6 th Grade Thinker and Team PRACTICE

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Brent Powers
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1 6 th Grade Thinker and Team PRACTICE

2 1. Last month Mrs. Smith made deposits in her checking account of $635.95, $800, and $ During the same month she wrote checks of $95, $8.17, $27.36, $31.17, $63, $128, and $ How much is now in her account if she started the month with $392.3? 2. Different strings of lights on a Christmas Tree in the department store downtown flash at different intervals. The blue lights flash every 9 seconds, the gold lights every seconds, and white lights every 10 seconds. It is now 1 p.m. and all three strings of lights have just flashed together. How many times will that happen again in the next two hours? The chart below lists facts about six colleges. Use it to answer question 3. Facts on Colleges A to F Colleges State Tuition Attendance A Virginia $12,200 1,800 B Vermont $2,000 1,600 C Rhode Island $18,365,325 D Ohio $12,000 2,130 E New York $15,200 2,30 F Massachusetts $1,975 3, Which college tuition would be closest to the mean tuition of colleges A to F? MATH BOWL th Grade Thinker and Team PRACTICE 1

. The shortest side of a triangle is 5. The next longest side is two more than twice the shortest side, while the longest side is two less than three times the shortest.

3 . The shortest side of a triangle is 5. The next longest side is two more than twice the shortest side, while the longest side is two less than three times the shortest. What is the perimeter of the triangle? 5 5. Below is the first 5 rows of Pascal s triangle. The 1 at the top of the triangle is classified as row 0. What is the sum of the numbers in the next row? Hint: Find the pattern. 6. If the pattern below continues, what letter would appear in the 00 th position? MATHISTHEGREATESTMATHISTH MATH BOWL th Grade Thinker and Team PRACTICE 2

7. A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit.

raspberries. How many cherries are there in the fruit salad? 8. A fish tank is 1 6 full of water.

The yearly Movie Club cost $10 to join. Once you join, the price of a movie is 50% off.

4 7. A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of 280 pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad? 8. A fish tank is 1 6 full of water. If 6 gallons of water are added, the tank is 1 2 full. How many gallons will the tank hold when full? 9. The yearly Movie Club cost $10 to join. Once you join, the price of a movie is 50% off. If the price of a ticket is $5, what is the fewest number of tickets you must purchase to start saving money? 10. A barn yard contains only ducks and pigs. If there are 30 heads and 80 legs, how many ducks are there? MATH BOWL th Grade Thinker and Team PRACTICE 3

5 11. The original price of a dress is $70. The dress is discounted 0%. You have a coupon for an additional 10% off the sale price. You must pay 7% sales tax on the final discounted price. If you pay for the dress with a fifty dollar bill, how much change will you receive back? 12. Use the table below to find how much Mrs. Larkin paid to park her car if she arrived at 8:5 a.m. and left at 1:17 p.m. PARKING 1 st half-hour $2 2 nd half-hour $1.50 Each additional hour or fraction of an hour $1.25 Maximum $18 per day 13. What s my number? Follow the clues below to find it. a) The number can be divided into 20 evenly. b) It is divisible by 12. c) It is greater than 25. d) It is less than 50. MATH BOWL th Grade Thinker and Team PRACTICE

6 1. Alice, Raul, and Maria are baking cookies together. They need cup of flour and cup of butter to make a dozen cookies. They each brought the ingredients they had at home. Alice brought 2 cups of flour and cup of butter, Raul brought 1 cup of flour and cup of butter, and Maria brought 1 cups of flour and cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make? 15. Which of the following boxes has the largest surface area? A. B C. D What is the last digit of 7 201? MATH BOWL th Grade Thinker and Team PRACTICE 5

7 17. Juan s test average after three chapter examinations is 75%. What must he score on his next chapter examination to raise his average to 80%? 18. Carlos started with an empty bank. Each day, he puts a penny, a nickel, and a dime into the bank. He kept this up until the bank contained an exact number of dollars, not a penny more or less. How many days did this take? 19. Grandma lives in Middletown and her five grandchildren all live within 25 miles. Scott lives 15 miles south of Grandma. Tom lives 20 miles north of Grandma. Robin lives 5 miles south of Scott. Byron lives 10 miles north of Robin. Caitlin lives 15 miles south of Byron. Grandma wants to visit each of her five grandchildren on five different days, traveling back home each day. How many total miles will she travel? 20. Suppose a farmer plants one plant the first day, two plants the second day, four plants the third day, eight plants the fourth day, and so on. If this pattern continues, how many total plants would he have planted after 8 days? MATH BOWL th Grade Thinker and Team PRACTICE 6

8 Solutions 1. Organize the facts: Mrs. Smith deposited $ $800 + $123.6 for a total of $ She wrote checks for $95 + $ $ $ $63 + $128 and $735.08, totaling $ If she deposited +$ and spent $137.78, the sum is equal to +$ She started with $ Therefore $ $18.63 = $ Make an organized list: Gold:, 8, 12, 16, 20, 2, 28, 180 Blue: 9, 18, 27, 36, 5, 5,..180 LCM = 180 White: 10, 20, 30, 0, 50,.180 So, 2( hrs.)(60min. per / hr.)(60sec. per / min) 7200sec. = = 0 times 180(sec.) 180sec. 3. Do the math: 12, , , , , ,975 = 16, ,123 6 College Tuition Difference A $12,200 $3923 B $2,000 $7877 C $18,365 $222 D $12,000 $123 E $15,200 $923 F $1,975 $118 So, College E. Draw a picture: 3(5) 2 = = 30 2(5) + 2 = 12 MATH BOWL th Grade Thinker and Team PRACTICE 7

9 5. Organize the facts: = 6 6. Find the pattern: There are 17 letters in the pattern Math is the greatest. Therefore, = 23 r9. The pattern will repeat itself 23 complete times plus 9 additional letters, so E is in the 00 th position. 7. Using a ratio table Below is a table showing different possible amounts of each fruit and the total number of pieces of fruit: Blueberries Raspberries Cherries Grapes Total pieces of fruit When there are 280 pieces of fruit, there are 6 cherries. Notice that for the table we successively doubled the number of blueberries which also successively doubles the number of pieces of the other fruits. Students may notice, after the second line, that if they quadruple 70, this will give the desired 280 pieces of fruit, making the table a little shorter. 8. Organize the facts: = must equal 6 gallons. Therefore, 3(6) = Do the math The price of a ticket is $5. 50% of $5 dollars is $2.50. Then, just divide $2.50 into $10 getting. So, tickets breaks you even and 5 tickets start to save you money. 5 MATH BOWL th Grade Thinker and Team PRACTICE 8

10 10. Make a guess and check table: Hint: The number of ducks and pigs must always equal 30. Duck Heads Duck Legs Pig Heads Pig Legs Total legs NO NO NO YES There are 20 ducks and 10 pigs. 11. Do the math: First, find 0% of $70 ($70 x 0. = $28). Secondly, subtract the $28 from $70 ($70 $28 = $2) to find the discounted price. Next, find 10% of $2 and then subtract it to find the final discounted price ($2 x 0.1 = $.20, then $2 $.20 = $37.80). To find the final price of the dress, calculate 7% of $37.80 and add it to $37.80 ($37.80 x 0.07 = $2.66 or $2.65, then $ $2.65 = $0.5). Finally, subtract the $0.5 from the fifty dollar bill to find the change ($50 $0.5 = $9.55 ) 12. Organize the facts: Time of day Time parked Cost 8:5 to 9:15 0:30 1 x $2.00 = $2.00 9:15 to 9:5 0:30 1 x $1.50 = $1.50 9:5 to 1:17 3:32 x $1.25 = $5.00 Total Cost: $ Organize the facts: Clue a: 1, 2, 3,, 5, 6, 8, 12,., 120, 20 Clue b: 12, 2, 8, 60, 120, 20 Clue c: 8, 60, 120, 20 Clue d: 8 MATH BOWL th Grade Thinker and Team PRACTICE 9

11 1. Fraction arithmetic The children bought = cups of flour and They have enough flour for x 5 Batches and they have enough butter for = 1 cups of butter. 1 x = Batches, so the butter is the limiting factor. Thus, they can make whole batches of a dozen cookies. 15. Do the math A) 2 sides x 5 = 20 x 5 = 20 top and bottom x 10 = 0 x 10 = 0 front and back 5 x 10 = 50 5 x 10 = 50 total C) 2 sides x 8 = 32 x 8 = 32 top and bottom front and back x 8 = 32 x 8 = 32 totals B) 2 sides top and bottom front and back totals total 96 totals D) 2 sides x 6 = 2 x 6 = 2 top and bottom x 10 = 0 x 10 = 0 front and back 6 x 10 = 60 6 x 10 = totals total 160 total 28 figure D MATH BOWL th Grade Thinker and Team PRACTICE 10

12 16. Students will be asked to work on mathematical practice 8- Express regularity and repeated reasoning. Students will need to make a table , , , ,76,801 Students will need to notice the pattern of the last digit in the sequence: 7, 9, 3, 1, 7, 9, 3, 1 Students will notice the pattern repeats after the first numbers. Therefore students will divide 201 by and know the sequence repeats 505 times with a remainder of 2. The two represents the second number in the pattern. Since the pattern is 7, 9, 3, 1, the last digit of is Do the math 1 st three tests th test Total points after tests 75(points) 3(tests) + X = 80(points) (tests) 75(3) + X = 80() X = 320 X = X = Make a table: Days $ $ MATH BOWL th Grade Thinker and Team PRACTICE 11

13 19. Draw a picture: G = Grandma T To Scott s 15 x 2 = 30 S = Scott To Tom s 20 x 2 = 0 T = Tom To Robin s 20 x 2 = 0 20 R = Robin To Byron s 10 x 2 = 20 B = Byron To Caitlin s 25 x 2 = 50 C = Caitlin G total = 180 miles 15 B S R C 20. Make a table: Days Plants Total Plants He would have 255 plants after 8 days. MATH BOWL th Grade Thinker and Team PRACTICE 12

MATH BOWL 33 rd Annual

MATH BOWL 33 rd Annual BAKERSFIELD CITY SCHOOL DISTRICT Education Center 00 Baker Street Bakersfield, CA 905 Curriculum and Instruction MATH BOWL rd Annual 6 th Grade The Super Star/Dynamic Duo PRACTICE . Evaluate the expression