Reducing Fractions, Part 1

Transcription

1 LESSON Name 81 Teacher Notes: page 526 Reducing Fractions, Part 1 Introduce Hint #50 Reducing Fractions (Manipulatives and Shortcuts). Review Tests for Divisibility on page 20 and Fraction Families Equivalent Fractions on page 18 in the Student Reference Guide. New Concept To find equivalent fractions, multiply by a fraction name for = 3 6 To reduce fractions, divide by a fraction name for = 1 2 (3 3 = 1) / (6 3 = 2) If both terms cannot be divided by the same number, the fraction cannot be reduced. 2_ cannot be reduced. 5 Lesson Practice a. Reduce by dividing by 4_ = = b. Which of these fractions cannot be reduced? (Circle one.) A 2 8 B 3 8 C 4 8 D 6 8 Saxon Math Intermediate Adaptations Lesson 81

2 Lesson Practice, continued Add, subtract, or multiply as indicated. Remember to reduce the answers. c = = d = = e = = f. 30 = Rewrite each mixed number with a reduced fraction. (Keep the whole number. Reduce the fraction.) g h i Find each sum or difference. Remember to reduce the answers. j = k = l = Written Practice page highest lowest 2. average 3. 1 ft = in. ( ) + = more 4... Saxon Math Intermediate Adaptations Lesson 81

3 page = prime numbers = 1 4 = + 12, 8. mm of length = width 9. a. 1 4 of members 1 members 4 b. 1 of answer to a. 2 c = members members members a. b. c. 10. rectangle in problem 8 Area = length width 11. Q R S? Draw 3 2. Saxon Math Intermediate Adaptations Lesson 81

4 page ) $ R 40 ) Divide 5280 by 9. Write the answer as a mixed number with a reduced fraction. 18. $10 ($ ) = = 20. Reduce = Convert = = 23. See page 532. A translation B rotation C reflection D slide Reduce. Convert. 24. a. $. collected from each b. total customers paid to company total profit a. b. Saxon Math Intermediate Adaptations Lesson 81

5 page number cube rolled once a. probability of an even number = b. different event with same probability: Probability of an number. 26. Number of Students Books Read Last Year Number of Books a. How many students read 12 books or more? b. How many students read 15 books or fewer? a. b. 27. All s are r, but some r are not s. A R S B R S C S R D R S Saxon Math Intermediate Adaptations Lesson 81

6 page fraction: 15% = Reduce: 5 5 = See page I used c numbers that were multiples of = Saxon Math Intermediate Adaptations Lesson 81

7 LESSON Name 82 Teacher Notes: page 534 Greatest Common Factor (GCF) Introduce Hint #51 Finding the Greatest Common Factor. Review Factors on page 8 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 82. New Concept Example To find the greatest common factor (GCF): 1. List the factors of the smaller number in order. 2. Starting with the largest factor, cross out any factor that does not divide evenly into the larger number. 3. Circle the first number that divides evenly into the larger number. This is the GCF. Find the greatest common factor (GCF) of 8 and List the factors of 8. 1, 2, 4, 8 2. Eight does not divide evenly into 20. Cross 8 out. 1, 2, 4, 8 3. Four divides evenly into 20. Circle 4 and stop. 1, 2, 4, 8 Four is the greatest common factor of 8 and 20. Lesson Practice Find the greatest common factor (GCF) of each pair of numbers: a. 6 and 9 factors of 6: 1, 2, 3, 6 b. 6 and 12 factors of 6:,,, Saxon Math Intermediate Adaptations Lesson 82

8 Lesson Practice, continued c. 15 and 100 factors of 15:,,, d. 6 and 10 factors of 6:,,, e. 12 and 15 f. 7 and 10,,,,,, Reduce each fraction by dividing the terms of the fraction by their GCF. (See problems a, b, and c.) g. 6 9 = h = i = Written Practice page a.m. to 2 p.m. = hours I used c hours dollars = 1? numbers to check my answer. $34.50 is close to. 6 = which is close to. Saxon Math Intermediate Adaptations Lesson 82

9 page Estimate the product. 3., 3452, 3552, 3652,, The height of most cars is about: A 4 to 5 feet B 8 to 10 feet C 40 to 50 feet D 20 to 25 feet Measure yourself compared to a car octagon sides 7. not prime each side = 12 in. perimeter = in. A 11 B 21 C 31 D a. List the factors of the smaller number (20):,,,,, Cross out those that are not factors of the larger number (30). The biggest factor is the GCF. Circle it. b. Divide both by the GCF = a. b. Saxon Math Intermediate Adaptations Lesson 82

10 page of a foot 4 is of =? See page 537. blue to gray A translation B rotation C reflection D flip 11. a. 1 3 of b. 2 of 12 3 is of =? Reduce: 6 12 = Divide both by the GCF. a. b = = Convert. Convert = $40.00 $ $ Saxon Math Intermediate Adaptations Lesson 82

11 page R 6 ) 4 3, = = 24. $ = Simplify. 25. Find the probability that with one spin the spinner will not stop on A. Write the answer as a reduced fraction. B A E C A F D E 26. All r are p, but some p are not r. A B C D R P R P R P P R 27. fraction: 22% = Reduce: = Saxon Math Intermediate Adaptations Lesson 82

12 page a. Soledad b. ft in. 1 0 = 5? Garret needs Heights of the Children Soledad James Garret Which child is exactly 5 feet tall? c. average d. range e. median 29. Mt. Blackburn Mt. McKinley (Mt. Blackburn ) Mt. Foraker (Mt. McKinley 890) I used c numbers = Height (in inches) Saxon Math Intermediate Adaptations Lesson 82

13 LESSON 83 page 539 Name Properties of Geometric Solids Teacher Notes: Introduce Hint #52 Faces on a Cube and Hint #53 Geometric Solids (Manipulatives). Refer students to Geometric Solids on page 17 in the Student Reference Guide. Use geometric solids to illustrate concepts in this lesson. New Concept Math Language A plane figure is a flat shape. Math Language Geometric solids are 3-dimensional shapes. They take up space. Example Geometric Solids Shape Name Cube Rectangular prism Pyramid Cylinder Sphere Cone The flat surfaces of solids are called faces. Two faces meet at an edge. Three edges meet at a vertex. face edge vertex A B D C G AB and CD Parallel Segments remain the same distance apart. CD and CE Perpendicular Segments intersect at right angles. H AG and EH Skew Segments on different faces do not intersect. F E Saxon Math Intermediate Adaptations Lesson 83

14 Lesson Practice Name the geometric shape of each of these real-world objects. a. brick b. soup can c. ice cream cone d. shoebox Use geometric solids for help. e. The pyramid has how many triangular faces? f. How many rectangular faces? g. Edges? h. Vertices? Use the rectangular solid to answer problems i k. i. Name a pair of parallel line segments. j. Perpendicular line segments: k. Pair of skew line segments: K L H M J O I N l. Which figure has faces that are perpendicular to its base? A B C D m. Which figure has six congruent faces? A B C D Saxon Math Intermediate Adaptations Lesson 83

15 Written Practice page time Alycia left: 2. Subtract the largest value coins first. Count hours forward. Count 1_ hour forward quarter dimes? nickels? pennies? 3. twenty-three million, two hundred eighty-seven thousand, four hundred twenty digits:,, 4. a. 1 of 24 3 b. 2 of 24 3 is of =? a. b. 5. prime numbers,,, 6. a. List the factors of the smaller number (4).,, Cross out those that are not factors of the larger number (8). The biggest factor is the GCF. Circle it. b. Divide both by the GCF. 4 8 = Saxon Math Intermediate Adaptations Lesson 83

16 page a. Shape? b. How many faces? 8. Shape of the earth? A circle C sphere B cylinder D plane a. b decimal number 10. distance across a circle A center B circumference C radius D diameter $ w = $ = Reduce. 6 8 = 18. Write the numerator as your answer. 3 4 = = Divide both by the GCF. 3 4 = w = Convert. Saxon Math Intermediate Adaptations Lesson 83

17 page = = = Reduce. Convert = Convert. 24. Age Price a. $4.50 Madison (12) Adults $10.00 $. Douglas (8) Age 9 12 $8.50 $. Mom Under 9 $ $. Dad b. $6.50 after 5 p.m. before 5 p.m. before 5 p.m. saved a. b. 25. Which takes up space? A B C D Saxon Math Intermediate Adaptations Lesson 83

18 page Estimate the area. 14 ft 2 in. 10 ft 3 in. 27. a. Which expense consumes about one third of the budget? b. About what fraction of the budget does food consume? 14 ft 2 in. ft 10 ft 3 in. ft Food Car Utilities Rent Entertainment a. b. 28. perimeter 29. Which transformation? 2.4 cm Rhombus A translation C reflection B rotation D flip 30. See page 545. a. range of the temperatures b. September October warmer or cooler? c. November October warmer or cooler? Saxon Math Intermediate Adaptations Lesson 83

19 LESSON Name 84 Teacher Notes: page 546 Review Hint #37 Average. Mean, Median, Mode, and Range Refer students to Statistics on page 20 in the Student Reference Guide. Review Average on page 9 in the Student Reference Guide. New Concept Statistics Median: the middle number of a set of numbers arranged in order Median middle 1, 3, 4, 4, 5, 6, 6 median = 4 Mode: the number that appears the most often in a set of numbers Mode most 3, 5, 8, 2, 5, 7, 6, 1 mode = 5 Range: the difference between the least and the greatest numbers in a set of numbers Range span 3, 5, 8, 2, 5, 7, 7, 6, = 7 range = 7 Lesson Practice Put the numbers into numerical order first. a. 3, 7, 9, 9, 4 Mean: Median: 3,,,, 9 Mode: Range: b. 16, 2, 5, 7, 11, 13 Mean: Median:,,,,, Mode: Range: Saxon Math Intermediate Adaptations Lesson 84

20 Lesson Practice, continued c. 3, 10, 2, 10, 10, 1, 3, 10,,,,,,, Mean: Median: Mode: Range: d. Name Andrei Raj Althea Mary Bedros Ann Yolanda Age ,,,,,, Mean: Median: Mode: Range: Written Practice page ) $ Shade 1 3. % shaded 3. one kilogram = grams 4. Estimate the product Saxon Math Intermediate Adaptations Lesson 84

21 page At which of these times do the hands of a clock form an acute angle? A 3:00 B 6:15 C 9:00 D 12: least to greatest , 0.01, 1.0, a. List the factors of the smaller number (8). Cross out those that are not factors of the larger number (12). The biggest factor is the GCF. Circle it. b. Divide both by the GCF =,,, a. b. 8. a. 1 4 of 80 = b. 3 of 80 = 4 is of =? a. b = Reduce. 4 6 = Divide both by the GCF. Saxon Math Intermediate Adaptations Lesson 84

22 page Mixed number and decimal $10.00 $ ) R = 16. $ = = = 19. Opposite faces are p. 4 Adjacent faces are p. 20. In rectangle MNOP, which segment is parallel to MN? 21. Which appears to be a right angle? A MP B PO C NO D MO O D M P N O A B A AOB C B BOC C BOD D AOD Saxon Math Intermediate Adaptations Lesson 84

23 page a. $3.10 eggs $0.00 juice $0.00 juice + $0.00 cereal b. average (mean) Milk Milk Milk Milk Apple juice Apple juice Eggs Cereal TOTAL c. median d. mode e. range a. b. c. d. e. 23. Draw the next figure in the pattern, and then count the dots. 24. perimeter in inches fraction: 90% = Reduce: = decimal:. 26. See page 2 in the Student Reference Guide. 212ºF water boils water freezes. Saxon Math Intermediate Adaptations Lesson 84

24 page It takes the moon about 29 1_ days to complete one cycle. Estimate the number of 2 cycles the moon completes in 365 days. Explain. I used c numbers. 365 is about and 29 1_ is about. 2 = 28. Draw a translation of the triangle shifted down 2 units y x See page 552. Write the names of the lakes on the graph. Depth (in feet) Maximum Depth of Lakes 30. area 16 feet 12 feet Saxon Math Intermediate Adaptations Lesson 84

25 LESSON Name 85 Teacher Notes: page 553 Units of Capacity Introduce Hint #54 Measuring Liquids and Capacities of Containers. Refer students to Liquids on page 1 in the Student Reference Guide. Review Equivalence Table for Units on page 1 in the Student Reference Guide. Display reference chart Liquids. New Concept Capacity is the amount of liquid a container can hold. Equivalency Table for Units of Liquid Measure U.S. Customary System 16 oz 1pt 2pt 1qt 4qt 1 gal Metric System 1000 ml 1L A liter is about 2 ounces more than a quart. Lesson Practice a. One fourth of a dollar is a quarter. What is one fourth of a gallon? b. How many pints equal 1 gallon? c. How many milliliters equal 2 liters? L ml 1 0 = 2? d. A cup is one half of a pint. A cup is how many ounces? Saxon Math Intermediate Adaptations Lesson 85

26 Written Practice page Shade all but prime number A prime number can t end in an even number. 5 = percent 3. length in centimeters and in millimeters cm minute = seconds heartbeats seconds =? 0 mm perpendicular to AB A BC B CD C DA D DC D C A B 6. a. List the factors of the smaller number (6). Cross out those that are not factors of the larger number (9). Circle the GCF. b. Divide both by the GCF. 6 9 = a. b. Saxon Math Intermediate Adaptations Lesson 85

27 page a. 1 5 of b. 2 of 60 5 is of 0 0 =? a. b. 8. Find AC. Label the figure. A B C? 9. least to greatest , 0, 0.01, qt pt 1 0 = 4?,,, 11. L ml 1 0 = 3? 12. Divide 100 by 6. Write the answer as a mixed number. Reduce. Saxon Math Intermediate Adaptations Lesson 85

28 page $17.56 $ $. 16. $ R 9 ) $ = 19. Reduce = Divide both by the GCF = = = = Convert. Saxon Math Intermediate Adaptations Lesson 85

29 page Count the 1_ 4 s a. 1 ft = in. Genaro (5 ) + in. Roberta (Genaro 4 in.) in. b. Stan (Roberta + 6 in.) in. a. ft in. b. ft in. 25. Double the previous number. 26. The probability of heads is what fraction? 4,,,, of 50 = , 85, 80, 90, 95, 90, 100 Put the numbers in order. a. range,,,,,, b. The mode is because it is the score that occurs often. c. The median is because it is the score. a. b. c. Saxon Math Intermediate Adaptations Lesson 85

30 page Maya Justin (Maya + 3) Coretta (Justin + 2) 29.,,,,,... a. Draw the next term of the sequence. b. Which transformation describes the change from term to term in this sequence? A translation B rotation C reflection D flip a. b Saxon Math Intermediate Adaptations Lesson 85

31 LESSON 86 page 559 Name Multiplying Fractions and Whole Numbers Teacher Note: For addtional practice, students may complete Targeted Practice 86. New Concept To multiply a fraction and a whole number: 1. Convert the whole number to a fraction. (Write the whole number over 1.) 2. Multiply the fractions. 3. Simplify the answer. Example What number is 2 3 of 4? 2 3 of = 8 3 = Lesson Practice Multiply. Simplify answers when possible. Reverse the order of factors to check your answer. a b c d. What number is 1 of 4? = = = = e. What number is 1 6 of 5? f. What number is 2 of 5? = = Saxon Math Intermediate Adaptations Lesson 86

32 Lesson Practice, continued g. Shade to show 1_ of 4. 3 Written Practice page Draw two horizontal parallel segments. Make the lower segment longer. Connect the ends. 2. Estimate the difference The sum of six and four is ten. 4. L ml 1 = 2? 5. fraction, decimal, and percent shaded 6. a. 1 of b. 2 of is of =? a. Saxon Math Intermediate Adaptations Lesson 86 b.

33 page Which segment names a diameter of this circle? A RS B RT C OS D OT 8. least to greatest Compare each to 1_ , 8 7, 7 16, 6 6, 5 8 S R O T,,,, = Convert of = = Convert Saxon Math Intermediate Adaptations Lesson 86

34 page ) Cancel matching final zeros. 18. $ = = 40 ) a. List the factors of the smaller number (60). Cross out those that are not factors of the larger number (100). Circle the GCF. b. Divide both by the GCF = a. b = Count the 3 _ 4 s. 2 3 = 12 Saxon Math Intermediate Adaptations Lesson 86

35 page a. Shape? b. How many vertices? a. b. 24. a. 12 goal Class Book Club Steven more Student Willis Steven Yuko Kent Beth b. books pages =? Number of Books Read c. median a. b. c. 25. What is the probability of rolling a number under 5? Reduce quart = 1 4 gallon 1 quart = percent of a gallon 1 2 Saxon Math Intermediate Adaptations Lesson 86

36 page quart 1 liter See page 1 in the Student Reference Guide morning evening one day 29.,,,... a. Draw the next term. b. Which transformation describes the change from term to term? A translation B rotation C reflection D slide a. b. 30. A 10 change on the Celsius scale is an 18 change on the Fahrenheit scale Label the blank tick marks. C F Saxon Math Intermediate Adaptations Lesson 86

37 LESSON 87 page 565 Name Using Manipulatives and Sketches to Divide Fractions New Concept Lesson Practice When dividing fractions, you can: Use fraction manipulatives. Make sketches. a. How many one sixths are in one half? b. How many one twelfths are in one third? Find each quotient. Try answering the problems mentally. c = d = How many fourths are in one? e = f = How many thirds are in two thirds? Saxon Math Intermediate Adaptations Lesson 87

38 Written Practice page a. perimeter 10 ft b. Area = length width 2. In which of these numbers does the 1 mean 1? 10 A B C D a. b. 3. least to greatest Find the least and greatest numbers. Then compare the other two. 1, 0, 1 2, 0.3 1_ 2 = qt oz 1 32 =?,,, 5. a. A quarter is what fraction of a dollar? b. one dollar = quarters c. quarters dollars =? 3 a. b. c. 6. fraction, decimal, and percent shaded. Saxon Math Intermediate Adaptations Lesson 87

39 page If a = 3, then 2a + 5 equals which of the following? A 10 B 11 C 16 D Find BC. 1 4 of 84 mm is mm. A B? C = = a. List the factors of the smaller number (20).,,,,, Cross out those that are not factors of the larger number (50). Circle the GCF. b. Divide both by the GCF = a. b of = How many 1 12 s are in 1_ 2? Use fraction manipulatives = Reduce. Saxon Math Intermediate Adaptations Lesson 87

40 page Cancel matching zeros = ) ) $ $ Divide 100 by 8. Write the answer as a mixed number. 21. How many 1_ 8 s are in 1_ 4? Use fraction manipulatives. 22. Count the 2_ 3 s. Reduce. 23. a. Marysville to Red Bluff Marysville to Sacramento Red Bluff 41 Chico 49 more than b. Sacramento to Chico Marysville Sacramento 40 halfway to Marysville still to go a. b. Saxon Math Intermediate Adaptations Lesson 87

41 page eggs cereal a. How many students ate cereal for breakfast? b. How many students ate eggs for breakfast? c. How many students ate both cereal and eggs for breakfast? d. Altogether, how many students ate eggs or cereal or both? e. How many of the 20 students ate neither eggs nor cereal for breakfast? highest lowest 8 greater 26. started eight hours before midnight started 5:32 drove stopped Saxon Math Intermediate Adaptations Lesson 87

42 page studied read total dozen made 4 dozen eaten dozen left 29. Use compatible numbers Use the data on page 571 to make a line graph. Mt. Wilson Temperatures Temperature :00 am 9:00 am noon 3:00 pm 6:00 pm Time Saxon Math Intermediate Adaptations Lesson 87

43 LESSON 88 page 572 Name Transformations New Concept Transformations Name Translation Reflection Rotation Movement sliding a figure in one direction without turning the figure reflecting a figure as in a mirror or flipping a figure over a certain line turning a figure about a certain point y y y rotation translation x reflection x x Rotations can be described by their direction and by their degree. clockwise same direction as clock hands counterclockwise opposite direction as clock hands full turn 360º half turn 180º quarter turn 90º 1 4 turn clockwise 1 4 turn counterclockwise Saxon Math Intermediate Adaptations Lesson 88

44 New Concept, continued Activity page 574 Describing Transformations This activity is optional. Lesson Practice a. Sketch an uppercase letter R after a b. Sketch an uppercase letter R after a reflection in its vertical segment. 180º counterclockwise rotation. Name the transformations that could be used to position triangle A on triangle B. c. y d. y A B r r B A x x e. y f. y A B r, r, A t r, B x x t Saxon Math Intermediate Adaptations Lesson 88

45 Written Practice page Lilah lives 1_ mile from school. How far does she travel each day going to school 4 and back? 1 4mi Home School 2. According to this calendar, what is the date of the first Friday in April 2070? S MARCH 2070 M T W T F S , a. one dollar = dimes. b. dimes dollars 1 1 =? 5. a. b of is of 1 1 =? gallon quart 1 2 gallon quart quart quart Saxon Math Intermediate Adaptations Lesson 88

46 page Which part of a bicycle wheel is most like a radius? tire A rim B spoke C hub D tire spoke rim hub = 0 6 = Reduce Find ST. a. fraction shaded R S? T Reduce. b. percent shaded 1_ 3 of 84 mm is mm. a. b In this drawing, which angle appears to be obtuse? D A A ABC B ABD C BDC D DAB C B Saxon Math Intermediate Adaptations Lesson 88

47 page = = How many 1_ 8 s are in 3 _ 8? Use fraction pieces. 15. a. How many 1_ s are in 1? 4 b. 1 6 = Convert. a. Reduce. b = Reduce = Reduce = 19. $6.57 $ $ = 22. School Schedule Subject Time Reading 8:00 8:50 Math 8:50 9:40 Recess 9:40 10:10 Language 10:10 10:50 Science 10:50 11:30 Lunch 11:30 12:30 a. reading language total b. lunch ends: Count hours forward. Counts minutes forward. a. b. Saxon Math Intermediate Adaptations Lesson 88

48 page ) $ area 30 ft. 30 ft , 1, 1 1 2, 2, 2 1 2, 3,,,, 27. probability of black R R W W W B B B B B B B B B B Reduce. 28. a. See page 16 in the Student Reference Guide. A P T B P T C P T D T P b. ; No p is a t, and no t is a p. 29. area of shaded portion 30. anniversary in. first flight (anniversary 200) 1 in. 3 4 in. 1 2 in. bicycle invented (first flight + 56) Saxon Math Intermediate Adaptations Lesson 88

49 LESSON Name 89 Teacher Note: page 580 Use geosolids to introduce this concept. Analyzing Prisms New Concept A prism is a three-dimensional solid with two congruent bases. Triangular prism 6 vertices 9 edges Rectangular prism 8 vertices 12 edges Trapezoidal prism 8 vertices 12 edges Pentagonal prism 10 vertices 15 edges Hexagonal prism 12 vertices 18 edges Octagonal prism 16 vertices 24 edges Lesson Practice Name each type of prism in a c. a. b. c. d. Look at the prism in problem a. How many perpendicular rectangular faces? Saxon Math Intermediate Adaptations Lesson 89

50 Lesson Practice, continued e. Look at the prism in problem b. How many pairs of parallel faces? f. Look at the prism in problem c. How many edges? g. Is this figure a prism?, because it does not have two p c bases. Written Practice page Thomas Jefferson wrote the Declaration of Independence wrote 25 later became president 2. Greater than or less than a year? a. $ days 1 = 10,000? b. Greater than or less than a year? a. b. 3. Which is divisible by both 4 and 5? Look down the 4s and 5s columns of the Multiplication Table. A 15 B 16 C 20 D 25 Saxon Math Intermediate Adaptations Lesson 89

51 page least to greatest a. one gallon = half gallons 0.5, 3, 1, 0, b. half gallons gallons 1 1 =? a.,,,, b. 6. one million, three hundred fifty-four thousand, seven hundred sixty,, = 6 8. = Reduce. a. fraction shaded (Reduce.) b. percent shaded a. b. 9. a. Shape? b. How many edges? a. b. Saxon Math Intermediate Adaptations Lesson 89

52 page length in centimeters and in millimeters of = cm mm Convert = = = Convert. Simplify. Simplify $10 (57 + $2.48) = = $ = ) Saxon Math Intermediate Adaptations Lesson 89

53 page w = = How many 1 10 s are in 1_ 2? Use fraction pieces. w = = 23. Divide 371 by 10. Write the answer with a remainder. Simplify. 24. Fill in the chart starting with Monty. Age Monty Noah Jenny Dad a. How old is Jenny? b. How old is Jenny s dad? a. b = + = Saxon Math Intermediate Adaptations Lesson 89

54 page A dime is tossed and then a quarter is tossed. List the possible outcomes. Dime heads Quarter tails 28. a. A pint is what fraction of a quart? b. What fraction of a gallon is a quart? c. What fraction of a gallon is a pint? d. The answers to a c show that one half of one fourth equals what fraction? 29. See page 585. and 30. Act it out. triangular faces rectangular faces Saxon Math Intermediate Adaptations Lesson 89

55 LESSON Name 90 Teacher Notes: page 586 Reducing Fractions, Part 2 Review Hint #50 Reducing Fractions (Manipulatives and Shortcuts) and Hint #51 Finding the Greatest Common Factor. Review Factors on page 8, Tests for Divisibility on page 20, and Fraction Families Equivalent Fractions on page 18 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 90. New Concept Example Example To reduce a fraction to lowest terms: 1. Find the GCF of the numerator and denominator. 2. Divide both by the GCF. Reduce 8 12 factors of 8: 1, 2, 4 GCF 8 12 = = 2 3 To write a percent as a reduced fraction: 1. Write the percent as a fraction. 2. Cancel matching zeros. 3. Reduce the fraction. Write 40% as a reduced fraction % = = = 2 5 Lesson Practice Reduce each fraction to lowest terms. Find the GCF first. a = b = c = Saxon Math Intermediate Adaptations Lesson 90

56 Lesson Practice, continued d = e. 12 = f. Cancel matching zeros. 16 Solve. Reduce each answer to lowest terms = g = h = i = Write each percent as a reduced fraction. j. 25% = k. 60% = l. 90% = Written Practice page See page Convert. 1 2 = = a. one gallon = quarts 4.. b. gal qt 1 0 = 6?. 0 a. b. Saxon Math Intermediate Adaptations Lesson 90

57 page decimal, reduced fraction, and percent shaded 6. How many vertices?. 7. Which segment is parallel to AB? 8. Classify triangle BCD by angles. y y D A D A x x C B C B A BC B CD C BD D DA 9. What transformation would move triangle DAB to triangle BCD? = = y D A x C B Convert and reduce. Convert and reduce. r Saxon Math Intermediate Adaptations Lesson 90

58 page = How many 1 10 s are in 2_ 5? Use fraction pieces = 14. Borrow and rename = Reduce = Reduce = = n = = How many 1_ 3 s are in 1? = Convert. n = Saxon Math Intermediate Adaptations Lesson 90

59 page = Extra Credit Magazine report 35 points 26. probability of orange TV report 50 points Book report Museum report 75 points 100 points a. book report 2 magazine reports TV report points earned B B R R R W W W W W O O O O O O b. 400 total earned needs Reduce. a. b. 27. area = 25 in. 2 a. each side b. perimeter a. b. Saxon Math Intermediate Adaptations Lesson 90

60 page ,,,... 3 sides, sides, sides, sides This is a pattern of regular p. The number of sides is i by. 29. a. factors of 16:,,,, b. Is the number of factors odd or even? c. What is the median of the factors? d. What is 16? 30. $24,575 $23,460 I used c numbers. $24,575 is about. $23,460 is about. = Saxon Math Intermediate Adaptations Lesson 90

61 INVESTIGATION 9 Name page 592 Focus on Performing Probability Experiments Teacher Notes: Review Hint #42 Probability and Chance. Each student will need a copy of Lesson Activity 30. A typical dot cube has six faces. Math Language Probability tells how likely something is to happen. It is expressed in fractions. Each time a dot cube is rolled there are 6 possible outcomes. Each outcome is equally likely. The probability of each outcome is 1_ 6. The total of the possible outcomes must add up to one = 6 6 = 1 The probability that the upturned face will be an even number is the sum of the probabilities of rolling a 2, a 4, or a = 3 6 = What is the probability that the upturned face is either 1 or 6? + = Saxon Math Intermediate Adaptations Investigation 9

62 INVESTIGATION 9 continued 2. What is the probability that the upturned face is less than 5? If we rolled our dot cube 24 times, we guess that we would roll a certain number 1_ 6 of 24 times = 4 times 3. If a standard dot cube is rolled 60 times, how many times would you guess that the upturned face will be 1? Explain how you got your answer. Since the outcome 1 can be expected to occur of the time, I divided 60 by. 4. If a standard dot cube is rolled 60 times, how many times would you guess that the upturned face will be either 1 or 6? Explain how you got your answer. Since one outcome can be expected to occur times in 60 rolls, then two outcomes can be expected to occur +, or times. Saxon Math Intermediate Adaptations Investigation 9

63 INVESTIGATION 9 continued Activity 1 page 593 Probability Experiment 1 Use the tallies on Lesson Activity 30 to answer problems Complete the Frequency column on Lesson Activity Which outcome occurred more frequently than you would guess? 7. How many times was the upturned face even? 8. Predict what the next roll would be. Saxon Math Intermediate Adaptations Investigation 9

64 INVESTIGATION 9 continued The table shows the results of 50 spins of the spinner shown above. Outcome Tally Relative Frequency Since 28 > , outcome 2 seems more likely than outcome 1. How does the spinner show the same probabilities? Region is larger than region. Since 17 > , outcome 1 seems more likely than outcome 3. How does the spinner show the same probabilities? Region is larger than region overestimates the true probability of stopping on Region 2 is slightly s than 1_ 2 ( or ) of the spinner. Saxon Math Intermediate Adaptations Investigation 9

65 INVESTIGATION 9 continued Activity 2 page 595 Probability Experiment 2 Complete Activity 2 with a partner. Use Lesson Activity 30 to answer problems Use the tallies to complete the Relative Frequency column on your table. number of tallies Look at your Relative Frequency table. Estimate the probability that you choose a T. 13. If a letter was written once, about how many times would you expect to choose it out of 30? If a letter was written twice, about how many times would you expect to choose it out of 30? 15. If a letter was written three times, about how many times would you expect to choose it out of 30? 16. Which of the letters do you think your partner wrote once? twice? three times? Saxon Math Intermediate Adaptations Investigation 9

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