2Integers (add this to small notebook) DefinitionIntegers are a set ofnumbers that include thefollowing:(… –3, –2, –1, 0, 1, 2, 3, …)FactsInclude positive and negative whole numbers.Successive integers differ by one.Every negative number is the opposite of the positive number of the same size.Represents the difference between two objects in a set.Can be represented on a number line.Examples–258Non-examples–2.764 1/30.2Integers
3Opposite Integers – Concept of Zero Earn $1, Spend $1 (need tiles)Have students share other similar examples. Introduce the term opposite integers and relate it to the example provided above.Earning $1 can be represented by +1. Spending $1 can be represented by and -1 are called opposite integers. Symbolically, (+1) + (-1) = 0.Have students draw a number line and place pairs of opposite integers on the number line. Through discussion, have them verbalize that opposite integers are equidistant from zero on the number line and when you add two opposite integers the sum is always zero.
4additive inverse Yellow (–) Red (+) students use the tiles to represent zero, draw diagrams and write number sentences. TT
5Which of the following would represent zero, using integer tiles? Yes or No
6use integer tiles to answer questions (+2) and (–2) = 0 (+3) and (–3) = __ (–5) and ( ) = 0 ( ) and (+4) = 0
7What does this equal?Can you arrange the tiles to show the same answer in a different way?
9Integers Warm UpPlace the following numbers on a number line: 3, –4, 0, 1, –5. Explain how these numbers are ordered.Write <, = or > in the boxes to complete the sentences below correctly.a) –15 – b) –46 – c) –2 5 – 5Name the negative integers that are greater than –20 and divisible by 3. Explain your answer.The temperature is -15o Celsius on Monday and -8o Celsius on Tuesday. Which day shows the higher temperature? How do you know?Explain why one negative integer is less than another negative integer by using a real world context.
10Show the same number using a different number of tiles Show the same number using a different number of tiles. What is the pattern?Integer+2-2+3-5Number of integer tiles2, 4, 6, 8, …3, 5, 7, 9…5, 7, 9, 11…
11Can you represent +3 with 121 tiles? why or why not!?If the integer is an even number, then an even number of tiles greater than or equal to the absolute value of the integer must be used to represent it because an even number plus an even number is an even number.If the integer is an odd number, then an odd number of tiles greater than or equal to the absolute value of the integer must be used to represent it because an odd number plus an even number is an odd number.
12Subtract numbers and take the sign of the larger number Adding Integers (+)Positive (+)Negative (-)Positive (+)Add the numbers and use the sign of the numbersSubtract numbers and take the sign of the larger numberExample 1: Positive + PositiveExample 2: Negative + NegativeExample 3: Positive + Negative
13Rule: The sum of two positive integers is a positive integer. =+11=+22=+45Do not confuse the sign of the integer with the operation being performed. Remember that:= +45 is read as Positive 29 plus positive 16 equals positive 45.
14Rule: The sum of two negative integers is a negative integer. =-11=-13=-20Do not confuse the sign of the integer with the operation being performed. Remember that:= -11 is read as Negative 2 plus negative 9 equals negative 11.
15To add a positive and a negative integer (or a negative and a positive integer), follow these steps: Find the absolute value of each integer.Subtract the smaller number from the larger number you get in Step 1.The result from Step 2 takes the sign of the integer with the greater absolute value.
16Adding IntegersYou earn $2 and then spend $5. How much is your profit or loss?Show this on a number line.Show this using integer tiles.
25On your own! (+2) – (+3) = __ (+2) – (–2) = __ I am $1 in debt and I spend $3 more. What is my debt/profit now?(–1) – (–3) = __I am $3 in debt and someone cancels a $2 debt that I owe him. What is my debt/profit now?
26For your small notebook: FACT: Any subtraction equation can be written as an equivalent __________ sentence.Subtracting IntegersFACT: The difference of two integers may be ___, ____, or ___ to either of the integers that are subtracted.Examples Not an example
27Class Practice Textbook p. 287 Regular #2-32 (evens), 42 or Challenge # 10, 26, 34, 47, 49GAME: Integers