LESSON Name 41 Teacher Notes: page 263 Introduce Hint #24 Regrouping Across Zeros. Subtracting Across Zero Review Missing Numbers on page 7 in the Student Reference Guide. Missing Factors For additional practice, students may complete Targeted Practice 41. New Concept Subtracting Across Zero Example $405 $126 3 9 $4 0 1 5 $1 2 6 3 9 $4 0 1 5 $1 2 6 $2 4 9 We can t subtract 6 from 5. Borrow one from 40, leaving 39. Subtract as usual. Borrow across all zeros in one step. Example Missing Factors 2 9 $3. 0 1 0 $1. 2 3 $1. 7 7 2 9 9 $3 0 0 1 1 $1 2 3 9 $ 2 To find a missing factor Divide. Math Language Factors are numbers that are multiplied. The product is the answer to a multiplication problem. factor factor = product a 4 = 36 36 4 = 9 a = 9 3 z 27 8 9 3 ) 27 z = 9 5n = 40 40 5 = 8 n = 8 Saxon Math Intermediate 4 265 Adaptations Lesson 41
Lesson Practice Subtract. Remember to write the dollar sign in money problems. a. $3.00 $1.32 b. $405 $156 c. 201 102 d. $4.00 $0.86 e. $304 f. $703 Find the missing factor in each problem: g. 8w = 32 h. p 3 = 12 i. 5m = 30 j. q 4 = 16 ) 32 ) ) ) w = p = m = q = Written Practice page 266 1. a. fraction: 1 100 b. decimal: 0. c. words: 2. $0.10 $. $. 3. 1 gal = qt See page 1 in the Student Reference Guide. Saxon Math Intermediate 4 266 Adaptations Lesson 41
page 266 4. 5. Five tenths equals one half. 4200, 4300, 4400,,,, 6. evening What time will it be 8 hours from the time shown? Start time: Count forward 8 hours. 11 10 9 8 12 1 7 6 5 2 4 3 7. Divide. 5w = 45 ) 8. 1.89 L words: w = 9. 10. Which letter below has no right angles? F E Z L Saxon Math Intermediate 4 267 Adaptations Lesson 41
page 267 11. Change to multiplication: 12. $1.25 + 1.25 + $1.25 + $1.25 inch 1 2 13. 1 meter = centimeters See page 1 in the Student Reference Guide. 14. Five dimes a. fraction b. value a. b. 15. Use fraction pieces. a. 0.5 0.50 16. a. 3 8 = b. 3 7 = c. 3 6 = 17. a. 4 8 = b. 4 7 = c. 4 6 = b. 1 2 1 4 d. 12 3 d. 12 4 a. b. a. b. a. c. c. b. d. d. Saxon Math Intermediate 4 268 Adaptations Lesson 41
page 268 18. m 8 64 19. 9 n 54 20. z + 179 496 m = n = z = 21. $3.00 + $1.84 22. $500 $167 23. w 297 486 w = 24. Subtract to find the rule., 28, 21, 14,,,,, 25. one million, fifty thousand,, 26. If the area of a square is 36 square inches, then how long is each side of the square? Area = length width A 6 in. C 12 in. B 9 in. D 18 in. 27. 1.4 words: Saxon Math Intermediate 4 269 Adaptations Lesson 41
page 268 28. 0. 2 7 0. 2 1 0. 2 4 0. 2 0 Look at the tenths. Look at the hundredths. fastest slowest 29. 402 153 I can use com numbers to see if my answer is r. 402 is close to, and 153 is close to. The sum of these is, which is close to my answer of. 30. 600 256 To find the d between the two heights, I s by borrowing across the z. Saxon Math Intermediate 4 270 Adaptations Lesson 41
LESSON Name 42 Teacher Notes: page 269 Rounding Numbers to Estimate Review Hint #12 Estimating or Rounding. Review Estimate on page 8 in the Student Reference Guide. New Concept To multiply by a multiple of 10 or 100: 1. Multiply the nonzero digits. 2. Copy the same number of zeros after the answer. 3 200 = 600 6 40 = 240 4 3000 = 12000 To round a number to the nearest hundred: 1. Underline the hundreds place. 2. Circle the digit to its right. 3. Ask: Is the circled number 5 or more? (5, 6, 7, 8, 9) Yes No Add 1 to the underlined number. The underlined number stays the same. 4. Replace the circled number and the number after it with zeros. 4 7 2 500 472 400 450 500 Saxon Math Intermediate 4 271 Adaptations Lesson 42
Lesson Practice Find each product: a. 50 7 b. 600 3 c. 7 40 = d. 4 800 = Round each number to the nearest hundred: e. 8 1 3 f. 685 g. 427 h. 25 7 3 i. 2 9 7 4 1 2 + j. 623 287 k. Round. l. 1 month = about 30 days 19 5 Written Practice page 273 1. square with 5 cm sides a. perimeter b. area a. b. Saxon Math Intermediate 4 272 Adaptations Lesson 42
page 273 2. 67 had 3. Appletown 42 km +? = 126 km ate? km had left 42 km Radical Whery 4. afternoon What time will it be in half an hour? start time: 11 10 9 8 12 1 7 6 5 2 4 3 half an hour later: 5. 1, 4, 9, 16, 25, 36, 49,,,, 6. a. 6 7 3 b. 67 3 7. a. b. 8. a. quarter inch b. centimeter a. b. Saxon Math Intermediate 4 273 Adaptations Lesson 42
page 274 9. Change to multiplication: $2.50 + $2.50 + $2.50 10. Are the line segments in a plus sign parallel or perpendicular? See page 16 in the Student Reference Guide. 11. 1300 1400 1500 1600 1700 12. greater than 500 odd 13. 6 80 = In your head: 1. Multiply the nonzero digits. 2. Copy the zero(s). 14. 7 700 = 15. 9 80 = 16. 7 600 = 17. z + 338 507 18. $4.06 $2.28 z = Saxon Math Intermediate 4 274 Adaptations Lesson 42
page 274 19. Divide. w 6 42 ) 20. n 422 305 21. 55 + w = n = 22. 5280 23. Ten nickels a. words: a. fraction b. tens place: b. value a. b. 24. Use fraction pieces. a. 0.5 b. 1 4 1 2 1 10 25. Find the sum. 3 squared 4 squared + 26. Which of these numbers does not describe the shaded part of this rectangle? A 5 10 B 1 2 C 5.0 D 0.5 Saxon Math Intermediate 4 275 Adaptations Lesson 42
page 275 27. 0.25 words: 28. 9. 1 2 8. 4 3 8. 5 7 Look at the ones. Look at the tenths. fastest (least time) slowest (greatest time) 29. Act it out. 30. Round. by 52 4 frame size area by Since 52 is close to frame size area, by a reasonable estimate is frame size Joleen could make area different, or passengers. frames. Saxon Math Intermediate 4 276 Adaptations Lesson 42
LESSON Name 43 Teacher Notes: page 276 Adding and Subtracting Decimal Numbers, Part 1 Refer students to Decimal Arithmetic Reminders Chart on page 9 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 43. New Concept Line up the decimal points. hundredths tenths ones 3.47 3.41 0.06 Example All decimal points are in line. Change all money amounts to the same form before adding or subtracting. Add these money amounts: $3.75 + $4 + 15 pennies dimes dollars $3.75 $4.00 + $0.15 $7.90 All decimal points are in line. Saxon Math Intermediate 4 277 Adaptations Lesson 43
New Concept, continued Activity page 278 Adding and Subtracting Decimals Use your textbook to complete this activity. Lesson Practice Find each sum or difference. Remember to write the dollar sign in money problems. a. $6.32 + $0.00 b. $3.25 $0.00 c. $0.46 + $0.00 d. $0.98 $0.00 e. $1.46 + $0.00 f. $6.32 $0.00 g. $6.32 + $0.00 h. $6.32 $0.00 Use the models to add and subtract. i. 0.50 + 0.75 = j. 0.75 0.50 = Written Practice page 279 1. 100 pennies 2. 3.78 liters had one pile poured out other pile left Saxon Math Intermediate 4 278 Adaptations Lesson 43
page 279 3. San Francisco 4. a. perimeter 3 cm 400 mi? mi Santa Barbara 110 mi Los Angeles b. area a. b. 5. a. 572 b. 572 6. a. fraction: b. decimal: a. c. words: b. 7. Are the rails of a railroad track parallel or perpendicular? 8. Show 3 3. Shade 2_ 9. 9. Use your student clock. Time now: Count back to 6:05 a.m. 11 10 9 8 12 1 7 6 5 2 4 3 Santo got to school hours after he woke up. Saxon Math Intermediate 4 279 Adaptations Lesson 43
page 280 10. 11. 2.45 140 150 160 170 + 0.00 12. $3.25 $0. 00 13. $2.15 $0.00 + $0.00 14. 3.75.0 0 15. 507 n 456 16. n 207 + 423 17. $5.00 $3.79 n = n = 18. In your head: 19. 4 300 = 20. 7 90 = 1. Multiply the nonzero digits. 2. Copy the zero(s). 6 80 = Saxon Math Intermediate 4 280 Adaptations Lesson 43
page 280 21. Divide. 22. 100 = 8n = 32 n = 23. Measure. 24. Circle the families. 1,080,000 words: 25. Which of these metric units would probably be used to describe the height of a tree? A millimeters B centimeters C meters D kilometers 26. Emily has a 2-liter bottle full of water and an empty half-gallon carton. She knows 1 liter is a little more than 1 quart. If she pours water from the bottle into the carton, what will happen? There are 2 quarts in a half gallon. Think: Which is greater: 2 quarts or 2 liters? A The bottle will be empty before the carton is full. B The carton will be full before the bottle is empty. C When the carton is full, the bottle will be empty. D The carton will be empty, and the bottle will be full. Saxon Math Intermediate 4 281 Adaptations Lesson 43
page 281 27. Order from highest to lowest. Start at the greatest place value. highest lowest 28. Which group is least to greatest? Look at the hundredths. A 0.23, 0.21, 0.25 B 0.25, 0.23, 0.21 C 0.21, 0.23, 0.25 D 0.21, 0.25, 0.23 29. Use fraction pieces. 1 1 2 + 2 = 1 1 2 + = 2 + = 30. 16.5 Ra Shawn seconds faster Since Sabrina ran faster than, she finished in l time. Saxon Math Intermediate 4 282 Adaptations Lesson 43
LESSON 44 page 282 Name Multiplying Two-Digit Numbers, Part 1 New Concept Lesson Practice Find each product. To multiply a two-digit number by a one-digit number: 1. Multiply ones. 4 2 4 2 2. Multiply tens. 3 3 6 126 a. 31 2 b. 31 4 c. 42 4 d. 30 2 e. 30 4 f. 24 0 Written Practice page 284 1. 3.78 L words: Saxon Math Intermediate 4 283 Adaptations Lesson 44
page 284 2. Write each number in digits. Then compare. forty-two thousand, three hundred seventy-six, forty two thousand, eleven,,, 3. $5.00 paid $. cost change Yes, my answer is r. If I round to the nearest d, $5 =. 4. 9 squared 9 5. Divide. 8m = 48 m = Saxon Math Intermediate 4 284 Adaptations Lesson 44
page 285 6. 8 fl oz = 1 cup 7. cups = 1 pint ounces = 1 pint 8. Find diameter to the nearest quarter inch. 9. a. Use the number line. 10 5 0 5 5 2 b. in your head 4 60 3 80 10. $4.03 $1.68 11. $4.33 + $5.28 12. $5.22 $2.46 13. $7.08 $0.59 Saxon Math Intermediate 4 285 Adaptations Lesson 44
page 285 14. 21 6 15. in your head 40 7 16. 73 2 17. 51 6 18. $2.00 $. + $. 19. 8.7. 20. 62 n 14 21. n 472 276 n = 22. Change to multiplication. 2.1 + 2.1 + 2.1 + 2.1 + 2.1 + 2.1 = n = Saxon Math Intermediate 4 286 Adaptations Lesson 44
page 285 23. 1760 24. 7 3 8 a. hundreds place: 1 8 3 b. words: c. 17 6 0 25. 1.50. 26. area = 6 sq. cm length = 2 cm A 3 cm B 4 cm C 10 cm D 12 cm 27. Round to the nearest dollar. a. $5.75 Round to the nearest whole number. b. 5.75 Saxon Math Intermediate 4 287 Adaptations Lesson 44
page 286 28. dollar bills $. dimes $. pennies +$. $ 1. 2 3 29. notebook t tax 30. Sutlej Po total longer Saxon Math Intermediate 4 288 Adaptations Lesson 44
LESSON Name 45 Teacher Note: page 287 Parentheses and the Associative Property Naming Lines and Segments Review Properties of Operations on page 22 in the Student Reference Guide. New Concept Parentheses and the Associative Property Do the work inside the parentheses first. 12 (4 3) = 12 1 = 11 The answer is different without the parentheses. 12 4 3 = 8 3 = 51 Associative Property of Addition Associative Property of Multiplication How you group the addends does not affect the sum. How you group the factors does not affect the product. (a + b) + c = a + (b + c) (a b) c = a (b c) The Associative Property does not apply to subtraction or division. Naming Lines and Segments To identify a line, name two points on the line. A B AB or BA line AB line BA To identify a segment, name its endpoints. R S RS line segment RS SR line segment SR Saxon Math Intermediate 4 289 Adaptations Lesson 45
Lesson Practice a. 8 (4 + 2) = b. (8 4) + 2 = c. 9 (6 3) = d. (9 6) 3 = e. 10 + (2 3) = f. 3 (10 + 20) = Compare. g. 2 + (3 + 4) (2 + 3) + 4 h. 3 (4 5) (3 4) 5 i. The A P is shown by the comparisons. j. The length of RS is 4 cm. The length of RT is 10 cm. R 4 cm S? T 10 cm What is the length of ST? Subtract. k. Which segment in this figure appears to be the diameter of the circle? M J L l. Which segments are perpendicular? K and m. In the figure below, name two segments that are parallel to BC. A E H B F and D C G Saxon Math Intermediate 4 290 Adaptations Lesson 45
Written Practice page 291 1. 1.1 + + 0.5 0.6 2. Half Divide by 2. 1 hour = 60 minutes half hour = minutes 3. 155 shuttle balloon higher 155 rounds to and 15 rounds to. =. 4. $5.00 paid $. costs 5. 12.5 words: change back Check a s problem by a. Saxon Math Intermediate 4 291 Adaptations Lesson 45
page 292 6. Negative sixteen is less than negative six. 7. Use your student clock. left for work a.m. Count back 35 minutes. ate breakfast 8. 4060 expanded form: words: 9. 10. a. 2 quarters half dollar b. Write the number in digits. Use digit lines 2,100,000 one million, two hundred thousand 11. Divide. 6w = 42 12. a. nearest inch b. nearest centimeter w = a. b. Saxon Math Intermediate 4 292 Adaptations Lesson 45
page 292 13. parentheses first 14. The Associative Property d 12 (6 3) (12 6) 3 n apply to subtraction. Changing the order of the subtractions gives d answers. 15. 4.07 2.26 16. $5.02 $2.47 17. $5.83 $2.97 18. $3.92 + $5.14 19. 42 3 20. 83 2 21. in your head 40 4 22. 41 6 23. $2.75 $0.00 + $0. 24. 3.50 + 0. Saxon Math Intermediate 4 293 Adaptations Lesson 45
page 293 25. 2 in. a. perimeter b. area 26. Which of the following segments is not a radius of the circle? R 27. first second T M d longer S A RS C MT B RM D MS d = 28. a. Subtract from. Then subtract the difference from. The answer is. b. Subtract from. Then subtract from the difference. The answer is. 29. maximum minimum 30. Round to nearest hundred. 702.9 warmer 101.7 Saxon Math Intermediate 4 294 Adaptations Lesson 45
LESSON Name 46 Teacher Note: page 294 Relating Multiplication and Division, Part 1 Review Multiplication Table on page 5 in the Student Reference Guide. New Concept To find a missing factor Divide. 12 3 4 4 w = 12 n 3 = 12 w = 12 4 n = 12 3 w = 3 n = 4 The Multiplication Table on page 5 in the Student Reference Guide can also be used to find missing factors. 0 1 2 0 0 0 0 1 2 0 2 4 0 3 6 0 4 8 3 0 3 6 9 12 4 0 0 1 4 2 8 3 12 4 16 4 3 0 3 6 9 12 Activity page 297 Using a Multiplication Table to Divide Use the multiplication table on page 297 of your textbook to complete the activity. 1. 36 items are divided into 4 equal groups. Find 4 ) 36 by tracing the 4 row to 36 with your finger. What number is at the top of the column? Saxon Math Intermediate 4 295 Adaptations Lesson 46
New Concept, continued 2. 30 students gather in groups of 5. Find 5 ) 30 by tracing the 5 row to 30. What number is at the top of the column? 3. 108 musicians arranged in rows and columns. There are 9 musicians in each row. How many columns are there? Lesson Practice Divide: a. 2 ) 12 b. 3 ) 21 c. 4 ) 20 d. 5 ) 30 e. 6 ) 42 f. 7 ) 28 g. 8 ) 48 h. 9 ) 36 Written Practice page 298 1. 495 first n second combined 495 2. 82 first second third in all 3. 3.78 Saxon Math Intermediate 4 296 Adaptations Lesson 46
page 298 4. a. 786 b. 786 5. Shade 2 1 3. a. b. 6. 1, 3, 5, 7, 9 7. It is morning. What time was it twelve hours ago? a. Find the sum. b. Find the square root of the sum. 11 10 12 1 2 9 3 8 7 6 5 4 time now: a. 12 hours ago: b. 8. What type of angle is shown by the hands of the clock in problem 7? See page 15 in the Student Reference Guide. 9. a. Find the length to the nearest quarter inch. b. What segment is parallel to AB? A B D C a. b. Saxon Math Intermediate 4 297 Adaptations Lesson 46
page 299 10. one BIG step = about 1 meter 11. two dozen BIG steps = 10 11 about meters 12. 64 + 13. $6.25 $. $. 14. $4.02 $2.47 15. $5.00 $2.48 16. n + 2.5 3.7 17. 4.3 c 3.2 n = c = 18. 42 3 19. 81 5 20. 6 ) 30 21. 7 ) 21 22. 8 ) 56 23. 9 ) 81 24. 7 ) 28 25. 3 ) 15 Saxon Math Intermediate 4 298 Adaptations Lesson 46
page 300 26. a. perimeter 3 in. b. area Area = length width 27. What is the radius? 6 ft A 12 ft B 4 yd C 3 ft D 2 yd 28. Name Coins Total Tyrique 2 dimes and 1 penny $. Dominic $. Tamasha $. List the amounts in order:,, least greatest Saxon Math Intermediate 4 299 Adaptations Lesson 46
page 300 29. 12, 24, 36, 48, 60,,,,,,, 30. Rule: The number of students is times the number of t. Number of Teachers 1 2 3 4 5 Number of Students 7 14 21 28 35 Saxon Math Intermediate 4 300 Adaptations Lesson 46
LESSON Name 47 Teacher Notes: page 301 Introduce Hint #25 Ways to Show Division. Relating Multiplication and Division, Part 2 Refer students to Division on page 8 in the Student Reference Guide. New Concept Here are three ways to show division: 3 ) 2 7 15 3 15 3 Follow the arrows. Say the greater number (dividend) first. The arrows show the order in which to read the numbers. All show fifteen divided by three. Multiplication and division problems can form fact families. 24 4 6 6 4 = 24 24 4 = 6 4 6 = 24 24 6 = 4 Lesson Practice Divide: a. 49 7 = b. 45 9 = c. 40 8 = d. 6 6 = e. 32 8 = f. 27 3 = Use digits and three different division symbols to show: g. twenty seven divided by nine ) 12 h. twenty eight divided by seven ) 12 Saxon Math Intermediate 4 301 Adaptations Lesson 47
New Concept, continued i. 12 3 4 ) 1 2 ) 1 2 j. Write two division facts using the numbers 36, 4, and 9. = = Written Practice page 304 1. $5.07 Brand B $0.00 Brand A more 2. 20 4 5 ) 12 ) 12 3. 2.3 4. greater than 8420. Even Saxon Math Intermediate 4 302 Adaptations Lesson 47
page 304 5. a. 1 1 2 1.75 6. area 4 ft 8 ft b. words: 7. 8. five dimes 10 0 10 a. fraction b. value a. b. 9. The length of segment PQ is 2 cm. The length of segment PR is 11 cm. How long is segment QR? P 2 cm Q? R 11 cm 10. What segment is perpendicular to AC? 11. 3296 A C B Saxon Math Intermediate 4 303 Adaptations Lesson 47
page 305 12. Circle the families. 13. 95 ( 7 64 ) = 15,000,000 words: = 14. $2.53 $. $. 15. n 5.1 2.3 16. in your head 40 3 n = 17. 51 5 18. 28 7 = 19. 81 9 = 20. 35 7 = Saxon Math Intermediate 4 304 Adaptations Lesson 47
page 305 21. 16 4 = 22. 28 4 = 23. 42 7 = 24. 48 8 = 25. 0 = 26. Which of these does not show 24 5 divided by 4? A 24 ) 4 B 24 4 C 24 4 D 4 ) 2 4 27. Round. a. $12.90 b. 12.9 a. Saxon Math Intermediate 4 305 Adaptations Lesson 47 b.
page 306 28. a. Divide by. Then divide 12 by. The answer is. b. Divide by. Then divide by 2. The answer is. c., the Associative Property apply to division because if the o is changed, then the answer ch. 29. 00$ Canada 30. Round to nearest hundred. 00$ Mexico 991 00$ more 507 Saxon Math Intermediate 4 306 Adaptations Lesson 47
LESSON Name 48 Teacher Notes: page 307 Multiplying Two-Digit Numbers, Part 2 Introduce Hint #26 Multiplication (Carrying on Fingers). For additional practice, students may complete Targeted Practice 48. New Concept Example When multiplying two-digit numbers: 1. Multiply by the ones digit. 2. Write the last digit. 3. Carry the first digit on your fingers. 4. Multiply by the tens digit. 5. Add the carried digit to that product. 6. Write the sum. 2 3 8 4 1. 8 3 = 24 2 3 4. 8 2 = 16 2. Write 4 in the ones column. 8 5. Add the carried 2 to that product. 3. Carry the 2 on your 184 6. Since 16 + 2 = 18, write 18. fingers. Lesson Practice Carry on your fingers to find each product. a. 16 4 b. 24 3 c. $45 6 d. 53 7 e. 35 8 f. 64 9 g. Use money manipulatives, or solve using pencil and paper. $14 3 = Saxon Math Intermediate 4 307 Adaptations Lesson 48
New Concept, continued h. Estimate. gallons 4 = quarts 19 19 gallons = about quarts A liter is slightly larger than a quart. quarts 19 gallons = about liters Written Practice page 310 1. 472 first 2. 42 miles hiked second fewer more in all 3. 15 3 5 4. between 8000 and 8350 ) ) odd 5. 306,020 Circle the families. expanded form: + + words: Saxon Math Intermediate 4 308 Adaptations Lesson 48
page 310 6. Shade 2 1 8. 7. 1 mile = ft See Equivalence Table for Units on page 1 in the Student Reference Guide. 8. Perimeter Add all sides. 9. A meter is cm long. 3 in. 3 in. 6 in. 5 in. cm 54 cm 5 in. 10. Find the length of segment BC. A B C cm 1 2 3 4 5 6 7 8 9 11. 100 + (4 50) = 12. $3.25 + = $. $. Saxon Math Intermediate 4 309 Adaptations Lesson 48
page 311 13. 4 9 14. Carry on your fingers. 33 6 15. 24 5 16. in your head 90 6 17. Carry on your fingers. $42 7 18. $5.06 $2.28 19. 1.45 + 2.70 20. 3.25 1.50 Saxon Math Intermediate 4 310 Adaptations Lesson 48
page 312 21. 14 28 45 36 92 + 47 22. 28 7 = 23. 5 ) 35 24. 6 ) 54 25. 63 7 = 26. A rectangle has an area of 12 sq. in. Which of these could not be the length and width of the rectangle? A 4 in. by 3 in. B 6 in. by 2 in. C 12 in. by 1 in. D 4 in. by 2 in. Saxon Math Intermediate 4 311 Adaptations Lesson 48
page 311 27. 5 (2 7) = (5 2) 7 This shows the Property of Multiplication. 28. ) 29. 39 9 invitations I rounded 39 to. Then I m 9 by. 30. Show 2, 3, 1.5, and 2 1_ 4. 1 2.5 1 4 3 4 Saxon Math Intermediate 4 312 Adaptations Lesson 48
LESSON 49 page 312 Name Word Problems About Equal Groups, Part 1 New Concept Example Azura bought 3 cartons of eggs. There were 12 eggs in each carton. How many eggs does Azura have? There are equal groups (cartons) of 12 eggs. Formula Number in each group Number of groups Total Problem 12 eggs in each carton 3 cartons 36 eggs Azura has 36 eggs. Example Tyrone has 5 cans of tennis balls. There are 3 tennis balls in each can. How many tennis balls does Tyrone have? There are equal groups (cans) of 3 tennis balls. Formula: Number in each group Number of groups = Total Problem: 3 tennis balls in each can 5 cans = 15 tennis balls Tyrone has 15 tennis balls. Saxon Math Intermediate 4 313 Adaptations Lesson 49
Lesson Practice a. There were 8 birds in each flock. b. There are 6 people in each car. There were 6 flocks. There are 9 cars. How many birds were there in all? How many people are there in all? number in each group number of groups number in each group number of groups flocks birds in flock cars people in car birds in all people in all c. A bakery display case contained d. One human hand has 27 bones. 4 dozen muffins. About how many bones are How many individual muffins in two human hands? were in the display case? number in group number of groups 27 bones in hand muffins in dozen dozens muffins in all hands bones in 2 hand Written Practice page 315 1. number in each group number of groups boys in row 2. number in each group number of groups girls in row rows rows boys in all Saxon Math Intermediate 4 314 Adaptations Lesson 49
page 315 3. 375 pounds llama coyote 4. 30 5 6 ) ) more 5. Shade 2 3_ 4. 6. 0 1 2 7. evening What time will it be two and one half hours from the time shown? start time: 30 minutes later: 2 hours later: 11 10 9 8 12 1 7 6 5 2 4 3 8. Shade 7_ 8. 4 cm 2 cm Saxon Math Intermediate 4 315 Adaptations Lesson 49
page 315 9. three million, seven hundred fifty thousand,, Which digit is in the hundred-thousands place? 10. 2.1 1.4 6.7 2.1 2.1 1.4 6.7 +. +... 11. 56 7 = 12. 64 8 = 13. 45 9 = 14. RT = 9 cm ST = 5 cm RS =? R? S 5 cm 9 cm T 15. $3.07 16. 4.78 17. (4 + 3) 64 = $2.28 3.90 = Saxon Math Intermediate 4 316 Adaptations Lesson 49
page 316 18. 7.07 n 4.85 19. c 2.3 4.8 n = c = 20. 403 (5 80) = 21. Divide. 6n = 30 = n = 22. (587 238) + 415 = 23. Carry on your fingers. 45 6 + = 24. 23 7 25. $34 8 26. The radius of a circle is 3 ft. Which of the following is not the diameter of the circle? A 36 in. B 6 ft C 2 yd D 72 in. See page 14 in the Student Reference Guide. 3 ft d 2r Saxon Math Intermediate 4 317 Adaptations Lesson 49
page 316 27. Which of these angles is acute? 28. a. 5 5 = A B b. 9 1 = C D c. 6 ) 0 = 29. number in group number of groups 27 bones in hand hands total hand bones 27 bones in foot feet total foot bones + = total hand bones total foot bones bones in all I used compatible n. Since 26 and 27 are both close to, a reasonable estimate is ( 2) + ( 2) =. There are about bones in two hands. 30. 239 Booker T. Washington Cabrillo total I used compatible n. Since 239 is close to, a reasonable estimate is + = total acres. Saxon Math Intermediate 4 318 Adaptations Lesson 49
LESSON Name 50 Teacher Note: page 317 Review Decimal Arithmetic Reminders Chart on page 9 in the Student Reference Guide. Adding and Subtracting Decimal Numbers, Part 2 New Concept Decimal place value from hundreds to hundredths: hundreds tens ones tenths hundredths. decimal point To add or subtract decimal numbers: 1. Line up the decimal points FIRST. 2. Put zeros in empty spaces. 3. Add or subtract. Example 3.75 12.5 2.47 Line up decimal points. 4.25 2.5 Line up decimal points. 1 1 3.75 12.50 2.47 18.72 Put a zero in the empty space. 3 1 4.25 2.50 1.75 Put a zero in the empty space. Saxon Math Intermediate 4 319 Adaptations Lesson 50
New Concept, continued Activity page 319 Adding and Subtracting Decimals Use your textbook to complete this activity. Lesson Practice a. Which digit in 23.5 is in the tenths place? b. Which digit in 245.67 is in the hundredths place? c. Which digit in 12.5 is in the same place as the 7 in 3.75? Find each sum or difference: d. 4.35 2.6 e. 4.35 2.6 f. 12.1 3.25 4.35. 4.35. 12.1. g. 15.25 2.5 h. 0.75 0.5 i. 0.75 0.7 15. 25. 0.75. 0.75. j. n + 1.5 = 4.75 4. 75 n = Saxon Math Intermediate 4 320 Adaptations Lesson 50
Written Practice page 319 1. number in each group number of groups people in boats boats 2. $6.98 cost $. tax total people in all 3. 620 Claire Ashanti 4. 48 4 12 ) ) more 5. Justin ran the perimeter of the block. 6. 58.7 How far did Justin run? words: 100 yd 50 yd 50 yd 100 yd 7. twelve million, seven hundred fifty thousand,, Which digit is in the hundred thousands place? Saxon Math Intermediate 4 321 Adaptations Lesson 50
page 320 8. 783 217 9. evening What time will it be 9 hours and 30 minutes from the time shown? start time: 30 minutes later: 11 10 9 12 1 2 3 9 hours later: 8 7 6 5 4 10. Change to multiplication: 11. (4 50) 36 = $3.75 + $3.75 + $3.75 + $3.75 = 12. 3.6.0. 13. $4.63 $.0 $.0 + $. Saxon Math Intermediate 4 322 Adaptations Lesson 50
page 320 14. Carry on your fingers. 43 6 15. 54 8 16. 37 3 17. in your head $40 4 18. 4.7.0.0.0.0. 19. $5.00 + $. 20. 7.03. 0 21. n 27.9 48.4 n = 22. 46.2 + c 52.9 23. 24 3 = 24. 36 9 = c = Saxon Math Intermediate 4 323 Adaptations Lesson 50
page 321 25. AB = 5 cm, BC = 4 cm, AC =? 26. Shade 3 3 8. A 5 cm B 4 cm C? 27. 1 minute 58.7 seconds 28. Which is more than one second but less than two seconds? 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2.0 2.25 A 0.15 sec B 1.5 sec C 2.1 sec D 2.15 sec 29. Order from least to greatest. Start at the greatest place value. least,,,, greatest 30. F higher temperature F lower temperature difference Saxon Math Intermediate 4 324 Adaptations Lesson 50
INVESTIGATION 5 Name page 322 Focus on Percents Teacher Notes: Introduce Hint #28 Percent. Introduce Hint #27 Fraction- Decimal-Percent Manipulatives, or use fraction-decimal-percent manipulatives. Refer students to Fraction- Decimal-Percent Equivalents on page 19 in the Student Reference Guide. A part of a whole can be named with a fraction, with a decimal number, or with a percent. 1_ of the square is shaded. 2 0.50 of the square is shaded. 50% of the square is shaded. fifty percent Percent means per hundred 50% = 50 100 Think of percents as fractions with denominators of 100. There is a close relationship between cents and percents. 50 = 1_ of a dollar 50% = 1_ of a whole 2 2 1_ of a dollar = 50 1_ 2 2 50% Shaded 1_ of a dollar = 25 1_ 4 4 25% Shaded 1 10 10 of a dollar = 10 1 10% Shaded Saxon Math Intermediate 4 325 Adaptations Investigation 5
INVESTIGATION 5 continued Naming Percents of a Dollar 1. A quarter is what fraction of a dollar? 2. A quarter is what percent of a dollar? % 3. A dime is what fraction of a dollar? 4. A dime is what percent of a dollar? 5. A penny is what fraction of a dollar? 000 100 6. A penny is what percent of a dollar? 7. A nickel is what fraction of a dollar? 000 100 8. A nickel is what percent of a dollar? Estimating Percents of a Whole 80% full 60% full 40% full 20% full 100% 50% In problems 9 12, estimate to find the best choice for how full each glass is. 9. This glass is about what percent full? A 20% B 40% C 60% D 80% Saxon Math Intermediate 4 326 Adaptations Investigation 5
INVESTIGATION 5 continued 10. This glass is about what percent full? A 25% B 50% C 75% D 100% 11. This glass is about what percent full? A 20% B 40% C 60% D 80% 12. This glass is about what percent full? A 20% B 40% C 60% D 80% Finding the Remaining Percent of a Whole The parts of a whole total 100%. If 25% of this circle is shaded, then 75% is not shaded. 25% 75% 100% 13. If 40% of this circle is shaded, 40% + c% 100% then what percent is not shaded? 14. Seventy-five percent of the 75% figure is shaded. + f% 100% What percent is not shaded? 15. If 80% of the answers were correct, then what 80% + a% 100% percent of the answers were not correct? 16. If the chance of rain is 10%, then what 10% + r% 100% is the chance that it will not rain? Saxon Math Intermediate 4 327 Adaptations Investigation 5
INVESTIGATION 5 continued Comparing Percents to One Half Complete each comparison in problems 17 19. State the reason for your answer. Remember that 50% = 1_ 2. 1 3 1 2 1 3 1 2 1 3 17. 48% 18. 52% 19. 50% 1 2 1 2 1 3 48% is than 50%. 52% is than 50%. 1_ 2 is than 1_ 3. 20. Forty percent of the students in the class were boys. Were there more boys or girls in the class? Explain your answer. 40% boys + % girls 100% students There were more in the class. Since 40% is l than 1_ 2, m than 1_ 2 of the students were girls. Finding 50% of a Number To find 50% (one half) of a number Divide number by 2. Example How many ounces is 50% of a cup? One cup is 8 ounces. Divide by 2. 8 2 = 4 Half of 8 ounces is 4 ounces. Saxon Math Intermediate 4 328 Adaptations Investigation 5
INVESTIGATION 5 continued Answer these questions about 50% of a number. 21. How many eggs is 50% of a dozen? One dozen eggs is eggs. Half of 12 eggs is eggs. 22. How many minutes is 50% of an hour? One hour is minutes. Half of minutes is minutes. 23. How much money is 50% of $10? Half of $10 is. 24. How many hours is 50% of a day? One day is hours. Half of hours is hours. Activity page 325 Percent Use your textbook to complete this activity. Saxon Math Intermediate 4 329 Adaptations Investigation 5