Mathematical+Reflections,+p.+52+0910

A.A Block B  4/20/10 Big Idea: Negative numbers help us to model many real-life situations. INV3 Essential Question: How do I find the difference between two integers? ** Mathematical Reflections **  ** In this investigation, you explored situations that involve subtraction of integers. You explore subtraction by using chip boards and number lines and by looking at patterns. These questions will help you summarize what you have learned: ** 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. ** My Strategy: First of all, if there are 2 ‘–‘signs, like 5 --4 (Five minus negative 4) then it’s actually an addition problem, the two numbers are added to each other. For 0, anything subtracting 0 is the number itself. For 2 positive numbers, if one smaller positive number is subtracting a bigger one, you subtract the smaller one from the bigger one and make it negative. If a bigger one is subtracting the smaller one, you move the amount of the smaller one’s spaces to the left. If it’s two negative numbers, then you can forget about all the negative signs and subtract it normally, like positive numbers but opposite. Be sure to put the appropriate signs on the differences. If it’s one positive and one negative number, if it’s the positive number subtracting, actually add the number to the positive number. If it’s the negative number subtracting, do the same but as negative. a. ** 5-9 ** Subtract five from nine so you get four. Make that four negative and the answer is -4. b. ** -5-+3 ** Add five to three so you get eight. Make that eight negative and the answer is -8. c. ** -5- -3 ** Add three to negative five so that you get -2, the answer. d. ** 5- -9 ** Add five to nine so that you get 14, the answer. 2) ** Without actually calculating the sum, how can you decide if the sum of two integers is positive? Negative? Zero? ** You can tell if the sum is going to be positive if two positive numbers are being added or if the absolute value of the positive number is greater than the negative number’s in a positive + negative number equation. You can tell that the sum is going to be negative if two negative numbers are being added or if the absolute value of the negative number is greater than the positive number’s in a positive + negative number equation. You can tell the sum is going to be zero if a number is added with its opposite.  3) ** Without actually calculating the difference, how can you decide if the difference of two integers is positive? Negative? Zero? ** You can tell if the difference is going to be positive if one positive number is subtracting another positive number with a lesser absolute value than it, or if one negative number is subtracting another negative number with a greater absolute value than it. You can tell the difference is going to be negative if one positive number is subtracting another positive number with a greater absolute value than it, or if one negative number is subtracting another negative number with a lesser absolute value than it. You can tell the difference will be zero if a number is subtracted from its opposite. 4) ** Describe how addition and subtraction of integers are related. ** Addition is the opposite of subtraction in every method, every way.  5) ** Describe how to find the absolute value of any number. ** You must measure the distance of the number away from zero. ** Think about your answers to these questions, discuss your ideas with other students and your teacher, and then write a summary of your findings in your journal. ** ** Summary ** In this investigation, we explored the subtraction of integers, including negative integers and positive integers. We found how to use chip boards, number lines, and patterns to learn about subtracting integers. We developed strategies for finding differences in problems with different combinations of positive and negative integers. We found how to predict if sums and differences were negative, positive, or zero before actually doing the problem. We also discovered how to find the absolute value of any number and how addition and subtraction are related.