Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Thank you for participating in Teach It First! This Teach It First Kit contains a Crosswalk Plus student lesson and teacher answer key. Also included is a teacher mini-lesson and worksheet. The mini-lesson was designed as an introduction to each chapter. Use the student lesson as your instructional tool or begin with the mini lesson if you feel your students need a refresher on the topic—you decide! Are you transitioning to the Common Core State Standards? If you are getting ready for change, or have already begun your shift to the new standards, Crosswalk Coach PLUS for the Common Core State Standards has you covered! This series is newly revised and better than ever—it now includes: •Two Common Core Practice Tests •Lots of additional practice •New item types that reflect the rigor of the new CCSS assessments Each lesson targets a single skill, promoting achievement through instruction and practice, and allowing you to assess mastery of discrete skills. You’ll get maximum flexibility in addressing areas of need. Plus, Coached Examples throughout strengthen comprehension. Everything you need to transition to the new standards is right here! We are happy to provide you this complimentary sample and would love to know what you think. Once you have read through this lesson, do what you do best— present it to your students. Then, don’t forget to complete a quick survey by going to www.triumphlearning.com/teach-it-first. By doing so, you will be entered into our quarterly raffle for one of five American Express $100 gift cards. Regards, Triumph Learning Join the conversation about Common Core today by visiting commoncore.com, the place where teachers, parents, and experts come together to share best practices and practical information for successfully implementing Common Core standards in the classroom. Learn it Today, Use it tomorrow. 136 Madison Avenue • New York, NY 10016 • p: 212.652.0215 • f : 212.857.8499 • www.triumphlearning.com Cr os s wa l kPl us , Ma t h, T e a c he rE di t i on, Gr a de8 Mini-Lessons Fraction-Decimal-Percent Equivalences Teach Explain how fractions, decimals, and percents are 1 of your spare used at different times. You might say __ 4 time is spent doing homework, that our school has 1.2 times as many students as last year, or that 35% of students take the bus. Explain: Each fraction can be equivalent to a decimal 1 5 0.25 5 25%. and percent. Example: __ 4 Model Explain why the number 1.2 is equivalent 1 and 120%. 1.2 can be written as 1.20, to both 1 __ 5 which becomes 120% when multiplied by 100. Remind students that to change a decimal to a percent, multiply by 100. Ask Students Ask students to explain why 6% is the same as 0.06 6 and why 6% is not the same as ___ . Explain that to 10 change a percent to a decimal, we divide by 100 (move decimal point 2 places to the left). 6 So, 6% 5 0.06. Show that ___ 10 5 0.6 and is not equal to 0.06 or 6%. Practice/Apply Distribute Reproducible R1. Ask students to do exercise 1. Then go over this exercise to make sure everyone understands it. Answers to Reproducible (R1) 1. B. 0.8 2. No. To convert 67% to a decimal, divide 67 by 100. Move the decimal point in 67 two places to the left. This gives 0.67. The decimal 6.7 is equal to 670%. 3. 0.25; 25 4 100 5 0.25 4. 37%; 0.37 3 100 5 37 5. B. 4% 5 0.4 6. B. 0.9 5 90% Mean Teach Practice/Apply Another word for the mean is the average. Mean is used to give us an idea of the overall picture for a set of numbers. We use the mean for scores, grades, and costs. Distribute Reproducible R2. Ask students to do exercise 1. Then go over this exercise to make sure everyone understands it. Model 1. B. 40 Answers to Reproducible (R2) Suppose you wanted to find the mean of 2, 5, 10, and 11. Explain the method: add the numbers and divide by 4 (the number of numbers). Sum 5 28, mean 5 7. 2. Multiply the mean by 7. Reason: The mean is the sum divided by 7, so the sum is the mean multiplied by 7. Ask Students 3. B. 8 Ask students to find the mean of 100, 500, 200, 700, and 1,000. Ask students to think of a situation in which they might need to find the mean. Then ask them to make up numbers for that situation and find the mean. 4. The sum of 100 numbers is 50(1,000) 1 50(500) 5 50,000 1 25,000 5 75,000. The mean of 100 numbers is 75,000 4 100 5 750. 5. The sum of the ages is 30 1 33 1 36 1 39 1 42 1 45 1 48 1 51 1 54 5 378. The mean age is 378 4 9 5 42. 13 T291NAG_Mth_G8_TG_PDF.indd 13 9/3/13 11:10 AM Name: Date: Fraction-Decimal-Percent Equivalences Every fraction can be written as both a decimal and a percent. 1. What is the decimal equivalent for __ 45 ? A. 4.5 B. 0.8 C. 0.45 2. Is 67% the same as the decimal 6.7? Explain. 3. Write 25% as a decimal. 4. Write 0.37 as a percent. 5. Which is not true? A. 60% 5 0.6 B. 4% 5 0.4 C. 125% 5 1.25 6. Which is true? 9 5 9% A. ___ B. 0.9 5 90% C. 90% 5 0.09 © Triumph Learning, LLC 10 R1 T291NAG_Mth_G8_TG_PDF.indd 16 9/3/13 11:10 AM Answer Keys (continued) 9. A.a2 ; a6 4 a4 5 a6 2 45 a2 B. quotient of powers property 10. Fraction: 723, 822 Whole Number: 13, 50 , 31 11.54 ,53 12. A: False, B: True, C: True, D: False, E: True, F: False 13. A: 1, B: 16, C: 64, D: 8, E: 2 14. A: No, B: Yes, C: No, D: Yes, E: No, F: No 15. B, D 1 , 1,024 16. ___ 625 Lesson 7 Coached Example Since the exponent is positive, this is a number greater than 1. The exponent of the second factor is 7. The exponent tells you to move the decimal point in 9.0 seven places to the right. The number 9.0 3 1 07in standard form is 90,000,000. About 90,000,000 passengers passed through the Hartsfield-Jackson Atlanta International Airport in 2008. Lesson Practice Lesson 6 Coached Example The area of the garden above is 121 square yards. To find the length of one side, take the square root of that area. On the lines below, try squaring numbers until you find one that results in 121. Possible work: 1025 10 3 10 5 100 Too low 1125 11 3 11 5 121 ✓ The length of each side, s, of the garden is 11 yards. Lesson Practice 1. B 2. B 3. B 4. D 5. C 6. A 7. C 8. C 9. A. (3.4 3 105)(3.8 3 1029) 5 (3.4 3 3.8)(1053 1029) B. 0.001292; Possible work: 3.4 3 3.8 5 12.92 1053 10295 105 1 (29)5 1024 1. B 12.92 3 1024 2. A 5 1.292 3 1013 1024 3. B 5 1.292 3 (101 1 (24)) 4. C 5 1.292 3 1 0235 0.001292 5. C 10. A: True, B: True, C: False, D: True 026, 8.6 3 103 11. 3.5 3 1 6. D 7. A 8. D 9. A. 8 centimeters; Possible work: 83 5 8 3 8 3 8 5 64 3 8 5 512 ✓ 3 ____ So, √ 512 5 8. B. 64 square centimeters; Possible work: Each edge is 8 centimeters. To find the area of one face, square the length of one edge: 82 5 8 3 8 5 64 sq cm. 3 __ 3 ___ ___ ___ 10.√ 7 , √ 55 , √18 , √95 11. A: True, B: False, C: True, D: False 12. A: 12, B: 8, C: 19, D: 3 13. A: No, B: Yes, C: Yes, D: No ___ 3 ____ 3 ____ 14. Less than 10: √50 , √ 400 , √ 900 ____ ____ 3 ______ Greater than 10: √ 200 , √ 144 , √ 1,200 15. 21, 11 12. A: 4,500,000,000; B: 0.000045; C: 4,500; D: 0.00045; E: 45,000 13. A: No, B: Yes, C: Yes, D: No 14. B 15. 170,000,000: (1.7 3 104)(1.0 3 104), 1.7 3 108 0.000017: (1.7 3 1022)(1.0 3 1023), 1.7 3 1025 Lesson 8 Coached Example The decimal point was moved 6 places to the right. The original number is less than 1, so the exponent will be negative. 0.000007 5 7 3 1026 Multiply to convert that number of square meters to square millimeters: (7 3 1026)(1 3 106) 25 T291NAG_Mth_G8_TG_PDF.indd 25 9/3/13 11:11 AM Cr os s wa l kPl us , Ma t h, S t ude ntE di t i on, Gr a de8 Domain 2 • Lesson 6 Common Core Standard: Square Roots and Cube Roots 8.EE.2 Getting the Idea Squaring a number means raising it to the power of 2. For example, 72 is equivalent to 7 3 7, or 49. So, we say that 49 is a perfect square. The opposite, or inverse, of squaring a number is taking its square root. We use the radical symbol (œw ) to represent square roots. To find the square root of a perfect square, think about what number, when multiplied by itself, will result in that perfect square. Example 1 Solve for y. 2 y 5 196 Strategy Step 1 Determine what number, multiplied by itself, results in 196. Take the square root of both sides of the equation. The opposite of squaring a number is taking its square root. __ ____ 2 196 √y 5 √ ____ y5√ 196 Step 2 Try squaring numbers until you find one that results in 196. 2 1 2 5 12 3 12 5 144 Too low 2 13 5 13 3 13 5 169 Too low 2 14 5 14 3 14 5 196 ✓ Step 3 Solve for y. ____ Duplicating any part of this book is prohibited by law. 2 1 4 5 196, so √196 5 14. ____ y5√ 196 5 14 Solution T291NA_Mth_G8_SE_PDF.indd 59 ____ Since √196 5 14, y 5 14. 59 13/09/13 9:53 AM Cubing a number means raising it to the power of 3. For example, 2 3 is equivalent to 2 3 2 3 2, or 8. So, we say that 8 is a perfect cube. The ___ opposite, or inverse, of cubing a number is taking its cube root. We use the symbol √ to represent cube roots. To find the cube root of a perfect cube, think about what number, when cubed, will result in that perfect cube. 3 Example 2 Solve for r. 3 r 5 125 Strategy Step 1 Determine what number, when cubed, results in 125. Take the cube root of both sides of the equation. The opposite of cubing a number is taking its cube root. __ 3 3 ____ 3 ____ 3 √ r 5 √ 125 r 5 √ 125 Step 2 Try cubing numbers until you find one that gives a result of 125. 3 You already know that 2 5 8. Start with 3. 3 3 5 3 3 3 3 3 5 27 Too low 3 4 5 4 3 4 3 4 5 64 Too low 3 5 5 5 3 5 3 5 5 125 ✓ Step 3 Solve for r. 3 ____ 3 5 5 125, so √ 125 5 5. 3 ____ r 5 √ 125 r55 3 ____ Since √ 125 5 5, r 5 5. The number under a radical sign is called the radicand. If you do not have a calculator handy, you may need to estimate the value of a square root or a cube root. To estimate a square root, find the two perfect squares between which the radicand lies. Take the square root of each to find the range of your estimate. To estimate a cube root, find the two perfect cubes between which the radicand lies. Then take the cube root of each to find the range of your estimate. Duplicating any part of this book is prohibited by law. Solution 60 • Domain 2: Expressions and Equations T291NA_Mth_G8_SE_PDF.indd 60 13/09/13 9:53 AM Lesson 6: Square Roots and Cube Roots Example 3 3 ____ Between which two consecutive integers is √ 500 ? Strategy Step 1 Find the two perfect cubes between which 500 lies. Then take the cube root of each to make your estimate. Try cubing consecutive positive integers. 3 You know from Example 2 that 5 5 125. Start with 6. 3 6 5 6 3 6 3 6 5 216 3 7 5 7 3 7 3 7 5 343 3 8 5 8 3 8 3 8 5 512 The radicand, 500, is between the perfect cubes 343 and 512. Step 2 3 ____ 3 ____ Estimate the value of √ 500 . 3 ____ 3 ____ 3 ____ √ 343 , √ 500 , √ 512 7 , √ 500 , 8 3 ____ Solution√ 500 has a value between 7 and 8. Roots can help you solve measurement problems, such as problems involving the area of a square or the volume of a cube. Coached Example The area of the square garden on the right is 121 square yards. What is the length, s, of each side of the garden? Garden s 2 Duplicating any part of this book is prohibited by law. The formula for finding the area, A, of a square is A 5 s , where s is the length of a side. s The area of the garden above is _________ square yards. To find the length of one side, take the _________ root of that area. On the lines below, try squaring numbers until you find one that results in _________. That is the value of s. ___________________________________________________________________________ ___________________________________________________________________________ The length of each side, s, of the garden is _________ yards. T291NA_Mth_G8_SE_PDF.indd 61 61 13/09/13 9:53 AM Lesson Practice Choose the correct answer. ____ 1. What is the value of √100 ? A. 4 B. 10 C. 25 D. 50 3 ___ 4. Between which two consecutive integers 3 ___ is √ 11 ? A. B. C. D. 0 and 1 1 and 2 2 and 3 4 and 5 2. What is the value of √ 27 ? A. 3 B. 5 C. 9 D. 13.5 3. Solve for y. 5. Solve for x. x 25 256 A. B. C. D. x56 x 5 15 x 5 16 x 5 128 3 y 5 216 y54 y56 y57 y 5 15 6. Between which two consecutive integers 3 ____ ? is √ 200 A. B. C. D. 66 and 67 20 and 21 6 and 7 5 and 6 Duplicating any part of this book is prohibited by law. A. B. C. D. 62 • Domain 2: Expressions and Equations T291NA_Mth_G8_SE_PDF.indd 62 13/09/13 9:53 AM Lesson 6: Square Roots and Cube Roots 7. Which statement below is true? __ 3 8. Which statement below is true? __ __ 3 __ A.√4 5 √ 4 __ ___ 3 B.√4 5 √ 27 ___ ___ 3 C.√16 5 √ 27 ___ ___ 3 D.√16 5 √ 64 A.√1 5 √ 1 __ __ 3 B.√2 5 √ 3 __ __ 3 C.√4 5 √ 9 __ ___ 3 D.√4 5 √ 27 9. The wooden block shown below is a cube. It has a volume of 512 cubic centimeters. s s s A. What is the length of one side, s? (Hint: the formula for the volume, V, of a cube is V 5 s3.) Show your work. B. Indira wants to paint the front face of the block. What is the area of one of the faces? Show your work. Duplicating any part of this book is prohibited by law. T291NA_Mth_G8_SE_PDF.indd 63 63 13/09/13 9:53 AM 10. Use the expressions shown below to label the points on the number line. 3 55 0 3 7 95 2 18 4 6 8 10 11. Select True or False for each equation. A. B. C. D. ____ 121 5 11 √ 3 ___ √ 81 5 27 ___ ____ 3 25 5 √ 125 √ __ 3 √ 9 5 3 ○ True ○ False ○ True ○ False ○ True ○ False ○ True ○ False A. 144 19 B. 3 512 12 C. 361 8 D. 3 3 27 13. Look at each square root or cube root. Is it equivalent to 4? Select Yes or No. A. B. C. D. __ √ 8 ___ 3 √ 64 ___ 16 √ 3 ___ √ 12 ○ Yes ○ No ○ Yes ○ No ○ Yes ○ No ○ Yes ○ No Duplicating any part of this book is prohibited by law. 12. Draw a line from each square root or cube root to its value. 64 • Domain 2: Expressions and Equations T291NA_Mth_G8_SE_PDF.indd 64 13/09/13 9:53 AM Lesson 6: Square Roots and Cube Roots 14. Determine whether each square root or cube root has a value greater than 10 or less than 10. Write the root in the correct box. 50 3 200 400 3 1,200 144 3 900 Less than 10 Greater than 10 15. Circle the number that makes each equation true. 9 17 19 21 Duplicating any part of this book is prohibited by law. 23 T291NA_Mth_G8_SE_PDF.indd 65 ____ 5√ 441 11 12 3 _____ 5 √ 1,331 13 65 13/09/13 9:53 AM