# Exploring Integers Chapter 2. Chapter 2 – Exploring Integers Chapter Schedule T - 2-1 Integers and Absolute Values B - Math Lab – 1-7 & 2-2 The Coordinate.

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Exploring Integers Chapter 2

Chapter 2 – Exploring Integers Chapter Schedule T - 2-1 Integers and Absolute Values B - Math Lab – 1-7 & 2-2 The Coordinate System FRIDAY - QUIZ 2A M - 2-3 Comparing and Ordering T - 2-4 Adding Integers B - Math Lab - 2-5 Subtracting Integers FRIDAY - Quiz 2B M - 2-6 Problem Solving: Look for a Pattern T - 2-7 Multiplying Integers B - Math Lab - 2-8 Dividing Integers FRIDAY - Quiz 2C M - No School – Columbus Day T- Chapter 2 Quiz Reviews B - Chapter 2 Review Math Lab FRIDAY - Chapter 2 Test M- Chapter 1 Review T- Chapter 2 Review Mid-Term Review THURSDAY/FRIDAY – MID-TERMS!!!!! – Report Cards – END OF 1 st Quarter M- MONDAY T- TUESDAY B- BLOCK F- FRIDAY

2.1 Integers and Absolute Value Objective: Graph integer on a number line and find absolute value Warm-up: Answers: 1)20 2)25 3)23 4)28 5)24 6)28 7)3 8)9

More  PEMDAS Answers: 9)1 10)1 11)8 12)1 13)8 14)4 NOTES:

2.1 Integers and Absolute Value What is an “Integer”?

2.1 Integers and Absolute Value Can you graph numbers on a number line? Graph these on a number line: A = - 2 B = 3C = 4 Which one has the largest ABSOLUTE VALUE? B = 4  Because it is the farthest from ZERO

2.1 Integers and Absolute Value The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive. On a number line it is the distance between the number and zero. ◦ The absolute value of -15 is 15. ◦ The absolute value of +15 is ALSO 15 The symbol for absolute value is to enclose the number between vertical bars such as |-20| = 20 and read "The absolute value of -20 equals 20“.

2.1 HOMEWORK P69 (18 - 48 EVEN)

Math Lab Section A – Individual Section A – Individual ◦ WS- One-Step Equations With Integers ◦ WS - One-Step Equations with Decimals Section B - Teacher Section B - Teacher ◦ 1-7 Ordered Pairs  P59 (50-55 ALL) ◦ 2-2 The Coordinate System  P74-75 (6-39 x3) Section C - Group Section C - Group ◦ Equation Scrabble FOR POINTS – Winners get EC!!!

1-7 Ordered Pairs 2-2 The Coordinate System Objectives: To locate and graph points on number line and in all quadrants of the coordinate plane

1-7 Ordered Pairs 2-2 The Coordinate System Objectives: To locate and graph points on number line and in all quadrants of the coordinate plane Team A – NEGATIVES!Team B – POSTIVIES! Rules: Play 1 coin per turn Must alternate (+) and (-) each turn First team past their 5 wins!

2.2 The Coordinate System NOTES: We will start off with the Rectangular Coordinate system. This is just the standard axis system that we use when sketching our graphs.

Sketch the Graph xy -25 0 0-3 1-4 2-3 30 45

Math Lab - HOMEWORK 1-7 Ordered Pairs ◦ P59 (50-55 ALL) 2.2 The Coordinate System ◦ P74-75 (14 - 38 EVEN)

2.3 Comparing and Ordering Objective: To compare and order integers Warm-up: (USE Graph Paper!) Graph the following coordinates X and Y Axes: 1. E (1, -3) 2. M (-4, 2) 3. I (0, -2) 4. L (2, 0) 5. Y (-3, -4) Graph the following inequalities individually: 6. J > -2 7. O < 6 8. E < 4 9. Y < -3 Answers: On Graph

Quiz 2A – Results! Period 1Period 2Period 3 Chapter 1 Test Average 91% A- 87% B 92% A- Quiz Average 80% B- 90% A- 85% B Binder Check Average 35/5030/50 27/30 (NO MATH Lab WS) Overall Class Average (as of 9/21) 70% C- 73% C 71% C-

2.3 Comparing and Ordering NOTES: Graphing Inequalities on a Number Line 1.X < 0 2.X < 0 3.Y >15 4.Y > 15

2.3 Comparing and Ordering NOTES: Graphing Inequalities with ABSOLUTE VALUES J) Is 4 < |-4| ? Answer: _______ O) Is -4 < |-4| ? Answer: _______ E) Is |4| < |-4| ? Answer: _______ Y) Is 4 < |4| ? Answer: _______ K) Is -4 < |4| ? Answer: _______ R) Is 4 < |4| ? Answer: _______

2.3 Comparing and Ordering P79 - 80 (15-42 x3 & 44)

2.4 Adding Integers Objective: To add integers Warm-up: Replace the ? with a, >, or = : 1. - 9 ? 8 2. 0 ? – 4 Write an inequality using the numbers in each sentence. Use “relation symbols”. 3. A turkey sandwich cost \$6 and a turkey dinner costs \$11. 4. The low temperature was - 42 ° F and the temperature now is - 46 ° F. Answers: 1)< 2)> 3)6 < 11 4)-42 > - 46

2.4 Adding Integers NOTES: Remember! If the signs are different, subtract their ABSOLUTE VALUES! Adding Integers Game

2.4 Adding Integers P86-87 (10 – 44 EVEN)

MATH LAB – 2.5 Subtracting Integers Section A – Individual WS Section A – Individual WS ◦ Inequalities and Their Graphs ◦ Solving One-Step Inequalities by Adding/Subtracting Section B – Teacher Section B – Teacher ◦ 2.5 Subtracting Integers Lesson Section C – Group Section C – Group ◦ Math Games Math Games

MATH LAB – 2.5 Subtracting Integers Objective: To subtract integers Warm-up: 1. Draw this “Magic Triangle” on your paper 2. Then look up “inverse”. How would it be useful when solving equations?

2.5 Subtracting Integers 9 – (- 3) = 9 + (+3) = 12 -7 – (-5) = -7 – (-5) = -7 + (+5) = -2 21 – (-19) = 21 – (-19) = 21 + (+19) = 40 3 - (+5) = 3 + (-5) = -2 -25 - (+25) = -25 + (-25) = -50 -10 + (+15) = 5 -10 - (-15) =

2.5 Subtracting Integers

Magic Triangle A magic triangle is an arrangement of six positive or negative integers such that the sum (+) of each side is the same. Solve the set of equations listed below. Then put the solutions to the equations into an empty magic triangle similar to the one pictured. 1.x = 4 + 5 - (-6) - 4 + 9 2.a = 20 + (-10) - 2 + 4 + (-2) 3.60 - (-2) - 22 + (-20) - 2 = n 4.z = 5 + (-6) - 3 5.-6 + 5 + 7 - 3 + 5 = h 6.-6 + 7 - (-2) - 5 = y 26

2.5 Subtracting Integers P 91-92 (6 – 45 x3)

2.6 Problem Solving: Look for a Pattern Objective: To solve problem by looking for a pattern Warm-up: Solve each equation 1. N = 9 – ( - 1) 2. X = - 3 – (21) 3. T = - 8 – (-3) Simplify each equation 4. 8m – ( - 6m) 5. - 15c – 17c Answers: 1)10 2)- 24 3)- 5 4)14m 5)- 32c

2.6 Problem Solving: Look for a Pattern P 96-97 (9 - 21 x3)

2.7 Multiplying Integers Objective: To multiply integers Warm-up: 1. Use the pattern below to find the product of 48 x 52 ◦ 8 x 12 = 96 ◦ 18 x 22 = 396 ◦ 28 x 32 = 896 ◦ 38 x 42 = 1596 Find the next two integers 1. 5, 10, 20, 40, _____, _____ 2. -2, 6, -18, 54, _____, _____ 3. N, O, R, S, V, _____, _____ 4. J, F, M, A, M, J, J, A, _____, _____ Answers: 1)2,496 2)80, 160 3)- 162, 486 4)W, Z 5)S (Sept.), O (Oct.)

2.7 Multiplying Integers NOTES: Multiplying Integers Rule 1: The product of a positive integer and a negative integer is a negative integer. Rule 2: The product of two negative integers or two positive integers is a positive integer.

2.7 Multiplying Integers NOTES: Multiplying Integers IntegersProductRule Used (+7) (+3) =+21 Rule 2 (+7) (-3) =-21 Rule 1 (-7) (+3) =-21 Rule 1 (-7) (-3) =+21 Rule 2

2.7 Multiplying Integers NOTES: Multiplying Two Integers IntegersProductRule Used (+8) (+4) =+32 Rule 2 (+11) (-2) =-22 Rule 1 (-14) (+3) =-42 Rule 1 (-9) (-5) =+45 Rule 2

2.7 Multiplying Integers NOTES: Multiplying Three Integers Integers Product of First Two Integers and the Third Product (+5) (+3) (+2) =(+15) (+2) =+30 (+8) (+2) (-5) =(+16) (-5) =-80 (-6) (+3) (+4) =(-18) (+4) =-72 (-9) (-3) (+2) =(+27) (+2) =+54 (-4) (-3) (-5) =(+12) (-5) =-60

2.7 Multiplying Integers P 102-103 (6 – 36 x3)

MATH LAB – 2.8 Dividing Integers Section A – Individual Section A – Individual ◦ Solving One-Step Inequalities by Multiplying/Dividing Section B - Teacher Section B - Teacher ◦ 2.8 Dividing Integers ◦ Math Games Math Games Section C – Group Section C – Group ◦ Climb the Cliff boardgame

MATH LAB – 2.8 Dividing Integers Objective: To divide integers Warm-up: Solve each equation 1. (- 5)(-3)(4) = a 2. (20)(- 6)(2) = b Find the product 3. (-8x) (-9) 4. (3xy)(-3)(7) 5. -9(-m)(-n) Answers: 1)60 2)-240 3)72x 4)-63xy 5)-9mn

2.8 Dividing Integers NOTES: Dividing Integers When we divide integers, the same rules for multiplying apply. Example: (+6) ÷ (+2) = +3 (+6) ÷ (–2) = –3 (–6) ÷ (+2) = –3 (–6) ÷ (–2) = +3 Calculate the following: A) (–8) ÷ (–2) = B) (12) ÷ (–4) = Solutions: A) (–8) ÷ (–2) = 4 B) (12) ÷ (–4) = –3

2.8 Dividing Integers P 106 -107 (6 - 45 x3)

Chapter 2 Test: Preparation Week Monday – NO SCHOOL Tuesday – Review Math Lab Packets Block- Math Lab – Quiz Reviews/Study Guides Friday – Chapter 2 Test (Substitute)

REMINDER: NEXT WEEK IS MID-TERMS !!

Chapter 2 Test: Math Lab Worksheets Graphing Inequalities: ◦ Draw your number line  --------I--------------I-----------------I--------  1 2 3 ◦ Mark this point with the appropriate notation (an open dot indicating that the point x=2 was NOT included in the solution) ◦ Then shade everything to the right, because "greater than" means "everything off to the right". x > 2

MATH LAB – Chapter 2 Test Preparation Section A – Individual Section A – Individual ◦ Chapter 2 Study Guide and Assessment  P110 – 112 (8-68 EVEN) Section B - Teacher Section B - Teacher ◦ Quiz Reviews (2A, 2B & 2C) Section C – Group Section C – Group ◦ Sequence Game (Pairs)

Chapter 2 Test Preparation A Game of Sequence: Recognizing number patterns is an important ability. By becoming familiar with them, you can save time in the future. Here’s a game that teaches you some of the most common sequences in mathematics.

Chapter 2 Test Preparation Examples: 1. 2, 4, 6, 8, 10 … “Multiples of 2” 2. 1, 4, 9, 16, 25 … “The squares” 3. 5, -10, 15, -20, 25 … “Multiples of 5, with alternating signs.” 4. 4, 12, 36, 108, 324… “Multiply each term by 3” 5. 1, 1, 2, 3, 5 … “Add the previous two terms” (Fibonacci) 6. 1, 2, 4, 8, 16 … “Powers of 2” 7. 5, -10, 15, -20, 25 … “Multiples of 5, with alternating signs.” 8. 3x + 1, 6x + 2, 12x + 4, 24x + 8, 48x + 16 … “Double the previous term.” 9. 1, 2, 2, 4, 8 … “Multiply the previous two terms.” WIN PLANNER POINTS!!  If you can find 20 patterns, you will receive a “Planner Sticker”.  For ever 10 more patterns, you will receive another sticker. (Max 50 patterns) NOTE: For a pattern to count, you must gave FIVE pieces of the pattern AND write the pattern

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