PROPERTIES OF OPERATIONS  The _________ Property states that the order in which numbers are added or multiplied.

The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes , 31, 43, 55,… , 64, 50, 36,… , 4.1, 4.8,

Lesson 1-4 Pages Properties Lesson Check 1-3.

Holt Algebra Simplifying Expressions 1-7 Simplifying Expressions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.

1.4 Properties of Real Numbers ( )

Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Pairs of Angles Example 1:Identify Angles Example 2:Identify Angles Example 3:Find a Missing.

Lesson Menu Main Idea Key Concept:Zero and Negative Exponents Example 1:Write Expressions using Positive Exponents Example 2:Write Expressions using Positive.

+ Properties of Real Numbers. + Properties Relationships that are always true fro real numbers are called properties. Properties are rules used to rewrite.

Name the property shown by each statement. 1. a + (b + c) = (a + b) + c 2. 3(ab) = (ab)3 3. z + y + 0 = z + y 4. 7 h 0 = 0 5. Dance lessons cost $100 per.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–6) Main Idea Key Concept: Multiplication Properties Example 1:Identify Multiplication Properties.

1-4 Properties How are real-life situations commutative?

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

Objective The student will be able to:

Simplifying Expressions

Main Idea and New Vocabulary Key Concept: Distributive Property

Main Idea and New Vocabulary NGSSS Key Concept: Pairs of Angles

Properties of Operations

Main Idea and New Vocabulary Key Concept: Product of Powers

Example 4: Divide Powers

Simplifying Expressions

Warm Up Simplify each expression – 5 ● ÷ 2 ● 4

Simplifying Expressions

Main Idea and New Vocabulary

Main Idea and New Vocabulary Key Concept: Volume of a Cylinder

Properties of Numbers Use mental math to simplify –2 • 13 • 5.

Equations and Inequalities

Main Idea and New Vocabulary Example 1: Write Expressions Using Powers

Key Concept: Zero and Negative Exponents

Example 1: Equations with Variables on Each Side

Main Idea and New Vocabulary Example 1: Solve Two-Step Equations

Properties of Real Numbers

Warm Up Evaluate · · · 3. ( ) + ( )‏ 4. 4(32) – 16(8)

Simplifying Expressions

Main Idea and New Vocabulary

Example 4: Divide Powers

MATH PROPERTIES LESSON OBJECTIVE: To identify and use various math properties. STANDARD: MCC6.EE.3 – Simplify & evaluate expressions using various math.

Simplifying Expressions

Simplifying Expressions

Main Idea and New Vocabulary Example 1: Write Expressions Using Powers

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Lesson 3 Properties of Operations

Example 1: Multiplication and Division with Scientific Notation

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Presentation transcript:

Lesson Menu Main Idea and New Vocabulary Key Concept:Commutative Properties Key Concept:Associative Properties Key Concept:Number Properties Example 1:Identify Properties Example 2:Find a Counterexample Example 3:Use Mental Math Example 4:Simplify Algebraic Expressions Example 5:Simplify Algebraic Expressions

Main Idea/Vocabulary Identify and use mathematical properties to simplify algebraic expressions. property counterexample simplify

Key Concept

Key Concept 1a

Key Concept 1b

Example 1 Identify Properties Name the property shown by the statement (3 m) 2 = 2 (3 m). Answer:The grouping of the numbers and variable did not change, but their order did. This is the Commutative Property of Multiplication.

Example 1 CYP A.Associative Property of Addition B.Associative Property of Multiplication C.Commutative Property of Addition D.Commutative Property of Multiplication Name the property shown by the statement 4 + (8 + x) = (4 + 8) + x.

Example 2 State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is associative. Find a Counterexample Write two subtraction expressions using the Associative Property. 4 ≠ 10Simplify. (12 – 5) – 3 = 12 – (5 – 3)State the conjecture. ? Answer:The conjecture is false. We found a counterexample: (12 – 5) – 3 ≠ 12 – (5 – 3). So, subtraction is not associative.

Example 2 CYP A.true B.false; (16 ÷ 8) ÷ 2 ≠ 16 ÷ (8 ÷ 2) State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is associative.

Example 3 Use Mental Math GARDENS In a museum garden, a decorative pool containing fish is 2 feet deep, 17 feet long, and 5 feet wide. Use mental math to find the volume of water in the pool. Write an expression for the volume. You can rearrange the numbers using the properties of math. Look for products that are multiples of × 17 × 5= 2 × 5 × 17 Commutative Property = (2 × 5) × 17Associative Property = 10 × 17 Multiply. = 170 Simplify. Answer:The volume of the water is 170 cubic feet.

Example 3 CYP A.50 pounds B.60 pounds C.70 pounds D.80 pounds ROCKS A landscaper bought four rocks to use in a landscaping project. The rocks weighed 15 pounds, 22 pounds, 8 pounds, and 25 pounds. Use mental math to find the total weight of the rocks.

Example 4 Simplify the expression 6 + (d + 8). Justify each step. Simplify Algebraic Expressions Answer: 6 + (d + 8)= 6 + (8 + d) Commutative Property of Addition = (6 + 8) + d Associative Property of Addition = 14 + d Simplify.

Example 4 CYP A.5m + 14; Commutative (+) and Associative (+) B.11m + 8; Commutative (×) and Associative (×) C.16m + 3; Commutative (+) and Associative (+) D.16m; Commutative (×) and Associative (×) Simplify the expression 5m + (3 + 11m). Name two properties you can use to justify the steps.

Example 5 Simplify Algebraic Expressions Simplify the expression a (9 b). Justify each step. Answer: a (9 b)= (a 9) b Associative Property of Multiplication = (9 a) bCommutative Property of Multiplication = 9ab Simplify.

Example 5 CYP A.9t; Commutative (×) and Associative (×) B.14t; Commutative (×) and Associative (×) C.14 + t; Commutative (+) and Associative (+) D.7t + 2; Commutative (×) and Associative (+) Simplify the expression 7 (t 2). Name two properties you can use to justify the steps.