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Using Multiple Representations to Introduce Integers Answer Key Susan Mercer Opposites Find the pair of opposites: up right empty white have backwards hot cold no full left negative loss down black south forwards owe north gain positive yes S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 1 Integers - Money During this unit you are going to use integers to represent situations that and problems include opposites. For example: having $5 is represented by +5 owing $5 is represented by –5 going up 4 steps is represented by +4 going down 4 steps is represented by –4 gain $12 is represented by +12 loss $12 is represented by –12 Use integers to represent the following situations: have $10 _+10_ owe $23 _–23_ up 5 steps _+5_ down 13 steps _–13_ loss $23 _–23_ gained $27 _+27_ loss $43 _–43_ have $1 _+1_ forward 10 steps _+10_ backwards 4 steps _– 4_ positive 7 __+7_ negative 16 _–16_ S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 2 Integers - Tiles The numbers .... –3, –2, –1 , 0, +1, +2, +3,.... are integers. The numbers +1, +2, +3 are positive integers. The numbers –3, –2, –1 are negative integers. When working with integers we are going to use the tile model. a white tile will represent +1 a black tile will represent a –1 a white tile and a black tile represent the number 0. Therefore represents the number –3. represents the number +5 represents the number +2 ( this is the same as 2 + 0 ) Using tiles, represent the following numbers: +4 –6 –3 +1 10 –10 0 S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 3 Integers - Number Lines During this unit you are going to use number lines. Label each number line and place the integer in its appropriate place. 4 0 0 -6 4 –6 2 0 -9 0 –2 –9 0 -7 0 0 7 7 and –7 +7 and –7 are opposites Place the number and its opposite. -5 0 -2 5 0 –5 -8 0 2 +2 0 8 –8 S. Mercer - Using Multiple Representations to Introduce Integers 0 ANSWER KEY page - 4 Integers - Sea Level During this unit you are going represent above and below sea level using integers. Represent each number. Remember to start at Sea Level. 0 +6 Sea Level Sea Level 0 (Sea Level) +6 (going up 6 steps) +4 Sea Level +4 -2 Sea Level –2 (going down two steps) +5 Sea Level Sea Level -5 –5 +5 +7 Sea Level +7 S. Mercer - Using Multiple Representations to Introduce Integers -2 Sea Level –2 ANSWER KEY page - 5 Addition of Integers Represent Using Tiles Represent Using a Number Line +5 +4 9 4 0 moved positive 4 then positive 5 and end at positive 9 9 positive tiles 4+5 Problem If you have 4 dollars and get 5 dollars you will end with 9 dollars +5 9 above sea level +4 Sea Level Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line +1 +6 01 7 7 positive tiles moved positive 1 then positive 6 and end at positive 7 1+6 Problem +6 If you have 1 dollars and get 6 dollars you will end with 7 dollars Represent Using Money +1 7 above sea level Sea Level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 6 Addition of Integers Represent Using Tiles Represent Using a Number Line -3 -2 --5 -3 0 moved negative 3 then negative 2 and end at negative 5 5 negative tiles –3 + –2 Problem If you owe 3 dollars and borrow 2 dollars you will end up owing 5 dollars Sea Level – 3 Represent Using Money –2 Represent Vertically 5 below sea level Represent Using Tiles Represent Using a Number Line -7 -1 --8 -1 0 moved negative 1 then negative 7 and end at negative 8 8 negative tiles –1 + –7 Problem If you owe 1 dollar and borrow 7 dollars you will end up owing 8 dollars –7 Represent Using Money – 1 8 below sea level Sea Level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 7 Addition of Integers Represent Using Tiles Represent Using a Number Line -5 -3 -3 -8 0 moved negative 3 then negative 5 and end at negative 8 8 negative tiles –3 + –5 Problem If you owe 3 dollars and borrow 5 dollars you will end up owing 8 dollars Sea Level -3 -5 Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line ZERO -3 ZERO ZERO 3 pairs and they equal 0 that leaves 3 positive tiles -3 0 3 moved negative 3 then positive 6 and end at positive 3 –3 + 6 Problem If you owe 3 dollars and get 6 dollars you will end with 3 dollars 3 above sea level +6 –3 Represent Using Money Sea Level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 8 Addition of Integers Represent Using Tiles Represent Using a Number Line -5 +5 5 0 Each line equals Zero. 0+0+0+0+0=0 moved positive 5 then negative 5 and end at 0 5 + –5 Problem at sea level -5 If you have 5 dollars and spend 5 dollars you will end with 0 dollars. +5 Sea Level Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line -6 -10 -4 0 10 negative tiles –4 + –6 Problem If you owe 4 dollars and borrow 6 dollars you will end up owing 10 dollars -4 -6 Represent Using Money Sea Level 10 below level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 9 Addition of Integers Represent Using Tiles Represent Using a Number Line -5 0 -5 move negative 5 and end at negative 5 5 negative tiles 0 + –5 If you have no money and borrow 5 dollars you will end up owing 5 dollars Problem Sea Level -5 5 below sea level Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line -7 -5 0 -12 move negative 7 then negative 5 and end at negative 12 12 negative tiles –7 + –5 Problem If you owe 7 dollars and borrow 5 dollars you will end up owing 12 dollars -7 -5 Represent Using Money 12 below sea level Sea Level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 10 Addition of Integers Represent Using Tiles Represent Using a Number Line -4 -3 +5 0 -2 ZERO Only 2 negative tiles are left +5 moved positive 5 then negative 3 then negative 4 and end at negative 2 5 + –3 + –4 Problem If you have 5 dollars and spend 3 dollars then spend another 4 dollars you will end up owing 2 dollars -3 +5 -4 Sea 2 below Level sea level Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line -4 +2 -8 0 -10 -8 10 negative tiles are left –8 + 2 + –4 Problem If you owe 8 dollars and make 2 dollars but then borrow 4 more dollars you will end up owing 10 dollars Represent Using Money -4 +2 -8 Sea Level 10 below sea level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 11 Addition of Integers Represent Using Tiles Represent Using a Number Line +2 -4 -4 2 negative tiles are left 0 -2 0 + –4 + 2 Problem If you have no money and spend 4 dollars but then make 2 dollars you will end up owing 2 dollars +2 Sea 2 below Level sea level -4 Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line -2 -6 +10 0 2 positive tiles are left 2 10 10 + –2 + –6 Problem -6 If you have 10 dollars and spend 2 dollars then spend another 6 dollars you will end with 2 dollars Represent Using Money -2 +10 2 above sea level Sea Level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 12 Word Problems 1) At 6:00am the temperature was 4˚ below zero. By 3:00pm the temperature had risen 15˚. What was the temperature at 3:00pm? Represent the problem using a picture 11 ˚ + 15˚ 0˚ - 4˚ 6:00 am Write a math expression of the problem - 4 + 15 = 11 -4˚ 3:00 pm Answer the question in a complete sentence. At 3:00 pm the temperature will be 11˚ above zero. 2) Sabrina went scuba diving. She descended 20 meters below the surface and then ascended 7 meters. How far below the surface was she? Represent the problem using a picture Write a math expression of the problem surface -20 + 7 = -13 -20 +7 -13 -20 Answer the question in a complete sentence. After ascending 7 meter she was at 13 meters below the surface. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 13 Word Problems 3) At midnight the temperature was 48˚F. By midday the temperature had risen 36˚. What was the temperature at midday? Represent the problem using a picture +84 ˚ Write a math expression of the problem + 36˚ +48 ˚ 48 + 36 = 84 48 ˚ 12:00am 0˚ 12:00 pm Answer the question in a complete sentence. At 12:00 pm the temperature will be 84˚ above zero. 3) Sabrina owes $5 to her mother and $16 to a friend, how much money does Sabrina have? Represent the problem using a picture Write a math expression of the problem 0 dollars -5 -5 -5 + -16 = -11 -16 -21 Answer the question in a complete sentence. Sabrina owes 21 dollars in total. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 14 Word Problems Comparing addition and subtraction 1) Sabrina earned $15 babysitting. She spent $6 in candy. How much money did she have left? Represent the problem using a picture Write a math expression using subtraction $15 -6 +15 1) $9 15 6 Write a math expression using integers no money Solve the problem. 1) 2) 2) 15 6 9 15 -6 9 2) 15 -6 Answer the question in a complete sentence. Sabrina has 9 dollars after buying the candy. Duncan invested in the stock market. The first year he gained $150. The second year he lost $80. What was his net gain? Represent the problem using a picture Write a math expression using subtraction $150 -80 +150 $80 1) 150 80 Write a math expression using integers no money Solve the problem. 1) 2) 150 80 70 150 -80 70 2) 150 -80 Answer the question in a complete sentence. After the second year has a net gain of 70 dollars. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 15 Word Problems Comparing addition and subtraction 1) Duncan has $30. He spends $12 on a CD. How much money does he have left? Represent the problem using a picture Write a math expression using subtraction $30 -12 +30 $18 1) 30 12 Write a math expression using integers no money Solve the problem. 1) 2) 2) 2) 30 -12 Answer the question in a complete sentence. 30 12 18 30 -12 18 Duncan has $18 left. Sabrina’s mom gained 15 pounds during the summer vacation. During fall she lost 12 pounds. What was her net weight loss or gain? Represent the problem using a picture Write a math expression using subtraction 15 -12 +15 1) 3 no weight gain Solve the problem. 1) 2) 15 12 Write a math expression using integers 2) 15 -12 Answer the question in a complete sentence. 15 12 3 15 -12 3 Sabrina’s mom net weight gain was 3 pounds. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 16 Subtraction of Integers 1-2-3-4 Method 1) 10 1) Copy the same number 5 2) Change subtraction to addition 3) Write the opposite 5 -5 10 4) Add the integers 2) 5 1) Copy the same number -2 2) Change subtraction to addition 5 3) Write the opposite 7 2 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 17 Subtraction of Integers 1-2-3-4 Method 3) -4 1) Copy the same number 8 2) Change subtraction to addition -4 3) Write the opposite -12 -8 4) Add the integers 4) -7 1) Copy the same number -1 2) Change subtraction to addition -7 3) Write the opposite -6 1 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 18 Subtraction of Integers 1-2-3-4 Method 5) 0 -5 2) Change subtraction to addition 1) Copy the same number 0 3) Write the opposite 5 5 4) Add the integers 6) 0 1) Copy the same number 8 2) Change subtraction to addition 0 3) Write the opposite -8 -8 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 19 Subtraction of Integers 1-2-3-4 Method 7) 15 10 2) Change subtraction to addition 1) Copy the same number 10 3) Write the opposite -15 -5 4) Add the integers 8) 3 -8 2) Change subtraction to addition 1) Copy the same number 3) Write the opposite 8 3 11 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 20 Subtraction of Integers 1-2-3-4 Method 9) -4 4 2) Change subtraction to addition 1) Copy the same number 3) Write the opposite -4 -4 -8 4) Add the integers 10) 6 -6 2) Change subtraction to addition 1) Copy the same number 6 3) Write the opposite 6 12 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 21 Review Addition and Subtraction of Integers Based on what you have learned so far, solve the following problems: 1) 10 + –8 = 2 2) –7 + –3 = –10 3) 4 + –9 = –5 4) –10 + 15 = 5 5) –3 + – 5 + – 9 = –17 6) 10 + –9 + – 4 = –3 7) 10 – 15 = –5 8) 10 – (–3) = 13 9) –5 – 10 = –15 10) –5 – (–3) = –2 S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 22 Multiplication of Integers Discover the Rules! Rule #1 –3 • 4 = – 12 5 • –2 = – 10 –6 • 3 = – 18 2 • –3 = – 6 Study the problems. What patterns do you notice? These are multiplication problems. All answers are negative. One number is positive and one is negative. 1 • –3 = – 3 –10 • 4 = – 40 Describe the rule and give two examples. A positive number multiplied by a negative number always equal a negative answer. So the answer is negative 12 if negative 3 is multiplied by positive 4 or if positive 3 is multiplied by negative 4. Rule #2 –3 • –4 = 12 5 • 2 = 10 –6 • –3 = 18 –2 • –3 = 6 1•3= 3 Study the problems. What patterns do you notice? These are multiplication problems. All answers are positive. both numbers are positive or both are negative. –10 • –4 = 40 Describe the rule and give two examples. If two positive or two negative numbers are multiplied the answer is positive. So the answer is positive 12 if positive 3 is multiplied by positive 4 or if negative 3 is multiplied be negative 4. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 23 Multiplication of Integers Discover the Rules! Rule #3 –3 • 4 • – 2= 24 4 • –5 • –2 = 40 –2 • – 2 • 3 = 12 –10 • 2 • –3 = 60 –2 • 1 • –3 = 6 Study the problems. What patterns do you notice? These are multiplication problems. All answers are positive. Each problem has two negative numbers and one positive. –5 • –2 • 4 = 40 Describe the rule and give two examples. If there is an even number of negative numbers being multiplied then the answer is positive. So the answer is positive 12 if positive 3 is multiplied by negative 2 and by negative 2 or if negative 3 is multiplied be negative 2 and a positive 2. Rule #4 3 • 4 • – 2= –24 Study the problems. What patterns do you notice? 4 • –5 • 2 = –40 –2 • 2 • 3 = –12 These are multiplication problems. –10 • 2 • 3 = –60 All answers are negative. 2 • 1 • –3 = –6 Each problem has two positive numbers and one negative. 5 • –2 • 4 = –40 Describe the rule and give two examples. If there are an odd number of negative numbers multiplied then the answer is negative. So the answer is negative 12 if positive 3 is multiplied by negative 2 and by positive 2 or if negative 3 is multiplied be negative 2 and a negative 2. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 24 Division of Integers Discover the Rules! Rule #1 –12 ÷ 4 = – 3 12 ÷ –4 = – 3 24 ÷ –6 = – 4 –24 ÷ 6 = – 4 15 ÷ –3 = – 5 Study the problems. What patterns do you notice? All the answers are negative. One number is positive and one is negative. These are division problems. –15 ÷ 3 = – 5 Describe the rule and give two examples. A positive number divided by a negative number is negative. A negative numbers divided by a positive is negative. Rule #2 –12 ÷ –4 = 3 12 ÷ 4 = 3 24 ÷ 6 = 4 Study the problems. What patterns do you notice? All the answers are positive. –24 ÷ –6 = 4 Both numbers are positive or both are positive. –15 ÷ –3 = 5 These are division problems. 15 ÷ 3 = 5 Describe the rule and give two examples. A positive number divided by a positive number is positive. A negative numbers divided by a negative is positive. S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 25 Positive or Negative? Looking at the problem, without doing the computation, decide if the answer to the problems is positive or negative. Explain you answer clearly. 1) –100 • –5 Positive or Negative Why? Because there is an even number of negative numbers 2) 15 • 4 • –3 Why? 3) 4) 6) 7) Positive or Negative Because there is an odd number of negative numbers 5000 ÷ –5 • –5 ÷ –5 Why? Positive or Negative Because there is an even number of negative numbers –100 ÷ –2 ÷ –2 Why? Positive or Negative Because there is an odd number of negative numbers –2• –2•–2•–2•–2•–2 Why? Positive or Negative Because there is an odd number of negative numbers –110 • 35 • 4 • 24 Why? 5) Because there is an add number of negative numbers –254 • –15 • –4 Why? Positive or Negative Positive or Negative Because there is an odd number of negative numbers S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 26 Review Multiplication and Division of Integers Based on what you have, solve the following problems: 1) 10 • –8 = –80 2) –7 • –3 = 21 3) 4 • –3 = –12 4) –5 • 10 = –50 5) –3 • – 2 • – 10 = –60 6) –3 • – 2 • 10 = 60 7) 10 ÷ –5 = –2 8) –10 ÷ –5 = 2 9) –25 ÷ –5 = 5 10) –25 ÷ 5 = –5 S. Mercer - Using Multiple Representations to Introduce Integers ANSWER KEY page - 27 Using Multiple Representations to Introduce Integers Name: ____________________ Period: ________ Date: ______________________ Opposites Find the pair of opposites: up right empty white have backwards hot cold no full left negative loss down black south forwards owe north gain positive yes S. Mercer - Using Multiple Representations to Introduce Integers page - 1 Integers - Money During this unit you are going to use integers to represent situations that and problems include opposites. For example: having $5 is represented by +5 owing $5 is represented by –5 going up 4 steps is represented by +4 going down 4 steps is represented by –4 gain $12 is represented by +12 loss $12 is represented by –12 Use integers to represent the following situations: have $10 ____ owe $23 ____ up 5 steps ____ down 13 steps ____ loss $23 ____ gained $27 ____ loss $43 ____ have $1 ____ forward 10 steps ____ backwards 4 steps ____ positive 7 ____ negative 16 ____ S. Mercer - Using Multiple Representations to Introduce Integers page - 2 Integers - Tiles The numbers .... –3, –2, –1 , 0, +1, +2, +3,.... are integers. The numbers +1, +2, +3 are positive integers. The numbers –3, –2, –1 are negative integers. When working with integers we are going to use the tile model. a white tile will represent +1 a black tile will represent a –1 a white tile and a black tile represent the number 0. Therefore represents the number –3. represents the number +5 represents the number +2 ( this is the same as 2 + 0 ) Using tiles, represent the following numbers: +4 –6 –3 +1 10 –10 0 S. Mercer - Using Multiple Representations to Introduce Integers page - 3 Integers - Number Lines During this unit you are going to use number lines. Label each number line and place the integer in its appropriate place. 4 –6 –2 –9 0 7 and –7 +7 and –7 are opposites Place the number and its opposite. –5 +2 –8 0 S. Mercer - Using Multiple Representations to Introduce Integers page - 4 Integers - Sea Level During this unit you are going represent above and below sea level using integers. Represent each number. Remember to start at Sea Level. Sea Level Sea Level 0 (Sea Level) +6 (going up 6 steps) Sea Level Sea Level +4 –2 (going down two steps) Sea Level Sea Level –5 +5 Sea Level Sea Level +7 S. Mercer - Using Multiple Representations to Introduce Integers –2 page - 5 Addition of Integers Represent Using Tiles Represent Using a Number Line 4+5 Problem +5 +4 Sea Level Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line 1+6 Problem Represent Using Money Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 6 Addition of Integers Represent Using Tiles Represent Using a Number Line –3 + –2 Problem –3 Sea Level Represent Using Money –2 Represent Vertically Represent Using Tiles Represent Using a Number Line –1 + –7 Problem Represent Using Money Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 7 Addition of Integers Represent Using Tiles Represent Using a Number Line –3 + –5 Problem Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line –3 + 6 Problem +6 –3 Represent Using Money Sea Level Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 8 Addition of Integers Represent Using Tiles Represent Using a Number Line 5 + –5 Problem Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line –4 + –6 Problem Represent Using Money Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 9 Addition of Integers Represent Using Tiles Represent Using a Number Line 0 + –5 Problem Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line –7 + –5 Problem Represent Using Money Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 10 Addition of Integers Represent Using Tiles Represent Using a Number Line 5 + –3 + –4 Problem Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line –8 + 2 + –4 Problem Represent Using Money Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 11 Addition of Integers Represent Using Tiles Represent Using a Number Line 0 + –4 + 2 Problem Represent Using Money Represent Vertically Represent Using Tiles Represent Using a Number Line 10 + –2 + –6 Problem Represent Using Money Represent Vertically For each representation, clearly label the answer. S. Mercer - Using Multiple Representations to Introduce Integers page - 12 Word Problems 1) At 6:00am the temperature was 4˚ below zero. By 3:00pm the temperature had risen 15˚. What was the temperature at 3:00pm? Represent the problem using a picture Write a math expression of the problem Answer the question in a complete sentence. 2) Sabrina went scuba diving. She descended 20 meters below the surface and then ascended 7 meters. How far below the surface was she? Represent the problem using a picture Write a math expression of the problem Answer the question in a complete sentence. S. Mercer - Using Multiple Representations to Introduce Integers page - 13 Word Problems 3) At midnight the temperature was 48˚F. By midday the temperature had risen 36˚. What was the temperature at midday? Represent the problem using a picture Write a math expression of the problem Answer the question in a complete sentence. 3) Sabrina owes $5 to her mother and $16 to a friend, how much money does Sabrina have? Represent the problem using a picture Write a math expression of the problem Answer the question in a complete sentence. S. Mercer - Using Multiple Representations to Introduce Integers page - 14 Word Problems Comparing Addition and Subtraction 1) Sabrina earned $15 babysitting. She spent $6 in candy. How much money did she have left? Represent the problem using a picture Write a math expression using subtraction 1) Write a math expression using integers 2) Solve the problem. 1) Answer the question in a complete sentence. 2) 2) Duncan invested in the stock market. The first year he gained $150. The second year he lost $80. What was his net gain? Represent the problem using a picture Write a math expression using subtraction 1) Write a math expression using integers 2) Solve the problem. 1) Answer the question in a complete sentence. 2) S. Mercer - Using Multiple Representations to Introduce Integers page - 15 Word Problems Comparing Addition and Subtraction 1) Duncan has $30. He spends $12 on a CD. How much money does he have left? Represent the problem using a picture Write a math expression using subtraction 1) Write a math expression using integers 2) Solve the equations. 1) Answer the question in a complete sentence. 2) 2) Sabrina’s mom gained 15 pounds during the summer vacation. During fall she lost 12 pounds. What was her net weight loss or gain? Represent the problem using a picture Write a math expression using subtraction 1) Write a math expression using integers 2) Solve the problem. 1) Answer the question in a complete sentence. 2) S. Mercer - Using Multiple Representations to Introduce Integers page - 16 Subtraction of Integers 1-2-3-4 Method 1) 10 1) Copy the same number 5 2) Change subtraction to addition 3) Write the opposite 4) Add the integers 2) 5 1) Copy the same number -2 2) Change subtraction to addition 3) Write the opposite 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers page - 17 Subtraction of Integers 1-2-3-4 Method 3) -4 1) Copy the same number 8 2) Change subtraction to addition 3) Write the opposite 4) Add the integers 4) -7 1) Copy the same number -1 2) Change subtraction to addition 3) Write the opposite 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers page - 18 Subtraction of Integers 1-2-3-4 Method 5) 0 1) Copy the same number -5 2) Change subtraction to addition 3) Write the opposite 4) Add the integers 6) 0 1) Copy the same number 8 2) Change subtraction to addition 3) Write the opposite 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers page - 19 Subtraction of Integers 1-2-3-4 Method 7) 10 1) Copy the same number 15 2) Change subtraction to addition 3) Write the opposite 4) Add the integers 8) 3 1) Copy the same number -8 2) Change subtraction to addition 3) Write the opposite 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers page - 20 Subtraction of Integers 1-2-3-4 Method 9) -4 1) Copy the same number 4 2) Change subtraction to addition 3) Write the opposite 4) Add the integers 10) 6 1) Copy the same number -6 2) Change subtraction to addition 3) Write the opposite 4) Add the integers S. Mercer - Using Multiple Representations to Introduce Integers page - 21 Review Addition and Subtraction of Integers Based on what you have learned so far, solve the following problems: 1) 10 + –8 2) –7 + –3 3) 4 + –9 4) –10 + 15 5) –3 + – 5 + – 9 6) 10 + –9 + – 4 7) 10 – 15 8) 10 – (–3) 9) –5 – 10 10) –5 – (–3) S. Mercer - Using Multiple Representations to Introduce Integers page - 22 Multiplication of Integers Discover the Rules! Rule #1 –3 • 4 = – 12 Study the problems. What patterns do you notice? 5 • –2 = – 10 –6 • 3 = – 18 2 • –3 = – 6 1 • –3 = – 3 –10 • 4 = – 40 Describe the rule and give two examples. Rule #2 –3 • –4 = 12 Study the problems. What patterns do you notice? 5 • 2 = 10 –6 • –3 = 18 –2 • –3 = 6 1•3= 3 –10 • –4 = 40 Describe the rule and give two examples. S. Mercer - Using Multiple Representations to Introduce Integers page - 23 Multiplication of Integers Discover the Rules! Rule #3 –3 • 4 • – 2= 24 Study the problems. What patterns do you notice? 4 • –5 • –2 = 40 –2 • – 2 • 3 = 12 –10 • 2 • –3 = 60 –2 • 1 • –3 = 6 –5 • –2 • 4 = 40 Describe the rule and give two examples. Rule #4 3 • 4 • – 2= –24 Study the problems. What patterns do you notice? 4 • –5 • 2 = –40 –2 • 2 • 3 = –12 –10 • 2 • 3 = –60 2 • 1 • –3 = –6 5 • –2 • 4 = –40 Describe the rule and give two examples. S. Mercer - Using Multiple Representations to Introduce Integers page - 24 Division of Integers Discover the Rules! Rule #1 –12 ÷ 4 = – 3 Study the problems. What patterns do you notice? 12 ÷ –4 = – 3 24 ÷ –6 = – 4 –24 ÷ 6 = – 4 15 ÷ –3 = – 5 –15 ÷ 3 = – 5 Describe the rule and give two examples. Rule #2 –12 ÷ –4 = 3 Study the problems. What patterns do you notice? 12 ÷ 4 = 3 24 ÷ 6 = 4 –24 ÷ –6 = 4 –15 ÷ –3 = 5 15 ÷ 3 = 5 Describe the rule and give two examples. S. Mercer - Using Multiple Representations to Introduce Integers page - 25 Positive or Negative? Looking at the problem, without doing the computation, decide if the answer to the problems is positive or negative. Explain you answer clearly. 1) –100 • –5 Positive or Negative Why? 2) 15 • 4 • –3 Positive or Negative Why? 3) –254 • –15 • –4 Positive or Negative Why? 4) –110 • 35 • 4 • 24 Positive or Negative Why? 5) –2• –2•–2•–2•–2•–2 Positive or Negative Why? 6) –100 ÷ –2 ÷ –2 Positive or Negative Why? 7) 5000 ÷ –5 • –5 ÷ –5 Positive or Negative Why? S. Mercer - Using Multiple Representations to Introduce Integers page - 26 Review Multiplication and Division of Integers Based on what you have, solve the following problems: 1) 10 • –8 2) –7 • –3 3) 4 • –3 4) –5 • 10 5) –3 • – 2 • – 10 6) –3 • – 2 • 10 7) 10 ÷ –5 8) –10 ÷ –5 9) –25 ÷ –5 10) –25 ÷ 5 S. Mercer - Using Multiple Representations to Introduce Integers page - 27