Rounding Mixed Numbers

LESSON Name 101 Teacher Notes: page 659 Review Hint #0 Comparing Fractions. Rounding Mixed Numbers Review Fraction Terms on page 19 in the Student Reference Guide. For additional practice, students may complete Fraction Activity I. New Concept To round a mixed number, compare the fraction to 1_ : If the fraction is greater than or equal to 1_, add 1 to the whole number. If the fraction is less than 1_, leave the whole number alone. These numbers are closer to 7. These numbers are closer to 8. 7 7 1 8 Halfway Example 7 3 4 6 5 8 because 3 4 > 1 6 because 5 < 1 Lesson Practice Round each mixed number to the nearest whole number. (Compare each fraction to 1_. Use fraction pieces or cross multiply.) a. 3 3 3 1 b. 7 1 8 1 8 1 Saxon Math Intermediate 5 661 Adaptations Lesson 101

Lesson Practice, continued c. 6 3 5 3 5 1 d. 6 1 4 1 4 1 e. 1 5 6 5 6 1 f. 5 3 10 3 10 1 g. Estimate the product of 9 4_ 5 and 5 1_ 3. h. Estimate the sum of 36 5_ 8 9 and 10. 10 i. Estimate the perimeter of this rectangle. 7 8 8 in. 1 5 4 in. Saxon Math Intermediate 5 66 Adaptations Lesson 101

Written Practice page 661 1. deer antelope 000 000 = 000 000 Cancel matching zeros. Reduce but don t convert.. 5 8 mc cm 1 100 =? 1 3. 186 five decades 4. 3 4 100 100 = Cross cancel. 5. length in millimeters and centimeters mm 10 0 30 40 cm 1 3 4 6. 1_ of centimeters. 7. Is $8.80 closer to $8 or to $9? $8. 8 0 80 is than 50, so $8.80 is closer to. Saxon Math Intermediate 5 663 Adaptations Lesson 101

8. Round the mixed numbers by comparing each fraction to 1_. 18 7 8 7 3 4 9. yd ft 1 1 =? 40 10. Find AD. 1_ of 60 mm is mm. 1_ of 60 mm is mm. 3 A 60 mm B C D? 11. 4 + 8.57 + 1.3 =.. +. 1. 16.37 1 = 16. 37. 13. $3.58 10 14. 4 = 15. 4300 5 = Think 3 0 ) 4 0 0 0. 16. 14w = $0.16 Saxon Math Intermediate 5 664 Adaptations Lesson 101 w =

17. 9 + 16 = 18. 5 6 = 1 1 19. 6 3 5 + 1 3 5 = 1 4 = 1 1 0. 8 5 6 1 1 6 = 1. 10 5 10 = Simplify. Cross cancel.. 4 5 = = 3. Write the missing number as your answer. 9 50 = 100 Cross cancel. 4. a. 1 second faster b. 1st place Faster means less time. 9. s nd place. 00 total a. b. 5. Reduce: 50 100 Saxon Math Intermediate 5 665 Adaptations Lesson 101

6. Write the coordinates: A (, ) B (, ) 5 4 3 y A C (, ) 1 B C 0 1 3 4 5 x 7. 14.0, 13.8, 13.7, 13.9, 14.1 in order: 8. 1 in. 1 ft median,,,, middle 9. length: width: perimter: 30. 7 read 10 not read Another name for 1 is, and 10 =. 10 Saxon Math Intermediate 5 666 Adaptations Lesson 101

LESSON Name 10 Teacher Notes: page 664 Subtracting Decimal Numbers Using Zeros Review Decimal Arithmetic Reminders Chart on page 9 in the Student Reference Guide. For additional practice, students may complete Targeted Practice 10. New Concept Example Line up the decimal points. Fill empty places with zeros. Put a decimal point on the back of any whole number. Subtract across the zeros. 0.4 0.31 3 1.3 3 9 0.4 0 1 0 0. 3 1 0.1 6 9 9 3.0 1 0 1. 3 1.7 7 Lesson Practice Subtract. a. 0.30 0.15 b. 0.3 0.5 c. 4. 0.4 d. 3.5 0.35 e. 10.0 6.5 f. 6.5 4.0 Saxon Math Intermediate 5 667 Adaptations Lesson 10

Lesson Practice, continued g. 1.0 0.9 h. 1.0 0.1 i. 1.00 0.5 j..5 1.0 k. Anisa poured 1. liters of cranberry juice from a full -liter container. How much cranberry juice was left in the container?.0 liters. l. 50.4 14.9 My estimate is reasonable because 50.4 rounds to to, 14.9 rounds, and =. Written Practice page 666 1.. 1 gal = pt It weighs how much? name: Now draw the figure again rotated 90 clockwise. Saxon Math Intermediate 5 668 Adaptations Lesson 10

3. Round the mixed numbers by comparing each fraction to 1_. 7 1 5 3 7 8 4. average 43 7 Is this the mean, median, mode, and/or range? 5. 5m = 100 m = m = and 6. decimal, reduced fraction, and percent shaded. 7. 1 5 = 40 8. 7 8 = + 40 = Convert. 1 10 10 100 9. Multiples: Think multiplication table. 10. a. length b. perimeter 6,,, a. b. Saxon Math Intermediate 5 669 Adaptations Lesson 10

11. United States 76.7 million bushels France (United States 3.8 million) United States + France 1. 0.4 0.1 =.. 13. 6. 0.71.. 14. 315 73 4197 586 9 + 3634 15. $4.36 9 16. 540 780 17. 6 ) 4 3 18. 1 ) 8 6 4 19. 5 1 3 + 1 3 = 0. 5 6 3 5 = Cancel. 1. 1 3 = = Saxon Math Intermediate 5 670 Adaptations Lesson 10

1 3 = 3. Write the missing number as your answer. = 1 50 = 100 4. a. total hours b. fraction sleeping Reduce. School 7 hr Play 4 hr Homework and chores hr Sleep 9 hr Meals hr a. b. 5..0 liters. 6.,.5,.8, 3.1, 3.4,,,,,???.5,.8, 3.1, 3.4, 7. top layer total blocks Saxon Math Intermediate 5 671 Adaptations Lesson 10

8. probability of pineapple 9. least to greatest Fruit Number Sold Pineapples 3 Strawberries 16 Kiwis 41 1. 0 1 10 =. 0. 0 0 1 1 100 =.,,, 30. First Season Team Wins Yellowjackets Eagles 5 Brahmas 3 Panthers 5 Tigers 1 a. Use the data in the table to complete the bar graph. 6 5 4 3 1 0 Yellowjackets Eagles Brahmas Panthers Tigers b. question: question: Saxon Math Intermediate 5 67 Adaptations Lesson 10

LESSON Name 103 Teacher Notes: page 670 Introduce Hint #59 Volume. Review Perimeter, Area, Volume on page 17 in the Student Volume Reference Guide. New Concept The volume of a shape is the amount of space the shape occupies. Volume is measured in cubic units. V = l w h height (h) length (l) width (w) Example Find the volume of this rectangular solid. cm cm 3 cm V = l w h V = 3 V = 1 cubic centimeters To estimate volume, round the measures before multiplying. Saxon Math Intermediate 5 673 Adaptations Lesson 103

Lesson Practice Find the volume of each rectangular solid. a. 4 in. b. 3 cm in. 4 in. 3 cm 3 cm c. Which type of unit records the volume of a rectangular prism: inches, square inches, or cubic inches? d. 6 in. 6 in. 6 in. Which formula can be used to find the volume of the above baseball case? A 4s B l w C l + w D l w h e. Use a formula to find the volume of the case in problem d. f. A box of wheat crackers measures 5 1_ by 1_ by 7 5_. What is a reasonable estimate 4 8 8 in cubic inches of the volume of the box? Explain. I can round 5 1_ 4 to, 1_ 8 to, and 7 5 _ 8 to. A reasonable estimate is, or cubic inches. Saxon Math Intermediate 5 674 Adaptations Lesson 103

Written Practice page 675 1. magazines children s books = Simplify.. 1_ of 1 1 oz 3 1 oz 3 oz ) oz 3. probability of prime number 1 3 = percent Simplify. 4. decimal and reduced mixed number 5. Which digit in 1.34 is in the same place as the 6 in 56.78? 1.34 56.78. 6. 30 cm d = r 7. 7 students seat themselves in rows of 6. How many rows of 6? How many students in the last row? ) Saxon Math Intermediate 5 675 Adaptations Lesson 103

8. Mr. Alfredson 30 minutes Son (Mr. Alfredson 15 minutes) Daughter (Mr. Alfredson + 10 minutes) Altogether, how many minutes did the family spend reading? + + = 9. Which arrow could be pointing to 5.8 on this number line? A B C D 5 6 10. Estimate the perimeter and area. 7 7 8 4 1 4 11. Draw a parallelogram with at least one obtuse angle. How many acute angles does it have? 1. 3.00.35 13. 10.00 4.06 14. 4.35 1.60 + 15.00 Saxon Math Intermediate 5 676 Adaptations Lesson 103

15. 7 47 360 = 16. 5 = 17. $47.00 0 = 18. 5 9 = 47 7 360 19. 16x = 11 0. 3 3 + 3 = 1. 1 4 1 4 = Cancel. x =. 1 7 5 = 3. 3 3 = 4. 4 10 5 10 = Cross cancel. = = 5. Write the missing number as your answer. 1 5 = 100 6. Reduce: 500 1000 = Saxon Math Intermediate 5 677 Adaptations Lesson 103

7. a. volume: Volume = length width height 3 cm b. number of faces: 3 cm 5 cm c. number of vertices: 8. 5 4 y A a. coordinates of each vertex A (, ) B (, ) 3 C (, ) B C 1 0 1 3 4 5 x b. On the grid, draw the position of the triangle after a rotation of 90º around point C. 9. See page 677. Use an inch ruler. See Triangles on page 15 in the Student Reference Guide. a. each side: b. perimeter: c. Classify the triangle: by sides: by angles: 30. a. median middle b. 11 Nebraska California c. Which three states? + + = 1 a. b. c.,, and Saxon Math Intermediate 5 678 Adaptations Lesson 103

LESSON Name 104 Teacher Notes: page 679 Rounding Decimal Numbers to the Nearest Whole Number Review Hint #9 Estimating or Rounding. For additional practice, students may complete Targeted Practice 104. New Concept Compare the number after the decimal to 5. These numbers are closer to 7. These numbers are closer to 8. 7 7. 7.5 7.8 8 Halfway Although 7.5 is halfway between 7 and 8, we round up if the digit after the decimal is 5 or more. Example 7. 6 8 (because 6 > 5) 7. 7 (because < 5) Round money amounts to the nearest dollar. Example $3. 9 5 $4 (because 9 > 5) $3. 1 6 $3 (because 1 < 5) Lesson Practice Round each money amount to the nearest dollar. a. $6. 4 b. $15. 0 6 c. $118. 5 9 d. Estimate the sum of $1. 8 9 and $6. 9 5. + = Saxon Math Intermediate 5 679 Adaptations Lesson 104

Lesson Practice, continued Round each decimal number to the nearest whole number: e. 4. 7 5 f. 1. 3 g. 96. 4 1 h. 7. 4 i. 45. 7 j. 89. 8 9 k. Estimate the product of 9. 8 and 6. 9 7. = l. Talisha ran one lap in 68.7 seconds. Round her time to the nearest second. m. Estimate the volume. Volume = length width height 9. 8 6. 1. 9 9.8 cm 6. cm 1.9 cm = Written Practice page 683 1. Draw a quadrilateral with two pairs of parallel sides and no right angles.. a. boys = girls b. boys + girls = students c. boys girls 000 000 = 000 000 a. Reduce but don t convert. b. c. Saxon Math Intermediate 5 680 Adaptations Lesson 104

3. 85, 90, 90, 80, 80, 80, 75 a. in order (lowest to highest):,,,,,, b. median: c. mode: 4. The product of one half and one third is one sixth. 5. tenths place 14.75 6. Division: Flip the second fraction. 1 1 3 1 3 1 1 0 00 1 3 0 00 7. Shade 5% Shade 50% Sum of shaded parts as a fraction: + + + = Shade 75% Shade 100% Sum of shaded parts as a decimal: + + + = Saxon Math Intermediate 5 681 Adaptations Lesson 104

8. 4 3 10 Compare the fraction to 1_. 9. a. $1 0. 4 9 b. $9. 5 1 a. b. 10. a. Multiples: Think multiplication table. b. common factors of and 7 a. 7,,,, b. 11. Which arrow could be pointing to 7. on this number line? A B C 7 8 1. Estimate the area and perimeter. 6.8 cm 6.8 3.9 cm 3.9 a. b. 13. 6.4. +. 0 14. $16.74 $15.74 ) 15. $5.64 10 16. 976 67 Saxon Math Intermediate 5 68 Adaptations Lesson 104

17. All these ratios are equal. What is the quotient of each division? 640 3, 30 16, 160 8, 80 4 18. 3 = 9 + 7 9 = Convert. 19. 5 3 + 3 1 3 = 0. 1 1 3 = Cancel. 1. 3 10 00 00 = Cancel.. Write the missing number as your answer. 4 5 = 100 3. Determine a possible pattern for this sequence, and draw the next figure.,,,... 4. See page 685. 5. 10 1 0 0 = a. Find the dot for Billings. A G4 B F4 C H D F5 b. What town do we find in region J3? c. What letter and number show where to find Evans? a. b. c. Saxon Math Intermediate 5 683 Adaptations Lesson 104

6. a. coordinates of each vertex A (, ) 5 4 y B (, ) C (, ) b. On the grid, draw the position of the triangle after a reflection across side AC. 3 C A 1 B 0 1 3 4 5 x 7. a. volume Volume = length width height b. number of vertices 8. Write as a reduced fraction. 8% = a. b. 9. Mariano 4 minutes Lon (Mariano + 5 minutes) Carson (Lon 3 minutes) Which expression can be used to find the length of time Carson rides the bus? A 4 + 5 3 B 3 (5 4) C 5 + 3 4 D 4 + 3 + 5 30. See page 686. Two thirds of the 18 students completed their homework. The other students read a book. Which diagram shows the number of students who read a book? Saxon Math Intermediate 5 684 Adaptations Lesson 104

LESSON 105 page 687 Name Symmetry and Transformations New Concept A line of symmetry divides a figure into mirror images (reflective symmetry). Figures often have more than one line of symmetry. Regular polygons have as many lines of symmetry as they do sides. Figures that look the same more than once during a full turn have rotational symmetry. Regular polygons have REFLECTIVE symmetry and ROTATIONAL symmetry. A C C C B B A B A Saxon Math Intermediate 5 685 Adaptations Lesson 105

Lesson Practice Find all lines of symmetry in each figure. a. b. c. d. e. A regular octagon has how many lines of symmetry? f. Which of these letters has rotational symmetry? (Circle one.) PLUS g. 6 5 y 4 3 1 0 1 3 4 5 x On the grid, draw the image of the figure reflected across the horizontal line y = 3. Saxon Math Intermediate 5 686 Adaptations Lesson 105

Written Practice page 693 1. boys girls 4 5 =. 3. Subtract the largest value coins first. 43 5 quarter 4. ten and twenty-three hundredths seconds dimes? nickels? pennies?. 5. comic books $ 0 50 =? 0 To find the answer, I multiplied and then divided the sum by to get comic books. 6. Write a fraction equal to 1_ that has a denominator of 10. Subtract it from 9 and reduce. 10 7. average Day Blanco Felicia 1 40 60 3 15 Saxon Math Intermediate 5 687 Adaptations Lesson 105

8. Estimate. 9. Estimate the quotient. 10. Faster means less time. $1.95 1 0. 8 6. 8 7 13.0 s opponent faster Gregory 11. See page 694. a. coordinates of each vertex b. area: A (, ) B (, ) c. perimeter: C (, ) D (, ) 1. The rectangle in problem 11 has how many lines of symmetry? 13. a. Which angle appears to be acute? D A b. Which two sides are parallel? c. What type of quadrilateral is quadrilateral ABCD? C B a. b. and c. 14. 1 100 + 9 100 = Cancel the matching final zeros. 15. 63 100 13 100 = Cancel the matching final zeros. Simplify. Saxon Math Intermediate 5 688 Adaptations Lesson 105

16. 5 10 5 10 = Cancel both ways. 17. 3 5 3 4 = 3 5 = Cancel. 18. 3.76 19. 00. 0. 6 4 + 3 6 = 1. 31 =. 00. + 00.. 8 ) 5 9 6 4 Think 30 ) 6 0 0 0. 3. 14m = 5964 m = 4. 3 0 = 15 100 5. Write the missing number as your answer. 7 5 = 100 Saxon Math Intermediate 5 689 Adaptations Lesson 105

6. Regular quadrilateral 7. a. Volume Volume = length width height b. Number of edges 10 in. Saxon-Os Saxon-Os Show 4 lines of symmetry. 7 in. in. a. b. 8. Afternoon Temperatures in Mexico City 8 Temperature ( F) 80 78 76 74 7 70 1 p.m. p.m. 3 p.m. 4 p.m. 5 p.m. Time a. and b. to ; c. 9. a. Which of these letters has rotational symmetry? TEN 30. 000 Election Results Dickenson County, Virginia Candidate Number of Votes Bush (R) 3,1 Gore (D) 3,951 b. Which letters have reflective symmetry? 3,1 3,951 + a. b. Saxon Math Intermediate 5 690 Adaptations Lesson 105