1.1 Integers And Absolute Value - Big Ideas Learning
English1.1SpanishIntegers and Absolute ValueHow are velocity and speed related?SSTATESTANDARDSMA.7.A.3.1On these two pages, you will investigate vertical motion (up or down). Speed tells how fast an object is moving, but does not tell the direction. Velocity tells how fast an object is moving and also tells the direction.If velocity is positive, the object is moving up.If velocity is negative, the object is moving down.1EXAMPLE: Falling ParachuteYou are gliding to the ground wearing a parachute.The table shows your height at different times.Time (seconds)0123Height (feet)4530150a. How many feet do you move each second?b. What is your speed? Give the units.c. Is your velocity positive or negative?d. What is your velocity? Give the units.a. For each 1 second of time, your height is 15 feet less.b. You are moving at 15 feet per second.c. Because you are moving down, your velocity is negative.d. Your velocity is 15 feet per second. This can be written as 15 ft/sec.2ACTIVITY: Rising BalloonsWork with a partner. The table shows the height ofa group of balloons.Time (seconds)0123Height (feet)04812a. How many feet do the balloons move each second?b. What is the speed of the balloons? Give the units.c. Is the velocity positive or negative?d. What is the velocity? Give the units.2Chapter 1Operations with Integers
EnglishSpanish3ACTIVITY: Finding Speed and VelocityyWork with a partner. The table shows theheight of a firework’s parachute.Time (seconds)Height (feet)048013602240312040a. How many feet does the parachute moveve each second?b. What is the speed of the parachute? Give the units.c. Is the velocity positive or negative?d. What is the velocity? Give the units.Inductive Reasoning4. Copy and complete the table.Velocity (feet per second) 1420 2025 15Speed (feet per second)5. Find two different velocities for which the speed is 16 feet per second.6. Which number is greater: 4 or 3? Use a number line to explainyour reasoning.7. One object has a velocity of 4 feet per second. Another object has avelocity of 3 feet per second. Which object has the greater speed?Explain your answer.In this lesson, you will study absolute value. Here are some examples:Absolute value of 16 16Absolute value of 0 0Absolute value of 16 16Absolute value of 2 28. IN YOUR OWN WORDS How are velocity and speed related?9. Which of the following is a true statement? Explain your reasoning.a. Absolute value of velocity speedb. Absolute value of speed velocityUse what you learned about absolute value to completeExercises 4 –11 on page 6.Section 1.1Integers and Absolute Value3
English1.1SpanishLessonLesson TutorialsThe following numbers are integers. . . , 3, 2, 1, 0, 1, 2, 3, . . .Key Vocabularyinteger, p. 4absolute value, p. 4Absolute ValueWordsThe absolute value of an integer is the distance betweenthe number and 0 on a number line. The absolute value ofa number a is written as a .4 units 5 41 2 101 4 4NumbersEXAMPLE 34 units2345 4 4Finding Absolute ValueFind the absolute value of 2.Graph 2 on a number line. 4 3 2 1012342The distance between 2 and 0 is 2.So, 2 2.EXAMPLE2Finding Absolute ValueFind the absolute value of 3.Graph 3 on a number line. 6 5 4 3 2 10123The distance between 3 and 0 is 3.So, 3 3.Find the absolute value of the integer.Exercises 4–194Chapter 11. 7Operations with Integers2. 13. 54. 14
EnglishSpanishEXAMPLEComparing Values3Compare 1 and 4 .RememberGraph 4 4 on a number line.Graph 1 on a number line.A number line can beused to compare andorder integers. Numbers to the left are lessthan numbers to theright. Numbers to theright are greater thannumbers to the left. 4 3 2 10123451 is to the left of 4 .So, 1 4 .Copy and complete the statement using , , or .Exercises 20–25EXAMPLE5. 2 16. 77. 10 118. 9 6 9 Real-Life Application4SubstanceFreezingPoint ( C )Butter35Airplane fuel 53Honey 3Mercury 39Candle wax55The freezing point is the temperature at which a liquidbecomes a solid.a. Which substance in the table has the lowestfreezing point?b. Is the freezing point of mercury or butter closer tothe freezing point of water, 0 C?a. Graph each freezing point.Airplane fuel Mercury 53 39Honey 3 60 50 40 30 20 100Butter3510203040Candle wax555060Airplane fuel has the lowest freezing point, 53 C.b. The freezing point of water is 0 C, so you can use absolute values.Mercury: 39 39Butter: 35 35Because 35 is less than 39, the freezing point of butter is closer tothe freezing point of water.9. Is the freezing point of airplane fuel or candle wax closer to the freezingpoint of water? Explain your reasoning.Section 1.1Integers and Absolute Value5
EnglishSpanishExercises1.1Help with Homework1. VOCABULARY Which of the following numbers are integers?129, 3.2, 1, —, 0.25, 152. VOCABULARY What is the absolute value of an integer?3. WHICH ONE DOESN’T BELONG? Which expression does not belong with theother three? Explain your reasoning. 6 6 6 66) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Find the absolute value of the integer.124. 95. 68. 159. 136. 107. 1010. 711. 1212. 513. 814. 015. 1816. 2417. 4518. 6019. 125Copy and complete the statement using , , or . 5 3 20. 223. 4 621.24. 4 1 722. 5 8 25. 5 9 5 ERROR ANALYSIS Describe and correct the error.26. 27. 10 10 5 428. SAVINGS You deposit 50 in your savings account. One week later, youwithdraw 20. Write each amount as an integer.29. ELEVATOR You go down 8 floors in an elevator. Your friend goes up 5 floors inan elevator. Write each amount as an integer.Order the values from least to greatest.30. 8, 3 , 5, 2 , 231.32. 12, 26 , 15, 12 , 10 33. 6 , 7, 8, 5 , 6 34 , 21, 17, 20 , 11 Simplify the expression.34.6 30 Chapter 135. 4 Operations with Integers36. 15
EnglishSpanish37. PUZZLE Use a number line.a. Graph and label the following points on a number line: A 3, E 2,M 6, T 0. What word do the letters spell?b. Graph and label the absolute value of each point in part (a).What word do the letters spell now?38. OPEN-ENDED Write a negative integer whose absolute value is greater than 3.REASONING Determine whether n 0 or n 00.39. n n 2n40. n n 041. CORAL REEF Two scuba divers explore the only living coralreef in North America, located just off the Florida Keys.a. Write an integer for the position of each diver relativeto sea level.14 feetb. Which integer in part (a) is greater?18 feetc. Which integer in part (a) has the greater absolute value?Compare this with the position of the diver farther fromsea level.42. VOLCANOES The summit elevation of a volcano is the elevationof the top of the volcano relative to sea level. The summit elevationof the volcano Kilauea in Hawaii is 1277 meters. The summitelevation of the underwater volcano Loihi in the Pacific Oceanis 969 meters. Which summit is closer to sea level?43. MINIATURE GOLF The table shows golf scores, relative to par.a. The player with the lowest score wins. Which player wins?b. Which player is at par?c. Which player is farthest from par?Determine whether the statement is true or false.Explain your reasoning.PlayerScore1 5203 44 15 244. If x 0, then x x.45. The absolute value of every integer is positive.Add.SKILLS REVIEW HANDBOOK46. 19 3247. 50 9448. 181 21750. MULTIPLE CHOICE Which value is not a whole number?A 5 B 0 C 4 Section 1.149. 1149 2021SKILLS REVIEW HANDBOOKD 113 Integers and Absolute Value7
1.1 Lesson 4 Chapter 1 Operations with Integers Key Vocabulary integer, p. 4 absolute value, p. 4 Absolute Value Words The absolute value of an integer is the distance between the number and 0 on a number line. The absolute value of a number a is written as a . 01 4 units 4 units 52 4 3 2 1 34 5
2 Integers and Introduction to Solving Equations 98 2.1 Introduction to Integers 99 2.2 Adding Integers 108 2.3 Subtracting Integers 116 2.4 Multiplying and Dividing Integers 124 Integrated Review—Integers 133 2.5 Order of Operations 135 2.6 Solving Equations: The Addition and Multiplication Properties 142 Group Activity 151 ocabulary CheckV 152
Write general rules for adding (a) two integers with the same sign, (b) two integers with different signs, and (c) an integer and its opposite. Use what you learned about adding integers to complete Exercises 8 –15 on page 12. 1.2 Lesson 10 Chapter 1 Operations with Integers Adding Integers with the Same Sign
students have mastered addition of integers, subtraction of integers may be introduced. 4 Subtraction of Integers In a subtraction equation, a b c,a is called the minuend ,b is the subtrahend , and c is the difference . Example 5 involves subtracting integers with same signs and Example 6 involves subtracting integers
Substituting Variable Values in Program Understand how real numbers and integers are treated by the CNC control Real numbers are any number rational or irrational Real numbers include integers 1.25, -.3765, 5, -10 are all real numbers Integers are whole numbers 2500, 3, 20 Numbers with decimals are not integers i.e. 1.25 Some NC words only allow integers
2010 AB2 BC2 maximum, minimum absolute extrema 2010 AB3 maximum, minimum absolute extrema 2009 AB2 BC2 maximum, minimum absolute extrema 2009 AB3 fundamental theorem absolute extrema 2009 AB6 maximum, minimum absolute extrema 2008 AB3 maximum, minimum absolute extrema 2008 AB4 BC4 maximum, minimum absolute extrema
CCBC Math 081 Textbook 3rd Edition Chapter Sections Page Chapter 1 Integers 1.1 Introduction to Integers 1.2 Absolute Value 1.3 Addition of Integers 1.4 Subtraction of Integers Mid-Chapter 1 Review 1.5 Multip
MGSE6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane MGSE6.NS.7: Understand ordering and absolute value of rational numbers.
Open Awards Level 2 Skills for Further Learning and Employment: Qualification Guide Page 4 of 46 Date Authorised: 03/10/2014 . www.openawards.org.uk Phone: 0151 494 2072 . Open Awards . Set up in 1981 as OCNNWR and now trading as Open Awards, we have been in business for over 30 years. During that time we have helped thousands of learners
