Time Date A nickel weighs about 5 grams (5 g). A liter of water weighs about 1 kilogram (1 kg). In Problems 1-7, circle a possible weight for each object. 1. A dog might weigh about 200 kg 2,000 kg 2. A can of soup might weigh about 4g 40 g 3. A newborn baby might weigh about 30 kg 300 kg 4. An adult ostrich might weigh about 1.5kg S 15kg 5. A basketball might weigh about 60 kg 6 kg 6. The weight limit in an elevator might be about 100 kg ~oo ~ 10,000 kg 7. A pencil might weigh about 45 g 450 g 8. Choose one of the problems above. Explain why you chose your answer. Sample answer: Problem 7-1 thought a pencil would weigh ab()ut the 286 sa~e as a nickel so I chose 4.5 grams. Time Date .(M~tric and Customary Weight··· __ ,_'" '"' '"",,' v,,- -, __' ... J -J" ~~,.....-::c.~-~~--, _ , -,_,-:"",-r-~~"""""-77":-"-'~I"7-"""--7-:'-""-~~~-::'-':--"_,,",-~~-~- ____ ~--'~ ____ ~_.-'O--~~---~--'-'''7--.- ._-:.,..':""'"'";_....,.."..---~""~""-~~~~.,..~,~--~-:"'_-,.-,...'-...~ ~ The number line below has ounces on the top and grams on the bottom. It shows, for example, that 7 ounces are about equal to 200 grams. ounces 0 2 I I I i I I i I 0 grams 4 I I i 6 II 8 I I I 200 100 i I 10 I I 12 I I I I I 300 14 I 16 I i I 400 20 I 18 I I I I 500 Use the number line to give the approximate weight of each object. Sample answers: 0 1. 2. PRETZELS . ~ . . . About .' '. 15 ounces 425 16 ounces grams About 3. 455 grams 4. 100 grams 3 About _ _ 500 grams _ 1 -=-_ 2 ounces About 17~ ounces Use the number line to help you determine which object weighs more. Circle the heavier object. s. 2.3 ounces 6. 5 ounces 454 grams 287 Date Time .1 Boxes~_ Math Explain how you know that the pattern below is an example of a translation. b. Draw the 'figure after it is translated to the right. I I i Sample answer: The figure is slid to the right. It was not turned or flipped. The size and shape are the ~ame. 2. Find the solution of each open sentence. 2 Y= a. 6 7 b. 4 Y= 7 3 9 a TO + a = TO r= J.... 10 3 c. 5 r= 5 10, 1 or "2 1 m V I ! I VI I 3. Circle the numbers that are multiples of 6. 8 38 ® ® @ ® 0 3~0 4. Insert parentheses to make each number sentence true. a. 14 *~8 - G3 - 6)* 5 = c. 48 / d. 150 5. If you use an average of 7 sheets of paper per day, about how many sheets would you use in 15)= 42 b. ~ + 2)= b. 4 weeks? 49 196 c. 52 weeks? 2~548 sheets 5~O96~ sheets a. 1 week? 56 - 21 10 - 4 /~o + 5)< 4 *4 d. 2 years? or 5,110 288 / Put an X through the numbers' that are multiples of 5. ----'~'--- 10 = ,~--'--=-_ / sheets sheets 0 Date Time Geometric shapes like these 3-dimensional ones are also called geometric solids. ~ Rectangular Prism IJ Cylinder m fj Triangular Prism Cone ~ ,.,.," Sphere & Square Pyramid Look around the classroom. Try to find examples of the geometric solids Rictured above. Draw a picture of each. Then write its name (for example: book). Answers vary. Example of rectangular prism: Example of cylinder: Example of triangular prism: Name of object: Name of object: Name of object: Example of cone: Example of sphere: Example of square pyramid: Name of object: Name of object: Name of object: 289 Date at Time Modeling a R~ctangular _Prism. After you construct a rectangular prism with straws and twist-ties, answer the questions below. vertices edges faces 6_ _ face(s) 1. How many faces does your rectangular prism have? __ 6_ _ face(s) How many of these faces are formed by squares? 0, or 2 face(s) 2. How many of these faces are formed by rectangles? _.. __ 3. 1__ face(s) 4. Pick one of the faces. How many other faces are parallel to it? _ _ 5. How many edges does your rectangular prism have? _1_2__ edge(s) 3__ edge(s) 6. Pick an edge. How many other edges are parallel to it? _ _ 8_ _ vertices 7. How many vertices does your rectangular prism have? __ 8. Write T (true) or F (false) for each of the following statements about the rectangular you made. Then write one true statement and one false statement of your own. a. ~ __T__ It has no curved surfaces. b. __F _ _ All of the edges are parallel. c. __T__ All of the faces are polygons. d. __F__ All of the faces are congruent. Answers vary. False Answers vary. e. True f. 290 Date Time 1. Estimate how many of each coin you think it will take to make a 1-ounce weight. Then use a balance or scale to determine exactly how many of each coin are needed. Estimated Number Actual Number of (oins of (oins Answers vary. 11 or 12 5 or 6 12 or 13 (oin . penny nickel dime · quarter 2. Describe how you estimated how many of each coin it might take to make a 1-ounce weight. Sample answer: I know there are about 28 g in 1 ounce, and a nickel weighs 5 g. Therefore, 6 nickels should weigh 30 9 (5 * 6 = 30), so 6 nickels equal about 1 ounce. I estimate that pennies weigh 1 as much as nickels, so it should take twice as many pennies, which is 12. Dimes are smaller than pennies, so I guessed 15 dimes. Quarters are heavier than nickels, so I guessed 4. . Try This ; I ""''''''''''''''''''F'~~='''''/ 3. Aboutwhat fraction of an ounce does each coin weigh? 1 1 penny = 12 oz 1 nickel = 1 6 oz 1 dime Sample answers: = 1 13 oz 1 quarter = 1 oz Explain how you found your answers. Sample answer: I used the number of coins that equal 1 oz as the denominator. For example, because 12 pennies equal 1 1 OZ, 1 penny equals 12 oz. 291 Date Time 1. The object below has the shape of a geometric solid. What is the name of the solid? Circle the best answer. 2. Draw the figure after it is rotated clockwise *~turn. @ rectangular prism B. cone c. cylinder D. square pyramid 3. Write a number model to estimate the answer. Then correctly place the decimal point. a. 0.97 *4 = 4. Insert <, >, or = to make a true number sentence. a. -12 3.88 1_*_4_ _4_ _ b. -44 Number model: __ c. -64 b. -19 26 -0.43 1 8.7= 74.8 -:- 4 Number model: 80 -;- 4 = 20 d. 5. Round each number to the nearest tenth. a. 2.34 b. 0.68 c. 14.35 d. 1.62 e. 5.99 2.3 0.7 14.4 1.6 6.0 > 0 -0.37 6. A cinnamon raisin bagel has about 230 calories. How many calories are in one dozen bagels? About a 4 1 2 e. -0.28 292 > < < 2,760 calories Date Time Polyhedrons are geometric solids with flat surfaces formed by polygons. For each problem below • Decide what the polyhedron should look like. • Use straws and twist-ties to model the polyhedron. • Answer the questions about the polyhedron. Look at page 102 of the Student Reference Book if you need help with the name. 1. I am a polyhedron. I have 5 faces. Four of my faces are formed by triangles. One of my faces is a square. a. After you make me, draw a picture of me in the space to the right. Square pyramid b. What am I? c. How many corners (vertices) do I have? 5 Square d. What shape is my base? 2. I am a polyhedron. I have 4 faces. All of my faces are formed by equilateral triangles. All of my faces are the same size. a. After you make me, draw a picture of me in the space to the right. b. What am I? Triangular pyramid, or regular tetrahedron c. How many corners (vertices) do I have? d. What shape is my base? 4 Triangle 293 Date Time Knowing how to draw is a useful skill in mathematics. Here are a few ways to draw a cube. Try each way. Tape your best work at the bottom of page 295. A Basic Cube Draw a square. Draw another square that overlaps your first square. The second square should be the same size as the Hrst. D @ Connect the corners of your 2 squares as shown. This picture does not look much like a real cube. One problem is that the picture shows all 12 edges, even though not all the edges of a real cube can be seen at one time. Another problem is that it is hard to tell which face of the cube is in front. A Better Cube Begin with a square. Next, draw 3 parallel line segments going right and up from 3 corners of your square. The segments should all be the same length. Finally, connect the ends of the 3 line segments. This cube is better than before, but it shows only the edges and corners, not the faces. If you want, try shading your cube to make it look more realistic. 294 D Date • Time Drawing a Cube continued A Cube with Hidden Edges Sometimes people draw cubes and other shapes with dashed line segments. The dashed line segments show edges that are hidden. Here is one way to draw a cube with hidden edges. Use a pencil. Draw a square. D Draw a faint square that overlaps your first square. The second square should be the same size as the first. Connect the corners of your 2 squares with faint line segments. Trace over 5 of your faint line segments with solid lines and 3 with dashed lines. The dashed line segments show the 3 edges that are hidden. Tape your best work here. See students' work. 295 Date Time Stephen wants to build a bookcase for his books. To help him design the bookcase, he measured the height of each of his books. He rounded each measurement to the nearest of an inch. His measurements are given below. i Book Heights (to the nearest ~ inch) 1111 7111111 13 62,94,78,72,8,68,94,94,9t,94,94,84,8,84,88' 11 7371 1177111 62,78,9,68,98,68,72,8,84,94,68,68,84,84,84 Plot the data set on the line plot below. Book Heights en .::£ 0 0 ro ..... 0 .... Q) ..c E :::::J Z ... X X X X X X X X X X X X X X X I 8 12 I 6 12 7 12 7 8 9 Height (inches) Sample number models are given. Use the completed plot to answer the questions below and on journal page 2958. Write a number model to show how you solved each problem. 1. a. What is the maximum book height? 983 inches 61 b. What is the minimum book height? _--=2_ inches 2Z c. What is the range of the data set? _--=8_ inches 3 1 7 8Number model: 28 9 295A 6'2 . . . I .. 9 12 Time Date 82 2. a. What is the median of the data set? _-----'-4_ inches b. How much longer is the maximum height than the median height? 1 1s 3 inches Number model: 1 1 = 1s 9s - 84" 3. Suppose that Stephen wants to make the space between the shelves on his bookcase i of an inch taller than his tallest book. a. How far apart should he make the shelves? 1a.?8' 0 r 102- 4 inches apart Number model: 9~8 + 78 = 10S2 b. If the thickness of the wood he uses for the shelves is i inch, what will be the total height of each shelf? (Hint: The totall1eight is the thickness of the wood plus the distance between shelves.) 7 2 5 7 1as inches Number model: 1as s 1as + = 4. Stephen decides to make the bookshelf two shelves high. He will put all the books that are 8 inches tall or shorter on the top shelf and all the books that are more than 8 inches tall on the bottom shelf. a. What will be tile difference in height between the tallest books on the top shelf and the shortest books on the top shelf? 1 1- 2 _----'=''-- inches 1 1 8 6= 1 2 2 Number model: _ _ _--=_ _-=-_ b. What will be the difference in height between the tallest book on the bottom shelf and the shortest books on the bottom shelf? 11 _--=:!_ inches 1 1 9~8 - 84 = 1 8 Number model: _~_ _-'--_-=_ 5. Make up and solve your own problem about the book height data. Answers vary. Number model: _ _ _ _ _ _ __ 2958 Date Time .-'.'-~'-".'.-' .. -~~ .......•. ..• _ ' , .", ___"-~l ,~" ___ , 2. Find the solution of each open sentence. 1. Draw the figure after it is translated to the right. a. -7 8 b. t + 14 = -12 c. -3 10 d. 6 s = -----=18==- 1 S = 8 t= m= 1 5 2 "8 + X 3 4 _ _4.:..,--_ 1 10 m= 4 1 54 60 x=8.t Or 2" Name the first ten multiples of each number. & 6 12 b. 86 172 , 258 , 344 , 430 , 516 , 602 , 688 , 774 , 860 l 18 24 30 + 1.7)* 2.5 + ~= a. 4 packs of gum? 250 10 packs of gum? 3 > 5 * 30 c. 16 packs of gum? 8.3 =(26.15 - 23.4)* 2 . d. 33 packs of gum? + 3.7)* 13.8 3.1 ~ 296 5. Gum costs $0.80 per pack. What is the b. b. 21.7 / (3 d. 48 cost of sentence true. c. (56.3 42 ------- 4. Insert parentheses to make each number a. (98.3 36 $3.20 $8.00 $12.80 $26.40 Date Time 1. The object below has the shape of a geometric solid. Name the solid. 2. Draw the figure after it is rotated counterclockwise ~-turn. cylinder 3. Write a number model to estimate 4. Insert the answer. Then correctly place the decimal point. < b. -123 > c. -8.9 < d. > a. a. 7.56 * 4 = 3 0.2 4 8*4 Number model: b. 563.2 -;- 4 32 = 1 4 0.8 Number model: 600 -•• 4 = 150 <, >, or = to make a true number sentence. e. -14 -6 -241 -5.7 1 2 5 3 9 1 0 -' 5. Round each number to the nearest tenth. a. 3.46 b. 0.71 c. 4.35 d. 9.60 e. 22.89 3.5 0.7 4.4 9.6 22.9 6. Jake can ride his bike 5 miles in 40 minutes. At this rate, how long does it take him to ride 1 mile? Circle the best answer. A. 200 minutes B. 40 minutes C. 20 minutes @ 8 minutes 297 Date Time 1. Write a formula for the area of a rectangle. In your formula, use A for area. Use I and w for length and width, or band h for base and height. A == I * w, or A == b * h 2. Draw a rectangle with sides measuring 3 centimeters and 9 centimeters. Find the area. 9 Number model: * 3 == 27 3. Find the height of the rectangle. Area 27 square centimeters 4. Find the length of the base of the rectangle. Area = 56 m2 Area = 84 in2 7 meters 56 : 7 8 Number model: 8_ __ m height = _ _ 84 - 12 == 7 7 _ _ in. length of base = _ _ _ Number model: _ _ _ - _ _ _ __ 6. Find the height of the rectangle. 5. Find the area of the rectangle. D}? 11.3 em 26 em 11 ·3 * 5 56.5 cm Number model: Area = 298 Area=403cm2 2 56.5 Number model: height = 403 -;- 26 == 15.~ 15.5 cm Time 1. What is the total number of cubes needed 2. Calculate the volume. to completely fill the box? 125 35 in cubes 25 in. Number model: 30,625 Volume = 3. When you roll a 6-sided die, about what (25 * 35) * 35 == 30,625 in 3 ~ 4. Complete. fraction of the time would you expect 4 1 a. 13 ft = _ _ _ yd _ _ _ ft a. a multiple of 2 to come up? 3 6' or ~ b. a factor of 20 4 or ~ to come up? 6' b. 18 ft 6 in. = c. 972 in. = d. 15,840 ft = e. 24,640 yd = ~ 5. Add. d. e. $71.08 b. c. -54 14 mi PJli\ ~ ----------------------------~ 6. If 4 shirts cost $76, what is the cost of -26 -62 + (-15) = -77 -88 = 51 + (-139) $63.89 = -$23.56 + $87.45 a. 6 _ in. 6 yd _ _ 27 yd 3 _ mi __ + 28 = + (-$85.79) a. 2 shirts? $38 $114 1 dozen shirts? $228 75 shirts? $1 ,425 b. 6 shirts? c. d. -$14.71 299 Time Date ~ : 138 ,'H . . " " Each picture at the bottom of this page and on the next page shows a box that is partially filled with cubes. The cubes in each box are the same size. Each box has at least one stack of cubes that goes to the top. Your task is to find the total number of cubes needed to completely fill each box. Record your answers in the table below. ( i Table of Volumes Placement of Cubes Box 1 Box 2 Box 3 Box 4 Box 5 Box 6 Number of cubes needed to cover the bottom 32 40 24 16 35 25 Number of cubes in the tallest stack (Be sure to count the bottom cube.) 5 7 4 5 6 5 Total number of cubes needed to fill the box l 160 280 96 '"" Box 1 300 i 80 210 125 ""~~~'" ,,' Box 2 Time Date -.-..--- ........... ~-~.....' ~ """,'," Box 3 Box 5 ","',.,_h,-_,,_>, , ' Box 4 Box 6 Formula for the volume of a rectangular prism: V= B* h B is the area of a base. h is the height from that base. , ) Volume units are cubic units. .. _-- base 301 Time Date 1~II~e~~~&tcking Problems continued • .: .. ~ .... 138 ~~_~, ••• ,,"_ . ·_v______ • __ , __ ,~~ ',_:,/ Find the volume of each stack of centimeter cubes. 2. 1. Volume = Volume / / 3. / / 4. / /1 II II II Volume / / ~/ L I Volume = / lI/ = Choose one of the problems from above. Describe the strategy that you used the volume of the stack of centimeter cubes. am Ie answer: For Problem 4 I found the volume of the tall part, which is 4 cm 2 * 6 em == 24 cm~, and then added the volume of the two extra squares to get 26 CI'Tl_3_.___ Try This 7. 6. 8cm 2cm Number model: Volume = 302 (2 18 * 3) * 3 == cm 3 18 Number model: Volume = (8 160 * 10) * 2 == cm 3 160 Time Date 1. a. What was the heaviest item in the class Gram and Ounce Museum? _ _ _ _ _ __ b. How much did it weigh? grams ounces Answers vary. 2. a. What was the lightest item in the class Gram and Ounce Museum? _ _ _ _ _ __ b. How much did it weigh? grams ounces Answers vary. Complete. 3.6 g = 6~000 mg 4. 3,000 g 7. 2.9 g = 2,900 mg 96 oz 9. 6 Ib = 56 oz 11. 3.5 Ib = 5. 3 kg = 6. 8. 10. 12. 7 g = 7,000 mg 8 kg = 8,000 g 4.5 kg = 4,500 g 9 Ib = 144 oz 8 T = 16,000 Ib Use the Rules of Thumb below to solve Problems 13-15. Write number models to show how you estimated. Rules of Thumb 1 kilogram equals about 2.2 pounds 1 ounce equals about 30 grams Sample answers: 13. A video camera weighs about 120 grams. About how many ounces is that? 1_2_0__:_3_0__4_ _ I\lumber model: _ _ 4 _ _ _ _ oz 14. A baby weighs about 3.5 kilograms at birth. About how many pounds is that? 3_.5_*_2_._2__7_._7_ _ Number model: _ _ _ 7_.7_ lb 15. An African elephant weighs 11,023 pounds. About how many kilograms is that? Number model: 11 000 -;- 2.2 == 5 000 5,000 kg 303 Time Date 1. The object below has the shape of a geometric solid. Name the solid. ch 'figure below shows the original figure rotated clockwise ~-turn? A A Original c 8 cone ~ 3. Write a number model to estimate the answer. Then correctly place the decimal point. 4. Insert * 32.9 = 1 9 7.4 Number model: 6 * 30 =180 b. c. b. 3 2.9 98.7 -;- 3 Number model: 99 -;- 3 . 33 d. e. 5. Round 8.99 to the nearest tenth. Circle the to make a true number sentence. a. a. 6 <, >, or < -9 -89 > -99 -2.99 < -2.9 -4" > -3 -9 > -2* -34 1 1 6. It takes 2 cups of 'flour to make about best answer. 20 medium-size peanut butter cookies. A. 8.0 How many cups of flour will you need to make about @9.0 4 cups 6 cups _L cups a. 40 cookies? C. 9.1 b. D. 8.09 c. 50 cookies? 60 cookies? d. 740 cookies? 304 0 18 74 cups ~ Date Time Math Message = 1 quart = 1 pint 1 half-gallon 1 gallon = = 2 2 2 4 cups pints quarts quarts Think: How can the picture above help you remember how many cups are in a pint, how many pints are in a quart, and how many quarts are in a gal/on? Units of Capacity 1. Circle the unit you would use to measure each amount. A large jug of milk milliliters orC@~ Water in a thimble A glass of juice Water in a water cooler milliliters or@~rv Water in a fish tank milliliters or<@~V milliliters orC@~v milliliters or@~v Liquid in a paper cup A tank of gas A spoonful of oil A large bottle of water A can of soup 2. Explain how you decided which unit to use for a can of soup. Sample answer: I chose milliliters because most cans hold less than a liter. 305 Time Date Comparing Capacities 1. Shade in the appropriate amount to show the capacity of each of your containers. Answers vary. ~ & ~ 1---2 L ·-2L 1---2 L 1---1 L 1---1 L 1---1 L Container _ _ Container _ _ Container _ _ e. d. f. l---2L 1---2L \---1 L 1---1 L Container _ _ Circle the container with the largest capacity. Was your prediction accurate? Container _ _ Units of Capacity u.s. Customary Metric 1 gallon (gal) = 4 quarts (qt) 1,000 milliliter (mL) = 1 liter (L) 1 quart (qt) = 2 pints (pt) 1 pint (pt) 1 milliliter (mL) = liter (L) = 16 fluid ounces (fl 2. Use the conversion table above to solve the problems. a. 6 qt c. = 3 12 pt pt = 48 noz b. 8,000 d. 6,450 mL e. 10 qt = 212 gal f. g. 4 gal = 64 c h. 32 mL 305A 500 = mL = 8 L = 6.450 mL L = 0.500 L 0.032 L Date Time Solve. You may draw pictures to help you. 1. Adaline filled her watering can with 1,250 mL of water. After watering her plants she had 485 mL left. How much water did she use? 765 mL 2. Betty and Don spent the morning squeezing oranges for juice. Betty squeezed 1 ~ L and Don squeezed 1t L. What is the total amount of juice? 3. There are 450 mL of syrup in 1 can. What is the total amount of syrup in 6 cans? 4. Dimitra poured 3~ or 3.250 L 2,700 mL i liter of water into a fish tank. William poured ~ liter of water into the 'fish tank. a. How much more water did William pour? b. How many milliliters is that? 2 5 L 400 mL 300 mL 1,800 mL 5. Raina brought a 1,500 mL jug of water to the school picnic. Her water jug has enough water to fill 5 glasses. How much does each glass hold? 6. The teacher set out 24 bowls of glue for the students to use for an art project. Each bowl holds 75 mL of glue. How much glue did the teacher need to fill all the bowls? 3058 Date Time 1. Use the data in the Largest Cities by Population table at the top of Student Reference Book, page 302 to complete the bar graph. Round each figure to the nearest million. Largest Cities by Population (/) c::: a E <D 0.. a <D c.. a l0 is E ::J Z 12 Tokyo Mexico City New York City Sao Paulo Mumbai (Bombay) Calcutta Shanghai Cities 2. Make three statements comparing the cities in the bar graph. Example: Abou.t 2/ million more people live in Toky.o than in Shanghai. Sample answers: About the same numbe_r_o_f__ people live in Mexico . City and New York City; about 1 million more people live in Sao Paulo ._ than Mumbai; about twice as many people live in Tokyo as SaC? Paulo. 306 Time Date 1. What is the total number of cubes needed 2. Calculate the volume. to completely fill the box? (2n-------n~::m 96 cubes gem Number model: (9 * 5) * 2 Volume = cm 3 90 = 90 3. When you roll a 10-sided die, about what fraction of the time would you expect a multiple of 3 to come up? 3 10 Use a probability term to describe the likelihood of this event. unlikely 3.21 m 560 mm b. 56cm = 172 in. c. 14ft4in.= 10,560 ft d. 2mi 321 cm = e. 5.3 km f. S. Add. m mi = 7,040 yd ~ 6. If you travel at an average speed -26 a. -46 + 20 = -41 b. -23 + (-18) = c. 16 = 33 + (-17) d. -$21.27 = $36.54 e. -$131.09 4 5~300 + (-$76.98) + (-$57.81) =-$208.07 of 50 miles per hour, how far will you travel in 150 miles 25 miles b. 21 hour.? c. 2~ hours? 125 miles d. 5~ hours? 280 miles a. 3 hours? ~ 47 307 Date Time Math Boxes 1. If you use the telephone an average of 4 times per day, about how many times would you use it in b. 4 weeks? 28 112 c. 52 weeks? 1 ,456 a. 1 week? 2. A cup of orange juice has about 110 calories. About how many calories are in a quart of orange juice? 440 times calories times times 0 3. Pears cost $0.55 each. What is the cost of a. 4 pears? b. 10 pears? c. 18 pears? $2.20 $5.50 $9.90 0 4. If you walk at an average speed of 3.5 miles per hour, how far will you travel in a. 2 hours? b. 6 hours? c. 21" hour.? 7 21 1.75 ~ 5. Miche"e can run 5 miles in 35 minutes. At this rate, how long does it take her to run 1 mile? 7 a. 5.87 d. 3.40 e. 93.29 308 miles 6. Round each number to the nearest tenth. c. 9.65 ~ miles ~ b. 0.32 minutes miles 5.9 0.3 9.7 3.4 93.3 ~
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