Grade 3-4 Individual Event (30 Minutes) 1) If Susie puts her pennies in piles of 4 she has 2 pennies left over. If she puts her pennies in piles of 5 she has 3 pennies left over. What is the least amount of pennies Susie can have? 2) This square is made of smaller squares. The area of the entire shape is 16 cm². What is the perimeter of the shaded region? 3) How many rectangles of any size are in this shape? 4) Jimmy bought 10 lollipops at 25 cents each. If Jimmy sells all the lollipops for the same price, how much will he have to sell each lollipop for in order to make a $1 profit? 5) Find the average of the numbers between 1 and 100 that end in 9. 6) Monika s resting heart rate is 50 beats per minute. For every minute she exercises, her heart rate increases 5 beats per minute. How long will it take her to reach a heart rate of 115 beats per minute? 7) The original price of a new sled is $140.00. If the sled is marked down 15%, what is the new price of the sled? 8) 13 + 24 + 35 + 46 + 54 + 65 + 76 + 87 =? 9) Barb made 48 snowman cookies. She put black hats on half of the cookies, baseball caps on one third of the cookies, and the remaining cookies had no hat. How many cookies had no hat? 10) Jerri ate one half of Jenny s cake. Jessie ate one fourth as much as Jerri did. Janice ate twice as much as Jessie. What fraction of Jenny s cake has not been eaten?
11) What is the average of the first 5 even numbers greater than 20? 12) 1000 x 200 13) 486 3² = 14) 17 x 58 = 15) 8 + 4 x 6 4 4 = INDIVIDUAL ANSWER DOCUMENT (Grades 3-4) SCORE Team # School Student Name Student Number 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Grade 3-4 Individual Event Solutions 1) Make a chart with multiples of 4 adding 2 and compare with multiples of 5 adding 3. When the number is the same for both, that will be the answer. The least number possible is 18 pennies. piles of 4 with 2 pennies left over 6 10 14 18 piles of 5 with 3 pennies left over 8 13 18 2) The shape is made of 16 cubes and the area is 16 cm². The length of each side of the small cubes are 1 cm. The dark region has 16 sides. Therefore, the perimeter of the dark region is 16 x 1cm or 16 cm. 3) Since a square is also a rectangle by definition, there are 9 possible rectangles in this figure. There are 4 small rectangles each made from 1 square, 4 rectangles each made from 2 squares, and 1 rectangle made from the 4 squares. 4) Jimmy originally spent 10 x.25 or $2.50. In order to make a $1 profit he must sell each lollipop for.35 to make.35 x 10 or $3.50. 5) Add up the numbers that end in 9: 9 + 19 + 29 + 39 + 49 + 59 + 69 + 79 + 89 + 99 = 540. Now divide 540 by 10 and the average is 54. 6) Take the final rate 115 and subtract her normal rate of 50. She must raise her heart beat 65 beats. It takes 1 minute to raise her heart beat 5 beats. Divide 65 by 5 and she must exercise 13 minutes. 7) The original price of a new sled is $140.00. $140 x 15% is $21. Subtract the 15% to find the new price of the sled: $140 -$21 = $119 8) Instead of doing regular addition, use smart addition and link numbers together. (13 + 87) + (24 + 76) + (35 + 65) + (46 + 54) = 100 + 100 + 100 + 100 = 400 9) Barb made 48 snowman cookies. Half (24) of the cookies had black hats, 1/3 (16) had baseball caps. 48 24 16 = 8 cookies remaining that had no hats. 10) Jerri ate 1/2. Jessie ate one fourth as much as Jerri which is 1/2 x 1/4 = 1/8. Janice ate twice as much as Jessie which is 2/8. The fraction of Jenny s cake that has not been eaten is: 1-1/2-1/8-2/8 = 1 7/8 = 1/8. 11) The average of the first 5 even numbers greater than 20 and then divide by 5 for the average: 22 + 24 + 26 + 28 + 30 = 130 / 5 = 26 12) 1000 x 200 = 200,000 13) 486 3² = 486 9 = 54 14) 17 x 58 = 986 15) 8 + 4 x 6 4 4 = 8 + (24) (1) = 31
INDIVIDUAL ANSWER KEY (Grades 3-4) Mark answers incorrect. Each correct answer is worth one point. Write the number that the student got correct in the SCORE box on their document. 18 1. 16 cm 9 2. 3. 35 cents 4. 54 5. 13 minutes 6. $119 7. 400 8. 8 9. 1/8 10. 26 11. 200,000 12. 54 13. 986 14. 31 15.
Grade 3-4 Team Event (20 Minutes) 1) The snow was falling 1 and ½ inches per hour. At this rate, how long would it take for 3 feet of snow to accumulate? There are 12 inches in 1 foot. 2) The perimeter of this large rectangle is 60 cm. What is the perimeter of 1 of the smaller squares? 3) The sums of each row and column are given. How much is 1 star worth? 16 60 20 32 36 28 4) Mary worked at the ice cream shop for 12 weeks this summer and got paid the same amount each week. She made a total of $2064. How much did she make each month?(1 month = 4 weeks) 5) A box of pencils can be divided equally among 3, 5, or 6 students. What is the least number of pencils in the box if there are more than 100? 6) Jane has a black, blue, red, and white shirt. She has black, blue, and red pants. How many shirt and pants outfits can she make if she cannot wear the same color shirt and pants together? 7) Leslie is baking cupcakes for the party. She bakes 15 per hour, but 2 get eaten every 15 minutes. How many hours will it take her to have a total of 210 cupcakes ready? 8) A spinner has 16 sections. Six spaces are red, five are green, and five are yellow. What is the probability that you will land on a red space? Reduce to lowest terms. 9) Molly bought a pair of shoes. The original price was $60, but the shoes were on sale for 15% off. How much did she have to pay for the shoes? 10) The printer has to hand-set the page numbers for the book. It takes him one minute to set a single digit on each page. If he starts on page 1 at 8:00 and finishes at 11:36 that morning, how many pages are in the book?
Grade 3-4 Team Event Solutions 1) Divide 36 inches by 1.5 inches per hour and it takes 24 hours for 36 inches or 3 feet of snow to accumulate. 2) Since the perimeter of the large rectangle is 60cm. The sides are all equal to 5cm because there are 12 equal sides. 60cm/12 = 5cm. The perimeter of one of the smaller squares is 4 sides x 5cm = 20 cm. 3) Since 3 smiley faces = 60, then 1 smiley face = 20. 2 Stars + 1 smiley face = 28. Subtract the smiley face (20) from the equation and the 2 stars are 8. One star = 4. 4) Since we are figuring the pay for a month divide the total by 3. $2064 3 = $688. 5) The least common multiple of 3, 5, and 6 is 30. Since there must be more than 100 pencils in the box, the lowest number that is divisible by 3, 5, and 6 is 120 pencils. 6) She could make 4 x 3 = 12 total outfits. However, she must subtract the three shirt/pant combinations of the same color black/black, blue/blue, and red/red. She can make 9 outfits. 7) She is baking 15 cupcakes each hour, but 2 are being subtracted every 15 minutes. So every hour 8 are subtracted. That means she is only gaining 7 cupcakes each hour. At that rate it will take her 210/7 = 30 hours to make the 210 cupcakes. 8) There are 16 total sections. Since 6 are red, the probability of landing on red is 6/16 or 3/8. 9) To find out how much she saved multiply $60 x.15 = $9. Subtract to find out how much she paid for the shoes $60 - $9 = $51. 10) First you must figure the time. It is three hours and thirty-six minutes or 180 + 36 = 216 minutes. The page numbers 1-9 take nine minutes to set. There are ninety pages in 10-99 so that is an additional 180 minutes. Subtract 216-189 = 27. Divide this by three and that will tell you the additional pages. There are 9 additional pages. So an additional 9 pages would be through page 108. Don t forget to count 100 as the first additional page of the 9 pages. There are 108 pages in the book.
TEAM ANSWER KEY (Grades 3-4) Mark answers incorrect. Each correct answer is worth one point. Write the number that the student got correct in the SCORE box on their document. 24 hours 1. 20cm 2. 4 3. $688 4. 120 5. 9 6. 30 hours 7. 3/8 (6/16 is incorrect) 8. $51 9. 108 10.
TEAM ANSWER DOCUMENT (Grades 3-4) SCORE Team # School Student Names Write answers clearly. Each correct answer is worth one point. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Grade 5-6 Individual Event (30 Minutes) 1) Connie and Tani had 60 jellybeans combined. Connie gave Tani 14 of her jellybeans, then they had the same number of jellybeans. How many jellybeans did Connie have to start with? 2) The cubes are glued together and dropped in a bucket of red paint. How many cubes have red paint on 5 sides? 3) How many rectangles of any size are in this shape? 4) Angie and Bobby have $27 combined; Bobby and Carl have $33 combined; and Angie and Carl have $30 combined. How much money does Carl have? 5) On planet Zurux they use three coin types: axps, daxps, and raxps. Four axps and one daxp equals one raxp. Two daxps and one raxp equals 10 axps. How many axps would equal one raxp? 6) Find the sum of the least and greatest prime number less than 50. 7) There are 75 students in the fifth grade. 27 like pizza, 46 like hamburgers, and 13 like both. How many students in the fifth grade class like neither pizza nor hamburgers? 8) In this multiplication problem different letters stand for different digits. What is the value of DCC? BC x 9 DCC 9) The sum of Sarah and Amy s ages is 39 years. Sarah s age is twice Amy s age. How old is Sarah? 10) 2 x 3 + 4 x 9 1 =
11) 13 + 24 + 36 + 57 + 43 + 64 + 76 + 87 = 12) What is the difference between 78% of 87 and 87% of 78? 13) What is one half of one third of 108? 14) What is the greatest common factor of 108 and 420? 15) If July 1 falls on Monday, what day of the week will Sept 2 fall on? INDIVIDUAL ANSWER DOCUMENT (Grades 5-6) SCORE Team # School Student Name Student Number 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Grade 5-6 Individual Event Solutions 1) In order for both girls to have the same amount of jellybeans, they would have 30 each in the end. So Connie started with 30 + 14 = 44 jellybeans, and Tani started with 30 14 = 16 jellybeans. Check this out by adding 44 + 16 = 60 total jellybeans. Connie started with 44 jellybeans. 2) The shape is made of 10 cubes. The cubes that have 1 block touching them have 5 sides showing. There are 3 cubes that have 5 red sides. 3) By definition a square is also a rectangle. There are 25 total rectangles in the shape. 4) A + B = 27 B + C = 33 A + C =30 2A + 2B + 2C = 90 Therefore, A + B + C = 45. Substitute (A + B) in the equation to solve for C. 27 + C = 45 C = 18 Carl has $18. 6) 2 + 47 = 49 Number of that Type type made from 1 shape 8 made from 2 shapes 9 made from 3 shapes 4 made from 4 shapes 3 made from 6 shapes 1 Total 25 5) Since 4 axps and 1 daxp equal 1 raxp, then 2 daxps plus 4 axps and 1 daxp equal 10 axps. If 3 daxps and 4 axps equal 10 axps, then 1 daxp equals 2 axps. Now 4 axps plus 2 axps equal 1 raxp or 6 axps. 4A + 1 D = 1 R 2D + 1 R = 10A substitute (4A + 1D) 2D + 4A + 1D = 10A 3D = 6A D = 2A 4A + 1D = 1R substitute (D = 2A) 6A = 1R
Grade 5-6 Individual Event Solutions 7) Use a Venn Diagram. The number of students who only like pizza is 27 13 = 14. The number of students who like only hamburgers is 46-13 = 33. To solve for Neither region subtract all the other regions from the total. There are 15 students who like neither. 9) The sum of Sarah and Amy s ages is 39 years. Sarah s age is twice Amy s age. Let X stand for Amy s age. Then Sarah s age is 2X. X + 2X = 39. Solve for X, 39/3 = X. X is 13 and 2X is 26. Therefore, Sarah is 26. 10) Use the order of operations PEMDAS. 2 x 3 + 4 x 9 1 = (2 x 3) + (4 x 9) 1 = 6 + 36 1 = 41 11) Use smart addition and group pairs together. (13 + 87) + (24 + 76) + (36 + 64) + (57 + 43) = 100 + 100 + 100 + 100 = 400 Both(13) Pizza(27) Hamburgers (46) 14 13 33 Neither = 75 - (14+ 13 + 33) = 15 8) There are only 2 possible solutions ( 0 or 5) for C since C x 9 = C. However, C cannot be zero because 9 x B would have to yield a zero. So C must be 5. Since C must be 5, then B x 9 + the 4 that carried yield D5. The only digit B can be is 9 since 9 x 9 + 4 would yield 85. The number DCC is 855. 12) 87% of 78 =.87 x 78 = 67.86 78% of 87 =.78 x 87 = 67.86 The difference is zero (0). 13) One half of one third of 108 is 108/3 = 36, 36/2= 18 14) 108/12 = 9 and 420/12= 35. If you do factors of 108 {2x2x3x3x3} and factors of 420 {2x2x3x5x7}, then the greatest common factor (GCF) is 12. 15) Both July and August have 31 days each. 31 + 31 = 62 days + 1 day in September that would be 63 days which is a perfect 9 weeks. September 2 will be on a Monday.
INDIVIDUAL ANSWER KEY (Grades 5-6) Mark answers incorrect. Each correct answer is worth one point. Write the number that the student got correct in the SCORE box on their document. 44 1. 3 25 2. 3. $18 4. 6 5. 49 6. 15 7. 855 8. 26 9. 41 10. 400 11. 0 12. 18 13. 12 Monday 14. 15.
Grade 5-6 Team Event (20 Minutes) 1) What is the sum of the first 7 prime numbers greater than 20? 2) If 3 darts land on this dart board, how many different point totals are possible? 3 4 444 5 4 3 23 3) Study the first two triangles. Using this pattern what is the missing number on triangle 3? 35 47 40 36 44 30? 46 4) Farmer Brown counted 19 animals in the farm yard. He counted legs and there were 62. If there were only cows and chickens, how many cows were out there? 5) The area of this shape is 72 cm². What is the perimeter? 6) A 900 seat stadium is divided into three sections. The first section has 350 seats. There are 150 more seats in section two than in section three. How many seats are in section 2? 7) The ratio of the length of Mary s throw to the length of Kyle s throw is 4:7. Mary s throw measures 16cm. How many more cm is Kyle s throw than Mary s? 8) How many blocks will it take to build a eight-step staircase? 9) A boy collected a total of 72 coins over three consecutive days. Each day he collected one more coin than the previous day. How many coins did he collect on the last day? 10) Tina starts with 10 cents and puts it in her piggy bank in January and then doubles it in February to put in 20 cents. If she keeps doubling the amount she puts in her bank each month, how much will she have in her bank by the end of December?
Grade 5-6 Team Event Solutions 1) The sum of first seven prime numbers greater than 20 is 23 + 29 + 31 + 37 + 41 + 43 + 47 = 251 2) Make an organized list. There are 7 different point totals that can be made from 3 darts landing. Dart 1 Dart 2 Dart 3 Point Total 5 5 5 15 5 5 4 14 5 5 3 13 5 4 4 13 5 4 3 12 5 3 3 11 4 4 4 12 4 4 3 11 4 3 3 10 3 3 3 9 3) The top number in each triangle is the average of the 2 bottom numbers. The average of the third triangle is 30 + 46 divided by 2 = 38. 4) Make a chart to compare the heads and legs and animal count. There were 12 cows and 7 chickens. Chickens 10 9 8 7 Cows 9 10 11 12 Total Animals 19 19 19 19 Chicken Legs 20 18 16 14 Cows Legs 36 40 44 48 Total Legs 56 58 60 62 5) The area is 72cm² and there are 8 squares so each square has an area of 9cm². This would make the lengths of each side of the squares 3cm. If you count the edges going around there are 14. Multiply this by 3cm and there are 42cm in the perimeter of the shape. 6) Subtract 900 350 = 550 seats left in section two and three. Since section two has 150 more seats than section three, use algebra to solve. Let X represent section three. X + (X + 150) = 550. 2X + 150 = 550. 2X = 400. X = 200. So section three has 200 seats and section two has (X + 150) = 350 seats. 7) The ratio of Mary s throw to Kyle s throw is 4:7. Mary s throw measured 16 cm. If she had 4 portions, then each portion is 4 cm. So Kyle s throw measured 7x (4 cm) or 28 cm. 28 16 = a difference of 12 cm. 8) Each layer of steps adds the number of cubes in the layer. So add 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 = 144 cubes. 9) Most students at this level will use trial and error. Try algebra. Let X stand for day 1. X + (X +1) + (X + 2) = 72. 3X + 3 = 72. 3X = 69. X = 23. 23 + 24 + 25 = 72. He collected 25 coins on the last day. 10).10 +.20 +.40 +.80 + 1.60 +3.20 + 6.40 + 12.80 + 25.60 + 51.20 + 102.40 + 204.80 = $409.50
TEAM ANSWER KEY (Grades 5-6) Mark answers incorrect. Each correct answer is worth one point. Write the number that the student got correct in the SCORE box on their document. 251 1. 7 2. 38 3. 12 4. 42 cm 5. 350 6. 12 cm 7. 144 8. 25 9. $409.50 10.
TEAM ANSWER DOCUMENT (Grades 5-6) SCORE Team # School Student Names Write answers clearly. Each correct answer is worth one point. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Grade 7-8 Individual Event (30 Minutes) 1) Kerry s average on 6 tests was 89. If he wants to make an average of 90, what must he score on the next test he takes? 2) In this magic square the sum of the numbers in each of row, column, and diagonal is the same. What number should be in the box marked X? 3) A picture frame is 18 x 16 inches. There is a 2 inch mat around the picture. What is the area of the mat (shaded region)? 4) If a roller coaster can accommodate 75 people in 25 minutes, how many people could ride the roller coaster in 2 hours? 5) A set of 10 consecutive odd numbers has a sum of 220. What is the third number in the set? 6) What number multiplied by itself is equal to the product of 16 and 144? 7) A certain number is divisible by three and also by five. When the number is divided by 7, the remainder is 2. What is the smallest number between 200 and 300 that satisfies all these conditions? 8) Mike shipped a package that weighed W pounds, with W being a whole number. To ship this package it costs a total of $1.75 for the first 5 pounds and.16 cents for each additional pound. If the package cost $6.39 to ship, how many pounds did it weigh? 9) A dune buggy has a front wheel with a circumference of 3 ft. and a back wheel with a circumference of 5 ft. How many more turns will the front wheel make than the back wheel in 2 miles? (1 mile = 5,280 ft.) 10) The numbers given represent the sum of the objects in each row or column. Find the value of the middle row. X 2 4 14 7 6 15 1 3 30 53 27 40 2 37? 66 2 2 2 2
11) Find the slope of the line segment joining the points ( 2, - 4 ) and ( - 4, 2 ). 12) 4 + 9 x 2 3 x 2 = 13) Find the difference between the sum of the three highest and the sum of the three lowest prime numbers between 0-100. 14) Nine people shake each other s hand only once at a meeting. How many handshakes take place altogether? 15) Suppose five days after the day before yesterday is Saturday. What day of the week will tomorrow be? INDIVIDUAL ANSWER DOCUMENT (Grades 7-8) SCORE Team # School Student Name Student Number 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Grade 7-8 Individual Event Solutions 1) Since he had an average of 89 on 6 tests his total points scored was 534. In order to make a 90 average on 7 tests, he must obtain a total of 630 points. Kerry must score 630-534 = 96 points. 2) Adding up the 4 numbers in the diagonal the sum is 34. Now you can solve for the top box 34 = (? +4 + 14 + 7). The top box is 9. Now to solve for X subtract the 3 numbers from 34. 34 (9 + 6 +3) = X. So, X = 16 3) The area of the entire frame is 18 x 16 = 288cm² and the inside area of the frame is 14 x 12 = 168cm². Subtract the inside area from the total area and that will give you the area of the surrounding mat. 288 168 = 120cm² 4) Using ratios, let X represent the number of people to ride in 2 housr. X :120 = 75:25. X/120 = 75/25. 25X = 9000 or X = 360. The roller coaster can accommodate 360 people in 2 hours. 5) The sum of 10 consecutive odd numbers is 220. Divide 220 by 10 and the average is 22 which would fall between the 5 th and 6 th numbers. So the 5 th number is 21. The numbers in the set are 13, 15, 17, 18, 21, 23, 25, 27, 29, 31. The third number in the set is 17. 6) Working backwards: 16 x 144 = 2304. The square root of 2304 is 48. The number multiplied by itself is 48. 7) Make a chart. Since the number is a multiple of 3 and 5, then it is a multiple of 15. List these and numbers that are multiples of 7 adding 2 and find the smallest number between 200-300. The answer is 240. 8) $6.39 - $1.75 = $4.64. The package weight for the remaining pounds can be calculated by 4.64/.16 = 29. So there were 5 pounds ($1.75) + the additional 29 pounds ($4.64) or 34 pounds. 9) Two miles would be 10,560 ft. Divide this by 3 and the front wheel turns 3,520 times. Divide total distance by 5 and the back wheel turns 2,112 times. To find out how many more times the front wheel turns than the back wheel subtract 3,520 2,112 = 1,408 times. 16 11 2 14 Multiples of 3 and 5 210 225 240 255 270 285 Multiples of 7 +2 205 212 219 226 233 240 5 9 4 7 6 15 1 12 3 10 8 13 10) Use the first column to solve for the star. 3stars = 30 so 1 star=10. Substitute this in the first row to solve for the moon. 3 stars + 1 moon = 37. So 1 moon = 7. Solve for the X by substituting the value of moon (7) in the second column. So 2X + 7 = 53. X is worth 23. Now to solve for the middle row: 1 star + 1 X + 2 moons = 10 + 23 + 14 = 47.
Grade 7-8 Individual Event Solutions 11) x 1 = 2, y 1 = - 4, x 2 = -4, and y 2 = 2. 2 (-4) -4-2 6 = -6 = -1 12) Use the order of operations PEMDAS. 4 + 9 x 2 3 x 2 = 4 + (9 x 2) (3 x 2) = 4 + 18 6 = 16 13) ( 97 + 89 + 83) (2 + 3 + 5) = 269-10 = 259 14) Since there are 9 people the answer is 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 handshakes. 15) Draw a diagram to help solve. Suppose five days after the day before yesterday is Saturday. What day of the week will tomorrow be? Tomorrow will be Thursday.
INDIVIDUAL ANSWER KEY (Grades 7-8) Mark answers incorrect. Each correct answer is worth one point. Write the number that the student got correct in the SCORE box on their document. 96 1. 16 120cm² 2. 3. 360 4. 17 5. 48 6. 240 7. 34 8. 1408 9. 47 10. -1 11. 16 12. 259 13. 36 14. Thursday 15.
Grade 7-8 Team Event (20 Minutes) 1) What is 30% of 20% of 300? 2) Barry wrote a number on the back side of each of these 2 cards. The sums of the numbers on both sides of each of the two cards are equal. The two numbers on the hidden sides are prime numbers. What is the sum of those two hidden numbers? 3) If each tiny square has an area of 4cm², what is the total combined perimeter of these shapes below? 32 59 4) The length of a rectangle is twice as long as it is wide. The perimeter is 108m. Find the area of the rectangle if the length and width are whole numbers? 5) There are 4 children in the Jones family. Amy is 10 inches shorter than John and he is 6 inches taller than Carmen. Wilson is 56 inches tall, which is 2 inches taller than Carmen. Find Amy's height. 6) ABCD stands for a four-digit positive number where each letter stands for a different digit. When the number ABCD is multiplied by four its digits appear in the reverse order. The first digit A is a quarter of the last digit D. The second digit B is one less than the first digit A. What number does ABCD represent? 7) Find the sum of the first 100 positive integers. 1 + 2 + 3 8) Fifty votes were cast in class election. Del got 1/5 of the votes. Marion got as many votes as Kyle and Luke put together. Luke got 1/3 as many votes as Kyle. How many votes did Marion receive? 9) The only way that 10 can be written as the sum of 4 different counting numbers is 1 + 2 + 3 + 4. In how many different ways can 20 be written as the sum of 5 different counting numbers? 10) Alan bought a box of popcorn and two bars of chocolate for $18. Jan bought 2 boxes of popcorn and a bar of chocolate for $21. Find the cost of a bar of chocolate.
Grade 7-8 Team Event Solutions 1).30 x.20 x 300 = 18 2) The only even prime number is 2 so it must be added to the card with 59 or otherwise an odd number added to it would make the sum even. There can be no even sum because a prime number added to 38 will yield an odd number. So the sum of each card must be 61. The card with 32 must add 29 because 61-32 = 29. The sum of the two hidden numbers is 29 + 2= 31. 3) These shapes are all pentominoes and they each have 12 sides. There are 6 shapes x 12 sides or 72 total sides. Since the area of each small square is 4cm², then each side is 2cm long. 72 sides x 2cm = 144cm. 4) Perimeter is equal to 2L + 2W. Let W stand for width and since the length is 2 times the width, length can be represented by 2W. 2 (2W) + 2W = 108. 6W=108. W is equal to 18m and the length is twice that or 36m. The area is length x width or 36 x 18 = 648m². 5) Work backwards. Wilson is 56 inches tall. He is 2 inches taller than Carmen. So Carmen is 54 inches tall. John is 6 inches taller than Carmen so he is 60 inches tall. Subtract 60 10 = Amy is 50 inches tall. 6) Since A is a quarter of D, 1 and 2 are the only possible answers for A and 4 and 8 are the only possible answers for D. The answer has to reverse so 1 cannot be the first number because the product DCBA cannot be odd since it is a multiple of 4. So A is 2 and D is 8, and B will be 1. Since AB is 21, then BA is 12. That would make B equal 7 since 4 x D is 32 and the 3 carries. 4 x 7 is 28 + 3 that carried would be 31. The 1 would end up in the digit for B and the 3 would carry in the product DCBA. ABCD is 2178. Check the answer, 2178 x 4 yields 8712, which is 2178 backwards.
Grade 7-8 Team Event Solutions 7) To find the sum of the first 100 integers, you first add 1 plus 100 (the first and last numbers of the set) and get 101. Do the same with the next two integers, 2 and... n(n+1)/2 100* (100 +1)/2 (100*101)/2 = 5050 8) You can solve this with algebra or make a chart. Del got 1/5 of the 50 votes so he got 10. Now make a chart to figure out the other 40 votes. Marion had 20 votes. Luke Total Votes (40) Marion= Kyle = 3L K + L 1 3 4 8 2 6 8 16 3 9 12 24 4 12 16 32 5 15 20 40 9) Make an ordered list of the possibilities. There are 7 ways to list 5 different counting numbers whose sum is 20. 1st # 2nd # 3rd # 4th # 5th # Sum 1 2 3 4 10 20 1 2 3 5 9 20 1 2 3 6 8 20 1 2 4 5 8 20 1 2 4 6 7 20 1 3 4 5 7 20 2 3 4 5 6 20 10) Let P stand for popcorn and C stand for chocolate. P + 2C = 18 2P + C = 21 3P + 3C = 39 Divide both sides by 3. (P + C) = 13. Substitute (P+C) back in the original known equation P + 2C = 18 and subtract to solve for C. (P + 2C) (P+ C) = C. (18) (13) = 5. The Chocolate costs $5.
TEAM ANSWER KEY (Grades 7-8) Mark answers incorrect. Each correct answer is worth one point. Write the number that the student got correct in the SCORE box on their document. 18 1. 31 2. 144cm 3. 648m² 4. 50 inches 5. 2178 6. 5050 7. 20 8. 7 9. $5 10.
TEAM ANSWER DOCUMENT (Grades 7-8) SCORE Team # School Student Names Write answers clearly. Each correct answer is worth one point. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.