Simplifying Improper Fractions

Transcription

1 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 To simplify improper fractions: 10 8 = Convert the improper ( top heavy ) fraction. 2. Add it to the whole number. 3. Reduce as necessary. Convert. Add = = Reduce. Activity page 599 Modeling Improper Fractions Use your fraction pieces. Write the mixed number = = = = Saxon Math Intermediate Adaptations Lesson 91

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

3 Written Practice page fathoms feetoms 2 2 = 10? 2. $ours hours =? 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 = = 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 Adaptations Lesson 91

4 page of A pentagonal prism has how many vertices? 10. Label the figure = A B C D? Convert and simplify = $10 ($ ) = Simplify. 3 8 = Convert. 15. $ ( ) = = Saxon Math Intermediate Adaptations Lesson 91

5 page ) m = $ = Convert and simplify. m = = How many 1_ 3 s are in 2_ 3? Use fraction pieces = How many 1_ 6 s are in 2_ 3? Use fraction pieces. 24. SumofNumbers Number of Ways 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 Adaptations Lesson 91

6 page 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? y A A translation C reflection B rotation D slide B x Range span 29. Reduce F = area = 784 sq ft. Saxon Math Intermediate Adaptations Lesson 91

7 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 ) R ) Use compatible numbers to estimate division. Example Estimate the answer for 24 ) Pick a number that is close to 24 and easy to work with. 24 is close to Round 868 up to a number that is compatible with rounds up to 875, which is compatible with Think of 875 as Every 100 is four 25s, so = is three 25s, so = 3. Since = 35, a reasonable estimate for 24 ) 868 is 35. Saxon Math Intermediate Adaptations Lesson 92

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

9 page decimal eggs cartons 24 2 =? 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 Adaptations Lesson 92

10 page Label the figure. 1_ of 40 mm is mm. 2 AD = A B C D? = $125 = = = R 24 ) = = of 5 = Convert and reduce. Convert = Convert = How many 1 6 s are in 5 10? Use fraction pieces = = Reduce. Saxon Math Intermediate Adaptations Lesson 92

11 page 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 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. $ 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 Adaptations Lesson 92

12 page 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 Suspension Bridges (North America) Length (ft) Bridge 30. How many degrees warmer? maximum minimum Saxon Math Intermediate Adaptations Lesson 92

13 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) 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 Population 700, , , , , , , Year 2000 Legend Austin Pittsburgh Saxon Math Intermediate Adaptations Lesson 93

14 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 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) Legend: Mia Lonnie Week Saxon Math Intermediate Adaptations Lesson 93

15 Written Practice page qt pt 1 1 = 2? It weighs how much? 2. Ibs $ 3 $2.55 = 4? 3. 1_ 2 of marbles ) 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 of n = 18, so n = So 2n = So 2n + 5 = A 23 B 17 C 31 D 14 Saxon Math Intermediate Adaptations Lesson 93

16 page 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 = = Convert. Simplify = How many 1_ 8 s are in 1? = = How many 1 10 s are in 1_ 5? Use fraction pieces. Simplify ( ) = 18. ($20 $6.55) 5 = = Saxon Math Intermediate Adaptations Lesson 93

17 page = R 31 ) = = = a. length cm 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? a. b. c.. Saxon Math Intermediate Adaptations Lesson 93

18 page (1889 ) Estimate the answer for 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 Adaptations Lesson 93

19 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 ) R 6 19 ) Lesson Practice a. 0 R 19 ) Think 20 ) 800. b. 30 ) Cancel matching zeros. c. 0 0 R 29 ) Think 30 ) 120. d. 0 R 29 ) Think 30 ) 900. Saxon Math Intermediate Adaptations Lesson 94

20 Lesson Practice, continued e. 0 R 48 ) Think 20) 800. f. 0 0 R 29 ) Think 30 ) g ) Think 30 ) 900. h. 0 R 18 ) Think 20 ) 800. i. 0 0 R 39 ) Think 40) Written Practice page prime numbers less than 50 that end with the digit = ) dividend 24,, 3. yd min =? 4 4. decimal ) Saxon Math Intermediate Adaptations Lesson 94.

21 page 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 B C D 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 Adaptations Lesson 94

22 page (101 10) = 13. $ = R 19 ) Think 20 ) = R 38 ) Think 40 ) = = 20. Reduce: 8 12 = Convert and reduce. Convert and reduce. Saxon Math Intermediate Adaptations Lesson 94

23 page = of 3 4 = Reduce. 23. Write a fraction equal to 2_ that has a denominator of Subtract it from 11 and reduce = 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 Adaptations Lesson 94

24 page a. 1 yd 3 ft b. 1 sq. yd 9 sq. ft of the students wore sneakers = 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 There would be about objects in each room. I used c numbers. 152 is close to and is divisible by 4. 4 = objects ºF 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 Adaptations Lesson 94

25 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 = The product of any number and its reciprocal always equals 1. Example = 6 6 = = 2 2 = 1 How many 1_ 2 s are in 1? means by a fraction = the fraction s reciprocal Example = = 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 g k h. l m. How many 3_ s are in 1? (Use the reciprocal.) 5 Saxon Math Intermediate Adaptations Lesson 95

26 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 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 Adaptations Lesson 95

27 page 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 B a. What is the reciprocal of 6? b. What is the reciprocal of 1_ 4? C D 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. $ ( ) = Saxon Math Intermediate Adaptations Lesson 95

28 page = R 31 ) Think 30 ) x = Reduce: = = Convert and simplify. x = = = = Simplify. Convert. Convert and simplify = How manys 1 10 Use fraction pieces. s are in 9 10? = = Divide 123 by 10 and write the answer as a mixed number. 24. a. perimeter b. area a. Saxon Math Intermediate Adaptations Lesson 95 b.

29 page temperature 10 0 C C F = 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 Adaptations Lesson 95

30 page 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 sq mi = sq mi + area of Denver sq mi Fort Worth sq mi Denver area of Denver = 67.7 sq mi + area of Honolulu sq mi Denver 67.7 sq mi Honolulu Saxon Math Intermediate Adaptations Lesson 95

31 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 = = 3 1 = 3 1 Example Cross cancel fractions to make multiplying and dividing fractions easier. Canceling fractions is another way to reduce = 2 (Cancel the 8 and the 4.) 3 1 Saxon Math Intermediate Adaptations Lesson 96

32 Lesson Practice Copy, change, and flip. If necessary, convert. a = b = c = 1 3 = 2 3 = 2 3 = d = e = f. Cross cancel. = = = = g = h = i. Cross cancel. = = = = 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 Shade 1 2. Shade of 1 2 = What percent is that? Saxon Math Intermediate Adaptations Lesson 96

33 page Cross cancel. 2 3 of = 4. Estimate the product digits ninety-three million, eight hundred fourteen thousand, two hundred,, 6. How many one tenths are there in three? A B = = + 20 C D 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 Adaptations Lesson 96

34 page Label the figure. A B C? D 12. decimal, reduced fraction, and percent 13. Copy, change, and flip = =. 14. Copy, change, and flip. 15. Copy, change, and flip. 16. m = = = = = m = 17. m 1.4 = = Write your answer with a dollar sign = m = Saxon Math Intermediate Adaptations Lesson 96

35 page = Think 20 ) R 30 ) m = $30.24 m = = Cross cancel = = 5 = , 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 Adaptations Lesson 96

36 page Michelle s birthday July 4 Mio s birthday July days = July Rusita s birthday Mio s birthday + 6 days = 29. Tyrone 21 miles per gallon Trina 26 miles per gallon = = 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: C I rounded the numbers. = Saxon Math Intermediate Adaptations Lesson 96

37 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 Reduce ratios like fractions: = 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 Reduce but don t convert: The ratio of boys to girls is 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 Reduce but don t convert. 114 b. What was the ratio of prairie dogs to jackrabbits? prairie dogs jackrabbits = Reduce. Saxon Math Intermediate Adaptations Lesson 97

38 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 = Reduce. d. What was the ratio of blue socks to red socks? blue socks red socks = 114 Reduce but don t convert. 114 Written Practice page pennies nickels = 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 Adaptations Lesson 97

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

40 page Copy, change, and flip Label the figure. A B? C D 12. Copy, change, and flip = = = = = Convert and simplify ($10 19 ) 9 = = Saxon Math Intermediate Adaptations Lesson 97

41 page = R 24 ) Reduce: = y = = Simplify. y = = 24. Write the missing number as your 4 answer = 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 Adaptations Lesson 97

42 page of What are the next three terms in this Fibonacci sequence? 1, 1, 2, 3, 5, 8, 13, 21,,,, = = = 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 Saxon Math Intermediate Adaptations Lesson 97

43 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 negative positive To calculate the difference between a positive temperature and a negative temperature: 1. Find the difference from the positive temperature to Find the difference from the negative temperature to 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 The difference from 2 C to 0 C is Add the differences = 8 There are 8 between 6 C and 2 C C Saxon Math Intermediate Adaptations Lesson 98

44 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 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) Low ( C) 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 Adaptations Lesson 98

45 Written Practice page cats dogs = 2. Reduce. a. name b. How many faces? a. b miles Start at 2ºF. Count down 5ºF F 5. A B C D 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 Adaptations Lesson 98

46 page K L J N M.. A JNK B KNL C KNM D LNM $ = = Think 20 ) $ = = Identity Property of Multiplication = of 25 = 5 Cross cancel. 21. Copy, change, and flip = = Saxon Math Intermediate Adaptations Lesson 98

47 page Write the missing number as your answer. 23. Reduce: = 7 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 a. List the factors of the smaller number (70). Cross out those that are not factors of the larger number (100).,,,, b =,,, a. b. Saxon Math Intermediate Adaptations Lesson 98

48 page a b 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 least to greatest ,,, Saxon Math Intermediate Adaptations Lesson 98

49 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 Lesson Practice Find each sum or difference: a. 4.3 b c. 6.4 d. 4.4 e f g. 8.2 h. 9.2 i j Saxon Math Intermediate Adaptations Lesson 99

50 Lesson Practice, continued k. Which digit in 24.7 is in the same place as the 6 in 16? l. Compare: Written Practice page 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 decimal and reduced mixed number 6. 10n = 100 X 3 4 n = n 2 =. Saxon Math Intermediate Adaptations Lesson 99

51 page one thousand, six hundred twenty and three tenths ft 11 in. Estimate the area. Area = length width 2 ft 11 in. 6 ft 10 in. 6 ft 10 in $ = Label the figure. Q R S? T Saxon Math Intermediate Adaptations Lesson 99

52 page = ) $ = Think 30 ) = = = Cross cancel. Convert and simplify. 21. Copy, change, and flip = 3 4 = 22. Write the missing number as your answer = Reduce: = Cross cancel. Saxon Math Intermediate Adaptations Lesson 99

53 page Gallons Fluid Ounces 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 ??? 3, 4, 7, 12, 19,, 3, 4, 7, 12, 19,,,,... Saxon Math Intermediate Adaptations Lesson 99

54 page 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? y A A translation C reflection B rotation D flip B x = Reduce. Saxon Math Intermediate Adaptations Lesson 99

55 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 = = Lesson Practice Simplify each decimal number: a = b = c = d = Simplify each answer. e f g = = = 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 Adaptations Lesson 100

56 Written Practice page carrots peas = 2. rolls $ =? = Cross cancel. 3 4 = percent Reduce 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 b. negative 2 10 A B C D = 12 a. b. 8. m cm 1 = 5? 3 4 = 12 Saxon Math Intermediate Adaptations Lesson 100

57 page Find AD. 1 of 40 mm is mm A B C D? = $1.75 = 15. $ = 16. Write the missing number as your answer = Reduce: = = w = 832 w = Saxon Math Intermediate Adaptations Lesson 100

58 page = = 22. Copy, change, and flip = Convert and reduce = 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 Adaptations Lesson 100

59 page a. How many faces? b. How many edges? a. b 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 Adaptations Lesson 100

60 page Elapsed Time (in minutes) Distance Traveled (in miles) a. line graph b. miles min = 44 miles min = 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 Saxon Math Intermediate Adaptations Lesson 100

61 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 Acute angles 90 Right angle 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 Adaptations Investigation 10

62 180 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 Step 3: Then read where the other side passes through the scale Step 2: Position one side here. Step 1: Position vertex here. Saxon Math Intermediate Adaptations Investigation 10

63 180 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 Saxon Math Intermediate Adaptations Investigation 10

64 180 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 Connect the dots to draw the other side of the angle. Draw angles with these measures: 5. 30º Saxon Math Intermediate Adaptations Investigation 10

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

66 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 = Find the exterior angle measurement for the angles in problems = = = Saxon Math Intermediate Adaptations Investigation 10