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Exploring Integers

Exploring Integers. Chapter 2. Chapter 2 – Exploring Integers. M- MONDAY T- TUESDAY B- BLOCK F- FRIDAY. 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

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Exploring Integers

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  1. Exploring Integers Chapter 2

  2. Chapter 2 – Exploring Integers M-MONDAY T-TUESDAY B-BLOCK F- FRIDAY 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 1st Quarter

  3. 2.1 Integers and Absolute Value • Objective: Graph integer on a number line and find absolute value • Warm-up: Answers: 20 25 23 28 24 28 3 9

  4. More  PEMDAS NOTES: Answers: 1 1 8 1 8 4

  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 = 3 C = 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 (18 - 48 EVEN)

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

  10. 1-7 Ordered Pairs2-2 The Coordinate System • Objectives: To locate and graph points on number line and in all quadrants of the coordinate plane

  11. 1-7 Ordered Pairs2-2 The Coordinate System • Objectives: To locate and graph points on number line and in all quadrants of the coordinate plane • Rules: • Play 1 coin per turn • Must alternate (+) and (-) each turn • First team past their 5 wins! Team A – NEGATIVES! Team B – POSTIVIES!

  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

  14. Math Lab - HOMEWORK • 1-7 Ordered Pairs • P59 (50-55 ALL) • 2.2 The Coordinate System • P74-75 (14 - 38 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: • E (1, -3) • M (-4, 2) • I (0, -2) • L (2, 0) • Y (-3, -4) Graph the following inequalities individually: • J > -2 • O < 6 • E < 4 • Y < -3 Answers:On Graph

  16. Quiz 2A – Results!

  17. 2.3 Comparing and Ordering • NOTES: Graphing Inequalities on a Number Line X < 0 X < 0 Y >15 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 • P79 - 80 (15-42 x3 & 44)

  20. 2.4 Adding Integers • Objective: To add integers • Warm-up: Replace the ? with a < , < , >, > , or = : • - 9 ? 8 • 0 ? – 4 Write an inequality using the numbers in each sentence. Use “relation symbols”. • A turkey sandwich cost $6 and a turkey dinner costs $11. • The low temperature was - 42°F and the temperature now is - 46°F. Answers: < > 6 < 11 -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 • Inequalities and Their Graphs • Solving One-Step Inequalities by Adding/Subtracting • Section B – Teacher • 2.5 Subtracting Integers Lesson • Section C – Group • Math Games

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

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

  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. x = 4 + 5 - (-6) - 4 + 9 a = 20 + (-10) - 2 + 4 + (-2) 60 - (-2) - 22 + (-20) - 2 = n z = 5 + (-6) - 3 -6 + 5 + 7 - 3 + 5 = h -6 + 7 - (-2) - 5 = y 26

  28. 2.5 Subtracting Integers • P 91-92 (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 • N = 9 – ( - 1) • X = - 3 – (21) • T = - 8 – (-3) Simplify each equation • 8m – ( - 6m) • - 15c – 17c Answers: 10 - 24 - 5 14m - 32c

  30. 2.6 Problem Solving: Look for a Pattern • P 96-97 (9 - 21 x3)

  31. 2.7 Multiplying Integers • Objective: To multiply integers • Warm-up: • 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 • 5, 10, 20, 40, _____, _____ • -2, 6, -18, 54, _____, _____ • N, O, R, S, V, _____, _____ • J, F, M, A, M, J, J, A, _____, _____ Answers: 2,496 80, 160 - 162, 486 W, Z 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. VIDEO???

  33. 2.7 Multiplying Integers NOTES: Multiplying Integers Integers Product Rule 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 Integers Product Rule 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 IntegersProduct 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 102-103 (6 – 36 x3)

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

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

  39. 2.8 Dividing Integers • NOTES: Dividing Integers When we divide integers, the same rules for multiplying apply. VIDEO??? 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 106 -107 (6 - 45 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-------- 1 23 • 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 • Chapter 2 Study Guide and Assessment • P110 – 112 (8-68 EVEN) • Section B - Teacher • Quiz Reviews (2A, 2B & 2C) • 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: • 2, 4, 6, 8, 10 … “Multiples of 2” • 1, 4, 9, 16, 25 … “The squares” • 5, -10, 15, -20, 25 … “Multiples of 5, with alternating signs.” • 4, 12, 36, 108, 324… “Multiply each term by 3” • 1, 1, 2, 3, 5 … “Add the previous two terms” (Fibonacci) • 1, 2, 4, 8, 16 … “Powers of 2” • 5, -10, 15, -20, 25 … “Multiples of 5, with alternating signs.” • 3x + 1, 6x + 2, 12x + 4, 24x + 8, 48x + 16 … “Double the previous term.” • 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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