Simplifying Improper Fractions

LESSON Name 91 Teacher Notes: page 597 Simplifying Improper Fractions Review Fraction Families Equivalent Fractions on page 18 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 91. For additional practice, students may complete Fraction Activity H. New Concept Example 2 10 8 To simplify improper fractions: 10 8 = 1 2 8 1. Convert the improper ( top heavy ) fraction. 2. Add it to the whole number. 3. Reduce as necessary. Convert. Add. 2 + 1 2 8 = 3 2 8 3 2 8 = 3 1 4 Reduce. Activity page 599 Modeling Improper Fractions Use your fraction pieces. Write the mixed number. 1. 1 2 + 1 2 + 1 2 = 2. 3 4 + 3 4 = 3. 5 8 + 5 8 = 4. 2 3 + 2 3 = Saxon Math Intermediate 5 595 Adaptations Lesson 91

Lesson Practice Simplify each fraction or mixed number. Reduce each fraction as much as possible. a. 6 4 1 4 ) 6 b. 10 6 6 ) 10 c. 2 8 6 6 ) 8 1 2 4 = 1 1 2 = = d. 3 10 4 ) e. 10 4 ) f. 12 8 ) = = = g. 4 14 8 ) h. 1 10 8 ) = = Simplify your answers. i. 1 5 6 + 1 5 6 j. 2 3 4 k. 5 3 3 2 = + 4 ) 3 4 ) ) = = l. Each side of this square is 5_ inches long. What is the perimeter of the square? 8 5 8 in. Saxon Math Intermediate 5 596 Adaptations Lesson 91

Written Practice page 600 1. fathoms feetoms 2 2 = 10? 2. $ours hours 6.50 1 =? 4 3. digits one hundred fifty-four million, three hundred forty-three thousand, five hundred fifteen,, 4. Use fraction pieces. a. 4 = 1 b. 4 = 5 a. b. 5. 3 4 = 8 + 5 8 = Convert. 6. mixed number 7. Which segment does not name a radius of this circle? A SO C TS T O R B OR D OT S Saxon Math Intermediate 5 597 Adaptations Lesson 91

page 601 8. 1 2 of 2 2 1 2 9. A pentagonal prism has how many vertices? 10. Label the figure. 11. 1 3 4 + 1 3 4 = A B C D? Convert and simplify. 12. 5 7 8 1 3 8 = 13. 3 3 8 14. $10 ($1.25 + 35 ) = Simplify. 3 8 = Convert. 15. $4.32 5 16. 416 740 17. 4.51 (2.3 + 0.65) = 18. 960 8 = Saxon Math Intermediate 5 598 Adaptations Lesson 91

page 601 19. 80 ) 9 6 0 0 20. 5m = $12.00 21. 5 2 2 3 = Convert and simplify. m = 22. 2 3 1 3 = How many 1_ 3 s are in 2_ 3? Use fraction pieces. 23. 2 3 1 6 = How many 1_ 6 s are in 2_ 3? Use fraction pieces. 24. SumofNumbers 2 3 4 5 6 7 8 9 10 11 12 Number of Ways 1 2 3 4 5 6 5 4 3 2 1 a. How many ways are there to total 6? List the different combinations. + + + + + different ways b. probability of rolling a sum of 7 with 1 toss of 2 number cubes Reduce. number of ways to roll 7 total number of ways to roll any sum = = c. Which outcome is more likely: a sum of 4 or a sum of 9? A sum of is more likely. There are combinations with a sum of, but only combinations with a sum of. Saxon Math Intermediate 5 599 Adaptations Lesson 91

page 602 25. Assuming that the sequence below repeats after every 3 terms, write the next 5 terms. 4, 4, 1, 4, 4,,,,,, 26. Sunday 6 Thursday 8 Monday 6 Friday 6 Tuesday 7 Saturday 8 Wednesday 9 In order: a. median: Median b. mode: Mode c. range: Range middle most span 6,,,,,, 9 d. Find the mean and write it as a mixed number. average 27. Which transformation would move triangle A to the position of triangle B? 5 4 3 y A A translation C reflection B rotation D slide 2 1 0 B x 1 2 3 4 5 28. Range span 29. Reduce. 30. 34 F 1 4 + 1 4 = area = 784 sq ft. Saxon Math Intermediate 5 600 Adaptations Lesson 91

LESSON Name 92 Teacher Notes: page 604 Dividing by Two-Digit Numbers Introduce Hint #55 Long Division, Part 2. Review Hint #40 Long Division, Part 1. New Concept Example Use long division when dividing by two-digit numbers: Divide, multiply, subtract, and bring down. Use zero as a placeholder. Place a digit above each digit. Round the divisor and the dividend before guessing. 32 ) 987 Think 30 ) 900 0 30 R 27 32 ) 987 96 27 Use compatible numbers to estimate division. Example Estimate the answer for 24 ) 868. 1. Pick a number that is close to 24 and easy to work with. 24 is close to 25. 2. Round 868 up to a number that is compatible with 25. 868 rounds up to 875, which is compatible with 25. 3. Think of 875 as 800 + 75. Every 100 is four 25s, so 800 25 = 32. 75 is three 25s, so 75 25 = 3. Since 875 25 = 35, a reasonable estimate for 24 ) 868 is 35. Saxon Math Intermediate 5 601 Adaptations Lesson 92

Lesson Practice Use compatible numbers to estimate problems a and b. a. 253 11 b. 253 21 ) 000 ) 000 Divide: 300 10 240 c. 0 31 ) 4 0 3 d. 0 R 12 ) 2 5 3 e. 0 12 ) 3 0 0 f. 0 R 23 ) 5 1 0 g. 0 12 ) 1 4 4 h. 0 R 30 ) 6 8 2 i. 0 R 32 ) 7 0 9 j. 0 R 43 ) 8 8 0 k. 0 22 ) 9 2 4 l. 0 R 22 ) 7 5 0 m. 0 0 21 ) 1 2 6 n. 0 R 21 ) 6 5 4 o. 0 R 41 ) 9 1 0 p. 0 0 R 21 ) 1 2 9 0 Written Practice page 607 1. Draw a quadrilateral with two horizontal segments that are the same length. 2. 1 hr = min ( ) + = Saxon Math Intermediate 5 602 Adaptations Lesson 92

page 607 3. decimal 3 9 10 4. eggs cartons 24 2 =?. 5. 6. Use fraction pieces. 4 in. 4 in. 4 in. a. How many 1_ s are in 1? 3 b. How many 1_ s are in 4? 3 top layer total cubes 7. Name this shape. How many edges does it have? 8. decimal. reduced fraction percent shaded 9. Which of these numbers does not equal 1_ 2? A 0.5 B 50% C 6 12 D 0.05 Saxon Math Intermediate 5 603 Adaptations Lesson 92

page 608 10. Label the figure. 1_ of 40 mm is mm. 2 AD = 11. 8.70 +.00 A B C D? 12. 12.75 13. 4 3 = 14. 8 $125 =.00 15. 100 64 = 16. 293 13 = 17. 0 R 24 ) 5 1 0 18. 3 5 8 + 1 7 8 = 19. 5 1 2 5 = 20. 1 3 of 5 = Convert and reduce. Convert. 21. 3 4 4 3 = Convert. 22. 6 10 1 5 = How many 1 6 s are in 5 10? Use fraction pieces. 23. 2 5 = 10 + 1 10 = Reduce. Saxon Math Intermediate 5 604 Adaptations Lesson 92

page 608 24. 3 ft 10 in. 2 ft 11 in. Estimate the area. 3 ft 10 in. 2 ft 11 in. 25. likely, unlikely, certain, or impossible? a. All of the upturned faces are heads. b. At least one of the upturned faces is heads. c. There is one more heads than there is tails. a. b. c. 26. 21.81 seconds. 27. a. Describe how to estimate the total cost of the items. What is your estimate? R each price to the nearest and then. $2.00 + b. $2.19 $1.19 $3.87 $1.39 a. c. If the girls share the cost evenly, how much will each girl pay? b. c. Saxon Math Intermediate 5 605 Adaptations Lesson 92

page 609 28. Assuming that the sequence below repeats after 5 terms, write the next 5 terms. 4, 4, 1, 4, 4,,,,,, 29. A graph is an appropriate type of graph for the data because it makes it easy to see the differences in the. 4500 Suspension Bridges (North America) 4000 3500 3000 Length (ft) 2500 2000 1500 1000 500 Bridge 30. How many degrees warmer? maximum minimum Saxon Math Intermediate 5 606 Adaptations Lesson 92

LESSON 93 page 610 Name Comparative Graphs New Concept Example Comparative bar graphs are used to display two or more sets of related data. Math Language A legend shows the names of the different sets of data. Like other bar graphs, comparative bar graphs can be horizontal or vertical. The average daily high temperature in January and July for five cities is displayed in the comparative vertical bar graph below. Temperature ( F) 80 60 40 20 00 Rome, Italy Average Daily High Temperatures Caracas, Venezuela Sydney, Australia Paris, France Tokyo, Japan January July Double-line graphs show how two or more things change in relation to one another. Example The double-line graph below shows the change in population of two cities from 1950 to 2000. Population 700,000 600,000 500,000 400,000 300,000 200,000 100,000 1950 1960 1970 1980 1990 Year 2000 Legend Austin Pittsburgh Saxon Math Intermediate 5 607 Adaptations Lesson 93

Lesson Practice a. Chinara, Alice, Terrell, and Manuel each wrote two stories. The number of paragraphs per story is shown in the table below. Complete the comparative horizontal bar graph to show the number of paragraphs. Student Story 1 Story 2 Chinara 8 8 Alice 3 6 Terrell 6 7 Manuel 7 10 Chinara Alice Terrell Manuel 0 2 4 6 8 10 Number of Paragraphs Story 1 Story 2 b. For a science project, Mia and Lonnie each planted a seed. A record of the height of each seedling is shown below. Week 1 Week 2 Week 3 Week 4 Mia s Seedling 1 cm 5 cm 11 cm 20 cm Lonnie s Seedling 2 cm 4 cm 10 cm 16 cm Display the data in a double-line graph. Height (cm) 20 18 16 14 12 10 8 6 4 2 Legend: Mia Lonnie 1 2 3 4 Week Saxon Math Intermediate 5 608 Adaptations Lesson 93

Written Practice page 613 1. qt pt 1 1 = 2? It weighs how much? 2. Ibs $ 3 $2.55 = 4? 3. 1_ 2 of 300 300 marbles ) 3 0 0 1 2 marbles marbles 4. decimal, reduced fraction, and percent shaded 5. Use fraction pieces. a. How many 1_ s are in 1? 5 b. How many 1_ s are in 3? 5 a.. b. 6. When nine is subtracted from twelve, the difference is three. 7. 2 3 of 3 3 2 3 8. 3n = 18, so n = So 2n = 2 3 3 1 2 1 3 So 2n + 5 = A 23 B 17 C 31 D 14 Saxon Math Intermediate 5 609 Adaptations Lesson 93

page 614 9. edges 10. Which of these angles appears to be a right angle? A AOB C COD B BOC D AOC A B C D O 11. 1 3 5 + 2 4 5 = 12. 4 5 8 1 8 = 13. 6 5 6 1 5 6 Convert. Simplify. 14. 1 1 8 = How many 1_ 8 s are in 1? 15. 8 10 5 10 = 16. 1 5 1 10 = How many 1 10 s are in 1_ 5? Use fraction pieces. Simplify. 17. 12.34 (5.67 0.8) = 18. ($20 $6.55) 5 = 19. 10 56 = Saxon Math Intermediate 5 610 Adaptations Lesson 93

page 614 20. 6 78 900 = 21. 0 R 31 ) 9 7 0 22. 9 2 9 = 23. 3 4 = 0 12 1 6 = + 0 12 24. a. length cm 1 2 3 4 5 b. The rectangle is 1 centimeter longer than it is wide. What is the perimeter of the rectangle? c. area a. b. c. 25. a. Write the next three terms of the repeating sequence below. E,,, E, E,,,,... E E b. The sequence repeats after every terms. c. What transformation is shown in the sequence? 26. a. If you spin this spinner 60 times, about how many times would you expect it to stop on 2? b. What percent of the spinner s face is region 2? c. What decimal part of the spinner s face is region 3? 1 3 2 a. b. c.. Saxon Math Intermediate 5 611 Adaptations Lesson 93

page 615 27. (1889 ) + 28. Estimate the answer for 31 4. About students will be on each team. I used compatible numbers. 31 is close to, which is divisible by 4. = students 29. year today 1756 Mozart was born about years ago. I rounded today s year to and then rounded 1756 to, which is compatible with. = 30. area = 10,000 sq m Enter and press the key. Each side is meters long. Saxon Math Intermediate 5 612 Adaptations Lesson 93

LESSON Name 94 Teacher Notes: page 616 Using Estimation When Dividing by Two-Digit Numbers Review Hint #40 Long Division, Part 1, and Hint #55 Long Division, Part 2. For additional practice, students may complete Targeted Practice 94. New Concept Example Use long division when dividing by two-digit numbers: Use zero as a placeholder. Place a digit above each digit. Round the divisor and the dividend before guessing. 19 ) 595 Think 20 ) 600 0 31 R 6 19 ) 595 57 25 19 6 Lesson Practice a. 0 R 19 ) 7 9 2 Think 20 ) 800. b. 30 ) 6 0 0 Cancel matching zeros. c. 0 0 R 29 ) 1 2 1 Think 30 ) 120. d. 0 R 29 ) 9 0 0 Think 30 ) 900. Saxon Math Intermediate 5 613 Adaptations Lesson 94

Lesson Practice, continued e. 0 R 48 ) 8 2 9 Think 20) 800. f. 0 0 R 29 ) 1 2 1 0 Think 30 ) 1200. g. 0 28 ) 8 9 6 Think 30 ) 900. h. 0 R 18 ) 7 8 2 Think 20 ) 800. i. 0 0 R 39 ) 1 2 0 0 Think 40) 1200. Written Practice page 618 1. prime numbers less than 50 that end with the digit 1 2. 8 = 24 24 8 ) dividend 24,, 3. yd min 660 3 =? 4 4. decimal 4 9 10 5. ) Saxon Math Intermediate 5 614 Adaptations Lesson 94.

page 618 6. a. A dime is what fraction of a dollar? b. one dollar = dimes c. dimes dollars 1 1 =? 4 a. b. c. 7. Which one says 19 ) 786? A 19 786 B 786 19 C 19 786 D 786 19 8. Use fraction pieces. 9. name a. How many 1_ s are in 1? 4 b. How many 1_ s are in 1? 3 a. b. 10. If LN is perpendicular to JM, then JNL is what type of angle? K L A acute B right C obtuse D straight J M N 11. $63.75 $. $. $. Saxon Math Intermediate 5 615 Adaptations Lesson 94

page 619 12. 1010 (101 10) = 13. $3.48 14. 25 2 = 15. 0 R 19 ) 7 8 6 Think 20 ) 8 0 0. 16. 36 + 64 = 17. 0 0 R 38 ) 1 2 0 0 Think 40 ) 1 2 0 0. 18. 5 6 + 5 6 + 5 6 = 19. 5 6 3 = 20. Reduce: 8 12 = Convert and reduce. Convert and reduce. Saxon Math Intermediate 5 616 Adaptations Lesson 94

page 619 21. 3 2 1 4 = 22. 1 3 of 3 4 = Reduce. 23. Write a fraction equal to 2_ that has a denominator of 12. 3 Subtract it from 11 and reduce. 12 11 12 2 3 = 12 12 24. a. 14th b. in. ft 1 1 =? 5 12th On which birthday? grew a. b. 25. a. Which of these terms does not describe 3 ft the figure? 3 ft 1 yd A rectangle C pentagon B parallelogram D regular quadrilateral 1 yd b. perimeter in feet perimeter in yards c. area in square feet area in square yards Saxon Math Intermediate 5 617 Adaptations Lesson 94

page 620 26. a. 1 yd 3 ft b. 1 sq. yd 9 sq. ft 27. 7 8 of the students wore sneakers. 1 7 8 = What fraction did not wear sneakers? My answer is reasonable because whole class, so only a s of the students is almost the fraction of the class did not wear sneakers. is a small fraction of the class. 28. Estimate. 152 4 4 There would be about objects in each room. I used c numbers. 152 is close to and is divisible by 4. 4 = objects. 29. 95ºF 44ºF 30. Don t count October 29. October 30 to October 31 days Number of days in November days December 1 + days Saxon Math Intermediate 5 618 Adaptations Lesson 94

LESSON Name 95 Teacher Notes: page 621 Reciprocals Introduce Hint #56 Reciprocal. Review Fraction Terms on page 19 in the Student Reference Guide. New Concept Reciprocal Flip the fraction. Example 5 6 6 5 4 3 3 4 4 = 4 1 1 4 The product of any number and its reciprocal always equals 1. Example 2 3 3 2 = 6 6 = 1 1 2 2 1 = 2 2 = 1 How many 1_ 2 s are in 1? means 1 1 2. 1 by a fraction = the fraction s reciprocal Example 1 3 4 = 4 3 1 1 2 = 2 (or 2) 1 Lesson Practice Write the reciprocal of each number. Leave improper fractions as improper fractions. a. 4 5 b. 6 5 c. 3 1 d. 7 8 e. 3 8 i. 2 1 f. j. 5 1 1 5 g. 3 10 k. 10 1 h. l. 5 12 1 1 1 m. How many 3_ s are in 1? (Use the reciprocal.) 5 Saxon Math Intermediate 5 619 Adaptations Lesson 95

Lesson Practice, continued n. Divide: 1 4 (Use the reciprocal.) 5 o. Think of a fraction and write it down. Then write its reciprocal. Multiply the two fractions. What is the product? = fraction reciprocal p. Is the following sentence true or false? If the product of two numbers is 1, then the two numbers are reciprocals. Written Practice page 624 1. average 35 Ib 42 Ib 34 Ib 2. Count on your hand. 4 fingers with 3 bones 1 palm with 5 bones total 3. decimal, reduced fraction, and percent shaded 4. Flip. 2 3 =. Saxon Math Intermediate 5 620 Adaptations Lesson 95

page 624 5. a. A quarter is what fraction of a dollar? b. one dollar = quarters c. quarters dollars 1 1 =? 5 6. What is the reciprocal of 3_ 4? What is the product? Flip. 3 4 = a. b. c. 7. Which one says 25 ) 5 0 0? A 25 500 B 500 25 8. a. What is the reciprocal of 6? b. What is the reciprocal of 1_ 4? C 25 500 D 500 25 a. b. 9. Which is an acute angle? K L A LNM B JNL J N M C KNL D KNM 10. ($20 $4.72) 8 = 11. $1.250 160 12. 25.45 (1.4 + 0.28) = Saxon Math Intermediate 5 621 Adaptations Lesson 95

page 625 13. 100 2 = 14. 0 R 31 ) 1 4 0 Think 30 ) 1 4 0. 15. 27x = 567 16. Reduce: 15 25 = 17. 1 5 6 + 1 5 6 = Convert and simplify. x = 18. 4 5 6 1 1 6 = 19. 3 8 = 20. 3 4 5 = Simplify. Convert. Convert and simplify. 21. 9 10 1 10 = How manys 1 10 Use fraction pieces. s are in 9 10? 22. 3 4 = 12 12 1 6 = 12 12 23. Divide 123 by 10 and write the answer as a mixed number. 24. a. perimeter b. area a. Saxon Math Intermediate 5 622 Adaptations Lesson 95 b.

page 625 25. temperature 10 0 C 10 26. 10 0 10 C F 27. 100 36 = 28. Ayanna tossed two standard number cubes. She needs to roll a 12 to win the game. What word best describes her chances of rolling 12 in one try? A certain B likely C unlikely D impossible Saxon Math Intermediate 5 623 Adaptations Lesson 95

page 626 29. a. A S R B S R C S R D R S b. Every s is a r, but some are not s. a. b. 30. Find the area of Denver first. 292.5 sq mi = 139.1 sq mi + area of Denver 292.5 sq mi Fort Worth 139.1 sq mi Denver area of Denver = 67.7 sq mi + area of Honolulu sq mi Denver 67.7 sq mi Honolulu Saxon Math Intermediate 5 624 Adaptations Lesson 95

LESSON Name 96 Teacher Notes: page 627 Using Reciprocals to Divide Fractions Introduce Hint #57 Canceling Fractions. Review Hint #56 Reciprocal. Review Fraction Terms on page 19 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 96. New Concept Example To use reciprocals to divide fractions: 1. Copy the first fraction. 2. Change the to a. 3. Flip the second fraction. 4. Cross cancel (if possible). 5. Multiply across. 2 1 2 3 = 1 2 1 3 2 = 3 1 = 3 1 Example Cross cancel fractions to make multiplying and dividing fractions easier. Canceling fractions is another way to reduce. 1 4 3 8 1 2 4 8 3 = 2 (Cancel the 8 and the 4.) 3 1 Saxon Math Intermediate 5 625 Adaptations Lesson 96

Lesson Practice Copy, change, and flip. If necessary, convert. a. 1 3 1 2 = b. 2 3 3 4 = c. 2 3 1 4 = 1 3 = 2 3 = 2 3 = d. 1 2 1 3 = e. 3 4 2 3 = f. Cross cancel. = = 3 3 4 = = g. 2 1 3 = h. 3 2 3 = i. Cross cancel. = = 10 5 6 = = j. How many 1_ 3 s are in 3_ 4? 3 4 = k. How much of 3_ 4 1 is in _ 3? 1 3 = Written Practice page 629 1. Shade 1 2. Shade 2 3. 2. 1 2 of 1 2 = What percent is that? Saxon Math Intermediate 5 626 Adaptations Lesson 96

page 629 3. Cross cancel. 2 3 of = 4. Estimate the product. 712 490 5. digits ninety-three million, eight hundred fourteen thousand, two hundred,, 6. How many one tenths are there in three? A 1 10 3 B 3 1 10 7. 1 4 = 20 1 5 = + 20 C 1 10 3 10 D 3 10 1 10 8. Copy, change, and flip. 9. Multiples: Think multiplication table. a. 1 = b. 3 = a. b.,,, 10. Cross cancel. 3_ of 10 tons 4 Saxon Math Intermediate 5 627 Adaptations Lesson 96

page 630 11. Label the figure. A B C? D 12. decimal, reduced fraction, and percent 13. Copy, change, and flip. 1 3 1 4 = =. 14. Copy, change, and flip. 15. Copy, change, and flip. 16. m + 1.4 = 3.75 1 4 1 3 = 3 1 2 = = = m = 17. m 1.4 = 3.75 18. 1 10 = 10 100 19. Write your answer with a dollar sign. 20 47 = m = Saxon Math Intermediate 5 628 Adaptations Lesson 96

page 630 20. 568 15 = Think 20 ) 6 0 0 21. 0 R 30 ) 4 2 7 22. 6m = $30.24 m = 23. 5 2 3 1 2 = Cross cancel. 24. 5 1 1 4 + 2 = 25. 100 5 2 2 3 1 2 = 5 = 26. 20, 18, 30, 20, 22, 28, 31, 20, 27, 30, 26, 31, 20, 24, 28 In order: 18,,,,,,,,,,,,,, 31 a. mode b. range c. median Mode most Range span Median middle a. b. c. 27. a. Classify triangle ABD by sides. A b. What single transformation would move triangle ABC to triangle ADC? D C B a. b. Saxon Math Intermediate 5 629 Adaptations Lesson 96

page 631 28. Michelle s birthday July 4 Mio s birthday July 4 + 14 days = July Rusita s birthday Mio s birthday + 6 days = 29. Tyrone 21 miles per gallon Trina 26 miles per gallon 500 21 = 500 26 = 500 = gallons 500 = gallons gallons Tyrone purchased gallons Trina purchased fewer gallons I used numbers. Tyrone purchased about gallons. Trina purchased about gallons. = 30. a. Range span b. metal that melts at coldest temperature c. melting temperature of ruthenium: melting temperature of gold: 1064.43 C I rounded the numbers. = Saxon Math Intermediate 5 630 Adaptations Lesson 96

LESSON Name 97 Teacher Note: page 633 Refer students to Ratio on page 21 in the Student Reference Guide. Ratios New Concept Math Language Ratio a way of comparing numbers by division Ratios can be written as fractions. 12 to 18 is written 12. 18 Reduce ratios like fractions: 12 6 18 6 = 2 3 Do not convert ratios. Leave them as improper fractions. Example There were 12 girls and 16 boys in the class. What was the ratio of boys to girls? boys 1. Write the ratio: 16 girls 12 2. Reduce but don t convert: The ratio of boys to girls is 4_ 3. 16 4 12 4 = 4 3 Lesson Practice There were 20 prairie dogs and 30 jackrabbits in a section of the Texas high plains. a. What was the ratio of jackrabbits to prairie dogs? jackrabbits prairie dogs 114 114 = 114 Reduce but don t convert. 114 b. What was the ratio of prairie dogs to jackrabbits? prairie dogs jackrabbits 114 114 = 114 114 Reduce. Saxon Math Intermediate 5 631 Adaptations Lesson 97

Lesson Practice, continued There were 8 red socks and 10 blue socks in George s drawer. c. What was the ratio of red socks to blue socks? red socks blue socks 114 114 = 114 114 Reduce. d. What was the ratio of blue socks to red socks? blue socks red socks 114 114 = 114 Reduce but don t convert. 114 Written Practice page 635 1. pennies nickels 114 114 = 114 114 2. The sum of one fourth and one fourth is one half. Reduce but don t convert. 3. $4.00 $0.00 $0.00 ) 00 $0.00 She has $ left. I to find the total amount of and divided by. Saxon Math Intermediate 5 632 Adaptations Lesson 97

page 635 4. How many 1_ 8 s are in 1_ 2? 1 2 1 8 Copy, change, and flip. Cross cancel. 5. decimal and reduced mixed number shaded. 6.. 7. a. A quart is what fraction of a gallon?. 0 b. one gallon = quarts c. gallons quarts 1 1 = 4? a. b. c. 8. 2 3 = 15 15 2 5 = 15 15 9. decimal number and fraction 0 10 10. Saxon Math Intermediate 5 633 Adaptations Lesson 97

page 636 10. Copy, change, and flip. 1 2 2 2 1 2 1 2 00 00 00 00 00 00 11. Label the figure. A B? C D 12. Copy, change, and flip. 3 2 3 = = 13. 2 3 3 = = 14. 7 10 + 7 10 = Convert and simplify. 15. 43.15 16. ($10 19 ) 9 = 17. 6 72 = 00.00 00.00 0000.00 Saxon Math Intermediate 5 634 Adaptations Lesson 97

page 636 18. 35 2 = 19. 0 R 24 ) 5 0 0 20. Reduce: 50 100 = 21. 12y = 1224 22. 5 3 4 3 1 3 4 = Simplify. y = 23. 1 1 4 + 1 1 4 + 1 1 4 + 1 1 = 24. Write the missing number as your 4 answer. 3 10 = 100 25. 26. area = 64 sq. in. inch 1 2 each side = in. The opposite of squared is square root. a. length b. perimeter a. b. Saxon Math Intermediate 5 635 Adaptations Lesson 97

page 636 27. 1 of 640 64 28. What are the next three terms in this Fibonacci sequence? 1, 1, 2, 3, 5, 8, 13, 21,,,, 1 + 1 = 1 + 2 = 2 + 3 = 29. a. factors of 64:,,,,,, b. Is the number of factors an odd or even number? c. What is the median of the factors? d. What is 64? 30. stripes stars 123 123 Saxon Math Intermediate 5 636 Adaptations Lesson 97

LESSON Name 98 Teacher Notes: page 638 Introduce Hint #58 Positive and Negative Numbers. Temperature Review Number Line on page 12 in the Student Reference Guide. Review Reference Chart Number Line. New Concept Math Language Positive numbers are greater than zero. Negative numbers are less than zero. Zero is neither negative nor positive. On a number line there are both positive and negative numbers. Negative numbers are written with a minus sign in front. 5 4 3 2 1 0 1 2 3 4 5 negative positive To calculate the difference between a positive temperature and a negative temperature: 1. Find the difference from the positive temperature to 0. 2. Find the difference from the negative temperature to 0. 3. Add the two differences together. Example How many degrees are there between 6 C and 2 C? 1. The difference from 6 C to 0 C is 6. 2. The difference from 2 C to 0 C is 2. 3. Add the differences. 6 + 2 = 8 There are 8 between 6 C and 2 C. 6 4 2 0 2 6 2 4 C Saxon Math Intermediate 5 637 Adaptations Lesson 98

Lesson Practice a. Write the temperature that is twelve degrees below zero on the Fahrenheit scale. b. What temperature is shown on this thermometer? 10 c. If the temperature shown is 14 lower than the high temperature for the day, then what was the high temperature? Count up 14. 0 10 C d. If the temperature falls 3 from the temperature shown, what will the temperature be? Count down 3. Use the table below to answer problems e and f. Daily Temperatures ( C) Day Sun Mon Tues Wed Thurs Fri Sat High ( C) 25 20 32 40 45 30 32 Low ( C) 11 13 15 23 25 15 15 e. What is the median of the low temperatures for the week? List the temperatures from least to greatest.,,,,,, median: f. What is the mean (average) of the high temperatures for the week? mean: Saxon Math Intermediate 5 638 Adaptations Lesson 98

Written Practice page 641 1. cats dogs = 2. Reduce. a. name b. How many faces? a. b. 3. 1.2 miles 4. 10 Start at 2ºF. Count down 5ºF.. 0 10 F 5. A B C D 5 4 3 2 1 0 1 2 3 4 5 a. Which arrow could be pointing to 2 1_ 3? b. Which arrow is pointing to negative three? a. b. 6. person mph trout (person + 10) mph sailfish (trout + 45) mph Saxon Math Intermediate 5 639 Adaptations Lesson 98

page 641 7. K L 8. 6.5 9. 4.26 J N M.. A JNK B KNL +. +. C KNM D LNM 10. 23.45. 11. 0.367. 12. $1.25 7 = 13. 608 750 14. 364 16 = Think 20 ) 4 0 0. 15. $7.20 20 = 16. 3 1 2 + 1 1 2 17. 5 8 15 4 7 15 = 18. 6 1 1 3 19. Identity Property of Multiplication 1 5 7 = 20. 4 of 25 = 5 Cross cancel. 21. Copy, change, and flip. 3 4 2 3 = 3 4 00 00 = Saxon Math Intermediate 5 640 Adaptations Lesson 98

page 642 22. Write the missing number as your answer. 23. Reduce: 30 100 = 7 10 = 100 24. 90 10 a. highest temperature b. lowest temperature 80 0 c. range of temperatures 70 difference from highest temperature to 0 F highest 10 F lowest difference from lowest temperature to 0 + sum of the differences a. b. c. 25. 9 2 + 81 26. a. List the factors of the smaller number (70). Cross out those that are not factors of the larger number (100).,,,, b. 70 100 =,,, a. b. Saxon Math Intermediate 5 641 Adaptations Lesson 98

page 642 27. a. 1 2 1 3 1 2 28. b. 1 2 1 3 1 3 Which transformation moves the first triangle to the position of the second triangle? A translation C reflection B rotation D slide 29. Which of these numbers is a composite number? A 3 B 5 C 7 D 9 30. least to greatest 0.376 0.037 0.38 0.367,,, Saxon Math Intermediate 5 642 Adaptations Lesson 98

LESSON Name 99 Teacher Notes: page 644 Adding and Subtracting Whole Numbers and Decimal Numbers Review Decimal Arithmetic Reminders Chart on page 9 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 99. New Concept Example Line up the decimal points. Fill empty spaces with zeros. Put a decimal point on the back of any whole number. 6.2 + 4.25 + 3 6.20 4.25 + 3.00 13.45 Lesson Practice Find each sum or difference: a. 4.3 b. 12.0 c. 6.4 d. 4.4 e. 5.2 +. +. +.. +.. +. f. 56.4 g. 8.2 h. 9.2 i. 4.75 j. 12.4 +.. +.. +... Saxon Math Intermediate 5 643 Adaptations Lesson 99

Lesson Practice, continued k. Which digit in 24.7 is in the same place as the 6 in 16? l. Compare: 12 12.0 Written Practice page 646 1. girls boys = Cancel the matching zeros. Don t convert. 2. ate total pieces 2 2 = What percent is that? Simplify. 3. pens $ 5 1 =? 4. Slower means more time. 13.8 0013.0 5. decimal and reduced mixed number 6. 10n = 100 X 3 4 n = n 2 =. Saxon Math Intermediate 5 644 Adaptations Lesson 99

page 647 7. one thousand, six hundred twenty and three tenths. 8. 2 ft 11 in. Estimate the area. Area = length width 2 ft 11 in. 6 ft 10 in. 6 ft 10 in. 9. 7 8 10. $7.13 3 4 = 8 11. Label the figure. Q R S? T Saxon Math Intermediate 5 645 Adaptations Lesson 99

page 647 12. 13.4 +. 13. 7.25. 14. 25 16 15. 60 2 = 16. 0 28 ) 9 5 2 17. $18.27 9 = Think 30 ) 1 0 0 0. 18. 4 5 8 + 1 7 8 = 19. 5 2 3 5 1 = 20. 3 4 1 3 = Cross cancel. Convert and simplify. 21. Copy, change, and flip. 3 4 3 = 3 4 = 22. Write the missing number as your answer. 9 10 = 100 23. Reduce: 20 100 = Cross cancel. Saxon Math Intermediate 5 646 Adaptations Lesson 99

page 648 24. Gallons 1 2 3 4 5 Fluid Ounces 128 256 384 512 640 a. Rule: the number of by. b. How many fluid ounces in 8 gallons? ounces in each gallon number of gallons 25. Use digits and symbols to write the temperature that is ten degrees below zero Fahrenheit. 26. 1 3??? 3, 4, 7, 12, 19,, 3, 4, 7, 12, 19,,,,... Saxon Math Intermediate 5 647 Adaptations Lesson 99

page 648 27. A standard number cube is rolled once. a. What is the probability that the upturned face is 3 or less? b. Describe a different event that has the same probability. The upturned face is an number. 28. two billion, six hundred million Expanded notation using powers of 10 See page 506. ( ) + ( ) 29. Which transformation would position triangle A on triangle B? 5 4 3 y A A translation C reflection B rotation D flip 2 1 0 B x 1 2 3 4 5 30. 3 8 + 3 8 = 00 00 Reduce. Saxon Math Intermediate 5 648 Adaptations Lesson 99

LESSON 100 page 649 Name Simplifying Decimal Numbers New Concept Example Get rid of the extra zeros in front and back. Keep the zero in front of the decimal. Don t remove zeros in the middle. 0 2. 0 1 0 0 = 2. 0 1 0 4 2. 0 0 = 0. 4 2 Lesson Practice Simplify each decimal number: a. 0 3. 2 0 = b. 0.320 = c. 32.00 = d. 3.020 = Simplify each answer. e. 3.65 + 6.35 f. 23.16 19.46 g. 4.23 3.18 = = = h. Attach a zero to the end of 2.5 without changing its value.. i. Attach a zero to the end of 6 without changing its value.. Saxon Math Intermediate 5 649 Adaptations Lesson 100

Written Practice page 651 1. carrots peas = 2. rolls $ 10 3.25 =? 3. 3 4 = Cross cancel. 3 4 = percent Reduce. 4. 5. Attach a zero to the end of 8 without changing the value of the number. Use a decimal. a. How many pins form the perimeter? b. How many small squares cover the rectangle? a. b.. 6. a. 7 3 4 b. negative 2 10 A B C D 0 10 7. 5 6 = 12 a. b. 8. m cm 1 = 5? 3 4 = 12 Saxon Math Intermediate 5 650 Adaptations Lesson 100

page 652 9. Find AD. 1 of 40 mm is mm. 2 10. 6.2 0.0 0 +.0 0 A B C D? 11. 10 3 10 2 = 12. 6.37. 13. 234 506 14. 10 $1.75 = 15. $17.50 10 = 16. Write the missing number as your answer. 1 50 = 100 17. Reduce: 40 100 = 18. 6 4 = 19. 16w = 832 w = Saxon Math Intermediate 5 651 Adaptations Lesson 100

page 652 20. 5 9 + 5 9 + 5 9 = 21. 9 10 9 10 = 22. Copy, change, and flip. 2 3 3 4 = Convert and reduce. 23. 3 3 4 = Cross cancel. 24. yd ft 1 = 10? 25. See page 3 in the Student Reference Guide. June (start on Jun. 21) July August September October November December (don t count Dec. 21) + Saxon Math Intermediate 5 652 Adaptations Lesson 100

page 653 26. a. How many faces? b. How many edges? a. b. 27. 10 0 10 C 5º colder than 0ºC 28. have a brother 7 6 have a sister 9 a. How many children have a brother? b. How many have a sister but not a brother? c. The numbers in the circles do not add to 30. What does that mean? children have siblings. Saxon Math Intermediate 5 653 Adaptations Lesson 100

page 653 29. Elapsed Time (in minutes) 0 10 20 30 Distance Traveled (in miles) 0 6 14 22 a. line graph b. miles min 22 30 2 2 = 44 miles min 44 2 2 = 88 A rate of 22 miles in 30 minutes is equal to a rate of 44 miles in minutes and 88 miles in minutes, which is about hours. 30. North Canadian River 1_ of North Canadian River 2 Wisconsin River 1_ of North Canadian River + 30 2 Saxon Math Intermediate 5 654 Adaptations Lesson 100

INVESTIGATION 10 Name page 654 Focus on Measuring Angles Teacher Note: Refer students to Angles on page 15 in the Student Reference Guide. Math Language One way to measure an angle is with degrees. Acute angles measure less than 90. Right angles measure 90. Obtuse angles measure more than 90 and less than 180. Straight angles measure 180. Read 30º as thirty degrees. 30 45 60 Acute angles 90 Right angle 90 120 150 180 Right angle Obtuse angles Straight angle A full circle contains 360º. Activity 1 page 654 Modeling Angles 1. Beginning with your arms extended forward 90 at 0º, raise one arm to form a 90º angle. 2. Beginning with your arms extended forward 180 at 0º, raise one arm up, around, and halfway down to form a 180º angle. Saxon Math Intermediate 5 655 Adaptations Investigation 10

180 0 INVESTIGATION 10 continued 3. Beginning with your arms extended forward at 0º, move one arm up through 90º, down through 180º, and continue around to 360º. 360 Use a protractor to measure angles. Step 1: Step 2: Step 3: Put the center point of the protractor on the vertex of the angle. Put one of the zero marks on one ray of the angle. The other ray passes through the scale. A protractor has two sets of numbers. If the angle is acute, read the smaller number. If the angle is obtuse, read the larger number. 40 140 50 130 60 120 70 110 80 100 90 90 100 80 110 70 120 60 130 50 140 40 Step 3: Then read where the other side passes through the scale. 30 150 150 30 20 160 10 170 0 180 160 20 170 10 Step 2: Position one side here. Step 1: Position vertex here. Saxon Math Intermediate 5 656 Adaptations Investigation 10

180 0 INVESTIGATION 10 continued Activity 2 page 656 Measuring Angles 4. What is the measure of each of these angles? a. b. c. d. Activity 3 page 656 Drawing Angles Protractors can help you draw angles. 1. Use the straight edge of your protractor to draw a long segment. Make a dot at one end. 2. Center the protractor over the dot. Line it up so that the segment passes through the 0º mark. 30 150 40 140 50 130 60 120 70 110 80 100 90 90 100 80 110 70 120 60 130 50 140 40 150 30 20 160 160 20 10 170 170 10 0 180 Saxon Math Intermediate 5 657 Adaptations Investigation 10

180 0 INVESTIGATION 10 continued 3. Find the number that matches the size of the angle you wish to draw (use the correct scale), and draw a dot at that number. 40 50 130 60 120 70 110 80 100 90 90 100 80 110 70 120 60 130 50 140 40 30 150 140 150 30 20 160 160 20 10 170 170 10 0 180 4. Connect the dots to draw the other side of the angle. Draw angles with these measures: 5. 30º Saxon Math Intermediate 5 658 Adaptations Investigation 10

INVESTIGATION 10 continued 6. 90º 7. 110º 8. 70º Angles have interior and exterior measurements. This angle has an interior measurement of 60. 60 Saxon Math Intermediate 5 659 Adaptations Investigation 10

INVESTIGATION 10 continued Extend one of the rays to make a line. exterior interior 60 Two ways to measure an exterior angle: Use a protractor. Use the formula: 180 interior angle = exterior angle Example 180 60 = 120 120 60 Find the exterior angle measurement for the angles in problems 9 11. 9. 15 180 15 = 10. 180 = 11. 130 180 = Saxon Math Intermediate 5 660 Adaptations Investigation 10