36Copyright © 2002 Mathematics Learning
Non-routine Problems
1. Three people are sharing a pizza. Sara wants 1/4 of it andPat wants 1/3 of it. What fraction of the pizza is left forWan? Who gets the most pizza? Why?
2. Six toy cars can be parked in a row 16 inches long. Howmany toy cars can be parked in a row 64 inches long? 40inches long? 104 inches?
37Copyright © 2002 Mathematics Learning
3. One day the Lugnut Car factory produced 315 cars. Thecars were silver, black or white. One-ninth of all the cars weresilver. For every three black cars made, two were white. Howmany of each color did they produce?
4. A student had 85% of the questions correct on a test of60 questions. How many questions were missed?
38Copyright © 2002 Mathematics Learning
5. An artist has a set of white tiles forming a rectangle twelvetiles across and eight tiles high. She wants to insert down themiddle a strip of red tiles that is two tiles wide and a strip ofred tiles across the middle that is three tiles high. How manytiles will she need to put in? Show two different ways of find-ing how many.
6. An artist has a set of white tiles forming a rectangle m tilesacross and n tiles high. She wants to insert down the middle astrip of red tiles that is two tiles wide and a strip of red tilesacross the middle that is three tiles high. How many tiles willshe need to put in?
39Copyright © 2002 Mathematics Learning
7. Fatima asked 50 fifth grade students to name their favoritecolor. 30 picked red. She also asked 80 eighth grade studentsand 50 of them picked red. Which group liked red best?Explain your reasoning.
8. You can buy 12 tickets for the park for $15.00 or 20 tickets for $23.00. Which is a better buy?
40Copyright © 2002 Mathematics Learning
9. Paul’s swimming pool is in the shape of a rectangle, 19 feetlong and 13 feet wide. There is a 2 foot wide walkway aroundthe pool. A fence is build around the walkway. What is thelength of fence needed?
10. Chan’s photo lab has some stools with 3 legs and somechairs with 4 legs. There are more chairs than stools. If there isa total of 26 legs on the stools and chairs, how many stools arein Chan’s lab?
41Copyright © 2002 Mathematics Learning
11. Kelly completed a survey of 100 students for the schoolnewspaper. 71 said they liked rock music, 52 said they likedcountry music and 30 said they liked both. How many studentsdid not say they liked either?
12. The dimensions of a Greek Temple are 48 meters by 32meters. It is in the shape of a rectangle. Eight meters fromthe walls, is a row of pillars. If the pillars are eight metersapart how many are there?
42Copyright © 2002 Mathematics Learning
13. We needed 138 balloons to decorate the gym for a classparty. We had five bags of balloons. They all held the samenumber of balloons. We found we needed 18 more balloons tofinish the job. How many balloons were in each bag?
14. Blocks measure 1 1/2 inches on each edge. A cube onefoot high, one foot wide, and one foot deep is made with thesecubes. How many little blocks are in large cube of blocks?
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15. At Pizza Hut, 14 girls equally shared 6 large pizzas and 6boys equally shared 2 large pizzas. Who gets to eat more piz-za, a girl or a boy?
16. Antwon and Erik are collecting baseball cards. Togetherthey have 62 cards. Antwon has 8 more cards than Erik.
a. How many cards does each have?
b. A month later they have 86 cards and Antwon has 12 more cards than Erik. How many does each have now?
c. Suppose they had 11, 238 cards and Antwon had 341 more cards than Erik?
44Copyright © 2002 Mathematics Learning
17. A rectangular box holds 36 cubes. When she opened thebox, Marcia could see 12 on the top. If she could open it at anend, how many cubes would she see?
18. A rectangular box holds 48 cubes. When you open the top,how many might you see? For each possibility, list how manyyou would see from an end.
45Copyright © 2002 Mathematics Learning
19. A 6 inch by 8 inch photograph is to be enlarged so thatthe base which was 6 is now 15 inches. How high will theenlarged photograph be?
20. The area of the floor of a rectangular room is 315 sq. ft.The area of one wall is 120 sq. ft. and the area of another is168 sq. ft. The floor and ceiling are parallel. What is thevolume of the room?
15"
6"
8"
?"
46Copyright © 2002 Mathematics Learning
22. Eleven pencils cost as much as three pens. If seven penscosts $9.24, what is the cost of one pencil? Write youranswer in cents.
21. Paula‘s swimming pool is in the shape of a rectangle, 32feet long and 23 feet wide. There is a 3 feet wide walkwayaround the pool. A fence is build around the walkway. Whatis the length of fence needed?
47Copyright © 2002 Mathematics Learning
23. Some hexagons are put together in a row asshown below. Each side of a hexagon is 7 cm long. Ifthe row has 43 hexagons, what is the distancearound the row? 2,349 hexagons? n hexagons?
24. A museum is holding a contest to see exactly how manydifferent ways four identical baseball cards can be puttogether on the wall as a unit (same side up). The rules alsostate that the cardsa. must lie flat,b. not overlap,c. all four cards must have top edge up, andd. each card must have an edge in common with anothercard.In how many different ways can this be done?
48Copyright © 2002 Mathematics Learning
26. A square piece of paper is folded in half to form arectangle with a perimeter of 12 cm. What is the area of theoriginal square?
25. Tashana has 16 coins that total to $1.85. She has onlynickels, dimes and quarters. How many of each coin couldshe have?
49Copyright © 2002 Mathematics Learning
27. A 12 ounce can of soda cost 42 cents. How muchwould a 16 ounce can cost at the same cost per ounce?
28. A 12 ounce can of soda cost 27 cents. How much woulda 20 ounce can cost at the same cost per ounce?
50Copyright © 2002 Mathematics Learning
29. Twenty-eight slices of pizza cost $12. How much would70 slices cost?
30. The sales manager for Chicken Shack Restaurants isstudying the sales figures of two new varieties of chicken sand-wiches recently introduced at eight of its restaurants. For fourweeks, the three restaurants have been selling lemon-roasted-chicken sandwiches, and for three weeks, the other five restau-rants have been selling barbecued-chicken sandwiches. Duringthis testing period, 6000 l-r-c sandwiches were sold, and 7200b-c sandwiches were sold. Which of the two new chickensandwiches should the sales manager report as having the bet-ter sales?
51Copyright © 2002 Mathematics Learning
31. Mr. Barnes built a fence around his square chicken yard.He used 24 post and placed then 10 feet apart. What is thearea of the space enclosed?
32. I am thinking of two numbers. When they are addedthe result is 56. When they are subtracted the result is 14.What is the result when the two numbers are multiplied?
52Copyright © 2002 Mathematics Learning
33. How much would 1.37 pounds of cheese cost at $2.85 per pound?
34. A floor, 9 feet by 12 feet, is to be tiled with 4 inch by 6inch tiles. How many tiles are needed to cover the floor?
53Copyright © 2002 Mathematics Learning
35. What fraction of the square shown below is shaded?Points P and Q are midway along their sides.
P
Q
36. There are 27 rows of coins with the same number of coinsin each row. Forty-eight coins fill 8 rows. How many coins are there in all?
54Copyright © 2002 Mathematics Learning
38, One day while I was at school, the electricity went out at home. When Ileft for school that morning, all the clocks were working and agreed that thetime was 6:30. When I got home they all showed different times. The wind-up clock, which was unaffected by the outage, read 5:21. The analog electricclock stops running when you unplug it from the wall and it starts up whereit left off when you plug it back in. That clock showed 3:50. My digital elec-tric clock, which resets itself to midnight electricity goes out and starts whenthe electricity comes back on, flashes until you correct the time. It was flash-ing 6:03 am. Assuming the electricity went out just once, what time did it goout and how long was it off?
37. A pizza in the shape of a rectangle is to serve 18 peo-ple. Everyone is to get the same amount of pizza. If thepizza is 30 inches by 12 inches, describe the piece eachperson will get.
55Copyright © 2002 Mathematics Learning
39. Two circles just touch a rectangle and each other as shownin the figure below. The area of the rectangle is 18 square cm.What is the radius of each circle?
40. Angela is deciding how many plants to buy for her gar-den. The diagram below represents Angela‘s garden. Thecurved area is a semi-circle. Find the area of her garden insquare feet.
42 ft.
28 ft.
56 ft.
14 ft.
56Copyright © 2002 Mathematics Learning
42. The arithmetic mean of ten scores is 91. When the lowestscore is dropped the mean of the remaining nine scoresbecomes 94. What is the lowest grade?
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41. The figures below are similar, that is, one has just been madelarger. Find the missing lengths.
57Copyright © 2002 Mathematics Learning
43. Venessa is playing a game where low score wins.After playing a number of games, she scores a 139which lowers her score from 157 to 156. What must shescore on the next round to lower her score to 155?
44. A block made of small cubes is dipped in paint. Theblock has four cubes on each edge as shown below. Howmany small cubes have paint on them?
58Copyright © 2002 Mathematics Learning
45. Marta made a stack of cubes 5 cubes across the front, 4cubes deep and 6 cubes high. The top and the four sides ofthe stack are painted red. How many cubes have paint onthem? How many cubes do not have paint on them?
5
6
4
46. One year Maria and Sonia send greeting cards.Altogether they send 56 cards. Maria sends 14 morecards than Sonia. How many cards does each girlsend? Explain your reasoning.
59Copyright © 2002 Mathematics Learning
47. A large cube made of 125 one centimeter cubes is placedon the floor and paint is poured down over the top and allsides. How many one centimeter cubes have paint on them?
48. Centimeter cubes are glued together to make a largercube (solid) that is several centimeters on each edge. Somefaces of this cube are painted. When the cube is taken apart,exactly 45 centimeter cubes have no paint on them. Howmany centimeter cubes were used to make the larger cube?
60Copyright © 2002 Mathematics Learning
49. The sum of five different positive whole numbers is 65.The median of the three numbers is 16. What is the largestany of the five numbers could be?
50. Sophie was raising Alaskan white mice. They wereunusual in that every two months the female had exactlytwo babies - a male and a female. When these babies weretwo months old, they had their first babies and continued tohave them every two months after that. Sophie began withone pair of mice on January 1, 2001 and her parents madeher sell all that she had on January 2, 2002, just after morebabies were born. Since none of the mice had died, she hadquite a few. How many?
61Copyright © 2002 Mathematics Learning
51. A long table for a party is made by putting square tablestogether that seat one person on a side. There are two rowsof small tables used. This table seats 38 persons. How manysmall tables were used?
52. Wanda Fish is planning a rectangular swimming pooland plans to use square tiles to cover the bottom. She willuse white tiles to form a rectangle in the middle and thenmake a uniform border of blue tiles. After the tiles havebeen delivered, she decides to put the blue tiles in the middleand use the white tiles for the border. As it so happens, thenumber of tiles was such that this was possible but the rect-angle did not necessarily have the same dimensions. What isthe smallest number of tiles that could have been delivered?
62Copyright © 2002 Mathematics Learning
53. Four women must cross a bridge over a deep ravine inenemy territory in the middle of the night. The treacherousbridge will hold only two women at a time and it is necessaryto carry a lantern while crossing. (persons must stay togetherwhile going across). One of the women requires 5 minutes tocross, one takes 10 minutes, a third requires 20 minutes andthe slowest requires 25 minutes (each of them can walk slowerif necessary but no faster). Unfortunately, they have only onelantern among them. How can they make the crossing if theyhave only 60 minutes before the bridge is destroyed? Notricks!
54. Main Bank was robbed this morning. A lone robbercarried the loot away in a big leather bag. The manager ofthe bank said most of the stolen bills were ones, fives, andtens. Early reports said the robber took approximately $1million in bills. The Channel 1 News team thinks this soundslike more money than one person could carry. What do youthink? Channel 1 News needs help in determining how hardit would be for one person to carry $1 million in small bills.Please investigate this question to determine if this is possi-ble. Prepare a report for Channel 1 News describing andexplaining your findings. Your report should help the inves-tigative reporter at Channel 1 better understand the situa-tion to plan for tonight’s broadcast.
63Copyright © 2002 Mathematics Learning
55. A square hall is covered with square tiles. When thenumber of tiles on two diagonals are counted, the number oftiles is 125. How many tiles are there on the floor?
56. The square to the right is divided into five congruentrectangles. If the perimeter of one of the rectangles is 30 cm,what is the area of the square?
65Copyright © 2002 Mathematics Learning
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66Copyright © 2002 Mathematics Learning
0 53 72
0 n43
43 + (- 9) = n n = ___- 9
0- 27 53
0- 85 - 57
0-100
38
53 - 72 = n 72 + n = 53
-100 + 38 = n
- 21 - (19) = n
-57 - (- 85) = n - 85 + n = -57
53 - (- 27) = n - 27 + n = 53
019 - 21
Adding and Subtracting Integers # 2
What added to 72 gives 53?
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67Copyright © 2002 Mathematics Learning
0
0
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29
0 36 74
0- 55 17
0- 35
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34 - (-26) = n - 26 + n = 34
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-55 - 17 = n
74 - 36 = n 36 + n = 74
0- 91 - 23
Adding and Subtracting integers # 3
What added to 29 gives - 43?
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Integer Math Squares
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7. 8. 9.
Copyright © 2002 Mathematics Learning
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Copyright © 2002 Mathematics Learning
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Copyright © 2002 Mathematics Learning
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Copyright © 2002 Mathematics Learning
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Integer Math Squares
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Copyright © 2002 Mathematics Learning
-8
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# 5
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Integer Math Squares
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Copyright © 2002 Mathematics Learning
-1
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# 6
1. 2. 3.
Integer Math Squares
76
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7. 8. 9.
Copyright © 2002 Mathematics Learning
-25
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1. 2. 3.
Integer Math Squares
77
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7. 8. 9.
Copyright © 2002 Mathematics Learning
-8
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# 8
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80Copyright © 2002 Mathematics Learning
++
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81Copyright © 2002 Mathematics Learning
++
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82Copyright © 2002 Mathematics Learning
++
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83Copyright © 2002 Mathematics Learning
++
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# 4
Integer Two Waysx x
x x
x x5. 6.
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84Copyright © 2002 Mathematics Learning
-1
3 5
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# 5
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85Copyright © 2002 Mathematics Learning
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# 6
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86Copyright © 2002 Mathematics Learning
-3
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# 7
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87Copyright © 2002 Mathematics Learning
-3 -27
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# 8
Copyright © 2002 Mathematics Learning 90
1
12
15
14
13
35
110
18
16
112
Fraction Bars
19
Copyright © 2002 Mathematics Learning 91
1 215
25
35
45
65
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85
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1 2?
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Adding Fractions
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 93
# 1
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 94
# 2
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 95
# 3
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 96
# 4
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 97
# 5
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 98
# 6
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 99
# 7
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 100
# 8
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 101
# 9
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 102
# 10
Fractions
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction names.
a. What fraction of the rectangle is shaded?
b. What fraction of the rectangle is NOT shaded?
c. Express your answer using other fraction name
a. What fraction of the figure is shaded?
b. What fraction of the figure is NOT shaded?
c. Express your answer using other fraction names.
Copyright © 2002 Mathematics Learning 103
# 11
1. 2.Fraction Balance #
Boxes that are the same size and shapemust have the same number in them.
3. 4.
5. 6.
7. 8.
Copyright © 2002 Mathematics Learning 106
10
6
181 10
1
127
124
342
342 3
42
143 1
451211
1233
4214
1. 2.Fraction Balance #
Boxes that are the same size and shapemust have the same number in them.
3. 4.
5. 6.
7. 8.
Copyright © 2002 Mathematics Learning 107
1 15
25
2
25
25
35
45
35
1 45 3 4
53 15 3 4
5
2 95 1 6
515
1. 2.Fraction Balance #
Boxes that are the same size and shapemust have the same number in them.
3. 4.
5. 6.
7. 8.
Copyright © 2002 Mathematics Learning 108
7 410 8 3
10
410 3 1
10
3
3 15
5 15
2 310 2 3
5
13 15
5 12 2 7
10
1 110
9 154 1
5
2 35
1. 2.Fraction Balance #
Boxes that are the same size and shapemust have the same number in them.
3. 4.
5. 6.
7. 8.
Copyright © 2002 Mathematics Learning 109
7 13
8
1 61
5 12
156
4
13
13
23
231
23
3 13 5 2
312 1
3
3 26
12
1. 2.Fraction Balance #
Boxes that are the same size and shapemust have the same number in them.
3. 4.
5. 6.
7. 8.
Copyright © 2002 Mathematics Learning 110
7 13
1 64
1 56
5
26
562
36
56
13
7 13
3 23 8 1
62 56
9 13
1 12
13
1. 2.Fraction Balance #
Boxes that are the same size and shapemust have the same number in them.
3. 4.
5. 6.
7. 8.
Copyright © 2002 Mathematics Learning 111
2 19 5 1
3
1313
156
39
6
56
12
39
23
1 19
6 162 2
3
16
9 19
16 1
3
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 113
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
0 1
6 14
1
32
3
8 34
5
145
3 7
3
3
122
253
123
1
123 1
24
5
4
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 114
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
76 9
5
2015
148
2
11 13
122
1211
2 142 7
82
1 131
236 86
162
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 115
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
1
4 5
6 1512
3
5
3
3413
414
135
1511
2
143 7
83
134 2
36
145 3
47 348
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 116
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
4
6 20
9
34
347 1
48
147 1
48 1410
144 3
45 348
582 5
85 5811
1 341 5
83
382 5
83 125
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 117
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
5
18
8123 1
29
181 5
82 383
381 1
24
183 7
86 7811
18
1467
81
5 7132
251 9
102 123
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 118
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
6
2
6123
11
2
143 3
410
8
141 7
83
142
784 1
27
3420
5
251 3 7
161 1
22 565
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 119
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
7
2
109
5
8126
3811
183 5
84
144
58
183 3
84
186 3
48
139
136 9
352 2
53 255
Fraction Sequence #
1) . . . . . . . . .
2)
What is the pattern?
. . . . . . . . .
. . . . . . . . .
3)
4) . . . . . . . . .
5) . . . . . . . . .
6) . . . . . . . . .
7) . . . . . . . . .
Copyright © 2002 Mathematics Learning 120
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
What is the pattern?
8
2
9
253
4
147
593 1
34
455 3
57
7881
88 389
345
1510 4
511
561 1
63 126
181 1
443
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 122
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
12
16
15
14
13
110
60
66242545
710
60 23
60
60
60
60
6060
60
60
3435
310 60
60 60
30
12
110
15
16
13
130
30
30
30 30
30
30
30
30 30
30
30
30
233546
730
254556
930
710
310
22
56
1010
1
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 123
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
12
112
16
14
13
24
323858567
12
24 233478141
1112
16
12
116
13
16
14
233438
58
78
716
128
18
24
24
24
24
24
24
24
24
24
2424
18
16
16
16
16
16
16
16
16
16
16
16
16
44
88
2
1216
121381
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 124
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
42
12
16
14
13
17
42 42
42
42
42
42
42
42
42
42
42
42
23
37132
56
342747
77
18
58
76
38
10
12
15
14
13
18
10 10
10
10
10
10
10
10
10
10
10
10
23
14558
25
343538
44
78
110
1510
3
121
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 125
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
156
12
16
14
13
18
156 156
156
156
156
156
156
156
156
156
156
156
23
58
56
343878
66
43
112
712
5121112
4
300
300 300
300
300
300
300
300
300
300
300
300
300
132
3556
12
15
14
13
2325
34
16
115
1515
4151415
165
715
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 126
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
100
12
15
14
100 100
100
100
100
100
100
100
100
100
100
100
25
35
34
45
55
180
12
15
14
13
16
180 180
180
180
180
180
180
180
180
180
180
180
23
45
25
343556
44
112
120
110
1100
710
310
346
920
320
1920
512
712
1112
1512
5
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 127
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
96
12
16
14
13
18
96 96
96
96
96
96
96
96
96
96
96
96
23
58
56
343878
77
126
12
16
14
13
17
126 126
126
126
126
126
126
126
126
126
126
126
23
3767
56
342747
99
89
29
116
19
109
516
178
1516
716
6
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 128
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
144
144 144
144
144
144
144
144
144
144
144
144
144
58
3878
6
16
18
6 6
6
6
6
6
6
6
6
6
6
6
58
3878
33
103
12
16
14
13
2356
34
18
12
14
13
2356
34
112
112
1212
5121112
106
712
1112
512 11
4
7
Fraction Benchmark #
Copyright © 2002 Mathematics Learning 129
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
l)k) of = x is
200
200 200
200
200
200
200
200
200
200
200
200
200
252
3538
240
15
16
240 240
240
240
240
240
240
240
240
240
240
240
45
3556
88
12
15
14
13
2325
34
18
12
14
13
2325
34
110
910
245
18
54
78
38
581
55
58
78
8
1. 2. 3.
Fraction Math Squares #
132
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
16
36
16
16
18
18
14
38
18
18
18
1
12
34
141
1 512 3
34
78
58
38
38
110
310
310
14
14
14
12
112
112
512
1 712
112
1112
512
1
1. 2. 3.
Fraction Math Squares #
133
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
14
12
34
782
18
381
14
18
5
35
15
1 710
127
16
56
581
38
3 1 2
5 46
4
1
14
34
12
341
58
381
2 16
56
127 1
6 2 12
58
581
38
5
110
2
1. 2. 3.
Fraction Math Squares #
134
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
234
4
14
139
161
23
38
15 23
14
183 1
2
3 34
34
123
38 6 3
4
1417
121
18
1 15
1 15
1 15
1 15
235
132 1
33
132 1
36
134
166
582
189
34
5 58
1 121 1
8
3
1. 2. 3.
Fraction Math Squares #
135
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
146
231
23
143 1
4
3 58
126 1
212
141
1 78
23
56
353
562
382
189
3 56
4 13
58
38
18
12
154
251 7
10
16
123 1
83
112
5127
131
233 5
6
2 18
1412
2 13
4
1. 2. 3.
Fraction Math Squares #
136
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
569
563 2
58
23
152
45
12 18
341
1214
161
124
29
23
384
782
564
187
121
3
1
4 38
4 14
2 14
161 1
62
163
10
165
162
17
13
23
585
342 2
5
710
59
5
1. 2. 3.
Fraction Math Squares #
137
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
3
56
58
129
10
563
2319
4 512 9 1
12
124 5 1
8
7 141 2
3
231
121
3
125
123
13
34
13
712
136
18
34
346
1351
21
15
7813
343 1
61
142 3
83
127
3418
6
1. 2. 3.
Fraction Math Squares #
138
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
10
11
17 18
781
24
141
6 12
8 14
134
198
582
184
341 5
61
232
1212
5617
125 1
41
343
1423
44
15
2 12 3 1
4
344
342
12
564
132
797 2
57
252 1
51
348
581
12
7
1. 2. 3.
Fraction Math Squares #
139
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
11 12
123
237
7 34
151
564
121
141
1210
1315
583
3811
44
9 12 4 1
8345 1
42
183
126
124
2 38 3 5
12
2 512
148
1 512
5 310 2 1
10
1414
4
122
5611
129
294
793 5
96
895
8
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
142Copyright © 2002 Mathematics Learning
8
2
2
1
648
36
1224
62 4
48
2
4
1
6
2
4
4
8
16
12
1
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
143Copyright © 2002 Mathematics Learning
16
8
12 18 13
10
3
14
12
24
16
4
6
12
12
3
4
72
24
6
2
20
4
12
2
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
144Copyright © 2002 Mathematics Learning
5
2
14
12
16
4
20
45
300
150
60
15
9030
6
20
40
60
2
9 3
18 6
9
3
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
145Copyright © 2002 Mathematics Learning
2
9 3 2 34
11
12
4 12
18
27
12
6 34
6
10
12
2
2 7
8
3
12
23
16
12
12
12
4
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
146Copyright © 2002 Mathematics Learning
4
6
5
4
12
1
7 2
113
9
3
6
12
18
19
2 38
12
38
12
58
12
23
12
34
13
12
5
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
147Copyright © 2002 Mathematics Learning
6
312
2
8 1 13
6
2
9
50
6
163 34
34
14
23
1122
14
122
25
127
4 12126 1
4
1
6
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
148Copyright © 2002 Mathematics Learning
18
5 14
3
6
49
13
34
121
1 12
12
2
1210
16
189
1
6
1
18
4
1648
2128
7
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
149Copyright © 2002 Mathematics Learning
12 30
5
1
34
122
12
12
2 12
16 20
2
440
20
9
15
3
14
1
14
2
19
3
8
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
150Copyright © 2002 Mathematics Learning
8 5
3
123
34
34
56 3
48
10
4
14
12
18
2
12
153
4 1
121
5
14
7
132
9
Fraction Two Ways # x x
x x
x x5. 6.
1. 2.
3. 4.
151Copyright © 2002 Mathematics Learning
8 69
15
4
18
12
22
12
5
4
14
64
13
3
12
6
141
124
2
1
30
13
20 12
10
Copyright © 2002 Mathematics Learning 155
!
"!
"#
"$
"%
"&
"'$
"(
.75
")
Decimal Bars
Copyright © 2002 Mathematics Learning 156
!
***
***
***
***
***
***
___
***
***
Decimal Bars
Copyright © 2002 Mathematics Learning 157
")
!
.8 + .8 = ___
Decimal Bars
.75 + .75 = ___
.5 + .5 = ___
4) .2 + .8 = ___
5) .7 + .8 = ___
6) .9 + .9 = ___
7) 1.2 + .9 = ___
1)
2)
3)
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 159
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 1
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 160
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 2
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 161
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 3
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 162
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 4
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 163
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 5
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 164
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 6
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 165
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 7
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 166
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 8
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 167
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 9
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 168
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 10
Decimals and Fractions1.
2.
3.
4.
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
c. What decimal part of the rectangle is NOT shaded?
Copyright © 2002 Mathematics Learning 169
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the rectangle is shaded?
b. What decimal part of the rectangle is shaded?
a. What fraction of the figure is shaded?
b. What decimal part of the figure is shaded?
c. What decimal part of the rectangle is NOT shaded?
c. What decimal part of the figure is NOT shaded?
c. What decimal part of the rectangle is NOT shaded?
# 11
Decimal Balances
1. 2.
3. 4.
5. 6.
171
Boxes that are the same size and shapemust have the same number in them.
Copyright © 2002 Mathematics Learning
.04.27
.06
3.2 3.8 3.81.8
.6.6 1.6
.2 .2 .5 .5
7. 8.
#1
Decimal Balances
1. 2.
3. 4.
5. 6.
172
Boxes that are the same size and shapemust have the same number in them.
Copyright © 2002 Mathematics Learning
.53.36
.907
7. 8.
.1.07
.73 5.4.8
.7 .7 .57 .57
2.1
#2
Decimal Balances
1. 2.
3. 4.
5. 6.
173
Boxes that are the same size and shapemust have the same number in them.
Copyright © 2002 Mathematics Learning
.231.021.777
8.
10.15.052.1
.3822.81.18
2.7 5 .93 .7
7.
#3
Decimal Balances
1. 2.
3. 4.
5. 6.
174
Boxes that are the same size and shapemust have the same number in them.
Copyright © 2002 Mathematics Learning
4.07 8.2 5.9
6.93
9.40
4.23.80 9.0813.80
3.65 1.350
7. Pedro and Zita had just enough money to buy two movie tickets. Pedro had $4.72 and Zita had $6.18. How much did one ticket cost?
8. 7.49 + 2.6 = 9. 20 - 15.020 =
#4
Decimal Balances
1. 2.
3. 4.
5. 6.
175
Boxes that are the same size and shapemust have the same number in them.
Copyright © 2002 Mathematics Learning
8.05 14.9 .06 .3
6.212.04 3.4 6.02
7. The heights of three girls are: Tanya 1.73 meters, Linda 1.57 meters, and Catalina 1.5 meters. What is the average height of the girls?
9.35 7.5 1.4 .60
8. 6.105 + .9 = 9. 17 - 8.07 =
#5#1
Decimal Balances
1. 2.
3. 4.
5. 6.
176
Boxes that are the same size and shapemust have the same number in them.
Copyright © 2002 Mathematics Learning
3.06 5.3 .7 .92
.36.8 2.07 3.53
7. Pat had $5.60, Sal had $3.92, and Wan had $4.08. They had just enough money to buy two pizzas. How much did one pizza cost?
.98 7.02 5.4 1.2
8. .206 + .84 = 9. 12.01 - 4.5
#6
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
178
Decimal Sequence #
1 2 4.5
1 1.5 3
1 1.2 1.7
1 1.4 2
1 1.1 1.16
1.011 1.016
1
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
179
Decimal Sequence #
8 23 60.5
.88 1 1.2
.3 .7 1.7
1.02 1.08 1.2
2 8 11
.25 .5 1
2
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
180
Decimal Sequence #
7 12 22
6 8 9.2
1.5 6 12
2.5 2.6 2.65
5.73 6 6.45
6.9 8 10.2
3
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
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6)
= Decimal word name =
. . . . . . . . .
181
Decimal Sequence #
1.7 2.3 3.5
.1 .2 .45
52 3.2
.992 1 1.02
1.15 2.65 6.4
3.5 12.5 17
4
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
182
Decimal Sequence #
4 11 28.5
.3 .8 2.05
4 5 5.4
1 1.03 1.06
0 .3 .4
.5 .56 .6
5
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
183
Decimal Sequence #
5 23 36.5
1.25 3.05 4.85
7.001 7.01 7.016
.875 1.125 1.5
6.05 6.5 7.1
1.05 1.5 1.68
6
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
184
Decimal Sequence #
1.002 1.01 1.022
2.5 6.25 10
8.99 9.08 9.2
.15 2.4 6.15
9.26 10.8
5.086 5.09 5.1
7
Name each point on the line with a decimal.
1)
= Decimal word name =
. . . . . . . . .
Copyright © 2002 Mathematics Learning
2)
= Decimal word name =
. . . . . . . . .
3)
= Decimal word name =
. . . . . . . . .
4)
= Decimal word name =
. . . . . . . . .
5)
= Decimal word name =
. . . . . . . . .
6)
= Decimal word name =
. . . . . . . . .
185
Decimal Sequence #
1.0021 1.004
1.6 4 9
1.75 7 9.1
0 .01 .04
.1 .18 .3
.1 1.5 5
8
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 187
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
1000
80
80
80
80
80
80
80
80
80
80
80
80
80
.09
.15
.60
1.25
.24 10.6
1000
10001000
10001000
10001000
1000
1000 1000
1000
.6
.75
1000
.90
.51 .501
.95
.99
3.671.25
.999
.90
.375
.06
.625
1
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 188
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
500
48
48
48
48
48
48
48
48
48
48
48
48
48
.35
.375
.60
.51
.24 2.50
500
500500
500500
500500
500
500 500
500
.3
.35
500
.15
.75 .06
.03
.9
3.1.009
.09
.15
.9
.95
.31
2
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 189
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
300
40
40
40
40
40
40
40
40
40
40
40
40
40
.6
.75
.06
.375
.35
2.5
.15
.9
.49 1.05
300
300300
300300
300300
300
300 300
300
.75
.15
300
.6
.06 .55
.35
.95
2.1.26
.4
3
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 190
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
30
120
120
120
120
120
120
120
120
120
120
120
120
120
.35
.09
.6
.135
.24 1.75
30
3030
3030
3030
30
30 30
30
.3
.35
30
.15
.75 .06
.03
.9
3.1.009
.09
.15
.9
.06
.3
4
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 191
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
60
160
160
160
160
160
160
160
160
160
160
160
160
160
.35
.09
.6
.375
.24 1.25
60
6060
6060
6060
60
60 60
60
.3
.6
60
.15
.125
.11
.06
.35
1.25
.51
.09
.15
.9
.06
.3
5
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 192
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
84
240
240
240
240
240
240
240
240
240
240
240
240
240
.15
.625
1.2
.375
.51 1.25
84
8484
8484
8484
84
84 84
84
.75
.15
84
.06
.6 .95
.35
.2
1.25.002
.02
.75
.6
.95
.40
6
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 193
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
50
320
320
320
320
320
320
320
320
320
320
320
320
320
.75
.625
.4
.375
.875 1.25
50
5050
5050
5050
50
50 50
50
2.05
.35
50
.15
.11 .06
.75
.9
.101.051
.26
.60
.95
.06
.04
7
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 194
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
20
96
96
96
96
96
96
96
96
96
96
96
96
96
.75
.99
.6
.625
.375 1.05
20
2020
2020
2020
20
20 20
20
.3
.90
20
.09
.75 .85
.03
.999
.499.009
5.05
.15
.9
.06
.3
8
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 195
l)k) of = x is
.51 .1.25 .001.05 .01
.51 .125.25 .01.1 .05
Decimal Benchmark #
70
200
200
200
200
200
200
200
200
200
200
200
200
200
.60
.09
.95
.007
.24 1.55
70
7070
7070
7070
70
70 70
70
.75
.49
70
.005
1.51 .101
.35
.011
3.6.499
.995
.15
.74
.51
.3
9
1. 2. 3.
Decimal Math Squares
198
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
.3 .05
.04 .2
.23
2.9
6
.08.620
.38
3
.026
.4 .1
.001 .02
.08 .009
.080
3.80
.306
.03 .001
.049
32.04 6.2
.3
.07.6
.2
.302
.08
.114
..03 10.060
.5
# 1
1. 2. 3.
Decimal Math Squares
199
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
2.1
10
2 3.9
1.4
9.7
4
3.2
.684
1
.24
.06
2.4
4.7 5.6
1.25 5.5
3.25 6
2.98
.2 .01
3.2 1.10
2.19
1.04
2.3
.01 1.2
2.9
8
3.08 1.02
1.3
1.01
.01
# 2
1. 2. 3.
Decimal Math Squares
200
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
.80 .2
.600
.24
.52
.16
.02
.3
2
.70 .3
.4 .3
.16 .07
1.07
.2
1.4
.2 .30
.900
.040
.07
.03
.06.009
.06
.03
.011
.400
.100
.030
.40
.3
.3
.3
# 3
1. 2. 3.
Decimal Math Squares
201
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
.40 .042
.030 .528
30.3
.001
61.17.055
8.32
.06
.300
3 .03
2.0 .20
.020 .002
10.106
100
9.894
.02
.680
9.99
2.7 1.005
5.34
.003
.3
43.43
5.680
20.02 10
.04 .345
161
39.03
# 4
1. 2. 3.
Decimal Math Squares
202
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
.19 .003
.007 .81
.071
.006
.129
3.99
.04
2.05
.999
10
.001
.900 .010
3
.09
.0101
.086 .8
.04 .006
20
6.020
5.009
.36
.104
.2039
.30
.104
.45
7
.010
100.0
.8
4.010
# 5
1. 2. 3.
Decimal Math Squares
203
4. 5. 6.
7. 8. 9.
Copyright © 2002 Mathematics Learning
.9090
.0002
3.101
.9993
.078
.080
.0005
.0005
.0407 .0603
.909 .101
.1234
.001 .8766
3.1010 .909
2
.0300
.05
.0500
.0030
.022
.0078 5.05
.0200 .0007
.0500
.05
.005.0005
.5.05
.0701
.7009
9.11
# 6
x
20
.6
.2
24
x
20
.6
.2
24
4
610
12 2
Decimal multiplication Two Ways
Carlos:“Across the top I thought that one- tenth of 20 would be 2 so two-tenths of 20 is 4.Down the right side, 6 times 4 equals 24. Across the middle, I would have to mul-tiply six-tenths by ten to get 6. Two-tenths of 10 is 2. Down the left side, one-tenth of 20 would be 2, so six-tenths of 20 would be 12. 12 x 2 = 24 so it checks.”
x
.1
.2
8
6.4
x
.1
.2
8
6.4!"
"
#$
%#%&
Pat“Across the top, what could I take one-tenth of and get 8? It would have to be 80.Down the left, 2 x .1 = .2. At first, I did not know what to do with .2 x __ = 6.4.Then I thought that five two-tenths is one and thus 30 x .2 = 6. Just two moretwo-tenths gives 6.4, so .2 x 32 = 6.4. Down the right side, I figured 8 x 8 = 64 so8 x .8 would = 6.4. Across the middle 2 x 4 = 8, so it would have to be .4. Nowto check, is .4 x 80 = 32? Well, one-tenth of 80 is 8 and I need four of them. Inow see that four-tenths of 80 = 32.”
Copyright © 2002 Mathematics Learning 206
Decimal Two Ways #+
5. 6.
1. 2.
3. 4.
207Copyright © 2002 Mathematics Learning
++
+
++
5.3
.2
6.2.40
.27
6.5
.02
5.32
.243.48
.08
3.6
.08
.4
.58
8.7 79.3
9.1
.04
2.95.1
4.8
1
Decimal Two Ways #+
5. 6.
1. 2.
3. 4.
208Copyright © 2002 Mathematics Learning
++
+
++
.0032.4001.36
.460
1.5 .01
.008
.001
.35 .65.7
.14.06 .35
.51
.5
2
.704 .046
.003
1
.09
.154.196
.083
Decimal Two Ways #+
5. 6.
1. 2.
3. 4.
209Copyright © 2002 Mathematics Learning
++
+
++
5.77
.6
.90
.200.12
.25
1.300
4.07
3.7 3.705
4
.115
.42
.82
.408 .092
3
.7
.335
1.02
2.8
1.25
.765
.300
1.050
Decimal Two Ways #+
5. 6.
1. 2.
3. 4.
210Copyright © 2002 Mathematics Learning
++
+
++
4.96.7.679
.019
.68
.005
4.955
4.99
7.38 2.57.6
9.5
.08 .003
2.407
.007
4
.008 .092 .002
1
.1
.417 .525 .999
Decimals Two Ways
6.
211
2.1.
5.
3. 4.
x
xx
xx
x
Copyright © 2002 Mathematics Learning
4 .15
20
.0840
.25
9
.215
.25 2
.2
1
.04
50
.3 3
.02
.12.05 4
.35100
.3
# 5
Decimals Two Ways
6.
212
2.1.
5.
3. 4.
x
xx
xx
x
Copyright © 2002 Mathematics Learning
4 .09
20.6
.25
4
8
.15 100
1000
.02 60
2
20
.12 3.6
.1 2
2.5.3
.75
.005
16.8
3
# 6
Decimals Two Ways
6.
213
2.1.
5.
3. 4.
x
xx
xx
x
Copyright © 2002 Mathematics Learning
12 .750
.0258
20
.6 18
.25
5.04
10
1.25
3
.4 12.0
.5
.08
100
.04
15.00
5 1.5
.25
2.400
# 7
Decimals Two Ways
6.
214
2.1.
5.
3. 4.
x
xx
xx
x
Copyright © 2002 Mathematics Learning
.1 .6
12.750
.250
5
.5
.001 2000
1000
.15
40
.02 .2
.4
1.2.6
5
.158
.05
.006
.4
1.5
# 8
Copyright © 2002 Mathematics Learning 216
Shade the given percent of the region.
50% 25% 75%
30% 60% 15%
28% 95% 1%
10% 20% 40%
Percent Units
Copyright © 2002 Mathematics Learning 217
Write the percent of each region that is shaded.
1.
4.
7.
10.
2.
5.
8.
11.
3.
6.
9.
12.
Write the percent that tells what part of the sciencearea is covered by each section.
Floor Plan
1. the office
2. the closet
3. the classroom
4. the laboratory
5. the storage room
6. the storage room, office, and closet together
7. the classroom and laboratory together
8. the classroom, office and closet together
9. the laboratory and storage room together
STORAGEROOM
OFFICECLOSET
CLASSROOM
LABORATORY
218Copyright © 2002 Mathematics Learning
Copyright © 2002 Mathematics Learning 220
!!!!!!Benchmark PercentsMark is a manager of The Athlete Shop and is in charge of pricing sale items. In his jobhe often needs to mentally compute percentages of a specific dollar amount Here's anexample of how Mark does his calculations using "benchmarks":
A jacket is currently priced at $80.00. Mark already knows the following:
1% of $80.00 is $ .8010% of $80.00 is $ 8.0025% of $80.00 is $20.00
Using only these benchmarks, he combines these amounts to figure other percentages.
2% of $80.00 is $1.60 (double the 1% amt.)3% of $80.00 is $2.40 (triple the 1% amt.)4% of $80.00 is $3.20 (4 times the 1% amt. or double the 2% amt.)5% of $80.00 is $4.00 (5 times the 1% amt. or half of the 10% amt.)20% of $80.00 is $16.00 (double the 10% amt.)75% of $80.00 is $60.00 (triple the 25% amt.)23% of $80.00 is $18.40 (20% + 3% or $16.00 + $2.40)
Try some!
50% of $80.00 is 30% of $80.00 is
100% of $80.00 is 60% of $80.00 is
90% of $80.00 is 15% of $80.00 is
70% of $80.00 is 9% of $80.00 is
40% of $80.00 is 49% of $80.00 is
12% of $80.00 is 33% of $80.00 is
Make up some of your own.
% of $80.00 is % of $80.00 is
% of $80.00 is % of $80.00 is
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 221
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
1000
1000
10001000
10001000
10001000
1000
1000 1000
100015%
60%
30%
26%
105%
75%
35%
20%
51%
99%
1000
$80
$80
$80$80
$80$80
$80$80
$80
$80 $80
$80
30%
90%
$80
15%
35% 70%
60%
40%
24%125%
75%
1
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 222
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
$60
$60
$60$60
$60$60
$60$60
$60
$60 $60
$60
75%
15%
$60
20%
40% 30%
55%
60%
35%
90%
600
600
600600
600600
600600
600
600 600
60035%
60%
55%
20%
3%
75%
15%
49%
30%
125%
600
127 %
2
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 223
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
200
200
200200
200200
200200
200
200 200
20035%
60%
55%
20%
2%
75%
15%
49%
30%
500%
200
$40
$40
$40$40
$40$40
$40$40
$40
$40 $40
$40
30%
90%
$40
15%
70% 35%
60%
225%
40%127 %1212 %
3
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 224
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
300
300
300300
300300
300300
300
300 300
30015%
60%
30%
26%
20%
75%
35%
11%
51%
99%
300
$18
$18
$18$18
$18$18
$18$18
$18
$18 $18
$18
60%
75%
$18
15%
95% 9%
30%
150%
49%
40%127 %
4
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 225
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
160
160
160160
160160
160160
160
160 160
16015%
60%
30%
35%
125%
75%
40%
20%
160
$50
$50
$50$50
$50$50
$50$50
$50
$50 $50
$50
30%
90%
$50
15%
70% 9%
60%
40%
125%
49%
127 %
1212 %
127 %
5
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 226
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
240
240
240240
240240
240240
240
240 240
24015%
60%
30%
90%
250%
75%
35%
20%
240
$36
$36
$36$36
$36$36
$36$36
$36
$36 $36
$36
30%
90%
$36
15%
35% 70%
60%
125%
40%
127 %
1212 %
127 %
1212 %
6
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 227
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
320
320
320320
320320
320320
320
320 320
32015%
60%
30%
26%
120%
75%
35%
125%
320
$24
$24
$24$24
$24$24
$24$24
$24
$24 $24
$24
30%
20%
$24
15%
75% 35%
60%
40%
250%
90%
127 %
1212 %
1212 %
7
Make up two of your own.
b)a) x = of is
d)c) x = of is
f)e) x = of is
j)i) x = of is
h)g) x = of is
l)k) x = of is
1.
Percent Benchmarks #
Make up two of your own.
b)a) of = x is
d)c) of = x is
f)e) of = x is
j)i) of = x is
h)g) of = x is
2.
Copyright © 2002 Mathematics Learning 228
l)k) of = x is
50%100% 10%25% 1%5% 122 %
50%100% 10%25% 1%5% 122 %
400
400
400
400400
400400
400400
400
400 400
40015%
60%
30%
26%
200%
75%
35%
3%
51%
99%
$72
$72
$72$72
$72$72
$72$72
$72
$72 $72
$72
75%
15%
$72
60%
35% 2%
55%
40%
125%
49%1212 %
8
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
2. 50%100% 10%25% 1%5% 122 %
1. 50%100% 10%25% 1%5% 122 %
Percent Benchmarks #
229Copyright @ 2002 Mathematics Learning
80
90
$64
85
60 80
200
$64 70
74%
49%
60
110%
10% 25%
55%
500% 80%
45
$1.05
20
$3.20
90
21
What percent of the cards in a 52 card deck are not face cards?
400
8
6
$15
35 75
44
$4 $4.50
0.5%
26%
60
175%
1% 600%
95%
15% 40%
$3.08
45
60
$1.60
7
$9
If 32% percent of a number is 128, find 40% of the number.
9
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
2. 50%100% 10%25% 1%5% 122 %
1. 50%100% 10%25% 1%5% 122 %
Percent Benchmarks #
230Copyright @ 2002 Mathematics Learning
7
$10
12.75
$7.20
80$1.04
$28
300 66
900%
35%
480
101%
50% 20%
99%
2% 300%
$3.55
8.4
52¢
210
12
22
Comfort Shoe Store marks up its prices 20%. What is thestore’s profit on a pair of shoes that sell for $144.00?
30
104
.5
$2.80
48$7
4
250 $9.70
65%
250%
$16
26%
8% 40%
45%
3% 200%
$3.20
12
$6.30
150
36
97¢
Darci got a 10% discount on a pair of jeans that was originallypriced at $44.90. How much did Darci pay for the jeans?
10
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
2. 50%100% 10%25% 1%5% 122 %
1. 50%100% 10%25% 1%5% 122 %
Percent Benchmarks #
231Copyright @ 2002 Mathematics Learning
20¢
120
$42
21
400$3.90
35
20 4
25%
600%
$401
49%
7% 175%
5%
30% 6%
$6.30
75
$1.95
14
160
20
$1.20
32
$240
54¢
45$21
670
240 $24
10%
90%
42
225%
35% 9%
12.5%
125% 60%
70
5
$10.50
180
30
$3
11
Abel paid $18.90 for a hat that was on sale. He paid 75% of theregular price. What was the regular price of the hat?
In the class election, 660 of the 750 students voted. What percentof the students voted? What percent of the students did not vote?
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
b)a) x = of is
d)c) x = of is
f)e)
j)i)
h)g) x = of is
l)k) % x = % of is
% x =
m)
% of is
x = of is
2. 50%100% 10%25% 1%5% 122 %
1. 50%100% 10%25% 1%5% 122 %
Percent Benchmarks #
232Copyright @ 2002 Mathematics Learning
$17
540
$12.50
15
400$25
200
$45 6
105%
51%
60
11%
750% 75%
4%
0.5% 5%
30
18¢
$7.50
$9
240
15
61
2
$20
28
55$48
205
50 $210
15%
40%
$8
350%
90% 70%
2%
4% 800%
$2.70
6
$12.00
45
44
$10.50
12
Laura spent 4 days of her 10-day vacation at Disney World.What percent of her vacation did she spend at Disney World?
Matt bought a $100 boom box at a 10% discount and then paid aa 10% sales tax. How much did Matt pay for the boom box?
12
Copyright © 2002 Mathematics Learning 233
1. Given the plate of doughnuts shown, answer the following questions.
a. Jessie ate 3 doughnuts. What percent of the plate of doughnutsdid she eat?
b. Jarrod ate 1 1/2 doughnuts. What percent of the plate ofdoughnuts did he eat?
c. What percent of the plate of doughnuts is left?
2. Two doughnuts were left on a plate in the cafeteria as shown below.
a. What percent of the partially eaten doughnut appears tobe missing?
b. What percent of the plate of doughnuts is missing(counting both doughnuts)?
c. If three of us want to split equally the remaining doughnuts,what percent of the plate of doughnuts could we each have?
Thinking in Percents
Copyright © 2002 Mathematics Learning 234
Estimating and Graphing Percents
1. The results of a Student Council election for President held last week were asfollows:
Sandy received 224 votesDoug received 150 votesAlex received 76 votes
Approximately what percent of the total number of votes did each candidatereceive?
Sandy ________ Doug ________ Alex _________
Draw a circle graph to show the voting results for class president. Title and labelyour graph.
2. The class wants to raise a total of $1,250 this year for the children’s home. Theyraised $620 from magazine sales and $130 from dances.
Approximately what percent of their goal of $1,250 have they raised?
Approximately what percent of their goal did the dances bring in?
Approximately what percent of their goal does the class still need to raise?
Draw a circle graph to show the parts in percent: magazine sales, dances, andamount still needed. Title the graph and label each part.
Copyright © 2002 Mathematics Learning 235
3. Passing a state budget is a long and complicated procedure. At times this pro-cess can nearly shut down the state government. One year a house of representa-tives rejected the governor‘s budget proposal and developed their own version.There were 74 democrats and 46 republicans in the house that summer.
If 44 democrats and 35 republicans voted to pass the house version of the budgetand all members voted, answer the following questions:
Approximately what percent of the democrats voted yes? ____________
Approximately what percent of the republicans voted yes? ___________
Approximately what percent of all representatives voted yes? ___________
4. Arnold works as a roofer for a construction company 40 hours a week andmakes $6.00 an hour. Federal income and social security taxes take approximately15% of his income. Most people spend approximately 30% of their income on aplace to live. Estimate how much Arnold has to spend on an apartment if he usesthe 30% guideline.
Total Income per week $___________ Taxes $__________
Amt. for housing $_________
5. Arnold recently married and decided to enter a training program to become awelder. When he completes the program, he will be making $13.50 an hour. If heworks 40 hours a week as a welder and taxes amount to about 20% of his income,estimate how much he will have available to spend on housing (still using the 30%guideline).
Total Income per week $__________ Taxes $__________
Amt. for housing $___________
After paying taxes and housing, how much money will Arnold have left?
___________
Copyright © 2002 Mathematics Learning 236
Refer to problems 1-3 on the previous pagesto do the following problems.
1. In some elections, where there are more than two candidates, a run-offelection is held between the top two vote getters if one of the candidatesdoes not receive more than 50% of the votes. Look at the Student Councilelection results and determine whether or not a run-off election is necessary.Use a calculator to determine the percent as closely as possible.
Sandy received what percent? ______ Alex received what percent? ______
Doug received what percent? ______ Is a run-off election necessary? _____
2. The class must file a financial report. The report must have results to thenearest whole percent. Based on the information given in problem 2 fromthe previous assignment, use your calculator to find the following percent-ages.
Percent of the total goal from magazine sales? ______________
Percent of the total goal from dances? ______________
What percent of the money must still be raised to meet this goal? ________
3. A governor can veto the a legislative budget. It takes 67% of the votes tooverride the veto. Assuming that all members of the house vote and nobodychanges their mind, use a calculator to determine if the house can overridethe veto.
What percent of yes votes does the house have? ___________
Will the veto override attempt succeed? Explain ____________________
_____________________________________________________________
Calculating Percent
Copyright © 2002 Mathematics Learning 237
Percentages are used in basketball to indicate a players fieldgoal average. The "Dream Team" worksheet providesstudents with some statistics on well known players. Manyof the percentages will need to be rounded and shouldpromote some discussion.
One of the more interesting ways of involving students in working with percentsis to arrange to show a video of the first half of an actual game. Ask yourbasketball coach if he/she has a video to watch or tape a recent game from acollege or pro team that is televised. Assign each student one or more players towatch and keep a tally of the shots made and shots attempted on the sheetprovided. Follow this activity with a class discussion.
Percents and Basketball Statistics
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Given some statistics from one of the Exhibition games during the historic 1992Summer Olympics, can you determine the following field goal percentages (to thenearest whole percent) of several of the players from the U.S. Basketball "DreamTeam"?
Player FG FGA % of shots made % of shots missed
Jordan 6 11
Bird 6 12
Mullins 7 13
Johnson 4 9
Barkley 5 12
Laettner 3 4
Ewing 6 9
Malone 4 13
How many shots would Bird have made if he attempted 100 baskets? What aboutMalone and Laettner?
Bird Malone Laettner
Describe the relationship between the percentage of shots missed and the percentageof shots made.
Find the team totals for each category.
FG FGA % of shots made % of shots missed
“Dream Team” and Percents
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Viewing a Basketball GameName
Game
Team
Select a team and record the information below.
Player ShotsMade
ShotsMissed
TotalShotsAttempted
Percentof shotsMade
Percentof shotsMissed
Copyright © 2002 Mathematics Learning 240
The purpose of the following activity is to familiarize students withthe % mode on a calculators.
Before introducing this activity, a class warm-up might include discussing ways ofwriting down calculator steps for basic arithmetic operations.
Warm-up 1
Say to the class "Add 17 and 8 on your calculator. What answer did youget? Now, write down each step that you took. Be specific."
Examples: 17 + 8 = OR 8 + 17 = OR 17 + 8 +
Warm-up 2
Say to the class, "Multiply 9 and 5 , then subtract 10 from the result. Whatis your answer? Record each step carefully."
Examples: 9 x 5 = - 10 OR 9 x 5 - 10 =
Make up more sample problems as needed. The introductory problem on thefollowing page is intended for students to experiment with their calculators untilthey find a way to use the % key and come up with a correct response. Possiblerecorded steps for this problem are shown below.
49.95 x 40 % =
40 % x 49.95 =
*40 x 49.95 %
*Some students will begin to see that when the % key is used, the decimal pointmoves 2 place; we want to encourage students to act meaningfully.
Teacher Notes on “Calculator-ing” Percents
Copyright © 2002 Mathematics Learning 241
Laurel wants to determine the exact amount of discount she will receive on apair of jeans that is advertised as 40% off the regular price. Using the percentbutton on her calculator, she finds the discount to be $19.98. If the regularprice is $49.95, show the steps that Laurel took on her calculator to determinethe amount of discount. Be specific!
Use your calculator to solve these problems.
1. Regular price: $7.00 2. Regular price: $65.00Discount 10% Discount 20%Sale Price $ Sale Price $
3. Regular price: $125.00 4. Regular price: $48.50Discount: 50% Discount 30%Sale Price $ Sale Price $
5. Regular price: $520.00 6. Regular price: $280.00Discount: 25% Discount: 60%Sale Price $ Sale Price $
7. Total restaurant bill: $45.30 8. Total restaurant bill: $72.00Tip: 20% Tip: 15%
9. Total sales: $350.00 10. Total sales: $15,750Sales tax 6%: Sales tax 7%:
11. Total sales: $1250.00 12. Total sales: $432.50Sales tax 6.5%: Sales tax 4.5%
13. In 1982, a belt sold for $11.50. Ten years later, the price of the beltincreased by 80%. How much more did it sell for in 1992? How muchwould the belt cost in 1992?
“Calculator-ing” Percents
Copyright © 2002 Mathematics Learning 242
Step 1
$65.95 is approx. $70.0010% of $70 is $720% of $70 is $14 (double the 10% amt.)$14.00 is the approx. discount
Step 2
To figure exactly 20% of $65.95, weneed our calculators. Experimentwith the % button on your calculatoruntil you come up with $13.19.
Actual Approx. Actual Approx.Reg. price: $18.90 Reg. price: $47.80Discount: 50% Discount: 30%Amt. of Disc: Amt. of Disc:Sale Price: Sale Price:
Actual Approx. Actual Approx.Reg. price: $137.90 Reg. price: $92.40Discount: 50% Discount: 30%Amt. of Disc: Amt. of Disc:Sale Price: Sale Price:
Actual Approx. Actual Approx.Reg. price: $203.00 Reg. price: $37.20Discount: 40% Discount: 25%Amt. of Disc: Amt. of Disc:Sale Price: Sale Price:
A pair of Guess jeans regularly sells for $65.95. It it is now selling at a 20%discount. Find the approximate discount first by using compatible numbersfor the dollar amounts and/or the percents. Then use a calculator to determinethe exact amount of discount and the sale price.
Step 3
Reg. price: $65.95 Amt. of Disc.: $13.19 Sale Price: $65.95 - $13.19 = $52.76
Discount
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Problem Solving with Percents
Solve the following problems. Show your work neatly and clearly and beable to verify your solution(s).
1. Which television would cost you less money? A $429 television setwith a 20% discount or a television set with no discount priced at $359?
2. The Miami Heat basketball team has won 13 games and lost 4 games.The Orlando Magic team has won 22 games and lost 9 games. About howmany games would each team win if they each play 100 games? Whowould have the better record?
3. You and a guest have eaten in a restaurant which had excellent service.Your bill comes to $23.00. If you leave exactly a 15% tip, what would theamount of the tip be?
4. A taxi driver gets to keep 25% of his fares. One day his fares totaled$358. How much money did the taxi driver keep?
5. You purchase an item for $28.50. You must also pay 6% sales tax.How much change should you receive if you give a salesperson a $50 bill?
10.
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2.
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Fraction-Decimal-Percent Two Ways #
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Write as a decimal.34
Change 10% to a fraction in simplest terms.
Write as percent.15
Write 0.25 as a fraction in simplest terms.
Change 37% to a decimal.
1
400%
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247
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2.
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Fraction-Decimal-Percent Two Ways # 2
Write 0.05 as a percent.
Write as a decimal.14
Change 60% to a fraction in simplest terms.
Write as percent.35
Write 0.4 as a fraction in simplest terms.
Change 110% to a decimal.
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24
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300%
Copyright © 2002 Mathematics Learning 252
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After solving the balance, write an equation for it.
Algebra Balances # 1
Boxes that are the same size and shape musthave the same number in them.
254Copyright © 2002 Mathematics Learning
255Copyright © 2002 Mathematics Learning
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Algebra Balances # 2
256Copyright © 2002 Mathematics Learning
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Algebra Balances # 3
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Thinking Algebraically #4
1. A printer is packaging books in identical box-es. She has filled seven boxes and all but 5books in another box. She has packed 51 books.How many books in a full box? Solve. Draw apicture for this problem. Now write an algebraicequation for the problem.
2. A printer is packaging books in identical box-es. She has filled five boxes and all but 4 booksin another box. She has packed 86 books. Howmany books in a full box? Solve. Draw a picturefor this problem. Now write an algebraic equa-tion for the problem.
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16 Point Grids
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. .. .. .
. .. .. .
. .. .. .
. .. .. .
2. Angle 1 o
9. Side 3 units long.
8. Side 2 units long.
7. Side 1 units long.
3. Angle 2 o
4. Angle 3 o
5. The sum ofthe three angles is .
o
11. Using your measurements,classify the triangle as either a:Scalene TriangleIsosceles TriangleEquilateral Triangle
10. The perimeterof this triangle is units.
6. Using your angle measures,classify the triangle as either a:Right TriangleAcute TriangleObtuse Triangle
1. The area of the above triangle is square units.
TRIANGLE #_____
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. .. .. .
. .. .. .
. .. .. .
. .. .. .
2. Classify the quadrilateral. Check all that apply.SquareRectangleParallelogramTrapezoid Rhombus None of the above
1. The area of the quadrilateral is square units.
Quadrilateral #_____
. .. .. .
. .. .. .
. .. .. .
. .. .. .
. .. .. .
. .. .. .
. .. .. .
. .. .. .
Quadrilateral #_____
Quadrilateral #_____
2. Classify the quadrilateral. Check all that apply.SquareRectangleParallelogramTrapezoid Rhombus None of the above
1. The area of the quadrilateral is square units.
2. Classify the quadrilateral. Check all that apply.SquareRectangleParallelogramTrapezoid Rhombus None of the above
1. The area of the quadrilateral is square units.
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A Different 16 Point Grid
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