Math 8 Ms. Campos Unit 1- Integers

Math 8 Ms. Campos Unit 1- Integers 2017-2018 Day Test Date: Lesson Topic Homework Schedule Sept W 6 First Day Return Signed Contract T 7 1 Introduction to Integers Lesson 1- page 4 F 8 2 Add and Subtract Integers Lesson 2 page 6 M 1 11 3 Multiply & Divide Integers Lesson 3 page 9 T 2 12 W 3 13 T 4 14 4 5 6 Order of Operations Lesson 4 page 12 Quiz Lesson 1-3 Evaluate Algebraic Expressions Lesson 5 page 15 Temperature Conversion Quiz Lesson 4-5 Lesson 6 page 18 F 5 15 7 Translating Algebraic Expressions Lesson 7 page 21 M 6 18 Combine Like Terms Lesson 8 page 25 8 Quiz Lesson 6-7 T 1 19 9 Perimeter Problems Lesson 9 page 27 W 2 20 Distributive Property Lesson 10 page 29 10 (Area Problems) T 21 NO SCHOOL F 22 NO SCHOOL M 3 25 Review Finish Review and Check Answers on Website Will be collected tomorrow T 4 26 Test Good Luck! Name # 1

Lesson 1 Aim: I can identify the determine the different number sets that make up the Real Number System Warm Up: What are the different types of numbers that make up the Real Number System? Number set Definition Examples Non-Examples Natural numbers Whole numbers Integers Rational numbers Irrational numbers 2

Guided Practice: Problem Set: Name the Integer 1) 5 degrees above 0 2) a loss of 2 yards 3) a withdrawal of $25 4) a deposit of $25 5) 3 inches of rainfall Put in order from least to greatest 6) 3, -8, 0, 11, -7 7) -11, 12, 9, -8, -1 Inequality Symbols < > Use < or > to make a true statement 8) -2-8 9) 0-6 10) -5-2 11) -8-10 3

Write the number that describes each situation: Lesson 1 Homework 1) loss of 5 kg 2) gain of 3 kg 3) rise of 1,500 ft in elevation 4) 15 feet below sea level 5) 12 inches of snowfall Put in order from least to greatest 6) 10, -5, 1, 12, 0 7) 55, -25, -11, 52, -74 Compare the integers using < or > 8) 7 4 9) 6-13 10) -6-3 11) 7-3 12) -2 11 13) -14-10 14) -4-9 15) -8 0 16) What type of numbers are used to represent temperatures below zero? 17) Circle all the numbers that are integers and explain why you chose them. 25 1½ -18 0 - " # 4 % " &# # -17 "' ( 18) List the first five non-negative integers. 19) List the first five positive integers. 20) 8 " & 21) 5 & ( 22) 8 ', 23) 6 & " 4

Aim: I can add and subtract integers Lesson 2 Warm Up: You buy a belt for $10 and some socks. Each pair of socks costs $3. The total shipping cost is $3. What is the total cost if you buy 11 pairs of socks? A) $36 B) $43 C) $46 D) 50 Guided Practice: Adding Integers 1) -2 + -3 2) -2 + 8 3) -6 + 1 4) -4 + 4 5) 6 + (-3) 6) 10 + -5 + 3 Subtracting Integers 1) 6 10 2) -3 8 3) 4 - -6 4) -2 (-8) 5) -2 - -2 6) 7 + -3 Problem Set: Adding Integers 1) 8 + -7 2) 8 + 2 3) -1 + -7 4) -3 + (-3) 5) 6 + (-6) 6) -2 + - 5 + 3 Subtracting Integers 1) -12-7 + 4 2) -5 6 + 2 11 3) 5-12 4) 8 (-9) 5) -7 (-10) 6) -4 - -4 7) -8 + 12 9 + 4 8) 5 6 + 2 11 9) 8 9 + 3 7 5

Lesson 2 - Homework Simplify: 1) -4 + (-4) 2) 8 + (-8) 3) -3 - (-8) 4) 5-9 5) -3 + 12 6) -6-10 7) -2 + 13 8) 8 + ( -9) 9) -8 + 12 10) -7 + 5 + 1 11) 1 6 8 12) -8 + 0 + 12 13) 7 9 8 5 14) 7 15 2 15) -14 + 16 1 16) -5 + 1 8 + 7 17) An elevator began on the fourth floor. It went up 6 floors, dropped 3 floors, and then went up another two floors. What floor did the elevator stop on? 18) On Monday afternoon the temperature was 6. That night it dropped 8. What was the temperature on Tuesday morning? 19) In the morning, Mrs. Boxer deposited $135 to her bank account. She withdrew $235 in the afternoon. What number describes her account s net change? 20) Circle all the numbers that are NOT integers and explain why you chose them. -40 57 %, & -6+6 % # %( & -6 13 21) 6 " & 22) 7 / ' 23) 3 % " 24) 9 & " 6

Aim: I can multiply and divide integers Lesson 3 Warm Up: 1) 6 12 2) 7 8 3) -9 4 1 4) -6 1 5) 8 ( 9) 6) 9 9 + 14 7) 0 15 + 12 8) -20 ( 22) Guided Practice: Multiplying and Dividing Integers 1) (-6)(-2 ) 2) (5)(-3) 3) (-5)(0) 4) (6)(-2)(3)(-1)(-4) 5) (-2)(1)(-3)(4) 6) (-1)³ 7) (-1) 246 8) (-1) 485 9) -25 5 10) -36-9 11) 0 8 12) 8 0 13) -32 4 14) (4)(-9) 15) (-4) 2 16) -4 2 17) -28 2 18) (-8)(-5) 19) -3 0 20) (-6)(7) 21) 0 ( 22) -2 0 12) (-38)(24)(96)(0) Zero Rules: When 0 is in the numerator of a fraction the answer is. When 0 is in the denominator of a fraction the answer is. *** Remember.. 0 Under is U 7

Problem Set: A. Multiply Fractions by Hand 1) 8 " & 2) 14 / ' 3) 7 % ' 4) 18 & " 5) 8 " # 6) 14 " & 7) 5 & ( 8) 12 ( / B. Fractions using a Calculator How to input fractions into the calculator You must use the a 8 9 button! Use ( ) if you need to make a number negative. 1) 1 4 + 2 3 2) 3 3 4 2 1 5 3) 6 3 4 1 2 4) 5 1 2 2 3 4 5) " + ' %D &D 6) ( # " # 7) & " ( # 8) % E 1 % " 8

Lesson 3 - Homework Simplify. Only use calculator on Fraction Problems 1) (-3)(9) 2) (-5)(-1) 3) (-9)(0) 4) (-7)(-3) 5) (-24)( (, ) 6) ( & " )(-18) 7) (3)(-1)(6)(-2) 8) (-4)(-23 ) 9) -55 5 10) -18-9 11) 0 7 12) 3 0 13) " ( & " 14) % ( % ) " " 15) ( E ' %( 16) % ( + ( % ( ) 17) ' / ( / 18) 0 # E 19) -2 " ' 20) 5 (, 4 & %D 21) -5 6 22) (-5)(-6) 23) (-2)(8) 24) -2 + 8 25) 12 - - 4 26) -4 + 12 27) -9 3 28) -9-3 29) Give an example of an irrational number. 30) Which of the following numbers are integers and explain why you chose them? -5, 0, 3, %# &, " ( 9

Aim: I can simplify numerical expressions Lesson 4 Warm Up: Does the order in which these operations are done make a difference? 6 + 3 x 4 6 + 3 x 4 9 x 4 = 36 6 + 12 = 18 Which is correct, and why? Order of Operations Guided Practice: 1) 5 + 2 x 6 2) 10 5 x 2 3) 7(1 + 2) 5 5 4) 3 4 + 8 15 2 5 5) -4 + (-5)(3) 6) -9 + (-4)(-2) 7) 8 + 5 (12-6 3) 8) 4 2-2 5 + (8-2) 10

Problem Set: 9) 3(2) 2 + 2(4) - 7 10) 4(5) + 16 3 2-3 2 11) 4-3 + 7(12-2 ) 12) 2 (9) - 4 3 13) 2(-3) 2 14) 2-3 2 15) 2 - (-3) 2 16) (-7)(4) 8 17) 0.34 + 2.4(3) 18) -3 2 19) (-3) 2 20) -3 3 21) (-3) 3 22) (-3) 4 23) 2 + 7 4 15 3 + 7 23) 20 4 + 3 6 12 4 24) 8(4) + 9 3 1 5 11

Lesson 4 Homework 1) 8 + 4 2 2) 16 32 4 3) 5 + 7(2) 4) 3(8 4) + 6 5) 7 8 4 2 + 5 6 6) 14 16 8 + 9(5) 7) ( E F%, " &F"(() 8) 9 14 2 + 3 4 9) ( # )(35) 14 7 10) (7 5)6 + 4 11) (0.9)(0.2) + (0.6)(0.4) 12) 10 3(5 2) ( 3 13) 2 (3 + 4) - 35 7 14) 15 + 2 4 5 15) 24 6 + 3 3 5(2) + (36 4) 16) How do we simplify a numerical expression? 17) Which operation would be performed first when simplifying 2 (3 8 + 5) 12? 18) Which set of numbers would be most appropriate to use to represent the number of household onlinedevices a family has in their home? A) integers B) whole numbers C) rational numbers 12

Aim: I can evaluate algebraic expressions Lesson 5 Warm Up: Simplify 1) -43 + 6 + 13 2)-5 + 1 8 + 7 3) 7 5 + 6 2 4) 60 3 4 2 Guided Practice: A. Algebraic Expression vs. Algebraic Equation B. Parts of an Expression 3x & + 5 Name the coefficient: Coefficient - Name the variable: Variable Name the exponent: Exponent Name the constant: Constant - Name the base: Base - C. Evaluating Algebraic Expressions 1-2 - Evaluate the following expressions: 1) 3x - 2 for x = 4 2) 5(x + 3) when x = 2 3) -13-5x if x = -2 4) 2a 5 if a = 3 5) (2a) 5 when a = 3 6) "G F / &8 H"9 if a = 8, b = 6, c = 2 13

Problem Set: 7) 5x 2y if x = 3; y = 6 8) & ( x + 3 for x = 20 9) 3x + 5y - 8 for x = 3.1; y = -.8 10) 19-2m for m = -6 11) ab 4 if a = 3; b = -2 12) 2x 2 if x = -3 13) (2x) 2 when x = -3 14) (4x + 3y)2 + 9 for x = - % & and y = - & " 15) "GH, &8F# for a = -2 and b = -3 14

Lesson 5 - Homework 1) x & for x = -5 2) 6x 4y for x = & ", y = -3 3) "JF&K &JFK for x = -4, y = 3 4) Given the formula h = 60t 5t 2, to answer the following question. If an object is shot upward from the ground, what is its height (h) above the ground after 5 seconds (t)? 5) The formula for area of a trapezoid is % & h(b % + b & ). Find the area of a trapezoid when h = 8, b % = 5, and b & = 7 6) Given: A = % B = -4 # Which of the following results as an integer? A) A + B B) A B C) AB D) A B 15

Lesson 6 Aim: I can convert Celsius and Fahrenheit temperatures. Warm Up: 1. Which scale do we use to measure the weather? 2. On which scale does water boil at 100? Guided Practice: A. The Fahrenheit Scale Customary System Report weather, cooking, house thermometers (swimming pool, bath tub, body temp) B. The Celsius Scale Metric System Used for scientific work Based on a scale of 100 Also called Centigrade Comparison of Temperature Scales Fahrenheit Celsius water boils body temperature water freezes Conversion Formulas C = ( (F 32) F = E C + 32 E ( 1. New York City s average high temperature for May is 68. What is New York City s average high temperature in May in degrees Celsius? 2. A recipe says that muffins should be baked at 180. What is this temperature in degrees Fahrenheit? 16

Problem Set: Convert the following temperatures using the given formulas C = ( (F 32) F = E C + 32 E ( Show all work- Non Calculator 3. 50 C 6. 56 C Show all work Calculator (round to the nearest tenth) 4. 77 F 7. 107 F 5. 194 F 8. 77 C 17

Lesson 6 - Homework Convert the following temperatures using the given formulas. Round to the nearest tenth when necessary. C = ( (F 32) F = E C + 32 E ( Show all work- Non Calculator 1. 35 C 4. 96 F Show all work Calculator (round to the nearest tenth) 2. 113 F 5. 97 C 3. 120 C 6. 75 F 7. The melting point for zinc is 787. What is the melting point of zinc in degrees Celsius? 8. The formula for area of a triangle is A = % bh. Find the area of a triangle where b = 7 and h = 12. & 9. Which of the following results in a negative number? A) (-3)(-4) B) (-3) 2 C) -3 2 D) (-3)(0) 10. Which of the following results in a positive number? A) -(-2) 2 B) (-2) 3 C) (-3)(0) D) (-2) 2 18

Lesson 7 Aim: I can translate verbal expressions to algebraic expressions Warm Up: 1) -4 + (-5)(3) 2) Which answer is greater? (3x)² or 3x² when x = 2 3) What is the difference between an expression and an equation? Guided Practice: x + 5 x 5 5x 5 x Remember. More Than / Less Than Subtracted From Translate and Simplify 1) The product of -2 and -6 2) 7 subtracted from -10 3) 8 less than 10 19

Write an algebraic expression for each 1) 3 times a number plus 6 2) 4 less than a number times 2 3) x divided by 8 4) 12 subtracted by x Math each phrase with the correct algebraic expression 5) n increased by 11 A) n 19 6) 11 less than n B) n + 11 7) the sum of n and 19 C) n + 19 8) 11 more than n D) n 11 9) n increased by 19 E) 19 n F) 11 - n Problem Set: Write each as an algebraic expression 10) m increased by 8 11) 4 less than c 12) the sum of b and 14 13) twice Don s age increased by 8 14) 40 more than Meg s bowling score 15) Abe s savings decreased by $540 16) Bill s batting average increased by 12 17) Bert s cab company charges $1.00 plus and additional $3.00 per mile for a ride. Write an expression to represent the total charge for m, miles. 18) Madeline s cab company charges $3.00 plus and additional $2.00 per mile for a ride. Write an expression to represent the total charge for m, miles. 19) To rent a paddleboat in Belmont State Park, the cost is $7.00 plus $3.50 per hour. Write an expression to present the cost of the rental for h, hours. 20) An amusement park charges $5 for admission and $2 for each ride. Write an expression for the total cost of admission and r rides. 20

Lesson 7 - Homework 1) w decreased by 4 2) the sum of m and 3 3) 9 less than x 4) 7 less than three times x 6) 5 decreased by 3 times a number 7) 12 more than twice m 8) 8 less than a number divided by 5 9) $60 more than 6 times Ben s salary 10) The sum of 25 and 3 times Joe s age 11) 3 more than the current temperature 12) 13 less than 6 times a number 13) 7 more than twice the length of a rectangle 14) A hot-air balloon is at a height of 2,250 feet. It descends 150 feet each minute. Write an expression for the balloon s height at m minutes. 15) A hiking club charges $60 to join and $12 for each hiking trip. Write an expression to model the total cost of h hiking trips. 16) A florist divides 60 roses into equal bunches of f, flowers. Write an algebraic expressions for the number of bunches the florist can make. 17) An object s weight on Mars is 0.38 times the object s weight on Earth. If e represent the weight of an object on the earth, write an algebraic expression for an object s weight on Mars. #18-20 Translate and Simplify: 18) The difference of 8 and -9 19) The quotient of -36 and 12 20) The sum of -5 and -8 21) An elevator began on the fourth floor. It went up 6 floors, dropped 3 floors, and then went up another two floors. What floor did the elevator stop on? 22) On Monday afternoon the temperature was 6. That night it dropped 8. What was the temperature on Tuesday morning? 23) Explain the difference between the way you represent 7 decreased by x and 7 less than x. Is there any value of x for which the two representations are the same? 21

Lesson 8 Aim: I can simplify algebraic expressions by combining like terms Warm Up: Phrase five more than twice a number the product of a number and 6 seven divided by twice a number three times a number decreased by 11 Expression Guided Practice: A. Identifying polynomials 6x-4+3 2 Monomial/Term- Like terms - Binomial - Trinomial - Polynomial - 22

1) What is the coefficient of p in a - 7p + 21? What is the constant? 2) What are the like terms of 7r + 5 + 3r? What is the constant? 3) What is the coefficient of a in the expression 4c + 5 + a? A) Are these like terms? Why or Why Not? 1) -4x and 6x 2) 7ab and 13ab 3) 3x and 3x 2 4) 4x 2 y 3 and 9x 2 y 3 5) 37x and 4 6) 4 and -9 7) 3x 2 y and 6xy 2 B) Simplify by Combining like terms 23

Problem Set: A. Determine if the following are like terms or unlike terms: 1) 3x + 2x² 2) 5xy + x 3) x²y - xy² 4) 4y² - 2y² 5) 0.1ab and 4ab 6) x 2 y and -5x 2 y 7) -2ab 2 and -2a 2 b 8) 3x 2 and 5x 4 B. Simplifying algebraic expressions: 1) 6x + 3x 2) 5x + x 3) 2x + 7 4) -9x + 4x 5) -2a 11a 6) -2a + 2a 7) -3x 2x + 5 8) 10y 3y y 9) 9y 3 + 6y 8 10) 9x + 4y 11) -7x + 7x + 3 12) -4x -3x 13) 8y 5a + 8y 5a 14) 4a 7 + 5a + 10 3a 15) 6x 2 + 3x 8x 2 16) 7 + 6y 2 4y 17) 8 + 11m 5 7m 18) x x + 2x 24

Simplify Lesson 8 - Homework 1) -6b + 5b 2) -3a - 4a 3) -5k + 5k 4) -8 + 5b + 2 b 5) 4a 6a a 6) 7k 8k k 7) 5t 6 t 8 8) -m 14 m + 6 9) g 5 +2g + 10 10) -7 z 3z + 2 11) 5c + 8 8c 9 12) -4k 3m + 6k + m Identify each polynomial: (monomial, binomial, trinomial) 13) a + 7p 21 14) 7r + 5 + 3r 15) 4xy 16) 3x 7y + 3z 17) 3x 2 7x 9 18) 6x + 8x 19) Mr. Torquato has $450 in his bank and deposits $20 per month. Write an algebraic expression to represent how much he has in m, months. 20) Pasquale got a job working at Subway and will be making $9.25 per hour. Write an expressions to represent how much he will make in h,hours. 21) The formula for volume of a cylinder is = πr & h. If the radius is 3 and the height is 12, express the volume in terms of π. 25

Lesson 9 Aim: I can express the perimeter of a polygon algebraically Warm Up: How much fencing does Jeremy need to make a dog run in his yard? 10ft 8ft Guided Practice: Perimeter of polygons Express the perimeter in simplest terms of x. 1) 2) 3) 5 4x + 3 x 3x - 1 9x 6x + 2 2x + 3 Problem Set: 4) 5) 2x 1 3x + 2 x 5) Express the perimeter of a triangle whose sides are x + 8, x + 5, and 2x 6 in simplest terms of x? 6) Find the missing side of the triangle if the perimeter is 6x + 8 represented as 15x + 12 2x - 1 26

Lesson 9- Homework Express the perimeter in simplest terms of x: 1) 2) 3) 2x + 3 4) 2x + 1 2x + 3 x 2x + 1 5x 7y 4x + 3y 5) Express the perimeter of a quadrilateral whose sides are 7x - 10, 4x + 8, 2x + 12, and 5x 10 in simplest terms of x. 6) Evaluate 5x 2y 7 for x = -2, y = 4 7) When is the sum of a positive integer and a negative integer negative? 8) Which expressions are equivalent? A) 6x + 7y 10x B) 7y +7x + 3x C) 8x + 2x + 7y D) -4x + y + 6y Rational or Irrational 10) -98 11) 16 12) 20 13) 5π 9) & E 27

Lesson 10 Aim: I can simplify algebraic expressions using the Distributive Property Warm Up: 1) Express the perimeter in terms of x: 2) Simplify and Evaluate: when x = 2 and y = 3 6 + 7x + 9y + 3x 2 4y Guided Practice A. Distributive Property : Express in simplest terms of x. 1) 2(x + 3) 2) 2(4x 5y) 3) 3(4x + 5y 6z + 8) 4) - (-2x + 4) 5) -6(7k +.5) 6) % (15x + 27) " 7) " (7n + 1) 8) -4(1 + 11x) + 20x 9) -3(5x 1) -8x # Problem Set: 10) 9(3 10n) 3(10n + 1) 11) 3 2(3x + 5) 12) 8 3(2x 7) + 5x 13) -4(3x 3) + 9(x + 1) 14) 10.8(x - 3.6) 15) ( ( 4n 3) 16) -2( -8x 10) # B. Area of rectangles : Express the area in simplest terms of x 1) 2) 3) 5 7 5 2x + 3 x + 6 28

Lesson 10 - Homework Express in simplest terms of x. 1) 5(3x 4) 2) 3(2x + 7y) 3) -6(1 + 11b) 4) -10(a 5) 5) - (-6x + 9) 6) -2(3x +.6) 10) 4(7 5n) 2(3n + 4) 11) 7(2x 2 3x ) + 10x 9) -9(3 10n) 3 7) % " (7n + 1) 8) 2(1 4.3k) 2 12) Express the area of the rectangle. 13) Express the perimeter of the triangle. 4 5x - 6 2x - 8 9x + 7 3x 14) It the width of a rectangle is 6 and length is (x + 7), express the area in simplest terms of x. 15) If Lisa s yard has a length of 9 and a width of x 2. A) Express the amount of fence she would need to enclose her yard in terms of x. B) Express the amount fertilizer she will need in terms of x. 29

Unit 1 Review Write the number that best describes the situation: 1) A gain of 20 yards 2) A withdrawal of 100 dollars Compare: Use < or > 3) -10-9 4) -1-7 Simplify (round to the nearest tenth if necessary) 5) -15 + 8 6) 5 (-6) 7) 10 + ( -6) 8) - 22 13 + - 6 9) - 9 & (-3) 10) (-4)(-5 % ) 11) (-1)(5)(-3) 12) 8 " & 0 13) 26-13 14) (-0.27)(-0.6) 15) 2 (, - # %& 16) The elevator begins on the fifth floor and goes up 5 floors, and goes down 7 floors. What floor is the elevator on now? Simplify (Show all work) 17) -25 + 3 7 18) 52 + (-5)(7) 19) 3 2 2 + 24 8 20) (15 3) 2 + 9 3 21) Evaluate 3x + 8y for x = -1 and y = -4 22) Evaluate " x - 6y for x = -5 and y = -4 ( 30

23) Evaluate 5x + 9 x - 6 for x = 3 24) Evaluate: 3.3p + 2 for p = 9 Given the following formulas: C = 5 (F-32) F = 9 C + 32 9 5 25) Convert 9 degrees Celsius to Fahrenheit. 26) Convert 59 degrees Fahrenheit to Celsius. (Round to the nearest tenth) Simplify each algebraic expressions 27) -5x 7x 28) 6x 9y + 4x y 29) 10x 6x 4x 30) 3(2x + 5) 5 31) (5x 8) 32) 25 (-5x + 10) 33) 6(10x + 2) + 3x 34) " # 3x 4 35) 3 2(4x 8) + 5x 36) -3(4x 9) + 2x 31

37) Express the area of a rectangle 38) Express the perimeter in simplest terms of x: in simplest terms of x, whose width is 4 and length is 2x 8 7x + 2 3x 8 38) You can estimate the stopping distance, needed for a car going at a speed of x mph by adding the reaction distance, x, and the braking distance ( ]^ ]^ ). The expression x + ( ) is used to represent the stopping "D distance. How much longer is the stopping distance for a race car going 120 mph than one going 90 mph? "D 39) A fitness club charges $100 to join and $33 for each month. Write an algebraic expression for the total cost of the fitness club for m months. Write an algebraic expressions for each phrase. 40) 3 less than the product of 8 and a number 41) the quotient of a number and 5 subtracted from 3 Identify each umber using: integer, rational, irrational 42) 49 43) -4 44) % ' 45) 24 46) 17 32