Sum Fun Tournament Meeting (Multiple Topics)

Transcription

1 Sum Fun Sum Fun Tournament Meeting (Multiple Topics) Sum Fun Topic There are a wide range of topics and difficulty levels covered during this meeting. Materials Needed The first four items listed below are available for download from on the MCP Members Only page of the Club Program section. Scorecard for each student Sheet for each round (Each student will need one copy of each question sheet.) Answer Key Rotate and Shuffle Rules OPTIONAL Prize(s) Meeting Plan This meeting plan is from the Sum Fun events that were started in Terre Haute, Indiana over 0 years ago. Created by a MATHCOUNTS coordinator and carried out today still by local teachers, Sum Fun is an engaging way to get your club members working together on math or to get your club members joining with students from other schools math clubs to have a great time while collaborating on math problems! The following guidelines will assume there are 0 math club members meeting for 4 minutes. Students are seated in groups of four at tables. Initial seating is arbitrary. Each table is numbered (-) and the four positions at each table are labeled (A-D). Each table is a team for one round, and the person at position A is the captain. Every student receives a copy of the round s four questions (see sample to the right) and is given five minutes to answer them. The team then works together to solve the problems and to agree on a single answer for each problem. A warning is given when there are 0 seconds left so that one answer for each problem can be recorded on the captain s sheet. These are the official answers for the table, and no other answers will be accepted. When time is up, the teacher will credit each student at a table with the number of questions their team collectively answered correctly. These points are recorded on each student s scorecard which each student carries with him/her throughout the meeting. This concludes a round of play. Students then are arranged in new teams. Three of the four students will rotate to other tables according to some rules, such as: () Cs go forward 4 tables to position C, () Bs go forward tables to position B and () As go forward table to position A. When students are at their new tables, the students at the table are shuffled according Round. Simplify ( ) +. Express your answer as a common fraction.. Joe tossed 4 splugs into an empty pot. Their average weight was 6 pounds. Then he tossed in more splugs whose average weight was 7 pounds each. Then he threw in a big splug. The overall average weight of the splugs in the pot was 7 pounds. What was the weight, in pounds, of the big splug?. The first four rows of Pascal s triangle are listed here. What is the sum of the numbers in the seventh row? 4. Express as a mixed number MATHCOUNTS Club Resource Guide 4

2 to some rule, such as: Arrange yourselves in ascending order according to the last letter of your last name. (The rotate and shuffle rules are changed every round.) Once the students are arranged, the next round of questions is distributed to each table. NAME: Round Number Table Number 4 A total of 4 rounds are conducted with rotations and shuffles between 6 each round. After the last round, 7 the scorecards are collected and 8 students are ranked by point total. (The sample scorecard to the right shows Pythagoras score after completing six rounds.) Ties can be Total All Rounds 6 broken using an arbitrary rule established before the meeting begins. For example, ties may be broken by comparing the scores in individual rounds starting with the last round completed. 4 Scorecard Pythagoras Smith Prizes can be awarded to the top finishers. The number of questions, number of rounds and time per round are arbitrary and can be adjusted for any situation. Similarly, when the number of total students is not divisible by 4, tables of three students each can be included. CONSIDERATIONS Enlisting the assistance of other teachers is extremely helpful. It is ideal to have a proctor/ point awarder for every two tables to speed up the scoring process. Any math problems can be used for the activity. If the problems provided for this activity (on are not the correct difficulty level for your students, you are encouraged to replace the problems with more appropriate ones. This is a fantastic activity to do in conjunction with other math clubs. The rules of Sum Fun () encourage students to meet students from other schools, () allow students of various ability levels to work together and () keep an all-star school from dominating the event. Though the scorecards have room for 8 rounds (which would take approximately hour, 0 minutes to complete), you can adapt the number of rounds you will use according to your timeframe. If Sum Fun is being conducted with multiple math clubs, prizes can be awarded to the high scorers from each club, the high scorers in each grade level, etc. This activity transfers well to the classroom. Sum Fun is perfect for the beginning of the school year when students don t know each other, for school days that have irregular schedules due to assemblies/delayed openings/holidays, etc. and for review days before quizzes or tests. Round Total Remember: There are Rotate and Shuffle Rules, Student Scorecards and multiple sets of problems/answer keys available for download from on the MCP Members Only page of the Club Program section. 4 4 Special thanks to MATHCOUNTS Indiana chapter coordinator Denis Radecki, P.E. for his creativity in putting Sum Fun together and for his generosity in sharing it with so many people. Thank you also to MATHCOUNTS Oklahoma chapter coordinator Tom Carlisle, P.E. for providing the many Sum Fun materials he has assembled over the years MATHCOUNTS Club Resource Guide

3 Sum Fun Rounds -8 Problem Sheets and Answer Key This material was originally used at the Sum Fun Event in Terre Haute, IN in November 998.

4 Sum Fun Round. What is the value of x x + when x =?. What number can be subtracted from both the numerator and denominator of 9 4 so that the resulting fraction will be equivalent to 4?. Your job is to number the pages of a book beginning with page. You have twenty of each of 0s, s, s, s, 4s, 6s, 7s, 8s and 9s. You only have four s. Under these conditions, what is the last page you can number? 4. What is the value of to the nearest millionth?

5 Sum Fun Round. What is the units digit when 7 is expressed as an integer?. Jim took a ride in a taxi that charges $.7 for the first mile and 0 cents for each additional quarter mile. Jim rode for 6 miles, paid the driver $0.00 and told him to keep the change as a tip. How much was the tip?. A student had an average of 88% after 6 tests. The next test counts as two tests (the score is counted twice). If 8% is the lowest B, what is the lowest score the student can get on the doubled test and still have a B average? 4. What is one-half the reciprocal of 0.008? Express your answer as a common fraction.

6 Sum Fun Round. Two concentric circles (having the same center) have radii of units and units. Two darts are thrown and they both land inside the larger circle. What is the probability that one dart lands inside the smaller circle and the other lands outside the smaller circle? Express your answer as a common fraction.. The total surface area of a closed right circular cylinder that is inches tall and 4 inches in diameter is qϖ square inches. What is the value of q?. If one marble is to be chosen from a bag that contains 0 red marbles, blue marbles and white marbles, what is the probability that the marble chosen will be blue or red? Express your answer as a common fraction. 4. What is the sum of the two whole numbers which the average of 7, 68 and 7 lies between?

7 Sum Fun Round 4. What percent of.87 is 87.?. If Zach had twice as many dollars as he has now and added half as many dollars as he has now, he would have $00. How many dollars does Zach have now?. Express 6% of 4 as a decimal. 4. How many different size squares can be formed by connecting 4 dots as vertices of the squares?

8 Sum Fun Round. If a b = a + b, what is the value of 4?. What is the positive difference between the numeric values of the area and the perimeter of polygon ABCDEFGH? All angles are right angles except angles ABC and HAB. A B 7 H 4 C 0 G 7 F. Customers at a particular yogurt shop may select one of three flavors of yogurt. They may choose one of four toppings. How many flavor-topping combinations are possible if one flavor and one topping must be chosen? E D 4. What is the positive difference between the product of 4. and 9.4 and the sum of 4. and 9.4? Express your answer as a decimal to the nearest hundredth.

9 Sum Fun Round 6. A rectangle has a perimeter of 48 feet. The length of each side is an integer. What is the greatest possible are of the rectangle?. Express the following expression in simplest radical form: What is the value of n if 4 4 = n? 4. If you may only move or, how many different paths can be found from A to B if you may only move on the segments given? A B

10 Sum Fun Round 7. What is the value of q for the equation = q?. What is the maximum number of equilateral triangles that can be made from 6 equal-length line segments if only the endpoints can coincide?. The numbers a and b are consecutive, even, positive integers. If a < 0 0 < b, what is the product ab? 4. What is the value of the expression number? + when written as a mixed + +

11 Sum Fun Round 8. What is the value of the sum common fraction. 0. +? Express your answer as a 9. What is the simplified value of the following expression: ?. What is the area, in square meters, of a triangle whose base is 000 cm and whose corresponding height is,000 mm? 4. What is the degree measure of angle ABC in this figure? 60 0? B 6 A C

12 Answers to Sum Fun Rounds -8 Round Round Round Round 4 Round Round 6 Round 7 Round 8 # ,000% # 4 $. 8 $ # page 44 76% # These problems were originally used at the November 998 Terre Haute, IN Sum Fun Event. We thank them for sharing these problems/answers with the rest of the MATHCOUNTS community!

13 Scorecard Scorecard NAME: NAME: Round Number Table Number 4 Round Total Round Number Table Number 4 Round Total Total All Rounds Total All Rounds Scorecard Scorecard NAME: NAME: Round Number Table Number 4 Round Total Round Number Table Number 4 Round Total Total All Rounds Total All Rounds

14 Sum Fun Sample Rotate & Shuffle Rules Round Position A Position B Position C Shuffle Forward table Forward tables Forward tables Alphabetically by first name Forward tables Forward tables Forward table Alphabetically by last name Forward tables Forward table Forward tables Numerically by birth month 4 Forward table Forward tables Forward tables Forward tables Forward table Forward tables 6 Forward table Forward tables Forward tables Numerically by day of the month of birthday Ascending order according to the last letter of last name Descending order according to first name 7 Forward tables Forward table Forward tables Ascending order by height 8 Forward tables Forward tables Forward table Ascending order by foot length

15 Sum Fun Rounds -8 Problem Sheets and Answer Key This material was originally used at the Sum Fun Event in Bartlesville, OK in September 994.

16 Sum Fun Round. What is the value of xy + xyz z if x = 4, y = /4 and z =?. In this figure, dimensions are in feet, and corners that appear to be right angles are right angles. What is the total area of the figure, in square feet? Express your answer as a decimal to the nearest tenth If a b = a b, what is the value of ( )? 4. Mary Baylor drove to work on Thursday at 40 miles per hour and arrived one minute late. She left at the same time on Friday, drove at 4 miles per hour and arrived one minute early. How far, in miles, does Ms. Baylor drive to work?

17 Sum Fun Round. How many cubic centimeters (cm ) are equivalent to 40 cubic meters (m )?. The length of a rectangle is increased by 0%. By what percentage would the width have to be decreased to keep the same area? Express your answer as a mixed number.. How long, in centimeters, is the slanted line in the figure shown? Express your answer as a decimal to the nearest tenth. 8 cm 4 cm 6 cm 4. The width of a particular rectangle is 4/ of its length. The perimeter is 6 cm. What is the area of the rectangle, in cm?

18 Sum Fun Round. An airplane has a wingspan of 47 feet. Suppose you decide to make a model of this airplane that is /0 the real size. What should the wingspan of the model be, in feet? Express your answer as a mixed number.. What is the area of the shaded region, in units? Use ϖ =.4. Express your answer as a decimal to the nearest hundredth. 6. What is 90% of 0% of 00? 4. A formula for the circumference of a circle is C = ϖr, and the formula for the area of a circle is A = ϖr, where r is the radius in each equation. If the area of circle P is 6ϖ square inches, what is the circumference of circle P, in inches? Express your answer in terms of ϖ.

19 Sum Fun Round 4. What is the value of ( ) + ()? Express your answer as a common fraction.. Joe tossed 4 splugs into an empty pot. Their average weight was 6 pounds each. Then he tossed in more splugs whose average weight was 7 pounds each. Then he threw in a big splug. The overall average weight of the splugs in the pot was 7 pounds. What was the weight, in pounds, of the big splug?. The first five rows of Pascal s Triangle are listed here. What are the numbers in the seventh row? What is the value of 4 + when expressed as a mixed number? + 6 7

20 Sum Fun Round. What percent of is 60?. What is the total area, in square units, of the shaded regions in this -by- unit square? All angles that appear to be right angles are right angles. Express your answer as a common fraction.. N is the number of buttons in a sewing box. N is more than 40 and less than 80. When N is divided by, the remainder is. When N is divided by 7, the remainder is 4. What is the value of N? 4. What is the ones digit when is simplified?

21 Sum Fun Round 6. There are three parks (A, B and C) in which boys and girls are playing. The areas of parks A, B and C are 00 m, 00 m and 00 m, respectively. The numbers of children playing in these parks are 60, 0 and 40, respectively. Which park is the most crowded with respect to children per m?. What is the simplified value of [4 + (7 4) (8) ] 0?. A one-foot-square tile costs $0.87. How much will it cost to cover a family room floor that measures 8 feet by feet with this type of tile? 4. How many triangles are created by the segments in this figure?

22 Sum Fun Round 7. Jim scored fewer points than Danny scored. Together they scored 7 points. How many points did Danny score?. The product of two positive numbers is 8 and one of their quotients is 8. What is the sum of the numbers?. A dealer has 0 cars and trucks. If two more cars are delivered, the dealer will have three times as many cars as trucks. How many trucks does the dealer have? 4. The table top shown has a square center section and semicircular end sections. If the area of the table top is 600 cm, what is the total length of the table top, in cm? Use ϖ = /7. Length

23 Sum Fun Round 8. If X pencils cost Y cents, how many pencils can be bought for D dollars? Express your answer as a common fraction in terms of X, Y and D.. What is the greatest common factor (GCF) of 40 and 46?. Marshmallows cost $0.06 each. A marshmallow weighs grams. What would be the price of a 0.4-kilogram bag of marshmallows? 4. When certain numbers are placed in the empty boxes, the sum of each row, each column and the two diagonals is the same. What number should be placed in the center box? 9 7

24 Answers to Sum Fun Rounds -8 Round Round Round Round 4 Round Round 6 Round 7 Round 8 # 6 40,000, C DX Y # #, , 6,, 0,, 6, 67 $ $.40 #4 880 ϖ 8 These problems were originally used at the September 994 Sum Fun Event in Bartlesville, OK. We thank them for sharing these problems/answers with the rest of the MATHCOUNTS community!