Rounding Mixed Numbers
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- Opal Bridges
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1 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 Halfway Example 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 b Saxon Math Intermediate Adaptations Lesson 101
2 Lesson Practice, continued c d e f g. Estimate the product of 9 4_ 5 and 5 1_ 3. h. Estimate the sum of 36 5_ 8 9 and i. Estimate the perimeter of this rectangle in in. Saxon Math Intermediate 5 66 Adaptations Lesson 101
3 Written Practice page deer antelope = Cancel matching zeros. Reduce but don t convert mc cm =? five decades = Cross cancel. 5. length in millimeters and centimeters mm cm _ of centimeters. 7. Is $8.80 closer to $8 or to $9? $ is than 50, so $8.80 is closer to. Saxon Math Intermediate Adaptations Lesson 101
4 page Round the mixed numbers by comparing each fraction to 1_ yd ft 1 1 =? Find AD. 1_ of 60 mm is mm. 1_ of 60 mm is mm. 3 A 60 mm B C D? = = $ = = Think 3 0 ) w = $0.16 Saxon Math Intermediate Adaptations Lesson 101 w =
5 page = = = 1 4 = = = Simplify. Cross cancel = = 3. Write the missing number as your answer = 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: Saxon Math Intermediate Adaptations Lesson 101
6 page Write the coordinates: A (, ) B (, ) y A C (, ) 1 B C x , 13.8, 13.7, 13.9, 14.1 in order: 8. 1 in. 1 ft median,,,, middle 9. length: width: perimter: read 10 not read Another name for 1 is, and 10 =. 10 Saxon Math Intermediate Adaptations Lesson 101
7 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 Lesson Practice Subtract. a b c d e f Saxon Math Intermediate Adaptations Lesson 10
8 Lesson Practice, continued g h i j 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 My estimate is reasonable because 50.4 rounds to to, 14.9 rounds, and =. Written Practice page gal = pt It weighs how much? name: Now draw the figure again rotated 90 clockwise. Saxon Math Intermediate Adaptations Lesson 10
9 page Round the mixed numbers by comparing each fraction to 1_ 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 = = + 40 = Convert Multiples: Think multiplication table. 10. a. length b. perimeter 6,,, a. b. Saxon Math Intermediate Adaptations Lesson 10
10 page United States 76.7 million bushels France (United States 3.8 million) United States + France = $ ) ) = = Cancel = = Saxon Math Intermediate Adaptations Lesson 10
11 page = 3. Write the missing number as your answer. = 1 50 = a. total hours b. fraction sleeping Reduce. School 7 hr Play 4 hr Homework and chores hr Sleep 9 hr Meals hr a. b liters. 6.,.5,.8, 3.1, 3.4,,,,,???.5,.8, 3.1, 3.4, 7. top layer total blocks Saxon Math Intermediate Adaptations Lesson 10
12 page probability of pineapple 9. least to greatest Fruit Number Sold Pineapples 3 Strawberries 16 Kiwis = =.,,, 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 Yellowjackets Eagles Brahmas Panthers Tigers b. question: question: Saxon Math Intermediate 5 67 Adaptations Lesson 10
13 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 Adaptations Lesson 103
14 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 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 Adaptations Lesson 103
15 Written Practice page 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? 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 Adaptations Lesson 103
16 page 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 Estimate the perimeter and area Draw a parallelogram with at least one obtuse angle. How many acute angles does it have? Saxon Math Intermediate Adaptations Lesson 103
17 page = = 17. $ = = x = = = Cancel. x = = = = Cross cancel. = = 5. Write the missing number as your answer. 1 5 = Reduce: = Saxon Math Intermediate Adaptations Lesson 103
18 page a. volume: Volume = length width height 3 cm b. number of faces: 3 cm 5 cm c. number of vertices: y A a. coordinates of each vertex A (, ) B (, ) 3 C (, ) B C 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 Adaptations Lesson 103
19 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 Halfway Although 7.5 is halfway between 7 and 8, we round up if the digit after the decimal is 5 or more. Example (because 6 > 5) 7. 7 (because < 5) Round money amounts to the nearest dollar. Example $ $4 (because 9 > 5) $ $3 (because 1 < 5) Lesson Practice Round each money amount to the nearest dollar. a. $6. 4 b. $ c. $ d. Estimate the sum of $ and $ = Saxon Math Intermediate Adaptations Lesson 104
20 Lesson Practice, continued Round each decimal number to the nearest whole number: e f g h i j k. Estimate the product of 9. 8 and = l. Talisha ran one lap in 68.7 seconds. Round her time to the nearest second. m. Estimate the volume. Volume = length width height cm 6. cm 1.9 cm = Written Practice page Draw a quadrilateral with two pairs of parallel sides and no right angles.. a. boys = girls b. boys + girls = students c. boys girls = a. Reduce but don t convert. b. c. Saxon Math Intermediate Adaptations Lesson 104
21 page , 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 Division: Flip the second fraction 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 Adaptations Lesson 104
22 page Compare the fraction to 1_. 9. a. $ b. $ 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 Estimate the area and perimeter. 6.8 cm cm 3.9 a. b $16.74 $15.74 ) 15. $ Saxon Math Intermediate 5 68 Adaptations Lesson 104
23 page All these ratios are equal. What is the quotient of each division? 640 3, 30 16, 160 8, = = Convert = = Cancel = Cancel.. Write the missing number as your answer. 4 5 = Determine a possible pattern for this sequence, and draw the next figure.,,, See page = 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 Adaptations Lesson 104
24 page 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 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 B 3 (5 4) C D 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 Adaptations Lesson 104
25 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 Adaptations Lesson 105
26 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 x On the grid, draw the image of the figure reflected across the horizontal line y = 3. Saxon Math Intermediate Adaptations Lesson 105
27 Written Practice page boys girls 4 5 =. 3. Subtract the largest value coins first 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 average Day Blanco Felicia Saxon Math Intermediate Adaptations Lesson 105
28 page Estimate. 9. Estimate the quotient. 10. Faster means less time. $ 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 = Cancel the matching final zeros = Cancel the matching final zeros. Simplify. Saxon Math Intermediate Adaptations Lesson 105
29 page = Cancel both ways = 3 5 = Cancel = = ) Think 30 ) m = 5964 m = = Write the missing number as your answer. 7 5 = 100 Saxon Math Intermediate Adaptations Lesson 105
30 page 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) 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 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 Adaptations Lesson 105
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