Monday, Aug. 24 th Chapter 1.1 – Chapter 1.2 – Monday, Aug. 24 th Chapter 1.1 – Simplifying and evaluating algebraic equations Chapter 1.2 – Properties of Real Numbers Essential Question: ◦ Can you identify, apply and solve equations and inequalities using algebra? Target: Students will be able to simplify and evaluate algebraic expressions as well as classify and use the properties of real numbers Agenda: ◦ COLORED Pens out please ◦ Homework Answers up for Quick Questions & Answers ◦ In class discussions and work problems ◦ Pencil and Calculators needed ◦ Homework – In class if time – DUE next class period

Grade Homework Teacher will collect and redistribute Students grade homework ◦ Sign on top of page ◦ Using colored pen, please correct as needed ◦ If student’s homework was completed – 4 pts ◦ If ¼ of it was not completed – 3 pts ◦ If ½ of it was not completed – 2 pts ◦ If only a problem or two – 1pt ◦ If none was completed – 0 pts Hand in to front of row for collection

The Sets of Real Numbers Rational Rational – ◦ Can be expressed as a ratio (m/n), where m and n are integers and n is not zero either or ◦ Decimal form of a rational number is either a terminating or repeating decimal ◦ i.e., 1/6, 1.9, …, -3, 0 Irrational Irrational - ◦ A real number that is not rational neither nor ◦ Decimal form of an irrational number neither terminates nor repeats ◦ i.e., π, …

Set of Rational Numbers Integers Integers - ◦ + or – Whole numbers {.., -3, -2, -1, 0, 1, 2, …} Whole Numbers Whole Numbers – ◦ Non-negative whole numbers {0, 1, 2,…} ◦ Every whole number n is equal to n/1

Practice Number Sets Look at examples on 1.1, page 1 and provide the abbreviation to the set(s) of number(s) to which each number belongs

Properties of Addition & Multiplication PropertyAdditionMultiplicationCommutative a + b = b + aa * b = b * a I can change the order Associative(a + b) + c = a + (b + c)(a * b) * c = a * (b * c) I can regroup Identitya + 0 = a = 0 + aa * 1 = a = 1 * a Adding 0 does not change original value Multiplying by 1 does not change the original value Inversea + (-a) = 0 = (-a) + aIf a ≠ 0, then a * 1/a = 1 = 1/a * a Adding the opposite results in 0Multiplying by the reciprocal results in 1 Distributivea(b + c) = ab + ac and (b + c) a = ba + ca

Properties of Addition & Multiplication

Practice Property Identification Look at examples on 1.1, page 2 and name the property for each illustration

Brain Break With a neighbor partner(s), take turns trying this exercise

Evaluate & Simplify Equations Exponents - a b = c a is the base b is the exponent c is the power Exponent represents the number of times the base is used as a factor Exponents represent repeated multiplication Exponents are applied immediately to the left

Absolute Value Absolute value represents the DISTANCE a number is from Zero (0) Distance is ALWAYS positive | | are the grouping symbols

Simplifying Expressions An expression is simplified when there are NO grouping symbols remaining and all like terms are combined Apply the distributive property when necessary and add/subtract like term coefficients

Order of Operations PEMDAS ◦ Simplify inside grouping symbols:  Parenthesis (or other grouping symbols:  ( ), [ ], { }, √, (a)/(b), | | ◦ Evaluate all Exponents ◦ Division/ Multiplication (Left to Right) ◦ Addition/ Subtraction (Left to Right)

Practice On Your Own Complete problems not worked on yet in class Practice on your own for 10 minutes before discussing with a neighbor or asking questions Homework Worksheets 1-1 & 1-2 Homework pages Due beginning of next class (Wed., Aug. 26 th )

Evidence of Understanding Name the at least 2 properties of REAL numbers ◦ Commutative ◦ Associative ◦ Identity ◦ Inverse ◦ Distributive Name 2 MAJOR classifications of numbers ◦ Rational & Irrational

Wed., Aug. 26 th Chapter 1.3 – Wed., Aug. 26 th Chapter 1.3 – Solving Equations Essential Question: ◦ Can you identify, apply and solve equations and inequalities using algebra? Target: Students will be able to solve equations using properties of equality. Students will solve absolute value equations. Agenda: ◦ COLORED Pens out please ◦ Homework Answers up for Quick Questions & Answers ◦ In class discussions and work problems ◦ Pencil and Calculators needed ◦ Homework – In class if time – DUE next class period

Grade Homework Teacher will collect and redistribute Students grade homework ◦ Sign YOUR NAME on top of page given ◦ Using colored pen, please correct as needed ◦ If student’s homework was completed – 4 pts ◦ If ½ of it was not completed – 3 pts ◦ If ¼ of it was not completed – 2 pts ◦ If only a problem or two – 1pt ◦ If none was completed – 0 pts Hand in to front of row for collection

Equation Equation Equation – A statement saying that two expressions are EQUAL General Rule General Rule – what you do to one side of the equation, you must do to the other (equal) Linear Equation Linear Equation – an algebraic equation in which each term is either a constant or the product of a constant and the first power of a single variable

To Solve an Equation: 1. Apply the Distributive Property or Fraction Bust 3(x-2) = 9 3x – 6 = 9 ◦ 3(x-2) = 9 is 3x – 6 = 9 (multiply 3 to each term) 1/3(x-2)=7 x – 2 = 21 ◦ or 1/3(x-2)=7 is x – 2 = 21 (multiply both by 3) 2. Clean up – combine like terms or either side of the equal sign 3x = 15 (add the 6 to both sides) ◦ 3x = 15 (add the 6 to both sides) ◦ x = 23 (add the 2 to both sides) 3. Isolate the variable – get it alone on one side x = 15/3 (divide by 3) ◦ x = 15/3 (divide by 3) ◦ x = Undo the Order of Operations x=5 ◦ x=5 ◦ x=23 5. Check your Answers! Substitute into the original equation 3(5-2)=9…. 3(3)=9….9=9 ◦ 3(5-2)=9…. 3(3)=9….9=9 ◦ 1/3(23-2)=7….1/3(21)=7… 7=7

Practice On Your Own Complete problems not worked on yet in class Practice on your own for 10 minutes before discussing with a neighbor or asking questions Homework Pg. 25 #41-65 Odd, 66, 67 ◦ Note – you will get NO credit if you do not copy problem and show ALL work Due beginning of next class (Fri., Aug. 28th)

Evidence of Understanding Name the at least 2 properties of REAL numbers ◦ Commutative ◦ Associative ◦ Identity ◦ Inverse ◦ Distributive Name 2 MAJOR classifications of numbers ◦ Rational & Irrational

Fri., Aug. 28 th Chapter 1.5 & 1.6 – Fri., Aug. 28 th Chapter 1.5 & 1.6 – Solving Linear Inequalities Essential Question: ◦ Can you identify, apply and solve equations and inequalities using algebra? Target: Students will be able to solve equations using properties of inequalities. Students will solve absolute value equations. Agenda: ◦ COLORED Pens out please ◦ Homework Answers up for Quick Questions & Answers ◦ In class discussions and work problems ◦ Pencil and Calculators needed ◦ Homework – In class if time – DUE next class period NOTE: Quiz Tuesday, Sept. 1 over 1.1 – 1.3

Grade Homework Teacher will collect and redistribute Students grade homework ◦ Sign YOUR NAME on top of page given ◦ Using colored pen, please correct as needed ◦ If student’s homework was completed – 4 pts ◦ If ½ of it was not completed – 3 pts ◦ If ¼ of it was not completed – 2 pts ◦ If only a problem or two – 1pt ◦ If none was completed – 0 pts Hand in to front of row for collection

Inequalities 1. Solve using the same process used to solve linear equations 2. The difference is in the sign. IF you multiply or divide by a negative number, then you MUST reverse the sign Information in Book – Chapter 1.5 & 1.6

Tues., Sept. 1 st Chapter 1.5 & 1.6 – Tues., Sept. 1 st Chapter 1.5 & 1.6 – Solving Linear Inequalities Essential Question: ◦ Can you identify, apply and solve absolute equations and inequalities using algebra? Target: Students will be able to solve absolute equations using properties of inequalities. Students will solve absolute value equations. Agenda: ◦ Quiz – please take out pencil & calculators ◦ COLORED Pens out please ◦ Homework Answers up for Quick Questions & Answers ◦ In class discussions and work problems ◦ Homework – In class if time – DUE next class period NOTE: Quiz today 1.1 – 1.3 Test Chapter 1 Sept. 9th NOTE: Quiz today 1.1 – 1.3 Test Chapter 1 Sept. 9th

Absolute Value The absolute value of a number is its distance from 0 on a number line Since distance is nonnegative, the absolute value of a number is always nonnegative They symbol |x| is used to represent the absolute value of a number x

Solving Absolute Value Equations For any real number (a) ◦ If (a) is positive or zero, the absolute value of (a) is (a) ◦ If (a) is negative, the absolute value of (a) is the opposite of (a) Example: ◦ |-3| = 3 and |3| = 3 Absolute value indicates DISTANCE from zero The absolute value bars | | act as a grouping symbol – perform any operations inside the absolute value bars FIRST Do NOT perform the distributive property

Evaluate an expression |5y-7| if y =3 Replace y with -3 then work through ◦ |5(-3)-7| ◦ |-15 – 7| ◦ |-22| ◦ ◦ 23.4 The value is 23.4 Remember to check

Solve an Absolute Value Equation |x-18| = 5 Case 1: a=b  x-18=5  x=23 Case 2: a=-b  x-18=-5  x=13 Check each case |23 – 18| = 5  |5|=5, 5=5 |13 – 18| = 5  |-5|=5, 5=5

Empty Sets or One Solution Empty Set ◦ Where you get no solution – meaning when you solve and check – it does not equal One Solution ◦ Where you have only one of the two solutions that works – meaning when you solve and check – only one answer works

Fri., Sept. 4 th Chapter 1.4 & 1.6 – Fri., Sept. 4 th Chapter 1.4 & 1.6 – Solving Absolute Equations and Inequalities Essential Question: ◦ Can you identify, apply and solve absolute equations and inequalities using algebra? Target: Students will solve absolute value inequalities and recall Chapter 1 concepts Agenda: ◦ Khan Academy ◦ 1.4 Homework Corrections ◦ 1.6 Absolute inequalities ◦ Chapter 1 Review Sheet NOTE NOTE: Test Chapter 1 Sept. 11th NOTE NOTE: Test Chapter 1 Sept. 11th

Khanacademy.org

Absolute Value Inequalities On a number line – solution is the absolute value distance from zero | a | < 4 (LESS THAN) Which means it can be LESS THAN 4 units in EITHER direction from Zero All the numbers between -4 and 4 are less than 4 units from 0 -4 < a < 4

Absolute Value Inequalities On a number line – solution is the absolute value distance from zero | a | > 4 (GREATER THAN) Which means it can be MORE THAN 4 units in EITHER direction from Zero All the numbers NOT between -4 and 4 are greater than 4 units from 0 4 >a or a< -4

Steps to solving Absolute Values 1. Isolate absolute value term to the left 2. List the 2 Cases where 1.IF |a| -b 2.IF |a| > b then a > b and a <-b 3. Solve each case as you would an equations to get your values 4. Replace the ORIGINAL equation with the value found and see if holds true 5. Your solution will be any condition that holds true when substituted back into the original equation. 6. Draw on the number line

Homework Pg. 44 #33-39 Khan Academy