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Mathematical Reasoning Lesson 9: Integers LESSON 9: Integers Computation and Word Problems Weekly Focus: integers Weekly Skill: addition, subtraction, multiplication, and division Lesson Summary: First, students will solve a word problem with percentages. In Activity 1, they will review vocabulary with true/false statements. In Activity 2, they will put numbers on the number line. In Activity 3, students will practice adding and subtracting integers. Activity 4, they will practice multiplication and division of integers. In Activity 5, they will do word problems. For Activity 6, they will do an application problem related to paying bills. There is an extra problem at the end. Estimated time for the lesson is two hours. Materials Needed for Lesson 9: Post-it notes 3 Worksheets with Answers (attached) Video (length 10 minutes) on 2 methods of adding and subtracting integers. The video is required for teachers and recommended for students. Fun music video on adding and subtracting integers (length 2:30) Video on multiplying and dividing integers (length 7:31). Required for teacher and recommended for students. Exit ticket (attached; use pencils, rulers, flyswatters, etc.) Mathematical Reasoning Test Preparation for the 2014 GED Test Student Workbook p. 10-13 Teacher Note: You may decide to have students complete only part of the worksheets in class and assign the rest as homework or extra practice depending on students’ needs and time. Objectives: Students will be able to: Review vocabulary related to integers Do computation of integers and word problems Solve a real-life application problem ACES Skills Addressed: N, CT, LS CCRS Mathematical Practices Addressed: Attend to Precision, Mathematical Fluency, Use Appropriate Tools Strategically Levels of Knowing Math Addressed: Intuitive, Pictorial, Abstract, and Application Notes: You can add more examples if you feel students need them before they work. Any ideas that concretely relates to their lives make good examples. For more practice as a class, feel free to choose some of the easier problems from the worksheets to do together. The “easier” problems are not necessarily at the beginning of each worksheet. Also, you may decide to have students complete only part of the worksheets in class and assign the rest as homework or extra practice. The GED Math test is 115 minutes long and includes approximately 46 questions. The questions have a focus on quantitative problem solving (45%) and algebraic problem solving (55%). Students must be able to understand math concepts and apply them to new situations, use logical reasoning to explain their answers, evaluate and further the reasoning of others, represent real world problems algebraically and visually, and manipulate and solve algebraic expressions. D. Legault, Minnesota Literacy Council, 2014 1 Mathematical Reasoning Lesson 9: Integers This computer-based test includes questions that may be multiple-choice, fill-in-the-blank, choose from a drop-down menu, or drag-and-drop the response from one place to another. The purpose of the GED test is to provide students with the skills necessary to either further their education or be ready for the demands of today’s careers. Lesson 9 Warm-up: Solve the percent problem Time: 10 Minutes Write on the board: Cindy wants to save 15% of her gross monthly income for retirement. Basic Questions: If she saves $235.00 a month, how much will she save in a year? ($235 x12 = $2820) At the end of two years, she had an emergency and had to spend ¼ of what she had saved. How much did she take out of her savings? ($2820 x 2 = $5640 divided by 4 = $1410) Extension Questions: If $235 represents 15% of her income, how much does she make monthly? (0.15x=235. X=235/0.15 = $1566.67) She wants to increase her monthly savings to 17%. How much is that? (0.17 x 1566.67 = $266.33) Lesson 9 Activity 1: Vocabulary True or False Time: 10 Minutes This activity can be projected on the board and done as a whole class. (attached) Have students volunteer to write answers. Then do some examples. Answers: 1. True 2. False. An integer is a whole number that is either positive or negative. Zero is also an integer. 3. True 4. True 5. False. Absolute value means the distance from zero. It is expressed with a positive number or zero and written with the symbol parallel bars symbol. Ex. l-4l = 4 and l4l = 4. Both positive and negative 4 are four units away from 0 on the number line. D. Legault, Minnesota Literacy Council, 2014 2 Mathematical Reasoning Lesson 9: Integers Lesson 9 Activity 2: Place the numbers on the line Time: 10 Minutes 1. Write a number line on the board from negative 5 to positive 5. 2. Write various positive and negative numbers on post-it notes and hand out to students. Choose the difficulty of the numbers you write according to your students’ skill level, but make sure to include a combination of + and – numbers as well as some easy-to-measure fractions (1/10, 2¼, ¾, -1½ for example) and decimals (0.3, -4.7, etc.) 3. Ask them to place the post-it note at about the correct place on the line. 4. As a class discuss whether the posted numbers are in the correct locations. 5. Now talk about absolute value. How far is each number from zero? That is its absolute value. Write a few examples, such as l-3/4 l = ¾. Have students come write more examples. 6. Don’t erase this line. Use it for the next activity to show addition and subtraction of numbers. Activity 3: Addition and Subtraction of + and - Numbers Time: 20-25 Minutes Use the number line to show how addition and subtraction of integers works. Some students prefer to see how the numbers move along the number line, whereas others prefer to know the rules. To add, go right on the number line. To subtract, go left on the number line. Here are examples of each: If integers have like signs, add and keep the common sign. If integers have different signs, find the difference. Then use the sign of the number with the greater absolute value. D. Legault, Minnesota Literacy Council, 2014 3 Mathematical Reasoning Lesson 9: Integers Example: To subtract an integer, go left on the number line. Example: -5 -4 = -9 If there are two negatives next to each other, they become a positive because you start going left on the number line, and then need to switch directions again for the second sign. Example: -9 - -4 = -9 + 4 = -5. Example: 18 - - 5 = 18 + 5 = 23 It is very helpful to watch the video assigned to this lesson for more explanations. Do Worksheet 9.1. Have students volunteer to do a few problems on the number using the number line. D. Legault, Minnesota Literacy Council, 2014 4 Mathematical Reasoning Lesson 9: Integers Lesson 9 Activity 1 Vocabulary: True or False 1. _____ A positive whole number is an integer. 2. _____ A positive fraction is an integer. 3. _____ Zero is an integer. 4. _____ A negative whole number is an integer. 5. _____ The absolute value of a number is always negative. D. Legault, Minnesota Literacy Council, 2014 5 Mathematical Reasoning Lesson 9: Integers Kuta Software - Infinite Algebra 1 Worksheet 9.1 Name___________________________________ Adding and Subtracting Positive and Negative NumbersDate________________ Period____ Evaluate each expression. 1) (-2) + 3 2) (-14) + (-7) 3) 3 - (-8) 4) (-9) + 14 5) (-8) - (-2) 6) 5 + (-8) 7) (-27) - 24 8) (-41) + (-40) 9) 38 - (-17) 10) (-44) + (-9) 11) (-16) - (-36) 12) (-6) - 24 13) (-16) - 6 + (-5) 14) 15 - 13 + 2 15) 16 - (-13) - (-5) 16) (-7) - (-2) - 9 ©U V240A1m2f 0KJuzt6ao ISGomfMtXwxaGr5eg 4LgL9CT.R Z FAtlHl3 jrvi0gOhOt6sK crwegsteorzvVeKde.R 7 1Mfa1dye1 XwKiNtrhk GI3n0fgiInuiXtveM KAml4gBefb2rgac 61s.y D. Legault, Minnesota Literacy Council, 2014 -1- Worksheet by Kuta 6 Mathematical Reasoning Lesson 9: Integers Kuta Software - Infinite Algebra 1 Worksheet 9.1 Answers Adding Name______________________________ and Subtracting Positive and Negative NumbersDate________________ Perio Evaluate each expression. 1) (-2) + 3 2) (-14) + (-7) 1 -21 3) 3 - (-8) 4) (-9) + 14 11 5 5) (-8) - (-2) 6) 5 + (-8) -6 -3 7) (-27) - 24 8) (-41) + (-40) -51 9) 38 - (-17) -81 10) (-44) + (-9) 55 11) (-16) - (-36) -53 12) (-6) - 24 20 13) (-16) - 6 + (-5) -30 14) 15 - 13 + 2 -27 15) 16 - (-13) - (-5) 4 16) (-7) - (-2) - 9 34 -14 7 D. Legault, Minnesota Literacy Council, 2014 ©g r2p0E1Q26 KKqu6t8aL pS6oWfAtOw1aFrUeO cL8L6C7.k g IAGlCl2 xr9iAgwh0tZsM Pr7efs4ewr4vceSdK.3 Y gMxaTd2ew hwtiBtEhg BIInxfniYn7idtCeK 2AflmgfeHblr Cac o1v.L -1- Works Mathematical Reasoning Lesson 9: Integers Lesson 9 Activity 4: Multiplication and Division of + and - Integers Time: 15-20 Minutes For multiplying and dividing integers: If the signs are the same, the answer will be positive. Example: (-2)(-6)= 12 If the signs are different, the answer will be negative. Example: -6/2 = -3 Do Worksheets 9.2 and 9.3. Choose a few problems to do on the board. Note to teacher: It is difficult to explain why the rules are such for multiplying and dividing + and – integers. This is one of the rare occasions it is easier just to know the rule. You can find the explanation if you search online. Lesson 9 Activity 5: Word Problems Time: 25-30 Minutes Do the word problems on pages 10-13 of the workbook. Choose a few more challenging problems for students (or you) to do on the board. Lesson 9 Activity 6: Application Problem Time: 10 Minutes Jason keeps track of his checking account every month. He uses his debit card to pay for his expenses so they are withdrawn immediately. Here are this month’s expenses: He started with a beginning balance of $1,000 on the first of the month He paid his rent of $825 on the 2nd of the month He bought groceries for $130 on the 6th of the month He put gas in his truck twice at $55 each time the week of the 10th He was paid $1,010 on the 15th of the month 1. How much money does he have at the end of the month? 2. Was he ever overdrawn on his account? If so, by how much? 3. Write an equation to show the changes to his account. D. Legault, Minnesota Literacy Council, 2014 8 Mathematical Reasoning Lesson 9: Integers 4. If he gets paid twice a month, what percent of his income goes toward rent? Lesson 9 Exit Ticket Time: 5 Minutes Write “Negative” and “Positive” on the board or on two pieces of paper. Give some students pencils, rulers or flyswatters and as you write an equation, have them race to hit one of the words to show that the solution is either negative or positive (you can divide them into teams or call students up two at a time). -5 + 8 (Positive) -1 – 3 (Negative) -10 – ( -11) (Positive) -41 + ( -11) + 51 (Negative) -8 / 4 (Negative) (-3) (-6) (Positive) Lesson 9 Extra Problem Time: 3-5 Minutes Write on the board: The temperature this morning was -8 and now it’s +15. How much did the temperature change from the morning until now? (23 degrees) Yesterday the temperature went from +2 to -12. What was the change in temperature? (14 degrees) Draw a vertical number line (thermometer) and have students use it to show how they obtained the answer. D. Legault, Minnesota Literacy Council, 2014 9 Mathematical Reasoning Kuta Software - Infinite Algebra 1 Name_____________________________ Lesson 9: Integers Multiplying and Dividing Positives and Negatives Date________________ Per Worksheet 9.2: Find the Quotient Find each quotient. 1) 10 5 2) -24 12 3) -20 -2 4) -300 -20 5) 65 5 6) -66 -6 7) 75 -15 8) -56 -14 9) 102 -17 10) -72 -4 11) 153 ¸ 17 12) 12 ¸ -3 13) 48 ¸ 6 14) -120 ¸ -20 15) 306 ¸ 18 16) -65 ¸ 13 ©1 92g0t1g2i wKEuBtFac 4SOoYf2tZwzalr6eh ELILtCV.j J yABlQly Wrcicgjh8tEsA ZrTeysHeMrCvyeadS.p 0 BMaaCdqeQ lwliftChI oIvnOfGiGnFiCtBeI CAIlhgoeHbzrYaJ v1P.R D. Legault, Minnesota Literacy Council, 2014 -1- 10 W Mathematical Reasoning Lesson 9: Integers Name___________________________ Kuta Software - Infinite Algebra 1 Multiplying Worksheet 9.2: Find the Quotient Answersand Dividing Positives and Negatives Date________________ P Find each quotient. 1) 10 5 2) -2 2 3) -20 -2 4) 65 5 6) 75 -15 8) 102 -17 -56 -14 4 -5 9) -66 -6 11 13 7) -300 -20 15 10 5) -24 12 10) -72 -4 -6 18 11) 153 ¸ 17 12) 12 ¸ -3 -4 9 13) 48 ¸ 6 14) -120 ¸ -20 6 8 15) 306 ¸ 18 16) -65 ¸ 13 17 -5 ©z m2b0x1Q2D rKsuVtzaA 8SSoIfatVw0asrIeY uL0LOCe.B y GAwloli Zrcizgzh4tPsC Sr9eAsXerrnvJeUd1.1 L ZMUasdce0 Tw7iutjht rIMnhf7ifnHihtpeR YA2llgweKbBr9ah M1d.X D. Legault, Minnesota Literacy Council, 2014 -1- 11 23) -8 ´ -11 24) -6 ´ 4 Mathematical Reasoning 25) -3 ´ -11 Lesson 9: Integers 26) -5 ´ -9 Worksheet 9.3: Find the Product 27) 9 ´ -7 28) -9 ´ -3 29) 12 ´ -12 30) 11 ´ -6 31) 6 ´ -5 ´ 3 32) 6 ´ -1 ´ 2 33) 8 ´ -6 ´ -3 34) -3 ´ 6 ´ -6 35) (3 )(3)(-1 )(3) 36) (-3)(3)(-3 )(-3) ©l 92h0k1p2r aKVuTt6a0 ASCoEfgt7wLagrjeI bLvLkCL.R F HAilwlC OrrikgAhitQsU HrDe6sjePrtvzeHdK.L I NMJa7dCeb qweiBtXha xIEn0f4iLnei6tGeH GA4lxgle2b9r2al b1E.U D. Legault, Minnesota Literacy Council, 2014 -2- Wor 12 23) -8 ´ -11 24)Mathematical -6 ´ 4 Reasoning -24 88 Lesson 9: Integers 25) -3 ´ -11 26) -5 ´ -9 33 45 Worksheet 9.3 Answers 27) 9 ´ -7 28) -9 ´ -3 -63 27 29) 12 ´ -12 30) 11 ´ -6 -144 -66 31) 6 ´ -5 ´ 3 32) 6 ´ -1 ´ 2 -90 -12 33) 8 ´ -6 ´ -3 34) -3 ´ 6 ´ -6 144 108 35) (3 )(3)(-1 )(3 ) 36) (-3 )(3)(-3 )(-3) -27 -81 Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.co Lesson 9 Activity 6 Application Problem Answers ©8 B2i0T1R2l vKJustxaz NSJovfutGwXaQrlev NLuLuCO.N U JAElXlm Nrci2gUhFtSsK 3r7eesleur4vYeadz.Z P aM7aAdBeM HwQiqtJhU SIvnUfci0nLiitBes nAeldgmepbLrsaC D1x.C -2- Wo Jason keeps track of his checking account every month. He uses his debit card to pay for his expenses so they are withdrawn immediately. Here are this month’s expenses: A beginning balance of $1,000 on the first of the month He paid his rent of $825 on the 2nd of the month He bought groceries for $130 on the 6th of the month He put gas in his truck at $55 each time twice the week of the 10th He was paid $1,010 on the 15th of the month 1. How much money does he have at the end of the month? $945 2. Was he ever overdrawn on his account? If so, by how much? Yes, by $65 3. Write an equation to show the changes to his account. D. Legault, Minnesota Literacy Council, 2014 13 Mathematical Reasoning Lesson 9: Integers $1,000 - $825 -$130- (2 x 55) + 1,010 = $945 4. If he gets paid twice a month, what percent of his income goes toward rent? $1,010 x 2 = $2,020. $825/$2,020 = 0.408 = 40.8% D. Legault, Minnesota Literacy Council, 2014 14