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Objective 6: Mathematical Processes and Tools used in Problem Solving 7.13A: Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. 2003 #4: Susan has 3 siblings: Ted, Kathy, and Jake. Susan is older than Jake Ted is younger than both his sisters but older than his brother. What information is needed to determine the order of the siblings from oldest to youngest? F G H* J Is Kathy older or younger than Ted? Is Jake older or younger than Susan? Is Susan older or younger than Kathy? Is Ted older or younger than Jake? 2003 #8: The net profit of a company for each of 5 consecutive years is shown in the table. Company Profit Year Net Profit (millions of dollars) 1984 12.5 1985 14.6 1986 13.1 1987 14.5 1988 12.2 Which statement is supported by the information in the table? F The net profit in 1987 was 20% greater than the net profit in 1986. G* The greatest increase in net
profit for 2 consecutive years occurred from 1984 to 1985. H The greatest decrease in net profit for 2 consecutive years occurred from 1985 to 1986. J The sum of the net profits for 1984 and 1985 was greater than the sum of the net profits for 1986 and 1987. 1 Objective 6: Mathematical Processes and Tools used in Problem Solving 2004 #3: Mrs. Vega needed to make 2 costumes for a school play The larger costume required 1 3 4 yards of material, and the smaller costume required yard less than the larger one. 4 4 Which equation can be used to find n, the number of yards of material needed for the smaller costume? A n=4 1 3 + 4 4 B n=4 1 3 · 4 4 C n=4 1 3 ÷ 4 4 D* n=4 1 3 − 4 4 2004 #48: Ms. Abbot went on a road trip The trip was 792 miles, and the average price of gasoline was $1.30 per gallon What information is needed to find the amount Ms Abbot spent on gasoline for the trip? F G H* J Number of hours the trip took Number of miles per hour the car traveled
Average number of miles the car traveled per gallon of gasoline Average number of miles Ms. Abbot drove per day 2006 #6 A farmer knows the length and width of his rectangular pasture. He also knows how many pounds of fertilizer to spread per square yard. What additional information does the farmer need to know in order to determine the number of bags of fertilizer he should buy? F G H J* The type of grass in his pasture The number of bags of fertilizer his truck will hold The price of each bag of fertilizer The number of pounds of fertilizer in each bag 2 Objective 6: Mathematical Processes and Tools used in Problem Solving 2006 #17 The drawing below shows the rotor of a helicopter. This helicopter has a rotor that moves at a rate of 500 spins per minute while flying. Which statement is best supported by this information? A B C D* The helicopter rotor will spin 2,000 times in 40 minutes. The helicopter rotor will spin 4,000 times before lifting the helicopter off the ground.
The helicopter rotor will spin 15,000 times in 3 hours. The helicopter rotor will spin 30,000 times in 1 hour. 3 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.13B: Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. 2004 #6: An equilateral triangle is divided into 4 congruent equilateral triangles. What method can be used to find the area of the larger equilateral triangle, given the area of one of the smaller triangles? F Multiply the area of the larger equilateral triangle by 4 G* Multiply the area of one congruent equilateral triangle by 4 H Subtract the area of one congruent triangle from the area of the larger equilateral triangle J Add the area of the larger equilateral triangle to the areas of the 4 congruent equilateral triangles 2004 #8: 4 Objective 6: Mathematical Processes and Tools used in Problem Solving Mr. Palmer started a
new business and hired 12 employees A list of the employees and their hourly wages is shown below. Employee Wages Employee Number Hourly Wage 774 $8.25 846 $6.85 616 $7.25 271 $9.15 806 $8.95 435 $7.25 736 $7.25 248 $9.15 192 $7.50 329 $8.60 685 $8.25 377 $6.95 What should Mr. Palmer do to organize the data in order to identify which employees earn less than the median hourly wage? F He should add up all the hourly wages. G He should list the employee numbers in order from greatest to least. H* He should list the hourly wages in order from least to greatest with their corresponding employee numbers. J He should list the employee numbers in order from least to greatest with their corresponding hourly wages. 2004 #18: Hilda bought 4 orders of french fries at $0.67 each, 3 hamburgers at $128 each, and 4 shakes at $2.25 each She paid 825% tax on the whole order What other information is necessary to find Hilda’s correct change? F Total cost of the order
H* Amount she gave the cashier 2006 #32 G Amount she paid in tax J Reason for buying the food 5 Objective 6: Mathematical Processes and Tools used in Problem Solving Stephanie makes cocoa mix to sell at the winter fair. She makes 230 cups of one flavor of cocoa mix and 180 cups of another flavor. To package the cocoa mix, Stephanie needs to purchase containers that hold 2 cups each. The containers are sold in boxes of 50. Which would be the correct order for Stephanie to do the following steps to find the number of boxes of containers she needs to buy? Step R: Divide the total number of cups of cocoa mix by 2. Step S: Find the sum of the numbers of cups of the two different types of cocoa mix. Step T: Divide the number of containers needed by 50 to find the number of boxes of containers to buy. F G* H J R, S, T S, R, T T, R, S R, T, S 6 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.13C: Select or develop an appropriate problem-solving strategy from
a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. 2003 #20: 1 1 of his Saturday earnings on a pair of shoes and of the remaining 2 2 amount on a CD. After he spent $535 on lunch, he had $1085 left How much did Jeffrey earn on Saturday? Jeffrey spent F G H J* $32.25 $36.45 $60.40 $64.80 2003 #38: ∆RST and ∆JKL are similar. Which choice shows the equations that can be used to find the area of ∆JKL? F* G H J 9 = 18 9 First use = 18 9 = First use 18 9 First use = 18 First use h 1 and then use area = (12h) 12 2 h and then use area = 12h 12 12 1 and then use area = (12h) h 2 12 and then use area = 12h h 7 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.14A: Communicate mathematical ideas using language efficient tools, appropriate units, and graphical, numerical, physical, or algebraic
mathematical models. 2003 #2: Which expression can be used to solve the problem below? To cater a luncheon, a hotel charges $50 per hour for use of a dining room plus $24.50 per person What is the total cost for a 2-hour luncheon for 45 people? F G* H J 2 × 50 + 24.50 + 45 2 × 50 + 24.50 × 45 2 × 24.50 + 50 × 45 2 × 45 + 50 × 24.50 2003 #23: Pilar spends a total of 60 hours per week at school and at her job. She attends school from 8:45 A.M until 3:45 PM, Monday through Friday Which equation can be used to find t, the maximum number of hours Pilar works at her job each week? A* B C D t = 60 − (5 × 7) t = 60 − (5 × 8) t = 60 − 7 + 7 + 7 + 7 + 7 t = 5 × 7 − 60 2003 #43: Luis is in charge of making props for a school play. He needs to make a large circular wooden clock that measures about 6 feet in circumference. Which equation can he use to find r, the radius of the clock? 6 A r= B r= C* r= 6 2π D r= 12 2π π 12 π 8 Objective 6: Mathematical
Processes and Tools used in Problem Solving 2004 #10: Mr. Cohen used 25 kilograms of fertilizer on his lawn The fertilizer contained 2 kilograms of nitrogen. Which equation can be used to find x, the percent of nitrogen in the fertilizer Mr. Cohen used? F* G H J x 2 = 100 25 x 25 = 100 2 x 27 = 2 100 25 x = 27 100 2004 #23: A sports-shop owner bought some baseball cards and then sold them for $7.50 each He sold 150 cards on Monday and 82 cards on Tuesday. What piece of information is needed to find the amount of profit he made from the sale of the baseball cards on Monday and Tuesday? A* B C D How much the shop owner paid for the baseball cards Number of cards sold on Wednesday Total number of cards sold Number of football cards bought by the shop owner 2006 #19 Arthur uses his own tractor while doing various jobs. He is paid a flat fee of $100 for each job. In addition to the flat fee, he is paid $20 for each hour he works with the tractor. Which shows how to find the amount
Arthur should be paid for working with the tractor for 10 hours? A B C* D Add 20 to 10 and then multiply the sum by 100 Multiply 100 by 10 and then add 20 to the product Multiply 20 by 10 and then add 100 to the product Add 20 to 100 and then multiply the sum by 10 2006 #47 Ed is reading the math problem shown below. Which is a correct way to read this problem? A B C D One and six tenths divided by three and two tenths Three and two tenths divided by one and six tenths Three and two hundredths divided by one and six hundredths One and six hundredths divided by three and two hundredths 9 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.15A: Make conjectures from patterns or sets of examples and nonexamples. 2003 #11: Mrs. Cotera wants to estimate the monthly operating expenses for the car she just bought, not including maintenance and repairs. Insurance will cost about $200 per month, and Mrs. Cotera expects to drive an average of 225 miles per week What
additional information does she need to estimate her monthly operating expenses? A B* C D The cost of fuel and the one-way distance to work The cost of fuel and the number of miles per gallon her car gets The cost of fuel and her weekly take-home pay The number of gallons of fuel needed per week 2003 #47: Mr. Zimmerman started a 6-week exercise program The first week he jogged 1 mile 1 each day, the second week he jogged 1 miles each day, and the third week he jogged 4 1 1 miles each day. If the pattern continues, how far will he jog each day of the sixth 2 week? A B* C D 1 mi 4 1 2 mi 4 6 mi 3 9 mi 4 1 10 Objective 6: Mathematical Processes and Tools used in Problem Solving 2004 #13: The table below shows the favorite sports of the students at Tompkins Middle School. Favorite Sports Sport Number of Students Cycling 950 Swimming 900 Basketball 675 Volleyball 450 Based on the information in the table, which of the following is a reasonable assumption? A About 3 times
as many students like cycling as volleyball. B Swimming is almost twice as popular as basketball. C* About 2 times as many students like swimming as volleyball. D Volleyball is the most popular sport. 2006 #2 The numbers in Set R share a common characteristic. Set R: 48, 54, 6, 66, 12, 24 The numbers in Set S do not share this characteristic. Set S: 9, 20, 39, 15, 63, 27, 44 Which best describes the characteristic that only the numbers in Set R share? F G H J* Numbers less than 70 Numbers greater than 5 Numbers that are composite Numbers divisible by 6 11 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.15B: Validate his/her conclusions using mathematical properties and relationships. 2004 #41: Mr. Jenkins wants to buy some rosebushes for his garden There are four stores in his neighborhood currently having sales on rosebushes. Rosebush Sales Store Sale Price Sheldon’s Plant Mart 4 rosebushes for $11.90 Rose Mart 3 rosebushes for $8.95
Kathleen’s Roses 2 rosebushes for $5.90 Rose Heaven 1 rosebush for $2.96 If Mr. Jenkins wants to save as much money as possible, at which store should he shop? A B C* D Sheldon’s Plant Mart, because he wants to buy 4 rosebushes Rose Mart, because each rosebush costs almost $3.00 Kathleen’s Roses, because each rosebush costs $2.95 Rose Heaven, because the selection is better 2006 #27 Mrs. Blackburn wrote the following riddle on the board for her mathematics class We are 2-digit numbers. Our greatest common factor is 16 Our difference is 48. Our sum is 112 What are the 2 numbers of the riddle? A B* C D 16 and 48, because their greatest common factor is 16 32 and 80, because their difference is 48 and their greatest common factor is 16 16 and 64, because their difference is 48 and their greatest common factor is 16 48 and 96, because their difference is 48 12 7.13A: Identify and apply Objective 6: Mathematical Processes and Tools used in Problem Solving mathemat ics to
2006 #45 A 10-ounce box of cereal costs $2.98, and a 20-ounce box of the same cereal costs $5.49 Which of these statements will help a shopper decide which box is the better buy? A B C D* The 10-ounce box is the better buy because it is less expensive per ounce of cereal. The 10-ounce box is the better buy because $2.98 is about $3, and $3 goes into $5.49 about 3 times The 20-ounce box is the better buy because it is more expensive per ounce of cereal. The 20-ounce box is the better buy because two of the 10-ounce boxes cost more than one 20-ounce box. 13
profit for 2 consecutive years occurred from 1984 to 1985. H The greatest decrease in net profit for 2 consecutive years occurred from 1985 to 1986. J The sum of the net profits for 1984 and 1985 was greater than the sum of the net profits for 1986 and 1987. 1 Objective 6: Mathematical Processes and Tools used in Problem Solving 2004 #3: Mrs. Vega needed to make 2 costumes for a school play The larger costume required 1 3 4 yards of material, and the smaller costume required yard less than the larger one. 4 4 Which equation can be used to find n, the number of yards of material needed for the smaller costume? A n=4 1 3 + 4 4 B n=4 1 3 · 4 4 C n=4 1 3 ÷ 4 4 D* n=4 1 3 − 4 4 2004 #48: Ms. Abbot went on a road trip The trip was 792 miles, and the average price of gasoline was $1.30 per gallon What information is needed to find the amount Ms Abbot spent on gasoline for the trip? F G H* J Number of hours the trip took Number of miles per hour the car traveled
Average number of miles the car traveled per gallon of gasoline Average number of miles Ms. Abbot drove per day 2006 #6 A farmer knows the length and width of his rectangular pasture. He also knows how many pounds of fertilizer to spread per square yard. What additional information does the farmer need to know in order to determine the number of bags of fertilizer he should buy? F G H J* The type of grass in his pasture The number of bags of fertilizer his truck will hold The price of each bag of fertilizer The number of pounds of fertilizer in each bag 2 Objective 6: Mathematical Processes and Tools used in Problem Solving 2006 #17 The drawing below shows the rotor of a helicopter. This helicopter has a rotor that moves at a rate of 500 spins per minute while flying. Which statement is best supported by this information? A B C D* The helicopter rotor will spin 2,000 times in 40 minutes. The helicopter rotor will spin 4,000 times before lifting the helicopter off the ground.
The helicopter rotor will spin 15,000 times in 3 hours. The helicopter rotor will spin 30,000 times in 1 hour. 3 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.13B: Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. 2004 #6: An equilateral triangle is divided into 4 congruent equilateral triangles. What method can be used to find the area of the larger equilateral triangle, given the area of one of the smaller triangles? F Multiply the area of the larger equilateral triangle by 4 G* Multiply the area of one congruent equilateral triangle by 4 H Subtract the area of one congruent triangle from the area of the larger equilateral triangle J Add the area of the larger equilateral triangle to the areas of the 4 congruent equilateral triangles 2004 #8: 4 Objective 6: Mathematical Processes and Tools used in Problem Solving Mr. Palmer started a
new business and hired 12 employees A list of the employees and their hourly wages is shown below. Employee Wages Employee Number Hourly Wage 774 $8.25 846 $6.85 616 $7.25 271 $9.15 806 $8.95 435 $7.25 736 $7.25 248 $9.15 192 $7.50 329 $8.60 685 $8.25 377 $6.95 What should Mr. Palmer do to organize the data in order to identify which employees earn less than the median hourly wage? F He should add up all the hourly wages. G He should list the employee numbers in order from greatest to least. H* He should list the hourly wages in order from least to greatest with their corresponding employee numbers. J He should list the employee numbers in order from least to greatest with their corresponding hourly wages. 2004 #18: Hilda bought 4 orders of french fries at $0.67 each, 3 hamburgers at $128 each, and 4 shakes at $2.25 each She paid 825% tax on the whole order What other information is necessary to find Hilda’s correct change? F Total cost of the order
H* Amount she gave the cashier 2006 #32 G Amount she paid in tax J Reason for buying the food 5 Objective 6: Mathematical Processes and Tools used in Problem Solving Stephanie makes cocoa mix to sell at the winter fair. She makes 230 cups of one flavor of cocoa mix and 180 cups of another flavor. To package the cocoa mix, Stephanie needs to purchase containers that hold 2 cups each. The containers are sold in boxes of 50. Which would be the correct order for Stephanie to do the following steps to find the number of boxes of containers she needs to buy? Step R: Divide the total number of cups of cocoa mix by 2. Step S: Find the sum of the numbers of cups of the two different types of cocoa mix. Step T: Divide the number of containers needed by 50 to find the number of boxes of containers to buy. F G* H J R, S, T S, R, T T, R, S R, T, S 6 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.13C: Select or develop an appropriate problem-solving strategy from
a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. 2003 #20: 1 1 of his Saturday earnings on a pair of shoes and of the remaining 2 2 amount on a CD. After he spent $535 on lunch, he had $1085 left How much did Jeffrey earn on Saturday? Jeffrey spent F G H J* $32.25 $36.45 $60.40 $64.80 2003 #38: ∆RST and ∆JKL are similar. Which choice shows the equations that can be used to find the area of ∆JKL? F* G H J 9 = 18 9 First use = 18 9 = First use 18 9 First use = 18 First use h 1 and then use area = (12h) 12 2 h and then use area = 12h 12 12 1 and then use area = (12h) h 2 12 and then use area = 12h h 7 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.14A: Communicate mathematical ideas using language efficient tools, appropriate units, and graphical, numerical, physical, or algebraic
mathematical models. 2003 #2: Which expression can be used to solve the problem below? To cater a luncheon, a hotel charges $50 per hour for use of a dining room plus $24.50 per person What is the total cost for a 2-hour luncheon for 45 people? F G* H J 2 × 50 + 24.50 + 45 2 × 50 + 24.50 × 45 2 × 24.50 + 50 × 45 2 × 45 + 50 × 24.50 2003 #23: Pilar spends a total of 60 hours per week at school and at her job. She attends school from 8:45 A.M until 3:45 PM, Monday through Friday Which equation can be used to find t, the maximum number of hours Pilar works at her job each week? A* B C D t = 60 − (5 × 7) t = 60 − (5 × 8) t = 60 − 7 + 7 + 7 + 7 + 7 t = 5 × 7 − 60 2003 #43: Luis is in charge of making props for a school play. He needs to make a large circular wooden clock that measures about 6 feet in circumference. Which equation can he use to find r, the radius of the clock? 6 A r= B r= C* r= 6 2π D r= 12 2π π 12 π 8 Objective 6: Mathematical
Processes and Tools used in Problem Solving 2004 #10: Mr. Cohen used 25 kilograms of fertilizer on his lawn The fertilizer contained 2 kilograms of nitrogen. Which equation can be used to find x, the percent of nitrogen in the fertilizer Mr. Cohen used? F* G H J x 2 = 100 25 x 25 = 100 2 x 27 = 2 100 25 x = 27 100 2004 #23: A sports-shop owner bought some baseball cards and then sold them for $7.50 each He sold 150 cards on Monday and 82 cards on Tuesday. What piece of information is needed to find the amount of profit he made from the sale of the baseball cards on Monday and Tuesday? A* B C D How much the shop owner paid for the baseball cards Number of cards sold on Wednesday Total number of cards sold Number of football cards bought by the shop owner 2006 #19 Arthur uses his own tractor while doing various jobs. He is paid a flat fee of $100 for each job. In addition to the flat fee, he is paid $20 for each hour he works with the tractor. Which shows how to find the amount
Arthur should be paid for working with the tractor for 10 hours? A B C* D Add 20 to 10 and then multiply the sum by 100 Multiply 100 by 10 and then add 20 to the product Multiply 20 by 10 and then add 100 to the product Add 20 to 100 and then multiply the sum by 10 2006 #47 Ed is reading the math problem shown below. Which is a correct way to read this problem? A B C D One and six tenths divided by three and two tenths Three and two tenths divided by one and six tenths Three and two hundredths divided by one and six hundredths One and six hundredths divided by three and two hundredths 9 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.15A: Make conjectures from patterns or sets of examples and nonexamples. 2003 #11: Mrs. Cotera wants to estimate the monthly operating expenses for the car she just bought, not including maintenance and repairs. Insurance will cost about $200 per month, and Mrs. Cotera expects to drive an average of 225 miles per week What
additional information does she need to estimate her monthly operating expenses? A B* C D The cost of fuel and the one-way distance to work The cost of fuel and the number of miles per gallon her car gets The cost of fuel and her weekly take-home pay The number of gallons of fuel needed per week 2003 #47: Mr. Zimmerman started a 6-week exercise program The first week he jogged 1 mile 1 each day, the second week he jogged 1 miles each day, and the third week he jogged 4 1 1 miles each day. If the pattern continues, how far will he jog each day of the sixth 2 week? A B* C D 1 mi 4 1 2 mi 4 6 mi 3 9 mi 4 1 10 Objective 6: Mathematical Processes and Tools used in Problem Solving 2004 #13: The table below shows the favorite sports of the students at Tompkins Middle School. Favorite Sports Sport Number of Students Cycling 950 Swimming 900 Basketball 675 Volleyball 450 Based on the information in the table, which of the following is a reasonable assumption? A About 3 times
as many students like cycling as volleyball. B Swimming is almost twice as popular as basketball. C* About 2 times as many students like swimming as volleyball. D Volleyball is the most popular sport. 2006 #2 The numbers in Set R share a common characteristic. Set R: 48, 54, 6, 66, 12, 24 The numbers in Set S do not share this characteristic. Set S: 9, 20, 39, 15, 63, 27, 44 Which best describes the characteristic that only the numbers in Set R share? F G H J* Numbers less than 70 Numbers greater than 5 Numbers that are composite Numbers divisible by 6 11 Objective 6: Mathematical Processes and Tools used in Problem Solving 7.15B: Validate his/her conclusions using mathematical properties and relationships. 2004 #41: Mr. Jenkins wants to buy some rosebushes for his garden There are four stores in his neighborhood currently having sales on rosebushes. Rosebush Sales Store Sale Price Sheldon’s Plant Mart 4 rosebushes for $11.90 Rose Mart 3 rosebushes for $8.95
Kathleen’s Roses 2 rosebushes for $5.90 Rose Heaven 1 rosebush for $2.96 If Mr. Jenkins wants to save as much money as possible, at which store should he shop? A B C* D Sheldon’s Plant Mart, because he wants to buy 4 rosebushes Rose Mart, because each rosebush costs almost $3.00 Kathleen’s Roses, because each rosebush costs $2.95 Rose Heaven, because the selection is better 2006 #27 Mrs. Blackburn wrote the following riddle on the board for her mathematics class We are 2-digit numbers. Our greatest common factor is 16 Our difference is 48. Our sum is 112 What are the 2 numbers of the riddle? A B* C D 16 and 48, because their greatest common factor is 16 32 and 80, because their difference is 48 and their greatest common factor is 16 16 and 64, because their difference is 48 and their greatest common factor is 16 48 and 96, because their difference is 48 12 7.13A: Identify and apply Objective 6: Mathematical Processes and Tools used in Problem Solving mathemat ics to
2006 #45 A 10-ounce box of cereal costs $2.98, and a 20-ounce box of the same cereal costs $5.49 Which of these statements will help a shopper decide which box is the better buy? A B C D* The 10-ounce box is the better buy because it is less expensive per ounce of cereal. The 10-ounce box is the better buy because $2.98 is about $3, and $3 goes into $5.49 about 3 times The 20-ounce box is the better buy because it is more expensive per ounce of cereal. The 20-ounce box is the better buy because two of the 10-ounce boxes cost more than one 20-ounce box. 13
