Adding & Subtracting Integers

Transcription

1 WARDEN AVE P.S. Adding & Subtracting Integers Number Sense & Numeration Unit #1 Grade 7 Math School Year This mini-unit will run from September and must be handed in on Friday Sept. 26th by 3:45 pm

2 PART A: INTEGERS What is an Integer? An integer is a number that has no fractional part, and no digits after the decimal point. We sometimes call them WHOLE NUMBERS. An integer can be positive, negative or zero. (Compare this to real numbers than can have digits after the point and can have fractional parts) Example integers: +12, +34, -4, 0 The following are real numbers and are not integers: 1.23 (cannot have decimal places) 12½ (cannot have a fractional part) Helpful ways to remember how Integers work: The Number Line Negative Numbers (-) Positive Numbers (+) (The line continues left and right forever.) Numbers on the left are smaller than numbers on the right. Examples: 5 is smaller than 8 1 is smaller than +1 8 is smaller than 5 Now its your turn to place numbers along a number line. Remember to use the guide above to help you if you are stuck or confused.

3 SKILL BUILDER Please place the following numbers on the number line in their correct place END OF LESSON Adding and Subtracting Integers Numbers Can be Positive or Negative: Negative Numbers ( ) Positive Numbers (+) " " is the negative sign. "+" is the positive sign No Sign Means Positive If a number has no sign it usually means that it is a positive number. Example: 5 is really +5 Adding Positive Numbers Adding positive numbers is just simple addition. Example: = 5 is really saying "Positive 2 plus Positive 3 equals Positive 5" OR You could write it as (+2) + (+3) = (+5)

4 Subtracting Positive Numbers Subtracting positive numbers is just simple subtraction. Example: 6 3 = 3 is really saying "Positive 6 minus Positive 3 equals Positive 3" OR You could write it as (+6) (+3) = (+3) Now for something a little different Subtracting a Negative is the same as Adding Example: What is 6 ( 3)? 6 ( 3) = = 9 Example: What is 14 ( 4)? 14 ( 4) = = 18 RULE OF THUMB If the operational sign (what it s asking you to do) matches the number s integer sign, then you are ADDING. And Positive and Negative Together... Example: What is 6 (+3)? Example: What is 5 + ( 7)? 6 (+3) = 6 3 = 3 5+( 7) = 5 7 = 2 Subtracting a Positive or Adding a Negative is Subtraction

5 RULE OF THUMB If the operational sign (what it s asking you to do) does not match the number s integer sign, then you are SUBTRACTING. QUICK REFERENCE OPERATION RESULT Now you get to try out your new skills with some practice sheets. Ready to do it? Go!!!

6 Name: Date: Add and Subtract Integers 1. Temperature is rising so we add a positive number. Addition sentence: a. Temperature was - 3 C. Then it rose 4 degrees. Now it is = 1 b. Temperature was -5 C. Then it rose 2 degrees. Now it is. c. Temperature was -9 C. Then it rose 4 degrees. Now it is. d. Temperature was -1 C. Then it rose 7 degrees. Now it is. e. Temperature was -2 C. Then it rose 5 degrees. Now it is. f. Temperature was -10 C. Then it rose 3 degrees. Now it is. 2. Temperature is dropping so we subtract a positive number. Subtraction sentence: a. Temperature was 3 C. Then it dropped 4 degrees. Now it is. b. Temperature was 7 C. Then it dropped 10 degrees. Now it is. c. Temperature was 5 C. Then it dropped 8 degrees. Now it is. d. Temperature was -1 C. Then it dropped 5 degrees. Now it is. e. Temperature was -7 C. Then it dropped 7 degrees. Now it is. f. Temperature was -10 C. Then it dropped 2 degrees. Now it is. 3. Fill, and observe the patterns. a. 5 4 = b. 4 0 = c = d = 5 5 = 4 1 = = = 5 6 = 4 2 = = = 5 7 = 4 3 = = = 5 8 = 4 4 = = = 4. Match the equations with the situations, and complete the missing parts. a. A diver was the depth of 20 ft. Then he rose 15 ft. Now he is at ft. b. John had $15. He had to pay his dad $20. Now he. c. John had a $15 debt. He earned $20. Now he. d. A ball was dropped from 15 ft above the sea; it fell 20 ft. Now the ball is at ft. e. Temperature was 20 C and fell 15. Now the temperature is C = = = = = Math Mammoth Grade 6 Worksheets Collection. Copyright SpiderSmart, Inc. and Taina Maria Miller

7 Two Ways to Solve a Word Problem Here are two quick methods to help you solve a word problem (hint of what s coming next). The two (2) approaches are called the C.U.B.E. method and the U.P.S. check method. Let s break them down. C.U.B.E. CUBE stands for: Circle the numbers. Underline important words. Box the question. Eliminate unnecessary information This is how it works: PROBLEM: Mr. Johnson's class has 21 students. If the seven of his students are absent due to heavy rainfall on a particular day, how many students does he have in his class on that day? CUBE APPROACH: Mr. Johnson's class has 21 students. If the seven of his students are absent due to heavy rainfall on a particular day, how many students does he have left in his class on that day? I underlined the word "left" because it helps us understand what type of problem we'll be doing. I realize you could classify other words in this word problem as "important," but the students I know only underline the important math words. They might also underline words such as remain, divide, in all, altogether, take away, etc. These are the "telling words" that tell students what kind of action they should perform to those numbers. Lots of teachers post these "key math words" on giant keys (aren't we clever?) on a math bulletin board somewhere in the room. I boxed the question so that we could focus on what answer we're supposed to find. I crossed out unnecessary information about the teacher's name and why the students were absent so that we could concentrate more easily on important info. You could do this to any word problem!

8 The other method mentioned above is the U.P.S. check Understand the problem. Plan how to solve the problem. Solve the problem. Check your answer Let s use the same problem as before but apply this method to it: PROBLEM: Mr. Johnson's class has 21 students. If the seven of his students are absent due to heavy rainfall on a particular day, how many students does he have in his class on that day? UPS APPROACH: Either way can work, you just need to find which one works for you. Here s a quick reference card to help you.

9 Practice Integer Word Problems 1. A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position? 2. Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations? 3. In golf, the average score a good player should be able to achieve is called "par." Par for a whole course is calculated by adding up the par scores for each hole. Scores in golf are often expressed at some number either greater than or less than par. Ms. Floop is having a pretty good day at the City Golf Club. Her score so far after 15 holes is -5. If par for 15 holes is 62, what is her score?

10 4. Dylan plays in the backfield of the Big Town football team. Last week he ran four plays from the running back position. He made "gains" measured in yards of 0, -5, 1, and -3. What were his average yards per gain? Round your answer to the nearest tenth of a yard. 5. There was a 100-mile race at the Toronto Race Track. The winning driver had a time of 57 minutes. The next four drivers in order of finish had times (relative to the winning time) of +2, +3.2, +3.8, and +4.5 minutes. The sixth place driver had a time that was 3 minutes slower than the driver ahead of him. What was the sixth place driver's time? Express your answer in hours, minutes, and seconds. 6. In 2011, Belter Books reported a net loss of $43.9 million. In 2012, the company had a net income of $33 million. How much more money did the company make in 2012 than in 2011?

11 PROJECT TIME Now that we ve learned all about how to add and subtract integers, it s time to show your understanding and share your newly acquired knowledge. That s right, its project time! For your project, you will be asked to explain the rules of adding and subtracting integers by creating a Your poster must have the following elements: A clear explanation of the rules (in your own words) Visual demonstrations to help explain An example for each rule (create your own questions and answers) A catchy title A clear sense of organization This is an individual project, but you can always have a partner look over your draft work. Below if your rough work space. You MUST complete your work here before moving on to the good copy. Good luck. The rules for Adding and Subtracting Integers (in my own words) are: Adding: Subtracting: Examples: 1) 2) 3) 4)

12 DRAFT OF POSTER (pencil sketch and layout)

13 Integers Rules Poster Teacher Name: Student Name: CATEGORY Graphics -Clarity Graphics are all in Most graphics are in Most graphics are in Many graphics are not None graphics are focus and the content focus and the content focus and the content clear or are too small. clear or are too easily viewed and identified from 6 ft. away. easily viewed and identified from 6 ft. away. is easily viewed and identified from 4 ft. away. small. Content - Accuracy At least 7 accurate facts (rules and examples) are displayed on the 5-6 accurate facts (rules and examples) are displayed on the 3-4 accurate facts (rules and examples)are displayed on the Less than 1-2 accurate facts (rules and examples) are displayed on the No accurate facts (rules and examples) are displayed on the Required Elements The poster includes all required elements as well as additional information. All required elements are included on the All but 1 of the required elements are included on the Several required elements were missing. All required elements were missing. Attractiveness Title The poster is exceptionally attractive in terms of design, layout, and neatness. Title can be read from 6 ft. away and is quite creative. The poster is attractive in terms of design, layout and neatness. Title can be read from 6 ft. away and describes content well. The poster is acceptably attractive though it may be a bit messy. Title can be read from 4 ft. away and describes the content well. The poster is distractingly messy or very poorly designed. It is not attractive. The title is too small and/or does not describe the content of the poster well. The poster is not presentable. There is no title on the poster