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Word Sort integers, addition, even numbers, odd numbers prime numbers, composite numbers, negative integer, positive numbers, whole numbers, subtraction, multiplication, division, 0, 12/2, –100, comparing, ordering, thermometer, debts/credits, above/below sea level. Suggestions: Venn Diagram, Web, Tree

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Integers (add this to small notebook) Definition Integers are a set of numbers that include the following: (… –3, –2, –1, 0, 1, 2, 3, …) Facts Include 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 – Non-examples – /3 0.2 Integers

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Opposite Integers – Concept of Zero

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additive inverse Yellow (–) Red (+)

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Which of the following would represent zero, using integer tiles? Yes or No

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use integer tiles to answer questions (+2) and (–2) = 0 (+3) and (–3) = __ (–5) and ( ) = 0 ( ) and (+4) = 0

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What does this equal? Can you arrange the tiles to show the same answer in a different way?

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Use integer tiles to show –2, +3 and –5.

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Integers Warm Up Place the following numbers on a number line: 3, –4, 0, 1, –5. Explain how these numbers are ordered. Write in the boxes to complete the sentences below correctly. a) –15 –20 b) –46 –31 c) –2 5 – 5 Name the negative integers that are greater than –20 and divisible by 3. Explain your answer. The temperature is -15 o Celsius on Monday and -8 o 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.

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Show the same number using a different number of tiles. What is the pattern? Integer Number of integer tiles 2, 4, 6, 8, … 3, 5, 7, 9…5, 7, 9, 11…

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Can you represent +3 with 121 tiles? why or why not!?

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Adding Integers (+) Positive (+)Negative (-) Positive (+) Add the numbers and use the sign of the numbers Subtract numbers and take the sign of the larger number Negative (-)Subtract numbers and take the sign of the larger number Negative (-) Add the numbers and use the sign of the numbers Example 1: Positive + Positive Example 2: Negative + Negative Example 3: Positive + Negative

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Rule: The sum of two positive integers is a positive integer. IntegersSum = = = + 45 Do 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.

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Rule: The sum of two negative integers is a negative integer. IntegersSum = = = - 20 Do 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.

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To 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.

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Adding Integers

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(+2) + (–5) = (–3) Another example?

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add using the integer tiles, drawing diagrams and writing the number sentences (+2) + (+3) = __ (–1) + (+4) = __ (–1) + (–3) = __ (+2) + (–4) = __

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Class Practice Regular Problems: P. 280 Evens from #2 – 40, 61 Or Challenge Problems: P. 281 #53, 55, 57, 58, 65, 66

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Operation Integers! Yellow cards are negative White cards are positive DIRECTIONS Turn over two cards and add them. Larger answer wins! (Record your addition sentence)

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Subtracting Integers You are $2 in debt and spend $4 more. What is your debt now? 1.Tiles 2.Number Line 3.Math Equation 4.Spokesperson

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-2 – 4 = = - +

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Sunny has $4 but spends $6. How much money does she have now? 1.Tiles 2.Number Line 3.Math Equation 4.Spokesperson

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+4 + (-6) = -2

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On 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?

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Subtracting Integers Examples Not an example FACT: The difference of two integers may be ___, ____, or ___ to either of the integers that are subtracted. FACT: Any subtraction equation can be written as an equivalent __________ sentence. For your small notebook:

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Class Practice Textbook p. 287 Regular #2-32 (evens), 42 or Challenge # 10, 26, 34, 47, 49 GAME: Integers

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