Fractions, Decimals, and. Percent. Name. A part of a whole can have different names. Fractions, decimals, and percents are three ways to name

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1 LESSON Name 71 Teacher Notes: page 457 Review Hint #17 Percent. Fractions, Decimals, and Percents Review Fraction-Decimal-Percent Equivalents on page 19 in the Student Reference Guide. Review reference chart Fraction- Decimal-Percent Equivalents. New Concept A part of a whole can have different names. Fractions, decimals, and percents are three ways to name part of a whole. Fraction Decimal Percent 1_ of the circle is shaded. 0.5 of the circle is shaded. 50% of the circle is shaded. Fractions, decimals, and percents all have numerators and denominators. Part of a Whole 1 Rules to Find Denominator The denominator of a fraction can be any number (except 0) and is expressed as a fraction. 0.5 The denominator of a decimal number is shown by the number of digits to the right of the decimal point. One digit to the right means a denominator of 10. Two digits to the right means a denominator of 100. Three digits to the right means a denominator of % The denominator of a percent is always 100. Math Language Both 5 10 and are equal to 1. To write a decimal or a percent as a fraction, find the denominator. 0.5 = % = Remember that your fraction pieces have the fraction name, decimal name, and percent name printed on them. Saxon Math Intermediate Adaptations Lesson 71

2 New Concept, continued Activity 1 page 459 Using Fractions and Decimals Use your textbook to complete this activity. Activity page 460 Writing Fractions, Decimals, and Percents Use your textbook to complete this activity. Lesson Practice Use fraction pieces to answer the problems. Remember to write the percent symbol in percent problems. a. Shade 5% of the circle. b. Write both 0% and 0. as fractions. The denominator of a percent is % = One digit to the right means a denominator of 10. What decimal part of the circle did 0% = you shade?. c. This square is divided into 100 d. Refer to problem c. equal parts, and 33 parts are shaded. Write the shaded portion as a fraction, as a percent, and as a decimal. Compare: How did you determine the comparison? fraction: 0.33 is l than 1_ 3 because 3 times 33 parts is percent: parts, which is decimal:. than the whole square. Saxon Math Intermediate Adaptations Lesson 71

3 Written Practice page $7.98 $.. (6 ) = Martin 4. half-dollars = $1 sister (Martin ) 5 dollars next year (sister + 1) Since Martin is t as old as his sister, I used the equation half-dollars in $1 half-dollars in $5 m =. 5. rolls 40 each + 6. factors of 7:, How many factors are there? Saxon Math Intermediate Adaptations Lesson 71

4 Written Practice, continued page not equal to 1_ A B C D Faster means fewer seconds. Allison Amy 1_ of 60 seconds 8.7 seconds Half a minute is equal to seconds, and 8.7 seconds is l than seconds. was faster because she swam for fewer seconds. 9. mixed number and decimal number 10. thousandths place See page 1 in the Student Reference Guide. 1. 4_ 5 of a dollar 100 ) Saxon Math Intermediate Adaptations Lesson 71

5 Written Practice, continued page Find AC. Label this figure with the information you know. A B C ? 15. $5.37 $8.95 $ $ $60.10 $ $ $ $ $ $ = ) = 3. Borrow and rename = Saxon Math Intermediate Adaptations Lesson 71

6 Written Practice, continued page a. Find the function. They are saving $ from their earnings. b. Use your rule from part a to solve. Total Amount Earned Earnings Left After Savings $1 $10 $9 $7 $8 $6 a. b. 5. Remember to write the dollar or cent sign. or 6. 1, 3, 9, 7,,, Is the sequence arithmetic or geometric? See page probability 8. Write as unreduced fractions. a. yellow b. not yellow G P P R R R Y Y Y Y a. 0.4 = 40% = b. 9. Perpendicular is square corners. 30. Round to the nearest ten. and are both names for parallelograms Round 1461 to and 14 to, and then s. with perpendicular sides. = years Saxon Math Intermediate Adaptations Lesson 71

7 LESSON Name 7 Teacher Notes: page 464 Review Hint #39 Area and Perimeter Vocabulary. Area, Part 1 Review Perimeter, Area, Volume on page 17 in the Student Reference Guide. New Concept To find the area of a rectangle, use this formula: Math Language The area is the number of square units needed to cover a surface. A = l w (Area = length width) Cover is a keyword for area. Label area as square units. The abbreviation for square is sq. Activity page 466 Using Area Models This activity is optional. Example in. Area = l w Area = 3 in. in. = 6 sq. in. 3 in. To estimate the area of a rectangle, round the length and width before multiplying. Example 14 ft 3 in. 1 ft 8 in. 14 ft 3 in. 14 ft 1 ft 8 in. 13 ft 18 sq. ft Saxon Math Intermediate Adaptations Lesson 7

8 Lesson Practice What is the area of each rectangle? a. b. 3 cm 3 ft 3 ft 4 cm c. d. in. m 5 in. 1 m Use the information below to answer problems e g. Lola s bedroom is 10 feet wide and 1 feet long. 10 ft 1 ft e. What is the perimeter of Lola s bedroom? P = l + w f. Circle the unit used to show the area of Lola s bedroom. square feet or cubic feet g. What is the area of Lola s bedroom? A = l w h. Estimate the area of the classroom floor. Measure the length and width of your classroom to the nearest foot. Saxon Math Intermediate Adaptations Lesson 7

9 Written Practice page juice boxes. boxes cents each 40 = t total cost c price per box $10.00 total cost 4c = c = t = 3. 4, 5, 8, 9, 1, 13,,,, 4. To find 1_, divide by 3. 3 ) 4, 1 3 5, 8, 9, 1, 13,,,,... Use your fraction-decimal-percent pieces. 3 = percent 5. 1 meter = 100 centimeters meters = centimeters words: Saxon Math Intermediate Adaptations Lesson 7

10 Written Practice, continued page Write a fraction as your answer. 1 = 1 8. factors of 16:,,,, 9. See page 1 in the Student Reference Guide Which digit is in the ones place? Write the quotient as a mixed number = 1. Find FG. Label this figure. 13. $10.35 $. F? G H $. $. + $. 14. $80.00 $ $ short division 7 ) $ Saxon Math Intermediate 5 47 Adaptations Lesson 7

11 Written Practice, continued page Cancel matching zeros. 60 ) ) m = 6000 ) = m = 1. Borrow and rename = = 4. Borrow and rename = 5. This rectangle is half as wide as it is long. What is the perimeter of the rectangle? cm Area = length width Saxon Math Intermediate Adaptations Lesson 7

12 Written Practice, continued page Label the spinner. A = 1 B = 1 4 C = D 8. Graph the data Average Annual Precipitation 10 Amount (inches) Albuquerque, NMCity and State 9. Round to the nearest dollar. milk.59 bread.39 cereal 4.89 juice.39 vitamins eggs 1.99 butter.9 a. 30. Count forward by minutes. b. c. Saxon Math Intermediate Adaptations Lesson 7

13 LESSON Name 73 Teacher Note: page 47 Adding and Subtracting Decimal Numbers Refer students to Decimal Arithmetic Reminders Chart on page 9 in the Student Reference Guide. New Concept Example To add or subtract decimal numbers: 1. Line up the decimal points.. Fill empty spaces with zeros. 3. Add or subtract digits with the same place value Sometimes you will need to use rounding or compatible numbers to add or subtract decimal numbers. Example Rounding: Compatible numbers: We rounded both numbers to the We used 8.63 because it s compatible nearest half. with and close to Saxon Math Intermediate Adaptations Lesson 73

14 Lesson Practice Add. Fill empty spaces with zeros. a b c Subtract. d e f Line up the decimal points and solve. Show your work. g = h = i. Estimate the perimeter of this square..4 cm j. The distance from Rodrigo s house to school is 0.8 mile. How far does Rodrigo travel going from his house to school and back again? Home 0.8 mi School Saxon Math Intermediate Adaptations Lesson 73

15 Written Practice page $ brother 18 Ling ( 1_ of brother ) sister (Ling ) ( ) = Ling s sister is years old to 4. Area = length width back 40 ft total 30 ft a. b. 5. Shade these circles of 1 4 = 8 = percent 1 4 = percent Think of quarters. Saxon Math Intermediate Adaptations Lesson 73

16 Written Practice, continued page Find BC. Label the figure. A B? C 8. Write the length and the units in words. 9. factors of 16:,,,, Cross out the numbers that are not factors of 0. cm 1 3,, 10. 3y = 1, so y must equal. Now what does y equal? Fill empty spaces with zeros. 13. $ Add digits with the same place value. 15. $ $0.70 Saxon Math Intermediate Adaptations Lesson 73

17 Written Practice, continued page ) $ ) $ w = = = = w = 4. a. 1 hrs 1 1 hrs b. $5.50 total hours worked per hour 5. Type of Exercise Frequency Bicycle riding 5 Roller-skating 7 Soccer 6 Swimming 10 Walking 5 Basketball Aerobics 4 paid in all First, I a the hours that Morgan worked, and then I m h the total number of by his hourly rate. a. What fraction of the 39 girls chose swimming? b. What fraction of the girls did not choose bicycle riding or rollerskating? Find the fraction of girls who did choose bicycle riding and roller-skating. Then subtract from a. b. a. b. Saxon Math Intermediate Adaptations Lesson 73

18 Written Practice, continued page Estimate the area. 10 ft 3 in. 7. $ $ 10 ft 3 in. ft tip is 1_ of that 5 Area = length width 8. Draw a rhombus that has a right angle. See pages 15 and 16 in the Student Reference Guide. 9. 7:59:10 is written in hour: minute: second form. + Hours Minutes Seconds Regroup more than 60 minutes as an hour. 30. Sketch a line graph to display the data from the table. Hourly Temperatures on Monday Time Temperature ( F) 86 Hourly Temperatures on Monday 8:00 a.m. 64 9:00 a.m :00 a.m :00 a.m. 69 1:00 p.m. 7 Temperature ( F) 1:00 p.m. 76 :00 p.m. 80 3:00 p.m :00 am 9:00 am 10:00 am Time Saxon Math Intermediate Adaptations Lesson 73

19 LESSON Name 74 Teacher Note: page 479 Review Equivalence Table for Units on page 1 in the Student Reference Guide. Units of Length New Concept Use the tables below to help convert units of length. Equivalence Table Units of Length U.S. Customary System Metric System 1 in. 1 ft 10 mm 1 cm 3 ft 1 yd 1000 mm 1 m 580 ft 1 mi 100 cm 1 m 1760 yd 1 mi 1000 m 1 km A meter is about 3 inches longer than a yard. 1 yd 1 yd 1 ft 1 ft 1 ft 3 ft 1 in. 1 in. 1 in. 36 in. Example Two yards is how many inches? yd in.? = Two yards equals 7 inches. To estimate equivalent lengths, round or use compatible numbers. Example About how many meters is 197 centimeters? The chart shows that 100 centimeters is the same length as 1 meter. Round 197 centimeters to 00 centimeters. Then divide by centimeters 100 = meters Saxon Math Intermediate Adaptations Lesson 74

20 Lesson Practice a. How many yards are in one fourth of a mile? To find 1_, divide by _ of 1760 = 4 b. Fifty millimeters is how many centimeters? Multiply the loop. Divide by the outside number. cm mm 1 1 =? 50 c. Dyami s height is 5 feet 1 inch. How many inches tall is he? 1 ft = in. ( ) + = d. A 10K race is a 10-kilometer race. How many meters is 10 kilometers? km m 1 1 = 10? e. The length of a pencil is best measured in. A centimeters B meters C kilometers D feet f. The height of a skyscraper is best measured in. A skyscraper is a very tall building. A inches B feet C miles D centimeters Saxon Math Intermediate 5 48 Adaptations Lesson 74

21 Written Practice page (6 ) 1 = price per pound pounds ) $3.43 total cost 7g = g = 5. Multiply the loop. mc cm 1 1 =? 6. Split the difference. Name the point: as a fraction words: as a decimal Saxon Math Intermediate Adaptations Lesson 74

22 Written Practice, continued page Multiply the loop. yd in. 1 1 = 3? 9. Find ST. Label the figure. R S? T Fill empty spaces with zeros $ ) $ = = 19. $1.00 $. $. $. $. $. + $ Write the quotient as a mixed number = Saxon Math Intermediate Adaptations Lesson 74

23 Written Practice, continued page Write a decimal number that is equal to.5 and has three decimal places. See Example 1 on page a. perimeter of square = 4 side length perimeter = 4 in. each side = in.? b. Area = length width area = area = a. b. 3. Grapes Grapes Per Pound Per Pound 4. Tyler Ramona Valley W N E a. Which street runs straight north and south? b. Which street is parallel to Ramona? Garvey S c. Which street is neither perpendicular nor parallel to Garvey? 5. a. b. Z, X, Y, T,,,... c. OPQRSTUVWXYZ Saxon Math Intermediate Adaptations Lesson 74

24 Written Practice, continued page a. One foot is what fraction of a yard? b. One foot is what percent of a yard? 7. Shade 1_. 1 = percent a. b Morning time is Evening time is : : From the morning time to noon is hours and minutes. From noon to the evening time is hours and minutes. hours minutes + hours minutes hours minutes 9. hummingbird degrees cooler mile = yards ) crocodile To find 1_, divide by 4. 4 Saxon Math Intermediate Adaptations Lesson 74

25 LESSON Name 75 Teacher Notes: page 485 Introduce Hint #45 Improper Fractions. Changing Improper Fractions to Whole or Mixed Numbers Review Mixed Numbers and Improper Fractions on page 18 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 75. New Concept A proper fraction is less than 1. An improper fraction is equal to or greater than 1. Less than 1 Equal to 1 Greater than Proper fraction Improper fractions To convert an improper fraction: 1. Divide the denominator (bottom number) into the numerator (top number).. Write the remainder as a fraction. 3. If necessary, add the mixed number to the whole number. Example Convert the improper fraction. 6 1 R1 + ) = 7 1 Write the remainder as a fraction. Add the mixed number to the whole number. Think of improper fractions as top heavy fractions. Saxon Math Intermediate Adaptations Lesson 75

26 Lesson Practice Convert each improper fraction. You may use fraction pieces. a. = ) b. 5 = ) c. 5 3 = ) d. 9 4 = ) e. 3 = ) f. 3 3 = ) g. 6 3 = ) h = ) i. 4 = ) j. 4 3 = ) k. 7 3 = ) l = ) Add. Simplify each answer. m = n = o = p = q. What is the perimeter of a square with sides 1_ inches long? 1 in. Written Practice page $0.49 $.10 $.39 $.39. Find the average ) Saxon Math Intermediate Adaptations Lesson 75

27 Written Practice, continued page Arrange from least to greatest.,,, 4. largest greatest least even difference 5. mixed number and decimal number Write 4.5 with the same number of decimal places as 6.5. See Example 1 on page Split the difference. Name the point: 0 1 as a mixed number. as a decimal number kilometer = meters km m 1 = 5? Multiply the loop. Saxon Math Intermediate Adaptations Lesson 75

28 Written Practice, continued page Find PR. P Q R Label the figure.? I can check my answer using the 1. Fill empty spaces with zeros equation + = Add digits with the same place value d = $ Associative Property of Multiplication = +. d = = 18. $ $10.00 $. $. $. + $. Saxon Math Intermediate Adaptations Lesson 75

29 Written Practice, continued page = = = Convert. Convert. Convert. 3. Perimeter = 4 side length 1 in. Find the perimeter in inches. Each side is what percent of the perimeter? 4. Area = length width a. Find the area in square feet. b. Find the area in square inches. a. b. 5. A rhombus has four congruent sides. 6. median middle mode most range span Day Miles Monday 41 Tuesday 67 Wednesday 13 Thursday 44 Friday 5 Saxon Math Intermediate Adaptations Lesson 75

30 Written Practice, continued page Use the graph to answer parts a c. Average Summer Temperatures in Portland, ME a. range span greatest temperature lowest temperature range b. How many months have an average temperature greater than 70ºF? Temperature (F) June July August Month c. July 47 lower January a. b. c. 8. Name the coin that is equal to half of a half-dollar. 9. Use a centimeter ruler to measure. a. Perimeter = l + w b. Area = length width a. b. 30. Richard 7 hours Detrina 3 more hours than Richard Pat hours less than Detrina A B 7 (3 + ) C (7 + 3) D 7 3 Saxon Math Intermediate 5 49 Adaptations Lesson 75

31 LESSON 76 Name page 491 Multiplying Fractions Teacher Note: For additional practice, students may complete Targeted Practice 76. New Concept To multiply fractions, multiply across. Example = = 8 15 Of is a keyword for multiplication. Example What fraction is one half of three fourths? one half of three fourths is three eighths = 3 8 Lesson Practice a. A semicircle is one half of a circle. Shade one half of the semicircle below. The shaded part of the semicircle shows that 1_ of 1_ is what fraction? 1 of 1 = 1 1 = b. A penny is what fraction of a dime? A penny is 1. A dime is 10. A dime is what fraction of a dollar? A dollar is 100. A penny is what fraction of a dollar? The answers above show that 1 of 1 10 is what fraction? 10 = Saxon Math Intermediate Adaptations Lesson 76

32 Lesson Practice, continued c. What fraction is three fourths of one half? = d. What fraction is one half of one third? = e. What fraction is two fifths of two thirds? = f = g = h. 3 3 = i. 1 = j. Half of the students were girls. One third of the girls wore red shirts. What fraction of the students were girls wearing red shirts? k. What is the area of a square with sides 1_ inch long? Written Practice page miles first day m second day total. 57 miles in 3 days 3m = 17 + m = m = m = Saxon Math Intermediate Adaptations Lesson 76

33 Written Practice, continued page List the factors of 6:. 0,,, Cross out the numbers that are not factors of 1..,,, 5. 3n = 18, so n must equal. 6. Area = length width What does n equal? 10 cm Arrange from least to greatest. Use fraction pieces. Compare each to 1_ ,,,, 9. a. 1_ of ) 6 4 b. 1_ of answer to part a 1 ) c. 1_ of 1_ = d. What percent of the squares had checkers on them? a. b. c. d. Saxon Math Intermediate Adaptations Lesson 76

34 Written Practice, continued page Find AB. Label the figure. A? B C 11. Fill empty spaces with zeros Subtract digits with the same place value m = $ m = w = $ w = = Convert = Convert of 3 5 = = 1. Multiply across =. Multiply across = Saxon Math Intermediate Adaptations Lesson 76

35 Written Practice, continued page Number of Concert Tickets Cost $35 $70 $105 $140 a. M the number of t by $. b. Use your answer to part a to find the total cost of 10 tickets. a. b. 4. Area = length width 3 8 in. 3 4 in. 5. a. Which number on the spinner is the most unlikely outcome of a spin? a. area = = 4 1 b. This rectangle s sides are twice the length of the rectangle s sides above. 3 Label the sides with lengths and units. b. Which outcomes of a spin have probabilities that are greater than 1_ 4? a. b. a. b., 6. a. A nickel is what fraction of a quarter? b. A quarter is what fraction of a dollar? c. A nickel is what fraction of a dollar? d. The answers to a c show that one fifth of one fourth is what fraction? a. b. c. d. Saxon Math Intermediate Adaptations Lesson 76

36 Written Practice, continued page factors of 100:,,,,,,,, 8. Use the data in the table to make a pictograph. Goals Scored by Soccer Teams Team Name Goals Goal Diggers 0 Buckies 16 Legends 15 Hornets 1 Goals Scored by Top Four Teams Teams Goals Key: goals 9. The colder temperature is farther away from 0ºF. 40 The colder temperature is range = span ºF Range between 80ºF and 47ºF is ºF. 80 F 30. Luis started 3 seconds after Jaxon. Luis finished 1 second before Jaxon. Jaxon s time was 3 seconds. Jaxon s time 10 seconds before and after seconds (Luis s time) Since Luis ran for seconds l than Jaxon, I can s 4 seconds from Jaxon s time. Saxon Math Intermediate Adaptations Lesson 76

37 LESSON Name 77 Teacher Notes: page 498 Converting Units of Weight and Mass Introduce Hint #46 Gram/Kilogram Manipulatives. Review Equivalence Table for Units on page 1 in the Student Reference Guide. New Concept Units of mass in the metric system: 1 mg 1 g 1 kg wing of a housefly paper clip pair of shoes 1 metric ton a small car Units of weight in the U.S. Customary System: 1 oz 1 lb 1 ton slice of bread a shoe a small car Use the table below to help convert units of weight and mass. Units of Weight and mass U.S. Customary System Metric System 16 oz 1lb 000 lb 1tn 1000 mg 1g 1000 g 1kg 1000 kg 1t On Earth a kilogram is about. pounds, and a metric ton is about 00 pounds. Example Six kilograms is how many grams? Multiply the loop. kilograms grams = 6? = kilograms = 6000 grams Saxon Math Intermediate Adaptations Lesson 77

38 New Concept, continued Example Lesson Practice Multiply 8 ounces by 4. How many pounds is that? 8 ounces There are 16 ounces in 1 pound. 4 3 ounces To find the number of pounds, divide by 16. pounds 16 ) 3 ounces 3 ounces is the same as pounds. a. One half of a pound is how many ounces? ) oz 1 b. If a pair of tennis shoes is about 1 kilogram, then one tennis shoe is about how many grams? 1000 g ) c. Ten pounds of potatoes weighs how many ounces? d. Sixteen tons is how many pounds? tons lb e. A roll contains 57 yards of fabric. Estimate the number of yards of fabric on 9 rolls. Use compatible numbers. 1 0 = 16? lb oz 1 0 = 10? 9 rolls 5 7 yards rolls yards = yards in all Saxon Math Intermediate Adaptations Lesson 77

39 Written Practice page Arrange from least to greatest..13, 1.3, 13., ,,, 4. a. 1_ of students b. 1_ of answer to part a joined the 4 students chess team. ) students students students 1 3 c. What fraction of the students scored 100%? a. b. c ton = pounds See page 1 in the Student Reference Guide. 6. Name the shaded part: as a fraction. as a decimal. as a percent. Saxon Math Intermediate Adaptations Lesson 77

40 Written Practice, continued page lb oz 1 0 =? 8. kg g 1 0 = 3? 9. Find AC. Label the figure = A B C? Convert = Convert = Convert Multiply across = 15. Multiply across = 16. Multiply across. 1 = $ Saxon Math Intermediate 5 50 Adaptations Lesson 77

41 Written Practice, continued page = X X X 1. ($5 + 4 ) 6 =. 64,75 8 = 3. 60w = 3780 ) w = 4. 1 dime nickels per stack + 6 pennies 4 stacks about in one stack total amount Each stack is about or one quarter, and four quarters is the same as $. 5. Lindsey 1. km Shamika (Lindsey 0. km) ( ) km Doug (Shamika 0.4 km) ( ) km Lindsey Shamika Doug 1. km 0.5 km 0.5 km 0.5 km Saxon Math Intermediate Adaptations Lesson 77

42 Written Practice, continued page a. How long is the rectangle? b. If the rectangle is half as wide as it is long, then what is the perimeter of the rectangle? c. Area = length width mm a. b. c. 7. Assume that this sequence repeats after every three terms. What are the next four terms of the sequence? 7, 3, 5, 7,,,,, 8. a. An inch is what fraction of a foot? b. A foot is what fraction of a yard? c. An inch is what fraction of a yard? d. The answer to parts a c show that 1 of 1_ 1 3 is what fraction? 9. The mass of a dollar bill is about. A 1 milligram B 1 gram C 1 kilogram D 1 metric ton a. b. c. d. 30. a. What fraction is shaded? 1 in. b. What is the area of the shaded region? c. Area is measured using s units. 1 in. a. b. c. Saxon Math Intermediate Adaptations Lesson 77

43 LESSON Name 78 Teacher Notes: page 503 Introduce Hint #47 Square Roots. Exponents and Square Roots Refer students to Exponents on page 1 in the Student Reference Guide. Review Expanded Notation on page 9 in the Student Reference Guide. New Concept Math Language A base is the factor in repeated multiplication. An exponent shows how many times the base is used = 5 3 In the expression 5 3, the base is 5 and the exponent is 3. The expressions 5, 5 3, and 5 4 are powers of five. Powers of ten can be used to show place value of numbers in expanded notation = = = = = = 1000 Example Write 4,500,000 in expanded notation using powers of ten. (4 1,000,000) + (5 100,000) = ( ) + ( ) Example If we know the area of a square, we can find the length of each side. When we find the side length by using the area, we are finding the square root. Math Language To find the square root of a number, ask: What factor multiplied by itself equals the original number? What is the square root of a square with an area of 5 sq. units? 5 squares in all 5 = 5 The square root of 5 is 5 because 5 5 = 5. 5 squares on each side Saxon Math Intermediate Adaptations Lesson 78

44 Lesson Practice a. This figure illustrates five squared, which we can write as 5. There are five rows of five small squares. Draw a similar picture to illustrate 4. b. This picture illustrates two cubed, which we can write as 3. Two cubed equals what whole number? Write each power as a whole number. Show your work. c. 3 4 = = d. 5 = = e. 11 = = f. If m = 10, then what does m equal? Write each number in expanded notation using powers of 10: g. 50,000 ( ) + ( ) h. 3,600,000 ( ) + ( ) i. 60,500 ( ) + ( ) Find each square root in problems j m. What factor multiplied by itself equals the original number? j. 1= k. 4= l. 16 = m. 49 = n. Solve each part and then compare. o. Find the square roots Compare: and then subtract: = Saxon Math Intermediate Adaptations Lesson 78

45 Written Practice page of 1 = = Use fraction-decimal-percent pieces. 1 6 = %. 00$ $ hours guests total guests 4. 1_ of 000 lb 5. 1_ of 16 oz lb lb ) 1 16 oz oz ) lb oz 6. Which shaded circle below is equivalent to the larger shaded circle at right? A B C D 7. Which of these fractions does not equal one half? 8. Find the length in millimeters and then in centimeters. A B C D 6 1 mm cm 1 3 Saxon Math Intermediate Adaptations Lesson 78

46 Written Practice, continued page factors of 6:,,, Cross out the numbers that are not factors of Find MN. Label the figure. L M? N, = = = 14. Fill empty places with zeros Convert. Convert. Convert. 15. $40.00 $ $ ) $ R 80 ) Write the quotient as a mixed number. + = 98 5 = ) Saxon Math Intermediate Adaptations Lesson 78

47 Written Practice, continued page of 1 =. Multiply across = 3. Multiply across. 1 3 = Convert. Reduce. 4. a. How far does Kiyoko travel going to school and back in 1 day? 5. Assume that this sequence repeats after every four terms. Home 1.5 mi School Write the next four terms of the sequence. b. If Kiyoko leaves her house at 7:55 a.m. and rides her bike, at what time will she get to school? 7, 3, 5, 7,,,,, leaves: Count minutes forward. a. b. 6. Area = length width A B 7. Which term does not apply to quadrilateral ABCD in problem 6? A rectangle D C B parallelogram C rhombus = D polygon See page 16 in the Student Reference Guide. Saxon Math Intermediate Adaptations Lesson 78

48 Written Practice, continued page A C A S L B E a. What is the probability that the letter selected is a vowel? b. What is the probability that the letter selected is A? c. What is the probability that the letter selected comes before G in the alphabet? a. b. c. 9. Write 5,000,000 in expanded notation using powers of 10. See page 506. ( ) + ( ) 30. Display the data in a horizontal bar graph. Planet Diameters Planet Diameter (miles) Mercury 3000 Venus 7500 Earth 8000 Mars 4000 Planet Diameters Mercury Planet Diameter (in miles) Saxon Math Intermediate Adaptations Lesson 78

49 LESSON Name 79 Teacher Notes: page 511 Finding Equivalent Fractions by Multiplying by 1 Refer students to Fraction Families Equivalent Fractions on page 18 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 79. New Concept Math Language Equivalent fractions are different names for the same number. When a number is multiplied by 1, the value of the number does not change. This is called the Identity Property of Multiplication. When a fraction is multiplied by any fraction name for 1, the result is an equivalent fraction. Example 3 4 = = = = 75% Lesson Practice Find the fraction name for 1 used to make each equivalent fraction: a. 3 4 = 9 1 b. 3 = 4 6 c. 1 3 = 4 1 d. 1 4 = Find the numerator (top number) that completes each equivalent fraction: e. 1 3 = 8 9 f. 3 = 3 15 g. 3 5 = h. Write a fraction equal to 1_ that has a denominator of 6: 1 = 6 6 Saxon Math Intermediate Adaptations Lesson 79

50 Lesson Practice, continued Write a fraction equal to 1_ that has a denominator of 6: = 6 6 What is the sum? i. Write 3_ 5 as a fraction with a denominator of 100: 3 5 = Write the fraction you wrote as a percent: The denominator of a percent is 100. Written Practice page ton = pounds pounds dayspo 50 1 =?? Multiply the loop.. 1 ft = in. 1 ft = in. ( ) + = 3. selling price Toshi paid profit Saxon Math Intermediate 5 51 Adaptations Lesson 79

51 Written Practice, continued page = Area = length width 7. factors of 9:,, Cross out the numbers that are not factors of = = 1 1 Convert Find AB. Label the figure., A? B C = 11. Borrow and rename = Convert. Saxon Math Intermediate Adaptations Lesson 79

52 Written Practice, continued page $ $10 4 = = $. ) m = w 6.35 = n = 655 m = w = n = 18. R 7 ) 4 3, ) R = 1. 1 of 1 5 = =. Multiply across. 3 4 = = Saxon Math Intermediate Adaptations Lesson 79

53 Written Practice, continued page a. How many fruit cups were sold in July? Fruit Cup Sales A 3 1 B 300 C 305 D 350 June July August b. June 100 fruit cups July August total sold a. b. 5. What is the probability of not rolling a 4? 6. Distributive Property 1 1 = 1 (0 + 1) (0 1) + (1 1 ) = Use mental math. 7. Fourteen books were packed in a box. Which is the most reasonable measure? A 15 milligrams B 15 grams C 15 kilograms D 15 metric tons Saxon Math Intermediate Adaptations Lesson 79

54 Written Practice, continued page This is an equilateral triangle. perimeter Add all sides. 1.5 cm g = mg 500 mg 1.0 g 500 mg mg 30. Round to the nearest $500. $ $ I r $7995 to $ and rounded $8449 to $. Then I s to find the difference. Saxon Math Intermediate Adaptations Lesson 79

55 LESSON Name 80 Teacher Notes: page 516 Prime and Composite Numbers Refer students to Prime Numbers on page 4 in the Student Reference Guide. Display reference chart Primes and Composites. New Concept Math Language A prime number is a counting number that has exactly two factors (1 and itself). A composite number is a counting number with more than two factors. The number 1 has exactly one factor, and is neither prime nor composite. Number Factors Type 1 1 1, prime 3 1, 3 prime 4 1,, 4 composite 5 1, 5 prime 6 1,, 3, 6 composite 7 1, 7 prime 8 1,, 4, 8 composite 9 1, 3, 9 composite 10 1,, 5, 10 composite An array is a rectangular arrangement of numbers or objects in rows and columns. Below are 3 different arrays for the number 1: 4 by 3 6 by 1 by 1 These arrays show us that 1,, 3, 4, 6, and 1 are factors of 1. Prime numbers have only one pair of factors. The only factors of 11 are 1 and 11. Here is the only array for the prime number 11. Saxon Math Intermediate Adaptations Lesson 80

56 New Concept, continued Activity page 519 Identifying Composite and Prime Numbers Use your textbook to complete this activity. Lesson Practice a. Use color tiles to make as many different arrays as possible for 14 and for 19. Draw the arrays you make using Xs. List the factors of 14:,,, List the factors of 19:, 14 is a number, and 19 is a number. b. Draw two arrays for the composite number 9. Use the factor pair 1 and 9 for one array. Use the factor pair 3 and 3 for the other array. c. List the factors of 15:,,, List the factors of 17:, Use color tiles to determine which number is prime and which is composite. can be drawn using more than two arrays, so it is. can be drawn using only two arrays, so it is. d. Use color tiles to make arrays for 10, for 11, and for 1. Which numbers can be arranged in more than two arrays? and Which number can be arranged in only two arrays? Which number is prime? Which numbers are composite? Saxon Math Intermediate Adaptations Lesson 80

57 Written Practice page ton = pounds pounds wheels 4 4 =? 1 Multiply the loop. 3. factors of 8: 4. List the next three prime numbers.,,, Cross out the numbers that are not factors of 1., 3, 5, 7, 11,,,,, = 9 1 Since 3 = 9 and 4 = 1, I used the fraction = A prime number has factors. All prime numbers have only 1 and 3 = 6 Convert. + i as f. 8. Arrange from least to greatest. Use fraction pieces or compare each to 1_.,,,, Saxon Math Intermediate Adaptations Lesson 80

58 Written Practice, continued page To find 1_ of a mile, 8 divide by Find XY. Label the figure. ) X? Y Z 11. $8.43 $8.43 $ $. 1. Fill empty places with zeros $1.00 $ $ w = $76.3 ) = w = 18. Write the quotient as a mixed number of 3 4 = = + = ) Saxon Math Intermediate 5 50 Adaptations Lesson 80

59 Written Practice, continued page Multiply across. 3 3 = 1. Write the numerator as your answer =? = Convert. Convert = = 5. It is evening. What time will be shown by this clock in 6 1_ hours? time shown: Count minutes forward Count hours forward. 6. Which digit is in the millions place? 9,956,000 Saxon Math Intermediate 5 51 Adaptations Lesson 80

60 Written Practice, continued page Write 150,000,000 kilometers in expanded notation using powers of 10. See page 506. ( ) + ( ) 8. Complete the sequence., 4, 8, 16,,, Is it arithmetic or geometric? See page What is the probability of heads with one coin toss? 30. Write as unreduced fractions. One digit to the right is a denominator of = The denominator of a percent is % = Saxon Math Intermediate 5 5 Adaptations Lesson 80

61 INVESTIGATION 8 Name page 5 Focus on Graphing Points on a Coordinate Plane Transformations Teacher Notes: Introduce Hint #48 Rectangular Coordinates and Hint #49 Coordinate Geometry. Refer students to Rectangular Coordinates on page 5 in the Student Reference Guide. Lesson Activity 41 Coordinate Plane has been incorporated into this intervention. Graphing Points on a Coordinate Plane Math Language The x-axis is the horizontal number line (first coordinate). The y-axis is the vertical number line (second coordinate). A coordinate plane has two perpendicular number lines that cross at their zero points. Coordinates are the numbers in parentheses that tell where a point is located. The origin is the point where the x-axis and the y-axis cross. The origin s coordinates are (0,0). To graph coordinates: 1. Start at zero.. Go left or right, and then up or down Draw a dot y (, 7) (7, 7) (7, ) (0, 0) x To graph (7, ): 1. Start at zero.. Count 7 places to the right. Then count places up. 3. Draw a dot. Saxon Math Intermediate 5 53 Adaptations Investigation 8

62 INVESTIGATION 8 continued 1. The coordinates of point A are (0, 0). This point is the o y C E D B A x Write the coordinates of each of these points. (Always start at the origin.). point B (, ) 3. point C (, ) 4. point D (, ) 5. point E (, ) Saxon Math Intermediate 5 54 Adaptations Investigation 8

63 INVESTIGATION 8 continued Below is a design drawn on a coordinate plane. To draw the design, we could start at (5, 9), draw a segment to (, 1), and then continue through the pattern back to (5, 9). We would connect the points in this order: (5, 9) (, 1) point F point G point H (5, 9) y G (5, 9) (,1) F H x Write the coordinates of each of these points from the star design above: 6. point F (, ) 7. point G (, ) 8. point H (, ) Saxon Math Intermediate 5 55 Adaptations Investigation 8

64 INVESTIGATION 8 continued Activity 1 page 53 Graphing Designs a. Graph each of the following points. Then make a design by connecting the points in alphabetical order. Complete the design by drawing a segment from the last point back to the first point. I (7, 10) M (4, 1) J (4, 10) N (7, 1) K (1, 7) O (10, 4) L (1, 4) P (10, 7) y I x b. This part is optional. Saxon Math Intermediate 5 56 Adaptations Investigation 8

65 INVESTIGATION 8 continued Transformations We can move figures on a plane by sliding them, turning them, or flipping them. These movements are called transformations. Names of Transformations Movement slide turn flip Name translation rotation reflection 9. This figure shows triangle ABC and the image of where triangle ABC would appear after a slide three units to the right. This is a transformation. 5 y 4 A 3 1 C B x Before the Translation Point A Point B Point C (, ) (, ) (, ) After the Translation Point A Point B Point C (, ) (, ) (, ) Saxon Math Intermediate 5 57 Adaptations Investigation 8

66 INVESTIGATION 8 continued 10. Triangle B is a mirror image of triangle A, so the transformation is a. This is also known as a f y A B x If triangle ABC is turned around point C, then it will move into the position of the image shown. The transformation is a r. Another word for a rotation is a t y A B C x Activity page 55 Transformations Use your textbook to complete this activity. Saxon Math Intermediate 5 58 Adaptations Investigation 8