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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.

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Presentation on theme: "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."— Presentation transcript:

1 Exploring Integers Chapter 2

2 Chapter 2 – Exploring Integers Chapter Schedule T Integers and Absolute Values B - Math Lab – 1-7 & 2-2 The Coordinate System FRIDAY - QUIZ 2A M Comparing and Ordering T Adding Integers B - Math Lab Subtracting Integers FRIDAY - Quiz 2B M Problem Solving: Look for a Pattern T Multiplying Integers B - Math Lab 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

3 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

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

5 2.1 Integers and Absolute Value What is an “Integer”?

6 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

7 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“.

8 2.1 HOMEWORK P69 ( EVEN)

9 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!!!

10 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

11 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!

12 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.

13 Sketch the Graph xy

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

15 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 > O < 6 8. E < 4 9. Y < -3 Answers: On Graph

16 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-

17 2.3 Comparing and Ordering NOTES: Graphing Inequalities on a Number Line 1.X < 0 2.X < 0 3.Y >15 4.Y > 15

18 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: _______

19 2.3 Comparing and Ordering P (15-42 x3 & 44)

20 2.4 Adding Integers Objective: To add integers Warm-up: Replace the ? with a, >, or = : ? ? – 4 Write an inequality using the numbers in each sentence. Use “relation symbols”. 3. A turkey sandwich cost $6 and a turkey dinner costs $ The low temperature was - 42 ° F and the temperature now is - 46 ° F. Answers: 1)< 2)> 3)6 < 11 4)-42 > - 46

21 2.4 Adding Integers NOTES: Remember! If the signs are different, subtract their ABSOLUTE VALUES! Adding Integers Game

22 2.4 Adding Integers P86-87 (10 – 44 EVEN)

23 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

24 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?

25 2.5 Subtracting Integers 9 – (- 3) = 9 + (+3) = – (-5) = -7 – (-5) = -7 + (+5) = – (-19) = 21 – (-19) = 21 + (+19) = (+5) = 3 + (-5) = (+25) = (-25) = (+15) = (-15) =

26 2.5 Subtracting Integers

27 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 = (-6) a = 20 + (-10) (-2) (-2) (-20) - 2 = n 4.z = 5 + (-6) = h (-2) - 5 = y 26

28 2.5 Subtracting Integers P (6 – 45 x3)

29 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) c – 17c Answers: 1)10 2)- 24 3)- 5 4)14m 5)- 32c

30 2.6 Problem Solving: Look for a Pattern P ( x3)

31 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.)

32 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.

33 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

34 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

35 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

36 2.7 Multiplying Integers P (6 – 36 x3)

37 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

38 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

39 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

40 2.8 Dividing Integers P ( x3)

41 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)

42 REMINDER: NEXT WEEK IS MID-TERMS !!

43 Chapter 2 Test: Math Lab Worksheets Graphing Inequalities: ◦ Draw your number line  I I I  ◦ 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

44 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)

45 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.

46 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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