Mathematical+Reflections,+p.+52+0910

Joshua Bodary Block D April 22, 2010 How do I find the difference between integers? **
 * Big Idea: ** Negative Numbers help us to model many real world situations.
 * ESSENTIAL QUESTION: **

To find the difference between integers is to it has it owns ways. If you want to find the difference of a negative number with another negative number or a positive number with another positive number is easily figure out since they are both the same side of the integers. You just need to subtract the positive number like subtracting ordinary whole numbers, to subtract negative numbers is like subtracting ordinary whole number but it is just in negative. But to find the difference between of a positive number and a negative number is a different way. If you finding the difference of a positive number with the negative number you need to just make the negative number like a whole number since subtracting a negative number is just like adding a positive number. If you want to find the difference of a negative number and positive number, it is just turning the positive to a negative number since we need to subtract the positive number by a negative number

** 1. Write a strategy for finding the difference of two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0. Verify your strategy by finding the following differences: **

A. 5 – 9 (answer = -4) Since the # 5 is smaller than the # 9. The answer is in negative. If 9 – 5 the answer is 4, so I just switch 9 and 5 and the answer is in negative. Furthermore, the answer is -4. ( 5 – 9 = 4)

B. -5 - +3 (answer = -2) Since the -5 is being subtracted by +3 which is also known as 3. Than -5 is being subtracted to 3 which concludes to answer of -8. (-5 - +3 = -5 – 3 = -8)

C. -5 - -3 = (answer = -2 We are looking for the difference between -5 and -3, just like how we find the difference of 5 -3 is 2. So if we do from the opposite side, which is -5 - -3, the answer will be the opposite of itself which is -2. (-5 - -3 = -2 / (5 -3 =2))

D. 5 - -9 = ( answer = 13) Since we are actually subtracting the -5, the integer needs to go higher. Subtracting a negative number is just like adding a positive numbers. (5 - -9 = (5 +9 =13)

** 2. Without actually calculating the sum, how can you decide if the sum of two integers is positive? Negative? Zero? **

// Positive = It only will be positive if // // A) Both numbers are positive numbers (2+2=4). // // B) One of the numbers is positive, and the positive number is higher absolute value than the other (-3 + 6=3). //

// Negative = It only be Negative If // // A) Both numbers are negative numbers (-7 + -8 = -15) // A) One of the numbers is Negative and the negative number is higher in absolute value than the other (-6 + 3 = -3)

// It only be Zero if // // A) Both numbers are zeroes (0 + 0 =0) // //  B) If the both absolute number line is being added. ( +5 + -5 = 0)  //

** 3. Without actually calculating the difference, how can you decide if the difference of two integers is positive? Negative? Zero? **

Positive = It only will be Positive if  A) If both in positive, If the first number is bigger than the other number ( 9 – 7 = 2) B) If both in negative numbers, the second negative number is bigger than the first number ( - 7 - -8 = 1). C) If only 1 number in negative and it is place in as the second number, the negative number is just adding up the number because subtracting a negative is like adding a positive number. ( +8 - -12 = -4)

It only be Negative If A) If both in positive, The second number is bigger than the first number ( 7 – 9 = -2) B) If both in negative, the second negative number need to be lower than the first negative number ( -9 - -6 = -3 ) C) If only 1 in negative number and it is place in as the first number, if a positive number is being subtracted by a negative number, it is like adding a negative number ( -6 – 4 = -10) Zero = It only be zero if

A) Both numbers is zero (0 - 0 = 0) B) If the positive number is both equal (5 – 5 = 0 )    C) If both negative number, the negative need to be the equal amount (-5 - -5= 0)

** 4. Describe how addition and subtraction of integers are related: **

Integers are like numbers but are like having an opposite side. Addiction and subtraction are related by is like a opposite world like adding 5 and 5 is 10, in the negative world -5 +-5 is -10. They are related by doing calculations that will end up a opposite answer.

** 5. Describe how to find the absolute value of any number: **

Using the integer line, the find the absolute value is to move the exact same unit but in the other direction. If you move to the right 7 unit, to find the absolute value I to go 7 unit to the left side. **Summary** TO modeling addition and subtraction of integers is a much more difficult way just to add or subtract normal whole numbers. Finding difference between integers are little bit complex, is also the same thing adding integers. Learning how to find sum and difference of integers and how it works it is like everyday life. It is like measuring how deep the ocean is (-238 feet from land) or measuring how high a mountain is (+386 feet from land). WE did also learn the inverse operation, the operation that can undo each other. Adding and subtracting are inverse operation. How we learned all this method of to add and subtract integers are a math process that we do to describe elevation and measures.