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Name: ________________________________________ Date: ____________________________ Period: _______ Mrs. Torres 6th Grade Lesson: 11-1: Exploring Integers Vocabulary Words: 1. Opposites – are two numbers that are the same distance from 0 on a numeric line, but in opposite direction. 2. Integers – are the set of positive numbers, negative numbers and the zero. Zero is not positive neither negative, it’s a neutral number. 3. Absolute Value – it is the distance of a number from zero, on a numeric line. The symbol for the absolute value of a number n is /n/. Representing situations with integers: Examples: 1. Dry ice is solid carbon dioxide which freezes at about 109 degrees below zero Fahrenheit. Which integer represents the freezing point of dry ice? a. -109 b. -19 c. +19 d. +109 “Below zero” is the clue word, which means going down, when something is going down, decreasing, that means that the answer is a negative number. So the answer will be a. -109 degrees. 2. The lowest elevation in New Orleans, Louisiana is 8 feet below sea level. Use a integer to represent this elevation: _______ 8 feet below sea level means going down, something that is below, so the integer will be a negative number, so the answer is -8. 3. He climbs 30 ft. = ______ Climbs means going up, increasing, so the answer is a positive number = 30 or +30. Practice: Write the integer that represents each situation: 1. 2. 3. 4. 5. 6. 7. 8. Lost three pencils = ______ Gain 10 pounds = ______ She has a debt of $25 = _______ 20 degrees below 0 = _____ He won $1,000 in the casino = ________ Lost 5 pounds = _____ 4 degrees above 0 = _____ He received a credit of $100 = ______ Identifying the Opposite: When you are going to identify the opposite, you have to change the direction of the units. If the number is positive, you are going to the right side of the numeric line. The opposite with be going to the left, so the number will be negative. If the number is negative, the opposite will be positive. 3 units Example: Write the opposite of 3 = -3 -3 -2 -1 3 units 0 1 2 3 Write the opposite of -5 = _____ If the number is negative, the opposite is positive, so the answer is 5 or +5. Write the opposite of 8 = _____ If the number is positive, the opposite is negative, so the answer is – 8. Practice: Write the opposite of the following integers: 1. 2. 3. 4. -10 = _____ 13 = _____ -21 = _____ – 1,215 = ______ 5. 14 = _____ 6. – 340 = _______ 7. 0 = _____ 8. -1 = _____ Finding the absolute value of an integer: /n/ The Absolute Value is the distance between a number and zero, in other words you have to count how many units are between the number and zero. Example: Find /-4/ = ______ 4 units -4 -3 -2 -1 0 1 2 3 4 The absolute value of 4 means, how many units are between 4 and 0? There are 4 units between 4 and 0, so the answer is 4. Find /2/ =____ -3 -2 -1 2 units 0 1 2 3 The absolute value of 2 means, how many units are between 2 and 0? There are 2 units between 2 and 0, so the answer is 2. Practice: Find the absolute value of the following numbers: 1. 2. 3. 4. /38/=_____ /-4/=_____ /-9/=_____ /-65/=_____ 5. /15/=_____ 6. /0/=_____ 7. /-12/=_____ 8. /10/=_____