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LESSON Name 61 page 387 • Using Letters to Identify Geometric Figures New Concept • To name a polygon using letters at its vertices: 1. Choose any vertex as the starting point. 2. Move around the perimeter in either direction, naming each vertex in order. 3. Stop after all vertices have been recorded. Naming Lines, Segments, and Rays Figure A Name Abbreviation line AB or line BA AB or BA segment AB or segment BA AB or BA ray AB (must name endpoint first) AB B A B A B • Name an angle using the letter of its vertex. If there is a chance for confusion, use three letters with the vertex as the middle letter. Example Look at the figure below. © 2008 Saxon B A C D E ∠ADC (angle ADC) is inside the figure. ∠CDE (angle CDE) is outside the figure. Both have D at their vertex. Saxon Math Intermediate 5 SM_H5_AD_L061_FF.indd 397 397 Adaptations Lesson 61 10/31/07 1:59:04 PM Lesson Practice ___ a. Which segment is parallel to JK ? ___ J K M L ___ b. If JK is 10___ cm long and if JM is half the length of JK, then what is the perimeter of the rectangle? Use words to show how each of these symbols is read and draw an example of each figure. ___ c. BC d. CD s r e. PQ l Refer to the figure below to answer problems f–i. B A M C D f. Angle AMD is an obtuse angle. Using three letters, what is another way to name © 2008 Saxon this angle? g. Which angle appears to be a right angle? h. Which ray appears to be perpendicular (forms a right angle) to MD? i. Name one angle that appears to be acute. Saxon Math Intermediate 5 SM_H5_AD_L061_FF.indd 398 398 Adaptations Lesson 61 10/31/07 1:59:07 PM page 391 Written Practice 1. 1 ft = in. × ( ) + = 2. _1_ absent 6 See “Fraction-Decimal-Percent Equivalents” on page 19 of the Student Reference Guide. _1_ 6 = percent fraction not absent 6 __ 6 – 4. (7 × 1000) + (4 × 10) 1959 1790 3. + 5. 56 23 × 6. Which of these fractions does not 1? equal __ 2 6 A ___ 12 12 B ___ 24 © 2008 Saxon _____ 2)1 Saxon Math Intermediate 5 SM_H5_AD_L061_FF.indd 399 = 2 _____ 2)2 399 48 D ___ 98 24 C ___ 48 4 _____ 2)4 8 _____ 2)9 8 Adaptations Lesson 61 10/31/07 1:59:09 PM page 391 Written Practice, continued 7. factors of 12: 1, , , , , 12 factors of 16: 1, , , , 16 , 3 10. 1 − __ = 4 3 + ___ 4 = 2 + ___ 1 + ___ 12. ___ 10 10 10 10 – 4263 q 1784 q= Saxon Math Intermediate 5 SM_H5_AD_L061_FF.indd 400 octagon 12 in. , 3 − 1 __ 2= 11. 3 __ 3 3 1= 1 − __ 5 14. Add all sides. 3 + 4 __ 1= 13. 5 __ 4 4 15. + $19.34 m $50.00 16. 58 39 24 16 52 + 11 © 2008 Saxon 9. Rename the 1. 8. Perimeter m= 400 Adaptations Lesson 61 10/31/07 1:59:11 PM Written Practice, continued 17. 389 × 470 page 392 _____ = 18. 5445 9 19. Write the quotient with a fraction. 25 ___ = 6 20. long division 22. (800 − 300) × 20 = 21. long division 894 ÷ 40 = 943 ÷ 30 = 1 1 = ___ 24. __ 23. 20 2 2 3 1 = 20 __ ___ 2 0 4 Use work area. © 2008 Saxon 25. Start counting with December. 15 months after November? 26. Find ST. Label the figure. R Saxon Math Intermediate 5 SM_H5_AD_L061_FF.indd 401 401 S ? T Adaptations Lesson 61 10/31/07 1:59:13 PM page 392 Written Practice, continued 27. Which angle in this figure on 28. Oregon page 392 appears to be a right angle? 1859 West Virginia (Oregon + 4) + Arizona (West Virginia + 49) + = = Use work area. 29. 65 guests are to be seated at 3 tables. What is a reasonable estimate of the number of guests per table? Explain. Using compatible , 65 is close to , which is a factor of 3. 66 ÷ 3 = is a reasonable estimate for the number of per table. Use work area. 30. a. How many months did he practice more than 20 days? c. mode most d. median middle e. range span © 2008 Saxon b. How many months did he practice between 15 and 20 days? Use work area. Saxon Math Intermediate 5 SM_H5_AD_L061_FF.indd 402 402 Adaptations Lesson 61 10/31/07 1:59:14 PM LESSON Name 62 Teacher Notes: page 394 • Review Hint #29 “Estimating or Rounding.” • Estimating Arithmetic Answers with Rounded and Compatible Numbers • Review “Estimate” on page 8 in the Student Reference Guide. • For additional practice, students may complete Targeted Practice 62. New Concept • An estimated answer is not an exact answer, but it is close. • Estimate to see if your calculated answers are reasonable. • Estimation can use rounded numbers to make the math easier. Example 29 30 $08.95 $ 9 × 21 × 20 $07.23 $ 7 600 $11.42 $11 + $06.89 +$ 7 $34 Lesson Practice Estimate each answer by rounding or using compatible numbers before doing the arithmetic. © 2008 Saxon a. 68 39 70 + 40 110 40 × 020 × 25 SM_H5_AD_L062_FF.indd 403 + f. 29 − Offset. Saxon Math Intermediate 5 c. 585 312 e. 94 d. 38 19 b. 41 23 312 × Offset. 403 Adaptations Lesson 62 10/31/07 2:00:51 PM Lesson Practice, continued _____ ) 123 h. 29 g. 685 59 − 391 Cancel matching zeros. _____ i. 703 ) 123 j. 31 96 − 497 k. Estimate the sum of: l. Estimate the perimeter: $12.95 $ 7.03 $ 8.49 57 41 × 2= 57 mm 41 mm Written Practice page 397 cups per dozen 1. 6 made 0020 left over eaten © 2008 Saxon made centuries ____ 1 = __ ? 2. _________ years 100 0 A century is Saxon Math Intermediate 5 SM_H5_AD_L062_FF.indd 404 years, and 100 × 404 = 1000. Adaptations Lesson 62 10/31/07 2:00:57 PM Written Practice, continued 4. Shade 3_1. 3. average 4 7 7 2 page 397 Name the fraction and percent not shaded. _____ ) 123 5. Estimate the product. 3 7. 1− __ = 8 6. Rename the 1. 1 = 1− ___ 10 39 41 3= 4 − 2 __ 8. 4 __ 4 4 11. 8 = 7 __ 6 10 − ___ 1 = 10. 6 ___ 10 10 1 + 1 __ 2= 9. 3 __ 3 3 12. Estimate the sum. © 2008 Saxon 586 317 numerator = Saxon Math Intermediate 5 SM_H5_AD_L062_FF.indd 405 405 Adaptations Lesson 62 10/31/07 2:01:01 PM Written Practice, continued 13. 89,786 26,428 57,814 + 91,875 14. page 397 $35,042 − $17,651 16. 5y = 4735 15. 428 × 396 17. 8 × 43 × 602 = 602 × 43 × 8 y= 18. Write the quotient with a fraction. 19. long division 967 ÷ 60 = 20. long division 875 ÷ 40 = 15 = ___ 8 0 1 > ___ b. __ 2 10 © 2008 Saxon 0 1 = ___ 21. a. __ 2 10 a. 0 1 < ___ c. __ 2 10 b. c. Saxon Math Intermediate 5 SM_H5_AD_L062_FF.indd 406 406 Adaptations Lesson 62 10/31/07 2:01:03 PM page 398 Written Practice, continued 22. $100 − ($24 + $43.89 + $8.67 + $0.98) = 23. Perimeter even 24. Add all sides. × 5 product Last digit? mm 10 20 30 When the numbers 0, 2, 4, 6, or A 15 mm B 40 mm C 60 mm D 100 mm 8 are multiplied by , product ends in the . 25. A flight leaves in the morning at the time shown. If it takes 3 hours and 20 minutes, what time will the plane land? time now: 11 10 20 minutes later: 12 1 2 9 3 4 8 © 2008 Saxon 3 hours later: 26. a. all possible outcomes: 7 , 6 5 , 1 2 b. probability of stopping on sector 3 with one spin: 3 c. probability of stopping on sector 1 with one spin: Use work area. Saxon Math Intermediate 5 SM_H5_AD_L062_FF.indd 407 407 Adaptations Lesson 62 10/31/07 2:01:04 PM Written Practice, continued page 398 27. Which angle in this figure appears to be an obtuse angle? X Y W Z M 28. Estimate the perimeter. 126 in. 32 in. 126 ×2= 032 ×2= + = Use work area. 29. half of 25 30. New York City 12:00 p.m. Chicago (New York City – 1 hour) © 2008 Saxon Los Angeles (Chicago – 2 hours) Saxon Math Intermediate 5 SM_H5_AD_L062_FF.indd 408 408 Adaptations Lesson 62 10/31/07 2:01:06 PM LESSON Name 63 Teacher Note: page 400 • For additional practice, students may complete Targeted Practice 63. • Subtracting a Fraction from a Whole Number Greater Than 1 New Concept • To subtract a fraction from a whole number greater than 1: 1. Line the number up vertically. 2. Borrow 1 from the whole number and rename the 1 as a fraction. 3. Subtract. Example 1 4 − __ 3 2 4 __ 2 − 3 4 2 1 __ 2 1 __ 2 2 2 3 Lesson Practice Subtract. Borrow from the whole number and rename. 3 4 4 __ a. 4 1 __ © 2008 Saxon − d. 2 Saxon Math Intermediate 5 e. c. 3 __ 4 − 4 − SM_H5_AD_L063_FF.indd 409 b. 0 3 0 40 1 − 2 __ 4 f. 4 − 6 − 409 Adaptations Lesson 63 10/31/07 2:02:22 PM Lesson Practice, continued g. At noon there were 3 pies. By 1:00 p.m., 14_3 of the pies had been served. Shade the circles below to show how much pie was served. Then tell how much pie remains. pies remain. page 402 Written Practice 1. 7 cm 34 cm 00000 + m00000 100 cm 7 cm 2. Borrow and rename. 6 0 in. 34 cm 1 in. − 1 __ 2 ? 100 cm 3. hamburgers per pound pounds 18 19 24 23 _____ ) 000 6. factors of 14: 398 1, 487 Cross out the numbers that are not factors of 21. , , 14 © 2008 Saxon 5. Estimate the sum. 4. average , Saxon Math Intermediate 5 SM_H5_AD_L063_FF.indd 410 410 Adaptations Lesson 63 11/8/07 11:29:29 AM page 402 Written Practice, continued 7. The distance around is called the A radius 8. + B diameter , , , 10. 60 11. 80 3 − 3 __ 4 1 − 2 __ 2 1 __ 3 − 2 __ 9 1 − __ 9 © 2008 Saxon D area 0 70 8 __ 9 13. 411 3 5 __ 2 3 __ 4 1 + 1 __ 4 + 0 Saxon Math Intermediate 5 SM_H5_AD_L063_FF.indd 411 C circumference , 9. Borrow and rename. 12. . 4 − 0 Adaptations Lesson 63 10/31/07 2:02:26 PM page 403 Written Practice, continued 14. 43,716 − 19,537 15. $6.87 × 794 16. $14.72 _______ 8 = 17. Write the quotient with a fraction. 20 ___ 9 18. long division _________ 20 ) 9 5 1 = 19. Cancel matching zeros. R ______ 50 ) 2 5 6 0 R _____ 2560 _____ 5) 50 R Add the zero back to the remainder. 21. Cancel matching zeros. 22. (400 + 400) ÷ 40 = 8 __ 8 23. 8_3 were not in the library. Name the fraction and the percent that were in the library. SM_H5_AD_L063_FF.indd 412 − % See “Fraction-Decimal-Percent-Equivalents” on page 19 of the Student Reference Guide. Saxon Math Intermediate 5 4736 2849 351 + 78 412 © 2008 Saxon 20. 50 × (400 + 400) = Adaptations Lesson 63 10/31/07 2:02:27 PM page 403 Written Practice, continued 24. least to greatest 5 ___ 10 1 __ 2 5 __ 8 1 __ 2 5 ___ 12 1 __ 2 25. What is the perimeter of this equilateral triangle? mm 10 , 26. 20 30 , Animal Average Weight (in pounds) Horse 100 100 Chimpanzee 100 100 100 100 Saltwater Crocodile Gorilla 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Key: 100 100 = 100 pounds a. least to greatest , b. 150w = 450 , missing factor , Divide. w= c. 2000 pounds = 1 ton © 2008 Saxon two animals that together weigh about 1 ton: , Use work area. Saxon Math Intermediate 5 SM_H5_AD_L063_FF.indd 413 413 Adaptations Lesson 63 10/31/07 2:02:28 PM Written Practice, continued 27. polar bear page 404 28. type of angle formed by hands arctic gull 11 10 12 1 2 9 3 4 8 7 6 5 29. Explain the best way to estimate 350 ÷ 4. Since 4 is a factor of 36, it is also a factor of to 350. Using c , numbers, 360 ÷ 4 = which is close . Use work area. 39 © 2008 Saxon 30. Saxon Math Intermediate 5 SM_H5_AD_L063_FF.indd 414 414 Adaptations Lesson 63 10/31/07 2:02:30 PM LESSON Name 64 Teacher Note: page 405 • Review “Place Value” on page 13 in the Student Reference Guide. • Using Money to Model Decimal Numbers New Concept • Money helps us understand decimal place value: Place-Value Chart Whole Numbers Decimals Place Name hundreds tens ones tenths hundredths Place Value 100 10 1 1 10 1 100 $100 bills $10 bills $1 bills dimes pennies Place Money Value of Place Example ones tenths hundredths $6 . 2 5 six two five dollars dimes pennies Lesson Practice © 2008 Saxon Name the place value of the 5 in each of these numbers. a. $25.60 b. $54.32 c. $12.75 d. $21.50 e. What combination of dollars, dimes, and pennies makes $3.84 using the fewest bills and coins possible? dollars Saxon Math Intermediate 5 SM_H5_AD_L064_FF.indd 415 dimes 415 pennies Adaptations Lesson 64 10/31/07 2:03:49 PM Lesson Practice, continued f. Is $12.63 closer to $12.60 or to $12.70? g. Is $6.08 closer to $6.00 or to $6.10? h. $1.49 $00000 × 000003 , $1.49 can be rounded to ×3= so e . page 409 Written Practice 1. is a reasonable , + , 2. 00$30.63 00$17.85 3. × © 2008 Saxon total empty filled Saxon Math Intermediate 5 SM_H5_AD_L064_FF.indd 416 416 Adaptations Lesson 64 10/31/07 2:03:51 PM Written Practice, continued 4. missing factor page 409 5. Estimate the product. Divide. 68 _____ ) 6h = 52 3 up 6. ___ 10 Name the fraction and the percent down. 7. Numbers written in dollars and cents (such as $54.63) have how many decimal places? 10 00___ 10 % 8. What combination of dollars, dimes, and pennies makes $3.25 using the fewest bills and coins possible? 9. Is $4.82 closer to $4.80 or $4.90? dollars dimes pennies Use work area. © 2008 Saxon 10. Divide 25 by 8. 11. factors of 20: Write the quotient with a fraction. 1, , , , , 20 Cross out the numbers that are not factors of 30. , Saxon Math Intermediate 5 SM_H5_AD_L064_FF.indd 417 417 , , Adaptations Lesson 64 10/31/07 2:03:52 PM page 409 Written Practice, continued 13. 360 − a = 153 12. What time is 12_1 hours before noon? 1 hour before noon: _1 2 hour before that: a= 14. 5m = 875 3 5 − z = __ 16. __ 5 3 15. Rename the 1. 3+f=1 __ 5 17. $30.48 ÷ 6 = z= f= 18. 20. Property of Zero for Multiplication ____________ 60 ) 1 5 8 SM_H5_AD_L064_FF.indd 418 6 19. $4.34 $0.26 $5.58 $9.47 $6.23 + $0.65 21. Borrow and rename. 5×4×3×2×1×0= Saxon Math Intermediate 5 R 70 2 – 3 __ 3 418 © 2008 Saxon m= Adaptations Lesson 64 10/31/07 2:03:54 PM page 410 Written Practice, continued 22. 1 1__ 3 2 __ + 2 3 23. Borrow and rename. 24. perimeter PQ = 12 mm 4 3 − 3 __ 4 P T Q S 25. Find the remainder. a. _____ 3 )1 R 0 b. R 26. What is the perimeter of this equilateral triangle? _________ 3 )1 0 R 0 inch 1 2 a. b. 27. What is the probability that the letter selected will be one of the letters that follows Q in the alphabet? © 2008 Saxon T C B F M R J Saxon Math Intermediate 5 SM_H5_AD_L064_FF.indd 419 419 Adaptations Lesson 64 10/31/07 2:03:55 PM page 411 Written Practice, continued 28. Display the below data in a line graph. April Day in Hershey, PA Time Temperature (°F) 60 12:00 a.m. 43 58 3:00 a.m. 46 6:00 a.m. 45 9:00 a.m. 48 12:00 p.m. 58 56 Temperature (ºF) 54 52 50 48 46 44 42 12:00 3:00 6:00 9:00 12:00 a.m. a.m. a.m. a.m. p.m. Time Use work area. 29. Wednesday 59º Tuesday (Wednesday – 7º) Monday (Tuesday + 12º) Use work area. 30. The hockey coach purchased six hockey pucks for $3.49 each. Explain how addition can be used to make a reasonable estimate of the total cost. , and $3.50 + $3.50 is the cost of two pucks is about + + . , the cost of six pucks is , or Since © 2008 Saxon $3.49 is about . Use work area. Saxon Math Intermediate 5 SM_H5_AD_L064_FF.indd 420 420 Adaptations Lesson 64 10/31/07 2:03:56 PM LESSON Name 65 Teacher Notes: page 412 • Review Hint #32 “Reading Metric Rulers.” • Review “Equivalence Table for Units” on page 1 in the Student Reference Guide. • Decimal Parts of a Meter New Concept • Meters can be divided into smaller units: Math Language decimeters (tenths) • The meter is the basic unit of length in the metric system. centimeters (hundredths) millimeters (thousandths) 1 meter 10 decimeters 100 centimeters 1000 millimeters cm 10 20 30 40 50 60 70 80 90 • The fractional parts of a meter can represent a decimal number. ó10 meter ó10 ó10 decimeter centimeter millimeter © 2008 Saxon Example How many millimeters equal 4 decimeters? 4 dm = 40 cm 40 cm = 400 mm Eduardo was 1 meter plus 35 centimeters tall. What was his height in meters? 1 m + 35 cm = 1 m + 3 dm + 5 cm = 1.35 m Saxon Math Intermediate 5 SM_H5_AD_L065_FF.indd 421 421 Adaptations Lesson 65 10/31/07 2:06:43 PM New Concept, continued Activity 1 page 414 Decimal Parts of Meter • This activity is optional. Activity 2 page 415 Measuring with a Meterstick • Use your textbook to complete this activity. Lesson Practice a. Which of these is the most reasonable measurement for the length of an automobile? (Circle one.) A 4.5 meters B 4.5 decimeters C 4.5 centimeters D 4.5 millimeters b. Alonso is 1 meter plus 43 centimeters tall. Use a decimal number to write Alonso’s height in meters. © 2008 Saxon c. A ruler is about 30 centimeters long. About how many decimeters long is a ruler? Saxon Math Intermediate 5 SM_H5_AD_L065_FF.indd 422 422 Adaptations Lesson 65 10/31/07 2:06:46 PM page 415 Written Practice 1. Draw a quadrilateral with one pair of horizontal segments and one pair of vertical segments. 2. number in each group × number of groups total players ____ 8) Use work area. 3. perimeter 100 yards 40 yards 4. _1 4 of a yard 36 in. 1 4 ____ in. ___ ) 36 1 __ 4 = ____ in. ____ in. percent ____ in. 5. Count on a clock the minutes from 7:45 to 8:30. 6. Estimate the sum. © 2008 Saxon 672 830 Saxon Math Intermediate 5 SM_H5_AD_L065_FF.indd 423 423 Adaptations Lesson 65 10/31/07 2:06:48 PM page 416 Written Practice, continued 7. a. fraction shaded b. fraction not shaded r c. My answers are + because = a. 10 __ , or 1 whole. 10 b. c. 8. height of refrigerator 9. half a meter = 1 m + 32 cm = 8 1, __ 2 11. How many factors? 2 __ 1, __ 2 3 , 12. Write the quotient as a mixed number. 5 ___ 1 __ 10 2 , factors of 10: , 13. greatest 3 4 5 15 = ___ 4 © 2008 Saxon 4 3 __ decimeters m 10. least to greatest 4, __ Use work area. odd Saxon Math Intermediate 5 SM_H5_AD_L065_FF.indd 424 424 Adaptations Lesson 65 10/31/07 2:06:50 PM page 416 Written Practice, continued 500 14. 15. 36,195 17,436 + 42,374 16. 41,026 − 39,543 more than 17. 608 × 479 18. 2637 ÷ 4 = 19. Cancel matching zeros. _____________ 40 ) $3 20. Cancel matching zeros. 3 + 5 __ 5 = 21. 3 __ 8 8 3360 _____ 22. Borrow and rename. 8 24. 6 × 42 × 20 = 25. $20 − ($5.63 + $12) = © 2008 Saxon 4 0 3 = 5 − 3 __ 20 3 −3= 23. 3 __ 3 . 6 Saxon Math Intermediate 5 SM_H5_AD_L065_FF.indd 425 425 Adaptations Lesson 65 10/31/07 2:06:51 PM Written Practice, continued page 417 27. By which of these numbers is 1080 divisible? 26. Use the Distributive Property. 2 2_1 dozen = 2 dozen + _1 2 dozen 2, 3, 5, 6, 9, 10 Check all the numbers. See “Tests for Divisibility” on page 20 in the Student Reference Guide. How many eggs? + 2 28. probability 1 2 3 4 a. even number b. less than 4 c. less than 5 a. b. c. 29. degrees cooler J’Ron 60 minutes © 2008 Saxon 30. Adolfo (J’Ron ÷ 2) Shaun (Adolfo ÷ 2) Saxon Math Intermediate 5 SM_H5_AD_L065_FF.indd 426 426 Adaptations Lesson 65 10/31/07 2:06:52 PM