# Integers

Mathematics Teacher at Mayamot National High School en Mayamot National High School
8 de Nov de 2012
1 de 11

### Integers

• 1. _____________________________________________ Operations With Integers -4 _________________ Middle Grades Mathematics Methods -8
• 2. Minus…What does it mean? In algebra, the minus sign can mean three things.  In front of a number, the minus sign means “negative”.  In front of any expression, the minus sign means “the opposite of”.  Between two expressions, the minus sign means “subtract” or “take away”.
• 3. Adding Integers Teaching the Idea: Integers are positive and negative whole numbers and zero. _________________________________________ When you add opposites, such as 3 and -3, the result is 0.
• 4. Adding Integers Teaching the Idea: Integers are positive and negative whole numbers and zero. _________________________________________ When you add opposites, such as 3 and -3, the result is 0. Three zero pairs. No counters are left, so the result is 0.
• 5. Example Problems: To model addition of integers, put on the first number, put on the second number, cancel what you can, and then count. 1. -10 + (-3) = 1. -8 + 9 = 1. 4 + (-7) = 1. -12 + (-6) = 1. 4 + 3 = 1. -5 + 2 = What patterns do you notice?
• 6. Subtracting Integers To model subtraction, put on the first number, take off the second number, and count. -2 - 5 (Sometimes there are not enough blocks to take off, so “zero” may be added until there are enough counters to remove.) Negative 2 put on, not enough to take five, so add five zero pairs, and then take five, count what is left.
• 7. Subtracting Integers To model subtraction, put on the first number, take off the second number, and count. -2 - 5 (Sometimes there are not enough blocks to take off, so “zero” may be added until there are enough counters to remove.) Negative seven left
• 8. Subtraction Examples: Put on, add zero as needed, take off, count. 1. -10 - 3 = 1. 6 - 9 = 1. 4 - (-7) = 1. -12 – (-6) = 1. 7 - 3 = 1. -5 - 2 = What patterns do you notice?
• 9. Multiplication of Integers Consider the four cases: 3(2) 3(-2) 3 sets of two is 6 3 sets of negative two is -6 -3(2) -3(-2) Opposite of 3 sets of two is -6 Opposite of 3 sets of negative two is 6
• 10. Minus…What does it mean? In algebra, the minus sign can mean three things.  In front of a number, the minus sign means “negative”.  In front of any expression, the minus sign means “the opposite of”.  Between two expressions, the minus sign means “subtract” or “take away”.
• 11. Division of Integers Recall there are four ways to write a division expression. Relate division of integers to multiplication: For example: 12/3 What times 3 equals 12?