VIEWS: 1 PAGES: 56 POSTED ON: 10/6/2011 Public Domain
Homework 1A1a Finish on worksheet 1-1, Expressions and Formulas p. 1 problems 3, 9, 12, 18 & 24 p. 2 problem 3 Finish on worksheet 1-2, Properties of Real Numbers p. 7 problems 4, 11, 14, & 20 p. 8 problems 3, 9 & 18 Find the Perimeter and Area of the Rectangle 2x 4x +5 Find the Perimeter and Area of the Rectangle 3x 7x -25 Vocabulary Builder Use the textbook to find and define the vocabulary for Unit 1: Solving Equations and Inequalities Lesson A2U1L1 a: Order of Operations Motivation: Order, Order, Order! What do the words ace, lost, bent, and below have in common? The letters of each word Hint : Look at the order of are in alphabetical order. the letters Order of Operations Objective: The student will: • use the order of operations and properties of real numbers to evaluate expressions; Order of Operations Going on a Trip Arrange the five sentence strips in the proper order. Close the car door. Unlock the car door. Buckle the seat belt. Drive the car. Open the car door. Order of Operations Going on a Trip This is the proper order. Unlock the car door. Open the car door. Close the car door. Buckle the seat belt. Drive the car. Order of Operations Arrange the four sentence strips in the proper order. Do all multiplications and/or divisions from left to right. Exponents. Evaluate all powers. Do all additions and/or subtractions from left to right. Parentheses - Evaluate expressions inside grouping symbols. Order of Operations This is the proper order. Parentheses - Evaluate expressions inside grouping symbols. Exponents. Evaluate all powers. Do all multiplications and/or divisions from left to right. Do all additions and/or subtractions from left to right. Order of Operations Evaluate the expression. 54 3 9 6 The correct answer is 6, because 3 Second First 33 = 27 (9 – 6) = 3 Our new expression is 54 / 27 * 3 Third Fourth 54 / 27 = 2 2*3=6 Kobe and Kameron are evaluating . Their work is shown below. Who is correct? Use what you know about order of operations to explain your answer. 3 8 5 3 20 2 2 3 3 8 5 3 20 2 2 3 Kobe Kameron 33 8 5 27 3 3 8 5 3 27 3 20 2 2 20 8 2 3 20 2 2 20 8 2 3 24 24 12 2 20 16 24 24 24 4 1 6 Work on the worksheet 1-1 Expressions & Formulas p. 1 problems 1-15 Only after you finish the first 10 problems, may you put one on the board for extra credit!! Evaluating Expressions Determine which keystroke combination is correct to evaluate the expression b+cd when a=1 b=4 c=2 & d=3 a+c2 4 23 1 2 2 Work on the worksheet Expressions & Formulas p. 1 problems 16-27 p. 2 problems 1, 2, & 4 Only after you finish the first 10 problems, may you put one on the board for extra credit!! Closer 1A1 #1 Evaluate: 60 48 2 43 Closer 1A1 #2 Evaluate the expression if x = 3, y = 5, and z = 8. 2 x y z Closer 1A1 #2 Evaluate the expression if x = 3, y = 5, and z = 8. 4 x( z y ) 6 x Lesson A2U1L1 b: Properties of Real Numbers Motivation: Write 5 different types of numbers Properties of Real Numbers Type of Number Points Whole Number 1 Negative Number 1 Zero 2 Rational Number 2 Irrational Number 5 Trancendental Number 10 Use the chart on 1-2 p. 7 to score your numbers Properties of Real Numbers Objective: The student will: • classify real numbers; • use the properties of real numbers to evaluate expressions; Classifications of Real Numbers RE Real Numbers All Rational and Irrational Numbers IR Irrational Numbers that cannot be expressed Numbers as a fraction. {all non-terminating, non-repeating decimals. RA Rational Numbers Numbers that can be expressed as a fraction. {a/b when b≠0} IN Integers {…,-5,-4,-3,-2,-1,0,1,2,3,4,5,…} W Whole Numbers {0,1,2,3,4,5,…} N Natural Numbers {1,2,3,4,5,…} Rules for Sets of Real Numbers All Natural Numbers are: • Whole Numbers, Integers, Rational Numbers, and Real Numbers. All Whole Numbers are: • Integers, Rational Numbers, and Real Numbers All Integers are: • Rational Numbers, and Real Numbers All Rational Numbers are Real Numbers All Irrational Numbers are Real Numbers No Rational Numbers are Irrational Numbers No Irrational Numbers are Rational Numbers Sets of Real Numbers Use the chart to place these numbers in the appropriate classification. 7 Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Real Numbers -6.3 Rational Numbers and Real Numbers π Irrational Numbers Sets of Real Numbers Use the chart to place these numbers in the appropriate sets. 17 Irrational Numbers 2/3 Rational Numbers and Real Numbers -3 Integers, Rational Numbers, and Real Numbers Properties of Real Numbers Use your skills and notes to determine the type of number for p. 7 1-2 Study Guide and Intervention Properties of Real Numbers problems # 1 - 20 Properties of Real Numbers Property Addition Multiplication Commutative x+y=y+x x*y=y*x Associative x+(y+z)=(x+y)+z x*(y*z)=(x*y)*z Identity x+0=x=0+x x*1=x=1*x Inverse x+ (-x)=0= (-x) +x x*1=1=1*x x x Distributive x (y+z) = xy + xz (y+z) x = yx + zx A number’s additive inverse is called it’s opposite number. A number’s multiplicative inverse is called it’s reciprocal. Properties of Real Numbers Read the chart at the top of p. 8 1-2 Study Guide. Use the chart to simplify each expression on p. 8 1-2 Study Guide problems # 1-18 Lesson A2U1L1 c Solving Equations Objective: The student will: • solve equations using the properties of equality Solving Any Equation Isolate the variable Step 1: Combine Like Terms Step 2: Add the Opposite Term. Step 3: Multiply by the Reciprocal of the Coefficient of the Variable. Solving Equations by using Multiplication and Division. Isolate the variable Step 1: Combine Like Terms Step 2: Add the Opposite Term. Step 3: Multiply by the Reciprocal of the Coefficient of the Variable. Solving Equations by Using Multiplication and Division. Isolate the variable Step Multiply by the Reciprocal Step 1: Combine Like Terms Step 3: 2: Add the Opposite Term. of There are no Like Terms to Combine. the Coefficient of the Variable. 1 1 8x 56 8 56 8 x 8 x7 The reciprocal of 8 is 1 / 8. Solving Equations by Using Multiplication and Division. Isolate the variable Step Multiply by the Reciprocal Step 1: Combine Like Terms Step 3: 2: Add the Opposite Term. of There are no Like Terms to Combine. the Coefficient of the Variable. 43 4 4 x 21 3 84 3 x 3 x 28 The reciprocal of 3/4 is 4 / 3. Solving Equations by using Addition and Subtraction. Isolate the variable Step 1: Combine Like Terms Step 2: Add the Opposite Term. Step 3: Multiply by the Reciprocal of the Coefficient of the Variable. Solving Equations by Using Addition and Subtraction. Isolate the variable Step Multiply by the Reciprocal Step 1: Combine Like Terms Step 3: 2: Add the Opposite Term. of the Coefficient of the Variable. There are no Like Terms to Combine. x 8 11 8 8 x 3 The opposite of +8 is – 8. Solving Equations by Using Addition and Subtraction. Isolate the variable Step Multiply by the Reciprocal Step 1: Combine Like Terms Step 3: 2: Add the Opposite Term. of the Coefficient of the Variable. There are no Like Terms to Combine. y 5 19 5 5 x 24 The opposite of – 5 is + 5. Solving Equations with the Variable on Each Side . Isolate the variable Step Multiply by the Reciprocal Step 3: 2: Add the Opposite Term. of Step 1: Combine Like Terms the Coefficient of the Variable. 3x 9 65 5x 5 x 9 9 5 x 8x 56 1 1 8 56 8 x The opposite of 98is – 9; The The reciprocal5x is 1 / 8. There are no Like Terms. opposite of –of7 5x. x 8 Solving Equations with the Variable on Each Side. Isolate the variable Step Multiply by the Reciprocal Step 1: Combine Like Terms Step 3: 2: Add the Opposite Term. of the Coefficient of the Variable. 21 9x 11x 13 13 9 x 9 x 13 1 1 8 2x 2 8 2 There are x 4 13. 2. of 13 is – The oppositeno Like Terms. The opposite of of 2 – 1 / The reciprocal 9x is is 9x. 2 Think-Pair-Share With a partner, solve Problems # 1, 2, & 3 on page 14 of worksheet 1-3 Study Guide and Intervention Solving Equations. One partner will write the problem and its solution on the board. The other partner will explain how the solution was found. Work on the worksheet 1-3 Solving Equations p. 13 problems 1-11 p. 14 problems 1-25 Only after you finish the first 8 problems, may you put one on the board for extra credit!! Solving for One Variable Using the TI-83 Calculator b + 9 = 17 Enter the leftthe letter graph Enter the ZOOM 6 of view any Substitute side to x for Press the right sideto the a Press ZOOM 3 of the the equation of the equation. equation in Y2: larger graph other in Y1: equationletter. x + 9 = 17 Solving for One Variable Using the TI-83 Calculator b + 9 = 17 b = 8. Press x + 9 = 17 x = 8. The value of value Therefore, the x is 8. of b is 8. Setting up and solving a problem involving a formula letter x for the Substitute the numbers for the variables (letters). unknown variable (letters). A = lw, when A= 48 & w=8 48 = l 8 48 = x 8, Solve for x. Solving for One Variable Using the TI-83 Calculator 48 = x 8 Enter thetheZOOM 6 to graph the the left ENTER the PressPressZOOM 3side of the PressEnter right side of to the the equationY1: view equation in ZOOMa3larger graph of the equation in Y2: ENTER to equation. view a larger graph of the equation. Solving for One Variable Using the TI-83 Calculator 48 = l 8 l = 6. Press 48 = x 8 6 = x. The value of value Therefore, the x is 6. of l is 6. Check worksheet 1-3 Solving Equations p. 13 problems 1-11 p. 14 problems 1-25 using the TI-83 Calculator. Only after you finish the first 8 problems, may you put one on the board for extra credit!! Setting Up Word Problems Step 1: Highlight math numbers/words Step 2: Create a number sentence. Step 3: Use the steps from Solving for One Variable Using the TI-83 Calculator. • Copy today’s notes into your “notesbook”! Setting Up Word Problems Step 1: Highlight math numbers/words Randy Anderson got a raise of 73¢ per hour. He now earns $8.45 per hour. What was his hourly rate before his raise ? Step 2: Create a number sentence. $8.45 = x + .73 Step 3: Use the steps from Solving for One Variable Using the TI-83 Calculator. Press 8.45 = x + .73 x = $7.72 The value of x is 7.72. Work worksheet 1-3 Solving Equations p. 16 problems 25-26 Check p. 16 problems 25-26 using the TI-83 Calculator. Only after you finish the first 8 problems, may you put one on the board for extra credit!! Closer A2U1L1 #1 Evaluate the expression -2b + a2c when a=4 b= -3 & c = 1/2 Closer A2U1L1 #2 Admission to Six Flags is $42. A chicken box costs $5.50. If you have only $70 total to spend for admission and pizza. How many chicken boxes can you buy? Closer A2U1L1 #3 The elements of set A consists of factors of 15. The elements of set B consists of factors of 21. What is A U B? a. { } b. { 1 } c . { 1, 3} d . { 1, 3, 5, 7 } e . { 3, 6, 9, 12, 15, 18, 21 }