Preguntas Capítulo Entero. 3. Crear un ejemplo debiendo dinero para comparar dos números negativos.

Transcripción

1 Preguntas Capítulo Entero 1. Qué es un número entero? 2. Explique lo que representa el valor absoluto. 3. Crear un ejemplo debiendo dinero para comparar dos números negativos. 4. Explicar cómo se puede utilizar un valor absoluto a sumar enteros. 5. Por qué los problemas de resta enteros se convirtieron en problemas de sumas? 6. Por qué son las reglas para multiplicar y dividir números enteros del mismo? 7. Por qué una respuesta diferente de (-3) 2 y -32? 8. Explique las reglas para multiplicar y dividir de los exponentes.

2 Problemas capítulo entero Definición Entero Trabajo de Clase 1. Nombre 5 enteros. 2. Nombre de 5 números que no son enteros. 3. Qué es lo opuesto a la 20? 4. Cuál es el opuesto de -13? 5. Escribir un entero para representar a cada situación: a. La temperatura cae 5 grados. b. El equipo gana 25 yardas. c. Usted deposita $ 100 en su cuenta de ahorros. d. Que retirar $ 75 dólares de su cuenta de ahorros. e. La montaña es de metros sobre el nivel del mar. 6. Utilizando el sistema de puntuación en el juego de Jeopardy (ganar puntos para las respuestas correctas y perder puntos por las respuestas incorrectas) lo que sería el resultado final después de los siguientes 5 respuestas: a. El jugador 1 responde a una pregunta correcta 200 puntos, 150 puntos una pregunta equivocada, una pregunta de 50 puntos correctos, una pregunta equivocada 150 puntos y 100 puntos la pregunta correcta. b. El jugador 2 responde a una pregunta de 100 puntos mal, una pregunta de 50 puntos correctos, una pregunta de 100 puntos correctos, una pregunta 150 punto correcto y 200 preguntas punto equivocado. c. El jugador 3 se trata de 200 puntos correctos, una pregunta de 200 puntos mal, una pregunta de 50 puntos mal, una pregunta 150 punto correcto y una pregunta de 200 puntos correctos. 7. Utilice el sistema de puntuación Jeopardy y crear una secuencia de cinco respuestas que le daría una puntuación de: a. 300 puntos b. -50 puntos c. 0 puntos Tarea 8. Cuál es el opuesto de -50? 9. Qué es lo opuesto a la 11? 10. Qué es lo contrario de 2? 11. Cuál es el opuesto de -7? 12. Escribir un entero para representar a cada situación: a. La temperatura se eleva de 11 grados. b. Las inmersiones submarinas 125 metros bajo el nivel del mar. c. El equipo pierde 15 yardas. d. Usted gana $ 35 de niñera. e. Una compañía pierde $ 12,000 en un mes.

3 13. Utilice el sistema de puntuación Jeopardy y crear una secuencia de cinco respuestas que le daría una puntuación de: a puntos b. 400 puntos c. 0 puntos Valor Absoluto Trabajo de Clase 14. Encontrar: a. -12 b. 25 c. -47 d Qué números tienen el número en particular como su valor absoluto? a. 150 b. 75 c. 14 d Cómo explicaría a un nuevo estudiante a encontrar el valor absoluto de -10 y +10? Tarea 17. Encontrar: a. 32 b. -35 c. -55 d Qué números tienen el número en particular como su valor absoluto? a. 72 b. 28 c. 155 d Cómo explicaría a un nuevo estudiante a encontrar el valor absoluto de 27 y -27? Comparing and Ordering Integers Classwork 20. Place the appropriate inequality symbol between the following pairs of integers: a. 3-7 b

4 c d. 7 7 e f Draw a number line and mark and label points for these numbers: 4, -7, 5, 0, -2, 1, Draw a number line and mark and label points for these numbers: -15, 0, 7, 4, -3, -1, If the temperature reading on a thermometer is 12 C, what will the new reading be if the temperature: a. Falls 15 b. Rises 3 c. Falls If the temperature reading on a thermometer is -7 C, what will the new reading be if the temperature: a. Falls 3 b. Rises 5 c. Rises 9 Homework 25. Place the appropriate inequality symbol between the following pairs of integers: a b c d e f Draw a number line and mark and label points for these numbers: 15, -3, 0, 5, -9, 7, Draw a number line and mark and label points for these numbers: -9, 1, 0, -3, 9, -1, If the temperature reading on a thermometer is 5 C, what will the new reading be if the temperature: a. Falls 15 b. Rises 3 c. Falls If the temperature reading on a thermometer is -10 C, what will the new reading be if the temperature: a. Falls 3 b. Rises 5 c. Rises 9 Integer Addition Classwork

5 30. Show the addition problem on a number line, and give the answer. a b. 4 + (-2) c d (-2) e Decide whether the statements below are always true, sometimes true, or always false. Give examples to support your answer. a. The sum of two positive numbers is a positive number. b. The sum of a negative number and a positive number is a positive number. c. The sum of two negative numbers is a negative number. 32. Explain the absolute values approach to solving a problem adding and positive and a negative number. 33. Find the sum. a. 2 + (-4) = b (-6) = c = d (-10) = e = f. 5 + (-5) = g = h (-1) = i. 4 + (-3) = j = k (-30) = l (-25) = m (-110) = n (-22) = o (-27) = 34. Write three addition problems that have a sum of: a. 15 b. 42 c. -27 d. -3 Homework 35. Show the addition problem on a number line, and give the answer. a (-4) b c d e Explain the absolute values approach to solving a problem adding two positives or two negatives. 37. Find the sum.

6 a = b (-4) = c = d. 5 + (-7) = e = f (-8) = g = h. 0 + (-8) = i = j (-9) = k = l (-32) = m (-98) = n (-61) = o (-82) = 38. Write three addition problems that have a sum of: a. -12 b. 5 c. -20 d. 33 Turning Subtraction into Addition Classwork 39. Decide whether the statements below are always true, sometimes true, or always false. Give examples to support your answer. a. The difference when a negative number is subtracted from a positive number is a negative number. b. The difference when a negative number is subtracted from a negative number is a negative number. 40. Convert the following subtraction problems into addition problems, then find the sum. a b. 12 (-2) c. -5 (-2) d e f. -15 (-7) g. -1 (-3) h i. 5 (-4) j. -2 (-4) k. 55 (-20) l (-99) m n (-45) o

7 41. Write three subtraction problems that have a difference of: a. 4 b. 17 c. -19 d. -2 Homework 42. Convert the following subtraction problems into addition problems, then find the sum. a. -5 (-4) = b. 4 (-3) = c = d = e. -7 (-2) = f. 5 9 = g. 3 (-3) = h. -2 (-2) = i. 7 (-10) = j. 9 (-2) = k. 50 (-25) = l = m = n. 63 (-33) = o = 43. Write three subtraction problems that have a difference of: a. 14 b. -22 c. -9 d. 23 Adding and Subtracting Integers Review Classwork (-8) = (-4) = 46. (-9) (-4) = = (-2) = = = =

8 = (-10) = (-10) = (-2) = = (-10) = (-2) = = = (-3) = (-2) = (-6) = (-28) = = (-94) = (-9) = (-44) = = (-64) = = (-64) = = Homework = =

9 (-3) = (-2) = (-10) = (-3) = (-6) = (-1) = (-7) = (-6) = (-2) = (-8) = (-1) = = = = = (-7) = (-2) = = (-58) = (-49) = = (-69) = (-2) = (-92) = =

10 (-58) = (-95) = = Multiplying Integers Classwork 104. Show the following multiplication problems on a number line: a. 3(3) = b. 2(-3) = c. 5(-2) = 105. (7)(-2) = 106. (8)(-3) = 107. (-8)(7) = 108. (6)(8) = 109. (3)(-7) = 110. (1)(7) = 111. (0)(-9) = 112. (-2)(-2) = 113. (8)(-9) = 114. (-4)(-1) = 115. (-7)(8) = 116. (8)(-6) = 117. (1)(-1) = 118. (-9)(-5) = 119. (4)(-9) = 120. (1)(-5) = 121. (5)(6) = 122. (3)(-1) =

11 123. (-4)(0) = 124. (-6)(-4) = 125. (-82)(-10) = 126. (-3)(46) = 127. (-33)(-13) = 128. (-77)(4) = 129. (20)(-40) = Homework 130. Show the following multiplication problems on a number line: a. 2(3) = b. 3(-2) = c. 4(-3) = 131. (-1)(-8) = 132. (1)(-2) = 133. (-7)(8) = 134. (9)(1) = 135. (-6)(3) = 136. (2)(-5) = 137. (0)(-5) = 138. (7)(-3) = 139. (-8)(-2) = 140. (-5)(-5) = 141. (-9)(-7) = 142. (-5)(3) = 143. (4)(-1) = 144. (4)(4) = 145. (-2)(9) =

12 146. (9)(-9) = 147. (-6)(-9) = 148. (6)(2) = 149. (-6)(4) = 150. (-4)(-5) = 151. (-67)(51) = 152. (13)(-50) = 153. (36)(-55) = 154. (-61)(-80) = 155. (-10)(45) = Dividing Integers Classwork 156. Show the following division problems on a number line: a = b = c = = = = = = = = = = = =

13 = = = = = = = = = = = = = Homework = = = = = = = = = =

14 = = = = = = = = = = = = = = Powers of Integers Classwork 207. What is the base and exponent in the following expressions? a. 5 3 b. 8 9 c = 36, what does this have to do with a square? = 216, what does this have to do with a cube? = 211. (-3) 2 = = =

15 214. (-3) 3 = = = 217. (-3) 4 = = = 220. (-3) 5 = = 222. After evaluating the above, what patterns do you notice? Is there a pattern if you look at the exponents in terms of odd or even? Homework 223. What is the base and exponent in the following expressions? a. 3 5 b. 5 8 c = 49, what does this have to do with a square? = 343, what does this have to do with a cube? = 227. (-5) 2 = = = 230. (-4) 3 = = = 233. (-3) 4 = = =

16 236. (-2) 5 = = 238. After evaluating the above with different bases are the patterns you noticed the same as in the classwork? Rules for Exponents Classwork 239. Write an explanation for multiplying exponents with the same base Complete each equation for the missing value: a. (5 2 )(5 5 ) = 5? b. (12 7 )(12 3 ) = 12? c. (3-2 )(3 5 ) = 3? d. (4 9 )(4-3 ) = 4? e. (5 4 )(5? ) = 5 12 f. (10 7 )(10? )(10-6 ) = Write an explanation for dividing exponents with the same base Complete each equation for the missing value: a = 3? b. c = 5? = 9? 9 d = 12? e ? = 10 3 f.? 2 3 = Complete each equation for the missing value: a. (12 4 ) 3 = 12? b. (9 5 ) 4 = 9? c. (34 2 ) 3 = 34? d. (5 7 ) 2 = 5? e. (3 12 ) 4 = 3? 244. Write an explanation for solving with an exponent of zero Evaluate: a. 2 0 = b. 5 0 = c = d. (-1) 0 =

17 e. (-4) 0 = f. (-22) 0 = 246. Write an explanation for evaluating an expression with a negative exponent Evaluate: a. 3-2 = b. 5-2 = c. 2-4 = d = e = f = Homework 248. Complete each equation for the missing value: a. (12 2 )(12 7 ) = 12? b. (2 5 )(2 2 ) = 2? c. (5-3 )(5 5 ) = 5? d. (15 8 )(15-5 ) = 15? e. (6 7 )(6? ) = 6 15 f. (11-6 )(11? )(11 8 ) = Complete each equation for the missing value: a = 7? b = 11? 11 c = 3? d. e = 2? 6 13? = f. 5? 5 6 = Complete each equation for the missing value: a. (8 6 ) 4 = 8? b. (11 3 ) 9 = 11? c. (4 3 ) 5 = 4? d. (2 6 ) 8 = 2? e. (12 4 ) 5 = 12? 251. Evaluate: a =

18 b. 7 0 = c. 6 0 = d = e. (-8) 0 = f. (-15) 0 = 252. Evaluate: a. 2-3 = b. 4-3 = c. 5-2 = 1 d. = e. 3 3 = 1 f. = 2 7 Integer Unit Multiple Choice Questions 1. What is the opposite of 15? a) 15 b) 0 c) What is the opposite of -9? a) 9 b) 0 c) What is 11? a) -11 b) 11 c) 0 4. What is -25? a) 25 b) -25 c) a) b) = c) a) b) = c)

19 a) b) = c) a) b) = c) a) b) = c) 10. If the temperature reading on a thermometer is 19 C, what will the new reading be if the temperature falls 10 C? a) 29 C b) -9 C c) 9 C d) 0 C 11. A submarine is cruising at -55 meters (55 meters below the surface). It descends 15 meters; then it rises 40 meters. What is the submarine s new depth? a) 0 m b) -20 m c) -110 m d) -30 m 12. The temperature in Atlantic City was -10 C at 4 A.M. It had fallen 7 C since 3 A.M. What was the temperature at 3 A.M.? a) -17 C b) -3 C c) 3 C d) 17 C 13. Convert the subtraction problem into an addition problem a) b) (-9) c) d) 12 + (-9) 14. Convert the subtraction problem into an addition problem. 3 (-7) a) b) -3 + (-7) c) d) 3 + (-7) 15. Which expression equals 25?

20 a) -5 2 b) (-5) 2 c) -5 5 d) (-5) Which expression does not equal -16? a) -4 2 b) (-4) 2 c) d) What is the missing value in the equation: (5 3 )(5 4 ) = 5? a) 7 b) 12 c) -1 d) What is the missing value in the equation: = 7? a) 3 b) 6 c) -3 d) What is the missing value in the equation: (6 15 ) 3 = 6? a) 5 b) 18 c) 45 d) Evalute 15 0 = a) 15 b) 1 c) 0 d) -1 Integer Unit Short Constructed Response Unit Review 21. Which two numbers have 56 as their absolute value? Write the addition sentence illustrated by each figure. 22.

21 Simplify

22 = (-5) = (-6) = (-6) = = (-18) = (-6) = (-9) = = (-1) = 36. (-4)(8) = 37. (-7)(-7) = 38. (-6)(-9) = 39. (3)(-7) = 40. (16)(0) = 41. (16) (-2) = 42. (-10) (-10) = = 18 3 = 45. (9) (-3) = Integer Unit Extended Constructed Response Unit Review 46. John had a balance of $105 in his bank account at the start of the week. He withdrew $45 on Monday, $76 on Wednesday, and $35 on Thursday. On Friday he deposited $120.

23 At the end of the week, does John have more or less money in his savings account than he had at the beginning of the week? How much more or less? Show all of your work to support your answers.

24 Answer Key 1. For example: 3, 4, 5, -2, For example: ½, -3/4, 0.4, 5, π a. -5 b. +25 c d. -75 e. +1, a. 50 b. -50 c Answers will vary a. +11 b c. -15 d. +35 e. -12, Answers will vary. 14. a. 12 b. 25 c. 47 d a. -150, 150 b. -75, 75 c. -14, 14 d , Answers will vary. 17. a. 32 b. 35 c. 55 d a. -72, 72 b. -28, 28 c. -155, 155 d , Answers will vary. 20. a. 3-7 b c d. 7 = 7 e f Order on number line: -7, -4, -2, 0, 1, 4, Order on number line: -15, -3, -1, 0, 4, 7, a. -3 b. 15 c a. -4 b. -2 c a b. -30 = -30 c d e f Order on number line: -9, -3, 0, 5, 11, Order on number line: -9, -8, -3, -1, 0, 1, a. -10 b. 8 c a. -13 b. -5 c a. 6 b. 2 c. -2

25 d. -6 e a. Always true b. Sometimes true c. Always true 32. Answers will vary 33. a. -2 b. -11 c. -2 d. -20 e. 0 f. 0 g. -3 h. -6 i. 1 j. 3 k. -5 l. -65 m. -5 n. 13 o Answers will vary 35. a. -10 b. -2 c. 10 d. 2 e Answers will vary 37. a. -5 b. -6 c. 7 d. -2 e. 7 f. -11 g. 0 h. -8 i. -4 j. -18 k. 3 l. -93 m. -87 n o Answers will vary 39. a. Always false b. Sometimes true 40. a. -14 b. 14 c. -3 d. -15 e. -4 f. -8 g. 2 h. 3 i. 9 j. 2 k. 75 l. -1 m. -60 n. 90 o Answers will vary 42. a. -1 b. 7 c. -16 d. 2 e. -5 f. -4 g. 6 h. 0 i. 17 j. 11 k. 75 l. -55 m n. 96 o Answers will vary

26 a. 9 b. -6 c a. 6 b. -6 c

27 a. 5 b. -4 c a. base = 5 exponent = 3 b. base = 8 exponent = 9 c. base = 11 exponent = is the area of a square with side lengths of is the volume of a cube with side lengths of If the negative sign is inside the parenthesis, and the exponent is odd, the answer is negative. If the negative sign is inside the parenthesis, and the exponent is even, the answer is positive a. base = 3 exponent = 5 b. base = 5 exponent = 8 c. base = 15 exponent = is the area of a square with side lengths of is the volume of a cube with side lengths of

28 Yes, if the negative sign is inside the parenthesis, and the exponent is odd, the answer is negative. If the negative sign is inside the parenthesis, and the exponent is even, the answer is positive Answers will vary 240. a. 7 b. 4 c. 2 d. 6 e. 8 f Answers will vary 242. a. 2 b. 3 c. -3 d. -2 e. 5 f a. 12 b. 20 c. 6 d. 14 e Answers will vary 245. a-f = Answers will vary 247. a. 1/9 b. 1/25 c. 1/16 d. 243 e. 64 f a. 9 b. 7 c. 2 d. 3 e. 8 f a. 4 b. 4 c. -2 d. -4 e. 4 f a. 24 b. 27 c. 15 d. 48 e a-f = a. 1/8 b. 1/64 c. 1/25 d. 16 e. 27 f. 49 Unit Review Questions 1. C 2. A 3. B 4. A 5. A 6. A 7. C 8. C 9. A 10. C 11. D

29 12. B 13. B 14. C 15. B 16. B 17. A 18. B 19. C 20. B , = = = = John has less money at the end of the week. He has $40 less.