Date Time Divide each shape into equal parts. Color a fraction of the parts. Write the name of the "whole" in the "whole" box. 1. Sample answers: Whole hex.agon Divide the hexagon into 2 equal parts. . Color ~ of the hexagon. 2. Whole -, rhombus i "!"'~'7~':"';'>_I'_"~~rp"'1'!/~(~f:?JttfIY- Divide the rhombus into 2 equal parts. Color ~ of the rhombus. 3. Whole trapezoid i r I ';'~''''''''Y'''''''''4"W~F';'~)",';_'''~:t'~~- Divide the trapezoid into 3 equal parts. Color ~ of the trapezoid. Divide the hexagon into 3 equal parts. Color of the hexagon. t 185 Date Time . _ 5. Fraction Review continued Whole hexagon Divide the hexagon into 6 equal parts. Color ~ of the hexagon. 6. Whole hexagon Divide each hexagon into thirds. Color 1 hexagons. i 7. Whole rhombus Divide each rhombus into 2 equal parts. Color rhombuses. 2t Grace was asked to color ~ of a hexagon. is what she did. What is wrong? m Ie answer: She did not divide the hexagon into . .~ equal part~_._ _ 186 • Date Time • . Fraction Review continued ~ Fill in the missing fractions and mixed numbers on the number lines. 9. ~4~1----------+----------+1----------+1----------+1~. 0I2 3 4 'f 1 4 10. ~4~1------------~1--------------+1--------------+1~. o 11. 4 1 2 3 3 1 I I I I I I o 1 2 3 5 1 6 6 6 6 III' 12. ~4~1----~1-----+1----~1-----+1----~1-----+1----~1-----+1~. 1 o 13. 14. 4 4 2 3 4 5 6 7 888 8 888 1 I I I I o 1 2 2~ 3 /~ / I I I I I o 1 2 5 3 5 4 5 5 2 I / III' 2 I I I 1~ 1~ 1~ 1~ 555 I III' 2 5 Try This 15. Enter the fractions above on your calculator. Record the keystrokes you used to enter j and 1 ~. Sample answer: On my TI-15, I pressed 2 ( n J 4 ( d J for ~. To enter 1i, I pressed 1wn:ID 1 QJJ 5GLJ. On my Casio fx-55 , I pressed 2 (hie] 4 for ~ and 10 1lEJ 5 for 11. 187 Time Date 1. What fraction of the clock face is shaded? or ~ 12 1 4' 2. LPOL is an 0 tuse (acute or obtuse) angle. o L The measure of LPOL is 145 3. Multiply. Use a paper-and-pencil algorithm. ~196 =94*34 ° 4. The five largest birds that are able to fly have the following weights: 16.3, 16.8, 20.9, 15.8, and 15.8 kilograms. a. What is the median weight? b. What is the mode? c. What is the range? d. What is the mean? 5. a. What city in Region 1 is located near 0 30 N latitude and 31°E longitude? Egypt kg kg kg side of the rectangle. 2. _ _ In. 1. 1 . _ _ In. _ _ In. 2· c. On which continent is the city located? Africa 15.8 5.1 17.12 6. a. Measure and record the length of each Cairo b. In which country is the city located? 16.3 kg _ _ In. b. What is the total distance around the rectangle called? Circle one. ~ ~ime~ 188 area . ~ Date 1. Time "-l Whole /6 nickels ( '~':l-',,-' T_""¥J'_'''I1'~~''i'':'':::)' '" a. Circle~ of the nickels. b. How much money is that? 0 . 60 $ 2. Whole 12 dimes a. Fill in the "whole" box. b. Circle ~ of the dimes. How much money is that? 1 . 00 $ 3. Whole ! 10 quarte~s "'~'>')'-",0' ,:;I; "~~"" .s, a. Fill in the "whole" box. b. Circle~ of the quarters. ;ow 1UCh mongo that? 189 8 c. 3" of 12 3 = 9 c. 3 = 27 c. :}of 36 54 = 20 c. iof32 = ~36 t of 24 = 16 c. 3 b. 5" of 15 9 b. 4" of 36 4 b. i 4 b. 7 10. of 22 = 11 11. What is t of 25? 121. % = b. 3" of 12 = 2 9. 4" of 14 2 4 of 32 5 i of 15 3 16 = 20 = 21 of 24 = 52 Explain. Sample answer: ~ of 25 is the same as dividing 25 by 2, which~_1_2-=-~._ _ _ _ _ _ _ _ 12. Michael had 20 baseball cards. He gave and i to his brother Dean. i- of them to his friend Alana, a. How many baseball cards did he give to Alana? __ ~_4_ _ cards __8__ cards b. How many did he give to Dean? 8 c. How many did he keep for himself? Try This 13. Maurice spent t of his money on lunch. He has $2.50 left. How much money did he start with? $5.00 14. Erika spent! of. her money on lunch. She has $2.00 left. How much money did she start with? 190 $8. 00 cards Time Date 1. What fraction of the clock face is shaded? 2. Draw angle ABC that measures 6So. Fill in the circle next to the best answer. ® t • 1~ © @ t f B LABC is an C _a_c_u_t_e_ (acute or obtuse) angle. 3. Mary has 27 pictures. She gives t of them 4. Divide. Use a paper-and-pencil algorithm. to her sister Barb and! to her cousin Sara. 962/12 a. How many pictures does Barb get? = 2 80 R2, or 80 12 __9_ _ pictures b. How many pictures does Sara get? _1_8_ pictures c. How many pictures does Mary keep? o ____ pictures ~ ~ ~------------------------------~ 5. There are 29 students in Ms. Wright's class. Each collected SO bottle caps. How many bottle caps did the students collect in all? 1 450 6. Find the area of the figure. D= 1 square centimeter v bottle caps Area '"/1 , _7_.5__ square cm 191 Time Date A deck of regular playing cards is placed in a bag. You shake the bag and, without looking, pick one card. 1. How many possible outcomes are there? 52 (Hint: How many cards are in the bag?) _.. possible outcomes 2. Are the outcomes equally likely? yes (Hint: Does each card have an equal chance of being chosen?) 3. Find the probability of each event. Probability of an event = ! I Favorable Outcomes Event i 26 Pick a red card Pick a club Pick a non-face card I i num~er Off favor~~le o~tcomes num er 0 POSS! e ou comes Possible Outcomes Probability em 52 52 I 13 52 40 52 [3] 52 40 52 I 3 Pick a diamond face card 52 52 I Pick a card that is not a diamond face card 49 52 I i i Pick the ace of clubs 1 52 1 52 52 52 52 52 I Pick a red or a black card I 1 I I Pick the 23 of hearts I I 49 52 0 0 52 52 i e the word or phrase that best describes the probability of picking a 5 a bag of 52 regular playing cards without looking. impossible @ unli~ even chance likely Sample answer: The probability of choosing a 5 card is only 4 out of 52. Explain why you chose your answer. 192 i I . Time Date 1. What fraction of the clock face is shaded? 1 3, 4 acu e 2. LMRS is an (acute or obtuse) angle. or 12 S The measure of LMRS is 35 3. Multiply. Use a paper-and-pencil algorithm. 8,987 = 19 * 473 ° 4. Cleo's friends ran the 50-yard dash in the following times: 7.9,12.1,8.5,11.7,8.3,11.7, and 9.8 seconds. What is the mean time? Fill in the circle next to the best answer. (IS) 11.7 seconds ® 9.8 seconds • 10 seconds @ 12.1 seconds 5. a. What city in Region 2 is located near 0 0 60 N latitude and 10 E longitude? Oslo 6. Measure the length and width of your journal to the nearest half-inch. Find its perimeter. a. Length 11 = b. In which country is the city located? Norway b. Width 8 = c. Perimeter = inches inches 39 inches c. On wl"lich continent is the city located? Europe 193 Time Date Use Math Masters, page 212. For Problems 1-6, Shape A is the whole. 1. Cover Shape A with trapezoid blocks. What fraction of the shape is covered by 1 trapezoid? 2. Cover Shape A with rhombuses. 1 3. Cover Shape A with triangles. What fraction of the shape is covered by What fraction of the shape is covered by 1 rhombus? 1 triangle? 1 3 2 rhombuses? 2 3 1 3 6, 3 triangles? 6 1 or "2 5 6 5 triangles? 4. Cover Shape A with 1 trapezoid and 3 triangles. With a straightedge, draw how your shapes look on the hexagon at the right. Label each part with a fraction. 5. Cover Shape A with 2 rhombuses and 2 triangles. Draw the result on the hexagon below. Label each part with a fraction. 6. Cover Shape A with 1 trapezoid, 1 rhombus, and 1 triangle. Draw the result on the hexagon below. Label each part with a fraction. 1 1 3 1 3 194 2 1 3 Time Date Use Math Masters, page 212. For Problems 7-12, Shape B is the whole. Whole I: Shape B: .• .#~9YE>le,~.~~a,QP~) 7. Cover Shape B with trapezoids. What fraction of the shape is covered by 1 1 trapezoid? _--,-4__ or 21 2 trapezoids? -=.4_,_ _ 2 = 3 trapezoids? 3 _----:..4__ 8. Cover Shape B with rhombuses. What fraction of the shape is covered by 1 1 rhombus? 6 3 rhombuses? orl 3 6, 2 5 5 rhombuses? 6" 9. Cover Shape B with triangles. What fraction of the shape is covered by 1 triangle? _1 12 2 triangles? .£. or 1 12 , 6 3 triangles? 1 3 or 4 _1__2_'__ 10. Cover Shape B with hexagons. What fraction of the shape is covered by 1 hexagon? 1 __ 2__ 1_ _ 2 hexagons? __ 11. Cover Shape B completely with 1 hexagon, 1 rhombus, 1 triangle, and 1 trapezoid. Draw the result on the figure at the right. Label each part with a fraction. 12. Cover Shape B completely with 1 trapezoid, 2 rhombuses, and 5 triangles. Draw the result on the 'figure at the right. Label each part with a fraction. 1 4 195 Time Date Use Math Masters, page 212. For Problems 13-16, Shape C is the whole. t Try This 1 Whole ~~,:;-'?'y~;,:'!!,:..t':,,~-""'1 13. Cover Shape C with trapezoids. What fraction of the shape is covered by 1 1 trapezoid? 2 _---"'S=---_ 2 trapezoids? 1 8', 0 r 4' 6 6 trapezoids? 3 8' ,or 4' 14. Cover Shape C with rhombuses. What fraction of the shape is covered by 1 rhombus? 1 12 3 rhombuses? 3 12 or 1 4' 6 rhombuses? 6 or 21 -,-1..; ; ; ;.2_'_---.;-' 15. Cover Shape C with triangles. What fraction of the shape is covered by _1 1 triangle? 24 3 triangles? ~ 24, or 1 S 12 triangles? 12 1 24, 0 r '2 16. Cover Shape C completely, using one or more trapezoids, rhombuses, triangles, and hexagons. Draw the result on the big hexagon below. Label each part with a fraction. Sample answer: 1 8 1 8 • 1 12 196 1 4 Date Time 1. What fraction of the clock face is shaded? 2 3", or LMN that measures 120°. 2. Draw angle 8 12 M N obtuse LLMN is an (acute or obtuse) angle. 3. a. In December, * of a foot of snow fell on Wintersville. How many inches of snow fell? 4. Divide. Use a paper-and-pencil algorithm. · 3 809/13 _62 R3, or 62"13 __9__ inches b. Tina's daughter will be ~ of a year old next week. How many months old will she be? _1_0_ months 5. Each student eats an average of 17 servings of junk food per week. About how many servings of junk food would a class of 32 students eat in a week? 6. Find the area of the figure. D= 1 square centimeter I _5_4_4_ servings i L VI Area .'" I i = __7_"_5__ square cm 197 Date Time Use pattern blocks to find fractions that add up to 1 whole. lines to show the blocks you used. Write a number to show that the sum of your fractions is 1. Sample answers: Whole hexagon 3 + 1 6 2 -- 1.2 + 1.2 = 1 2. Use pattern blocks to find fractions that add up to ~. Draw lines to show the blocks you used. Write a number model to show that the sum of your fractions is ~. Solve. You may use pattern blocks or any other method. 1 3 2 3. 6-6 5. ~ - t: 198 - -6 i, or ~ 4. i 5 6. 6 ~ = 1 -"2 1 _---..::2=--_ ~, or i 1 Date Time .[F!,~~!~!,Cllld Mixed-Number Sums & 7. Use pattern blocks to find three different pairs of mixed numbers 2l Use your Geometry Template to illustrate the that add up to mixed numbers. Write a number model to show that the sum of each pair of mixed numbers is Sample answers: 2l Differences Whole hexagon a. 1 1 24 13 +_13 6 Number model: _ _ --=-_ ---=_ _ _--=-_ b. 1 16 + 13 = \ 7 246 6 _ _-=--_ l\lumber model: _ _--=_ _--'=_ c. 0 0 Number model: 7 r------7,\ 1 24 - _----'''---_ 221 6 6 _ _---"'-'---_-"'-_ + Solve. You may use pattern blocks or any other method. 9. 10. 1i - t = 5 6=--_ _--.e 11. 1~ -1t = 1 _--,3=-_ ~ ~ = _~=-'--,_o_r--=~::.- 1 _ 198A Time Date 1. Rithik ate ~ of a cheese pizza. He then ate ~ of a veggie pizza. 4 f' a. What fraction of a pizza ~d he eai in all? . loa pizza, ors3 0f a.Plzza + · = 6 2 amp le num ber models are given. 6 Number model: _ _----==~_---=-. 6 _ _= _ __ _ b. Did he eat more or less than a whole pizza? _ less How do you know? Sample answer: ~ would be 1 whole pizza, and 2. Karina walked t < ~. t of a mile to school. After school, she walked t of a mile to the store, and then t of a mile back3to her home. mile 4 _ _ _ _ __ a. How far did she walk after school? _ _~--=- 213 Number model: '4 b. How far did she walk in all? Number model: + '4 = '4 ~ mile, or 1 mile 121 4 _ _4L--+~--,4--,+,---4-,----__4,---_ 3. Stephana is making pancakes and waffles for his guests. a. He needs ~ cup of milk for the pancakes and ~ cup of 4, 3 milk for the waffles. How much milk does he need in all? _ __ 0r 1-31 CU pS 224 '3 Number model: + '3 =.. ""'3_ __ b. Stephana has 1 ~ cups of milk. Will he have any left over? If so, how much milk will be left? Number model: 132 - Yes. i cup 113 ---=3=--_ 1 Try This 4. Kumba has one dollar. He spent t of the dollar on a pencil and 1~ of the dollar on an eraser. 7 a. What fraction of the dollar did he spend? 1 Number model: _ _.. . . 2 2 + TO = 10__ b. What fraction of the dollar does he have left? Number model: 1988 1- ~ = TO 7 3 ______ 1_0_____ 3 1.0_ .. _ Time Date 1. Circle ~ of all the triangles. Mark Xs on ~ 2. Insert parentheses to make these number sentences true. of all the triangles. a. 8.2 -(5.2 + 2.5) = 0.5 b. 13.6-~+8)=0.6 c. 9.1 =(28.4 - 1.1) -:- 3 d. 9 *(2.5 + 3.5)= 54 4. Draw and label a 3. Plot and label each point on the 45° angle. coordinate grid. A (5,0) 5 1--+--+--+=-+----+- 8 C E 3 t-=-+--+--+--+--+--- B (3,5) 4 c (1,4) 2 I--+---t--+--+--+--- o (1,1) 1 I----t>-=O:+-+-+-A-=--l0 0 1 2 3 4 5 5. A bag contains red blocks, blue blocks, green blocks, and orange blocks. You put your hand in the bag and, without looking, pull out a block. About what fraction of the time would you expect to get a blue block? 4 2(5, R This angle is an acute Y (acute or obtuse) angle. E (2,4) 6 4 7 3 T Sample answer: 1 or 5" 6. If 1 centimeter on a map represents 10 kilometers, then b. 6_0__ km. 19.5 cm represent _1_9_5 __ km. c. __3__ cm represent 30 km. d. __5_"_5__ cm represent 55 km. a. 6 cm represent __ e. 0.5 cm represent 5 km.~ ~ 199 Date Time 1. Which fraction is another name for ~? Fill in the circle next to the best answer. t • ! ® 2. A bag contains 2 blue blocks, 3 red blocks, 5 green blocks, and 10 black blocks . You put your hand in the bag and, without looking, pull out a block. About what fraction of the time would you expect to get a black block? © 1~ @ ~ ~ 10 20, or 1 2 ~ ~------------~~--------------~ 3. Use pattern blocks to help you solve these problems. a. LTAPis an 0 use (acute or obtuse) angle. 4 or 23 t + ~ = _6=----,_ _-= 5 b. t + 1= _----.;6=---_ 1 1 §- i = ~, 0 r ! c. "3 - "3 = d. 3 -----==-- 2 ~ ~ 5. Next month 486 students, teachers, and parents are going on a field trip to the zoo. Each bus holds 35 people. How many buses are needed for the trip? 14 buses p A The measure of LTAP is 135 0 6. Tell if each of these is closest to 1 inch, 1 foot, or 1 yard. a. the length of your smile b. the length of your journal 1f c. the distance from your waist to your feet 1 inch t 00 1 d YCJ._r_ _ 1 inch d. the width of your wrist --~-- ~ 200 Date Time Use pattern blocks to help you solve the problems. 1. i +i = 7. 9. 4. 1t+t= 1t or 2 11 2TO 1 1 10 1 TO, or 11"0 + 1"0 = 6. 1 ~ ~ = _--,9~,=---o_r------,,3,"---_ 4 6 2 11. "8 - "8 = 13. 1 ~ 10. 1 8, or 2 --=------=--- 12. 1~ 4 t + - __----"5=---_ _ 5 2 3 3 12 112 + 212 = ----=-==-- 61 4~, or + 1"21 = - =----= 1 2 1 3 "3 - "3 = - - - ' ' ' " - - - t -t = 1 _ _ _-=-7_ __ 1- 41 = - - - - -11 =--- 16. 4~ - 2% = ___1~ ~ = _ _ _--=--_ _ is. 10% - ---=----- 4 8. 3"2 --'---=-----"-=- 3 ~, or 1 4 2 2. "6 + "6 = ~, or 1~ 3• ~ 2 +.1 2 5. 2 _ _---"3""--_ _ 14. 5 4 6~ = _ _ _ _ __ --=-_ __ 17. Ryan and Reggie baked an apple pie that was cut into 12 equal pieces, Ryan had 5 ?2 of the pie, and Reggie ate 12' Who ate more? Reggie 8 What fraction of the pie did the boys eat all together? -12, or _--::...;;;;;:=---_--=-_ 18. Alice and Cherice run at the same park. On Saturday, Alice ran ran t of a mile. ~ of a mile, and Cherice A_Ii_c_e_-------. Who ran the shorter distance? _ _ How far did Alice and Cherice run all together? _O_,_o_r_1_1_ miles _18 200A Time Date Add and subtract. Use pattern blocks to help you. 2 5 3 2 4 8 2. a-8+a=--- 4 2 5 3 4 7 6 , or 73 4. 76 + 16 - 16 = ---:8-'--- 1 1• 14 + ~4 _14 = 4' or 2 3. 5. 1~ - 122 - 1~ = 1 12 2 1 4~-~ + 11 = 54' or 52 4 4 ~ ~_ 7. 2+2 4 9. (29 6. 1 2' or 12 43 1 _ 2----- 2 + 9) - 1 (9 + 193 ) = 8. 2 19 ---- 3 s 1 428 11. (a-a) (a-a) =- - - 10. ± + ~ + 3~ = 38 , 0 r 4 8 8 8 4 1 2 4 1 (a3 a) + (a-a) =-8'-or -2 10 5 11 _1 _ ~ _ 1 _ 5 12 , or 56 (1012 + 12) (5 12 12 - - - - 5 3 12. (5 1 2 1 -, or 1 + 5) + (5 - 5) = ~. .- -- 13. Paulo, Regina, and Ted picked a bucket of apples on the ls of the apples, field trip to the apple orchard. Paulo took Regina took 1~ of the apples, and Ted took 1~ of the apples. They decided to give the rest of the apples to the teacher. Who took the most apples? Regina What fraction of the apples did their teacher get? How do you know? Sample answer: I added fs + ~ + ~ and I got i¥. Since I know that the total number of apples was I subtracted i¥ from that and I got fs. That's how many the teacher gets. .. 14. Julie was making a quilt. She had . .... ~ yard of fabric. She bought another ~ yard of fabric. She gave: yard of the fabric to her friend. How many yards of fabric does she have left? 2008 *, 8 8 ' or 1 yard _=--____ .. Time Date Color the squares and write the missing numerators. 1of each large square. 1. Color IJl _L2.J_ is colored. 1 square 1 2 1 is colored. 4 2 2. Color Whole t of each large square. 1 1 is colored. 4 f21. ~ colored. _ _ IS 8 f4l. L::!J __ IS colored. 16 3. Color! of each large square. ~ is colored. 4 [ [ ] is colored. 8 1121 is colored. 16 201 Time Date 1. Circle -i of all the squares. Mark Xs on i of all the squares .. 2. Insert parentheses to make these number sentences true. Sample answer: rtJD[jDD~ DDDDD~ ~DODD~ DDDDD~ a. 2 *(3 + 10)= 26 b. 12 = 6*(6 - 4) c. (24 - 5)* 2 d. 12 + 24 = 3*(6 + 6) 4. Draw and label a 3. Plot and label each point on the 38 1250 angle. coordinate grid. A (0,2) B (4,0) 5 D (5,5) T 4 1--1---1---f----1f-:=E=+- 3 C (1,5) Sample answer: ~--=C=-'I---'f----1r=D4- A 2.---1----'---I---+--t- 1 0 o f--+--+-+---l--=B::+0 1 E (5,3) 2 3 4 p 5 ~ This angle is an obtuse !:Ftl ~________________________~~_-~l«~-~Ir-~(a~c~u~te~or~o~b~tu=s~e~)~an~g~le~.______~~14~J~ 5. A bag contains 5 6 1 3 green blocks, red blocks, blue block, and yellow blocks. You put your hand in the bag and, without looking, pull out a block. About what fraction of the time would you expect to get a blue block? 1 15 202 6. If 1 inch on a map represents 40 miles, then how many inches represent 10 miles? Fill in the circle next to the best answer. ® 2in. • l' '4 In. © tin. @ 4in. Date Time , Whole f large square) ~~~",,~Yt~~r::,~t?'~ , ,, ,, ,, ,, , , ,,, , ,, ,, ,, ,,, ,,, ,, ,,, ,, ,, ,,, ,, ,,, ,, :, :, ,, ,, ,, :, , ,,, , , ,, ,, ,, ,, ,, , ,, ,, , , , ,, ,, ,, ,, ,, , :, ,, ,,, ,,, ,, ,, ,, ,,, ,, , , : ,,, ,,, ,,, , ,,, : ,,, ,, , : ,,, : ,, :, ,, ,, : :,, ,,, ,, :, , , , , , : ,, ,, :, ,, ,,, lo of the square is shaded. 2 How many tenths? ,, ,, ,,, ,,, 2 10 1 10' or 0.1 2 o.--=- t is shaded. ~oT5nJ tenths? 5 2- 3 5. "5 10 i is shaded. 10 8 [[] "5 10 1 100' or 10 .g. is shaded. How many tenths? 1 0.-- []]=0._6_ 6. 4 "5 5 2 2 0.--""'-'--- 0.01 How many tenths? 2 "5 @] 4 4 o.---=- 10 -i is shaded. t is shaded. 1 "4 [25] 100 25 0.--- 3 "4 [Z§J 75 0.-- 100 203 Time Date 1. Complete the name-collection box. 2. A bag contains 4 "'---_ _ _5_ _____: 8 blue blocks, 2 red blocks, 1 green block, and 4 orange blocks. Sample 3 + .1 ' answers: 55, 0.8 You put your hand in the bag and, without looking, pull out a block. About what fraction of the time would you expect to get a red block? 8 10 9 1 1(5-1(5 2 15 3. Use pattern blocks to help you solve these problems. 2 b. c. %- d. 1 6 64 - 2" = -----'''--- i= LARTis an 6, 4 6, acute (acute or obtuse) angle. 6 3 t t= ~ +i = a. 4. A i, or 1 or~ R 1 ~ T - The measure of LART is 40° ~ r-------------------------------~ 5. There are 252 pages in the book Ming is reading for his book report. He has two weeks to read the book. About how many pages should he read each day? _.18 204 pages 6. Tell if each of these is closest to 1 inch, 1 foot, or 1 yard. 1 yard b. the width of your journal 1 foot c. the length of l' h your largest toe Inc d. the length of your shoe 1 foot a. the height of the door Time Date Math Message: Eating Fractions Quinn, Nancy, Diego, Paula, and Kiana were given 4 chocolate bars to share. All 4 bars were the same size. 1. Quinn and Nancy shared a chocolate bar. Quinn ate Nancy Who ate more? t of the bar, and Nancy ate f. 1 How much of the bar was left? _ _ _4-=--_ _ 2. Diego, Paula, and Kiana each ate part of the other chocolate bars. Diego ate ~ of a bar, Paula ate t of a bar, and Kiana ate i of a bar. Diego How do you know? Sample answer: Diego ate ~, which is more than ~. Paula ate ~ which is less than 1. Who ate more, Diego or Paula? Comparing Fractions with ~ Turn your Fraction Cards fraction-side up. Sort them into three piles: t fractions equal to t • fractions less than • • fractions greater than You can turn the cards over to check your work. When you are finished, write the fractions in each pile in the correct box below. Less than ~ Equal to 1 1 0 1 2 2 2 3 0 3, 4, 5, 5, 5, 4 3 234 2, 4, 6, 8, 5 6 10,12 6, 8, 9, 10, 2 1 4 10,10,12,12 ! Greater than ! 2 3 345 3, 4, 5, 5, 5, 4 6 6 6 6, 8, 9, 10, 8 10 8 9 10,10,12,12 205 Date Time Write the fractions in order from smallest to largest. 1. 4 7 8 2 1 TO, TO, TO, TO, TO 1 10 4 2 10 10 7 10 1 .1 2' 1 1 100 9' 5' 1 100 1 9 1 5 1 4" 2 2 2 2 100 2' 9' 5' 2 2 100 9 2 5 2 4 smallest 4 4. 25' 1 25' 1 25 1 2 largest smallest 2 3. 4' 10 largest smallest 1 2. 4' 8 2 2 largest 7 6 7 8' 12' 15 4 25 7 15 6 12 7 8 largest smallest 5. Choose 5 fractions or mixed numbers. Write them in order from smallest to largest. Answers vary. smallest largest Which fraction is larger: ~ or ~? 2 5" Explain how you know. ample answer: ~ has a smaller denominator than ~, so each fifth is bigger than each seventh. --------------~~------------------------------ 206 Date Time t of the day at school. Lunch, recess, music, gym, and art make up t of 1. Sari spends 2. Multiply. Use a paper-and-pencil algorithm. 5,152 her total time at school. How many hours are spent at these activities? 2 = 92 * 56 hours Show how you solved this problem. Sample answer: 8 hr; 1 4 of 8 hr 1of 24 hr = = 2 hr 3. Adena drew a line segment t t inch long. Then she erased inch. How long is the line segment now? Fill in the circle next to the best answer. ® ® • ~ l!l 4. Write an equivalent fraction, decimal, or whole number. Decimal 4'In. '6 a. 0.40 2' 2 m. b. 1 . 4 m. c. ~ 55-5: . @ 1141n. 5. Complete the table and write the rule. Rule: + 5.73 in out 6.19 11.92 12.03 17.76 3.26 0.01 8.99 4.41 10.14 40 JOO 0.3 1.0 d.0.6 100 100 ~ 6. Complete. = b. 43 in. c. 6 ft = d. 11 ft = e. 73yd a ...a. 10 6 jQ a. 17 in. 5.74 Fraction = 1 ft 5 3 ft 7 2 yd 3 yd 2 219 ft in. in. ft ~ 129' 207 Date • Time What Is the ONE? Math Message 1. If the triangle below is . ~, then what is the whole-the ONE? Draw it on the grid . . . 2. If ~ of Mrs. Chin's class is 8 students, then how many students does she have altogether? 32 " students Use your Geometry Template to draw the answers for Problems 3-6. 3. If 6. If <> iS~, D.:J iS~, then what is the ONE? then what is the ONE? I 208 4. If a s ~, then what is the ONE? is 2 then what is the ONE? Date Time 1111 What is the ONE? continued Solve. If you wish, draw pictures at the bottom of the page to help you solve the problems. 00 0 0 0 00 15 counters 16 counters ~, then what is the ONE? 25 counters 10. If 12 counters are ;, then what is the ONE? 16 counters 7. If 8. If 0 0 iS~, then what is the ONE? iS~, then what is the ONE? 9. If 10 counters are 11. If ~ of the cookies that Mrs. Jackson baked is 12, then how many cookies did she bake in all? 12. In Mr. Mendez's class, 60 cookies ! of the students take music lessons. That is, 15 students take music lessons. How many students are in Mr. Mendez's class? 20 students 13. Explain how you solved Problem 12. Sample answer: I divided 15 by 3, which told me that each fractional pa.rt is equal to 5 students. So, the whole is 4 * 5, which is 20 students. is an equivalent fraction to ~. 19 209 Time Date f ,J ~_" ":..,..r~/{ Veronica collected 15 insects for a science project. She measured the length of each insect to the nearest ~ inch. Her measurements are shown in the table below. Length (to the nearest inch) Insect I Insed t , 1.12 Darner dragonfly Red 3 Length (to nearest inch) t .I. "<;;J<;;J Boreal fi refly 8" Yellow bumblebee "4 Damselfly 1.1 4 Paper wasp 1~ American cockroach 3 i 7 8" i Ground beetle 8" 7 Field cricket 8" 7 Green lacewing 1 Indian meal moth 8" Lady bug 8" 5 Katydid 1~ 4 3 1~ 4 Carolina mantid " ~4J:lj£"'i}t+1':WWMi,iiYi'"", Plot the insect lengths on the line plot below. Then use the completed plot to answer the questions on the next page. Insect Lengths I I en ..... I I 0 i Q) en c: I 0 ' Q) I X Xi XI X XIX X X X ..0 E X .. XI ::::l z I 3 I 1 8 2 I 5 8 I 3 4 I 7 8 1 1 I 18 1"4 Length (inches) 209A 1 X X .X X : I 1~ 8 I 13 4 ... Date Time Use the line plot on journal page 209A to answer the questions. Write a number model Sample number models are to summarize each problem. 1. a. What is the maximum insect length? 13 4" b. What is the range of the data set? 7 2. a. What is the median of the data set? in. '8 4 - Number model: in. 4 3 "8 - '8 Number model: 1 7 _--=8__ 7 4" - '8 1 or '2 in. in. b. How much longer is the maximum length than the mode length? 13 138 = '2 3. a. What is the mode of the data set? Number model: "8, given. in. 13 3 _ b. How much longer is the median length than the minimum length? 7 '8 in. The minimum? 3 18 3 . 7 _--"",8__ in. = "87 1 4. Two insects have the maximum length. What is the difference in length between these insects and the next-longest insects? _---"-__ in. Number model: 143 -1 12 - 14 5. There are three insects in Veronica's collection that are from t inch to ~ inch long. If these three insects were placed end to end, how long would the line of insects be? 1§. 8 , 0 r2 in. Number model: 5 8 + 85 + 3-2 4 6 insects less than t inch long were placed end to end? 8, 333 6. How long would the line of insects be if all the Number model: "8 3 or 4" in. + "8 = 4" 7. Make up and solve your own problem about the insect data. Answers vary. Number model: 209B Date Time 1. Name the shaded area as a 'fraction and a decimal. 2. Which number sentence is true? Fill in the circle next to the best answer. a. fraction: 27 100 b. decimal: 0.27 @ ..£.=~ 12 6 ~ ~ 3. Write 6 fractions equivalent to 7 28 "8 32 21 70 24 80 35 168 40 ~:. 4. Divide. Use a paper-and-pencil algorithm. _ 51 R9, or 51 ~2: 9 14 192 Sample answers ~ : 2223 179 5. Multiply. Use a paper-and-pencil algorithm. 8,432 = 68 * 124 6. Compare. 12 times as long as 2 hours. b. 6 years is 18 times as long as a. 1 day is 4 months. 6 c. 3 gallons is 8 cups. d. 8 cm is 40 e. 1 meter is 210 times as long as 2 mm. 50 long as 2 cm. times as much as times as Date Time • • MakingSpinners 1. Make a spinner. Color the circle in 6 different 12 colors. Design the spinner so that the paper clip has the same chance of landing on each of the colors. 3 Sample answers: 12 2. Make another spinner. Color the circle red, blue, and green so that the paper clip has • a i chance of landing on red and • a ~ chance of landing on blue. 9 a. What fraction of the circle did you color 3 1 2 1 red? 6 blue? 6, '3 green? 0r 3 0r b. Suppose you plan to spin the paper clip 24 times. About how many times would you expect it to land on red? 4 blue? 8 green? 12 c. Suppose you plan to spin the paper clip 90 times. About how many times would you expect it to land on red? 15 blue? 30 green? 45 211 Time Date Math Boxes' 1. According to a survey of 800 students at -i Martin Elementary, about of them chose pizza as their favorite food. Of those who chose pizza, ~ liked pepperoni topping the best. How many students liked pepperoni topping the best? 300 2. Multiply. Use a paper-and-pencil algorithm. 71 2,698 * 38 = students ~ ~ 3. a. Hannah drew a line segment 1 ~ inches long. Then she erased ~ inch. How long is the line segment now? 1~ inches -i ~ -2.96 70 100 9 9 2 10 d. 0.2 ~ 6. Complete. a. 5 ft = b. 40 in. = 100.54 97.58 c. 80 in. = 55.91 52.95 72.03 69.07 70.4 67.44 59.21 56.25 d. 108 in. a 25 100 b. 0.25 c. 1.0 out in Fraction a. 0.70 5. Complete the table and write the rule. 212 whole number. inches i Rule: 4. Write an equivalent fraction, decimal, or Decimal b. Joshua drew a line segment inch long. Then he added another inch. How long is the line segment now? 1~ 181: 1 e. 3yd = = 1 3 2 9 12 yd ft yd 2 4 8 ft in. in. ft in. ~ Date Time 1. If this spinner is spun 24 times, how many times do you expect it to land on each color? a. Fill in the table. I ! Color Expected Number in 24 Spins 8 8 red blue i 4 4 yellow green i Total 24 b. Explain how you determined the expected number of times the spinner would land on each color. Sample answer: Red and blue each cover ~ or of the circle. of 24 yellow each cover 4 spins. ! ins is 8 s ins. Green and i of the circle. i of 24 spins is ,":. 2. If a six-sided die is rolled 12 times, how many times would you expect to roll a. an odd number? 6 b. a number less than 4? c. a6? _6__ _2__ _4__ a triangular number? _6 __ a prime number? _6 __ d. a square number? e. f. 213 Time Date Getting Ready 1. Follow the directions for coloring the grid on Math Masters, page 238. You may color the squares in any way. The colors can even form a pattern or a picture. 2. For this experiment, you are going to place your grid on the 'floor and hold a centimeter cube about 2 feet above the grid. Without aiming, you will let it drop onto the grid. You will then record the color of the square on which the cube finally lands . • If the cube does not land on the grid, the drop does not count. • If the cube lands on more than one color, record the color that is covered by most of the cube. If you cannot tell, the toss does not count. Making a Prediction white 3. On which color is the cube most like/yto land? ~llow 4. On which color is it least like/yto land? 5. Suppose you were to drop the cube 100 times. How many times would you expect it to land on each color? Record your predictions below. Predicted Results of 100 Cube Drops Color I Number of Squares yellow red 4 green 10 blue 214 1 I I 35 white 50 Total 100 I i I Predicted Results Fraction Percent 1 100 4 100 i ! 10 100 35 100 50 100 1 I i 1 % 4 % 10 0/0 35 0/0 50 % 100% .. Date IIDlY Time A Cube-Drop -Experiment continued Doing the Experiment You and your partner will each drop a centimeter cube onto your own colored grid. 6. One partner drops the cube. The other partner records the color in the grid below by writing a letter in one of the squares. Drop the cube a total of 50 times. Write y for yellow, r for red, 9 for green, b for blue, and w for white. Sa.mple a.nswer: w w w b IW r Y W b W W b W· 9 W W b W W b W b W· W I :Pw 9 b b b r W b W b b b W W b b W W1W W W W b I I 7. Tl1en trade roles. Do another 50 drops, and record the results in the other partner's journal. My Results for 50 Cube Drops Sample a.nswers: 8. Count the number for each color. Number of Drops Percent white 1 2 3 16 28 20/0 4% 60/0 32% 56% Total 50 100% Color yellow red Write it in the "Number of Drops" column. Check that the total is 50. 9. When you green blue I : , have finished, fill in the percent column in the table. Example: If your cube landed on blue 15 times out of 50 drops, tl1is is the same as 30 times out of 100 drops, or 30% of the time. 215 Time Date 1. Write these numbers in order from least to greatest. 964 9,460 96,400 400,960 94,600 964 9,460 94,600 96,400 400 960 0 7 hundreds place, ten-thousands place, ones place, thousands place, and tens place. 7 with the following digits: 5 5 in the 7 in the o in the 9 in the 8 in the Write the number. 3. Write the greatest number you can make 3 2. A number has 9 9 5 8 o 4. What is the value of the digit 8 in the numerals below? 2 _.975,320 a. 807,941 __ 80 b. 583 8,00_0_ c. 8,714 80,000 d. 86,490 5. Write each number using digits. a. four hundred eighty-seven thousand, sixty-three 800,00_0_ 6. I am a 5-digit number. • The digit in the thousands place is the result of dividing 64 by 8. 487,063 • The digit in the ones place is the result of dividing 63 by 9. b. fifteen thousand, two hundred • The digit in the ten-thousands place is the result of dividing 54 by 6. ninety-seven 15,297 • The digit in the tens place is the result of dividing 40 by 5. • The digit in the hundreds place is the result of dividing 33 by 11. What number am I? 9 216 8 3 8 7 Date Time 1. Name the shaded area as a fraction and 2. Write <, >, or = to make each number a decimal. sentence true. a. fraction: 63 a. 8 - - 8 < 7 5 < 5 12 - - 6 1 1 > 4 - - 15 3 b. b. decimal: c. 0.63 500 8 d. 1000 - - 16 .§. < ~ e. 7 - - 20 3. Write 6 fractions equivalent to 2 12 3 4 5 i. 4. Divide. Use a paper-and-pencil algorithm. 769 15 - 51 R4, or 51 ~ -----------=-=- 24 6 36 100 600 Sample answers ~ 5. Multiply. Use a paper-and-pencil algorithm. 9,476 = 46 * 206 r-------------------------------~ 6. Compare. a. 1 day is _4_ times as long as 6 hours. b. 6 years is 36 times as long as 2 months. c. 3 gallons is 4 cups. 12 times as much as 16 times as long as 5 mm. e. 1 meter is 10 times d. 8 cm is PJ\ ~ as long as 10 cm. 217 Time Date For Problems 1-3, fill in the blanks to complete an equation describing the number line. 1.... ~~~~~ I 0 Equation: 5 I I I I I 1 8 2 8 3 8 4 8 5 8 1 8 * I .. 1 7 8 6 8 5 8 - ~~~ 2. • I I I I o 1 6 2 6 3 6 3 6, 3__ *6 1_ Equation: _ _ I 4 6 5 6 1 5 3 6 3 orl2 ~~~~ 3. • .. I I I o 1 3 2 3 4 I I I 3 3 3 4 1 4 _ _ * _--=3__ = 3", or Equation: _ _ 11 ... 3 For Problems 4-6, use the number line to help you multiply the fraction by the whole number. 4. ... ~~ I I I 0 1 4 2 4 2 4, Equation: 2 * l = 5. • ... 3 4 1 or 1 ~~~~~.~ I I I I I I I 3 4 1 2 5 6 0 10 10 10 10 10 10 I ... 10 7 8 9 10 10 10 10 8 5 9 5 10 10, or~ 6 Equation: 6 * 1ri = ~~~~~~~ 6. • I I I I I I o 1 2 5 3 5 4 5 5 Equation: 7 217A 5 *i = t, or 1~ 5 6 5 I I 7 5 5 .. Time Date Example 1: Equation: 6 -1 5 *~ -1 5 = ~ -1 5 5 5 5 ~~~~~~ ... I I I I I I o Example 2: Equation: 3 * %= 2 5 ... I I 5 5 ... 10 5 ~ 2 5 2 5 - I I 5 5 o ... 10 5 Write an equation to describe each number line. 1 1 1. a." 1 _-----==6=----_ 1 6 * __4-=--_ - _ _4-=--_ 4 I 4 4 3 4 4 * 1 4 I 4 4 6 4 3 - 111 4 1 1 333 1 3 ~,...----.,...,...----.,...,...----.,...~~~~ I I o 8 I I ~ 1 * 3 - 2 3 I I I I I ~ 8 I o 4 I 2 3 I ~ 2 * 3 - ... 3 2 3 I I 9 3 2 3 ~~~~ b. III ... 8 1 3 ... 8 4 3 333 a.... 1 4 I I O 2 2. 1 444 I o b .... 1 .......---...........---...........---...........---...........---...........---.... I I I I I 4 I 8 I I I I ~ I III 9 3 3 3. Study the pairs of number lines above. Use the patterns you see to describe a way to multiply a fraction by a whole number. Sample answer: If I take the whole number, multiply it by the numerator of the fraction and then write the product over the denominator, that is my answer. 2178 Time Date Use number lines to help you solve the problems. 1.5* 5 ~ "6 = 11111 6 6 6 6 6 ~~~~~ .. I I I 1 3 .. I 1 I 1 I "8 3. 8 3, 4 4.2*"3=_- Sample answer: I 4 8 4 3 1 1 1 1 o 3 3 6 9 ¥, 0 r31~, 0 r 13 ~ = 4 *~ 8 - 8 8 3" 3 8 6 3 3 - 8 4 8 12 8" 8 8 10, 0 r '5 6. = 3 * 120 222 10 10 10 .. ~~~ I o 217C I I I I ... 3" ~~~~ I 1 I I 1 I 1 I i I I I i o ... 8 8 3 .. 3" ~ 223" or 4 - ... 9 ~~~ I I I I o 5. .1 3" =3* 1 1 1 888 .. 1 6 3" 3 ... 1 3 3 o .. 1 3 ~~~~~~ I 1 6 111 3 3 3 - I 6 * 1= ----'=--~----- 6 I Q,or2 o 2. I I 5 10 I ... 16 8 Sample answer: I I 10 10 .. Time Date Suma and her sister Puja are making 12 blueberry-wheat muffins for breakfast. The recipe lists the following ingredients: 1 cup flou r 1 egg t cup whole-wheat flour t cup skim milk 2 teaspoons baking powder ~ cup honey ~ cup blueberries ~ cup cooking oil t teaspoon salt ~ teaspoon cinnamon Use the list of recipe ingredients to help you solve the number stories below. For each problem, write an equation to show what you did. 1. The sisters decided to double the recipe. a. How many cups of whole-wheat flour do they need now? 2 2, or 1 cup(s) Equation: 2 * 12 == 22 b. How many cups of blueberries do they need now? or 12 2 * 34 14 , cup(s) Equation: or 12 c. How many cups of honey do they need now? 6 4, 4 3, or 113 cup(s) Equation: 2 6 4" * 32 4 3 2. Suma and Puja decide to make 48 muffins instead of 12. a. How many teaspoons of salt do they need now? 4 4, or 1 teaspoon(s) 4 Equation: * 14 4 4" b. How many teaspoons of cinnamon do they need now? .1£ or 14 1 8, teaspoon(s) or1 8 , c. How 4 2, 4 Equation:· * 38 12 If ma~ cups of skim milk do they need now? or 2 cup(s) Equation: 4 *1 '24 2170 Time Date The Hillside Elementary School walking club meets every Monday after school. The table below shows how far some students walked at their last meeting. ( . I Student Katie Mahpara 1 Miles Cole Jack 4 2" "4 10 Maria 5 5 9 3" Nikhil 5 3" 6" Use the information in the table to solve the number stories. 2 3. a. If Katie walks the same distance atevery meeting, how far will she walk after 2 meetings? _..... b. After 7 meetings? ~, 0 r 2~ miles '3 miles . c. After 7 meetings, Katie will have walked between _ _ _ __ Circle the best answer. 1 and 2 miles ~nd 3 m~ 4. a. If Jack walks the same distance at every 3 and 4 miles ~5, 0 r 2 ~, 0 r 21 meeting, how far will he walk after 3 meetings? _____ miles b. After 3 meetings, Jack will have walked between _ _ _ _ __ Circle the best answer. 1 and 2 miles ~d 3 m~ 8. a. If Mahpara walks the same distance at every 3 and 4 miles ~g, 0 r 3 160 , 0 r 3 ~ meeting, how far will she walk after 4 meetings? _____ miles b. After 4 meetings, Mahpara will have walked between _ _ _ _ __ Circle the best answer. 1 and 2 miles l Try This 2 and 3 miles ~nd4m~ -' "b:~r""'>'4l:Jt'i't,*",y?,"j;<!IJr:ry:*-'l'~'4\~r~;*:;o;!f' 6. If Cole walks the same distance at every meeting and wants to walk a total of ~ 7. Make up your own multiplication number story about Nikhil or Maria. Answers '217E 3=-__ meetings miles, how many meetings will he need to attend? _ _ Date Time 1. Karen used 60 square feet of her back i yard for a garden. Vegetables fill of her garden space. Tomato plants fill of the space taken up by vegetables. How many square feet are used for tomatoes? i 2. Multiply. Use a paper-and-pencil algorithm. 3,74 1 = 87 * 43 __6__ square feet :, .. a 1819 Lukasz drew a line segment that was inches long. Then he extended it another 2-i inches. How long is the line segment now? 2i 5 4 8 inches _---""'-- 4. Write an equivalent fraction, decimal, or whole number. Decimal Fraction a. 0.60 3i inches long. Then she extended it another 2t inches. How long is the line segment now? 57 P\ _---"8'"--- inches b. Sybil drew a line segment 0.65 c. 1.0 b. d. 0.9 -60- 100 65 100 50 50 - 9 ~ 10 ~ 5. Complete the table and write the rule. Rule: -3.49 in out 104.16 100.67 87.35 83.86 45.72 42.23 51.92 55.41 77.69 I 74.20 6. Complete. 3 192 b. 16 ft 5 c. 67 in. = 7 d. 22 ft = 1 4 e. 12 yd = a. 42 in.= a 162-1~ ft 6 in. in. ft yd ft 7 1 6 in. ft in. ~ 129' 217F Date Time 1. Measure the length and width of your desk to the nearest half-inch. Find its perimeter. a. Length b. Width = inches = 2. Find the area of the figure. D = 1 .square centimeter c. Perimeter = v v inches Answers vary. Area 3. If 1 centimeter on a map represents 20 kilometers, then 160 km. b. 3.5 cm represent 70 km. c. 1.5 cm represent 30 km. d. 2.5 cm represent 50 km. e. 0.5 cm represents 10 km. 2 4 b. 57 in. = = e. 8 yd = 1 ~ard the width of your ankle 1 inch c. the length of 1 inch your little finger ~ 3 5 24 ft 2 in. ft 9 in. d. the length of your forearm 1 foot ~ 130 ~ times as long as 12 hours. b. 3 years is ~ times as long as a. 1 day is 6 months. yd yd 1 c. 12 cm is ft d. 1 m is 60 times as long as 2 mm. ~ times as long as 20 cm. ft ~ 218 square cm 6. Compare. a. 26 in. = d. 16 ft 10 4. Tell if each of these is closest to 1 inch, 1 foot, or 1 yard. b. 5. Complete. = = IV a. the width of a door . a. 8 cm represent c. 9 ft '"v inches e. 3 gallons is 24 times as much as 2 cups. ~

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