2009–2010 MATHCOUNTS Club Resource Guide 41 Sum Fun Tournament Meeting (Multiple Topics) 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 www.mathcounts.org on the MCP Members Only page of the Club Program section. Scorecard for each student Question 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 20 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 20 math club members meeting for 45 minutes. Students are seated in groups of four at tables. Initial seating is arbitrary. Each table is numbered (1-5) 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 30 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: (1) Cs go forward 4 tables to position C, (2) Bs go forward 3 tables to position B and (3) As go forward 1 table to position A. When students are at their new tables, the students at the table are “shuffled” according ♦ ♦ ♦ ♦ ♦ Round 1 1. Simplify (–1) 3 + 3 –1 . Express your answer as a common fraction. 2. Joe tossed 4 splugs into an empty pot. Their average weight was pounds. Then he tossed in 5 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? 3. The first four rows of Pascal’s triangle are listed here. What is the sum of the numbers in the seventh row? 4. Express 1 4 3 1 + + as a mixed number. 1 1 1 1 2 1 1 3 3 1 S u m F u n S u m F u n
Transcript
2009–2010 MATHCOUNTS Club Resource Guide 41
Sum Fun Tournament Meeting(Multiple Topics)
TopicThere are a wide range of topics and difficulty levels covered during this meeting.
Materials NeededThe first four items listed below are available for download from www.mathcounts.org on the MCP Members Only page of the Club Program section.
Scorecard for each studentQuestion Sheet for each round (Each student will need one copy of each question sheet.)Answer Key Rotate and Shuffle Rules
OPTIONALPrize(s)
Meeting PlanThis meeting plan is from the Sum Fun events that were started in Terre Haute, Indiana over 20 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 20 math club members meeting for 45 minutes.
Students are seated in groups of four at tables. Initial seating is arbitrary. Each table is numbered (1-5) 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 30 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: (1) Cs go forward 4 tables to position C, (2) Bs go forward 3 tables to position B and (3) As go forward 1 table to position A. When students are at their new tables, the students at the table are “shuffled” according
♦♦♦♦
♦
Round 1
1. Simplify (–1)3 + 3 –1. Express your answer as a common fraction.
2. Joe tossed 4 splugs into an empty pot. Their average weight was � pounds. Then he tossed in 5 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?
3. The first four rows of Pascal’s triangle are listed here. What is the sum of the numbers in the seventh row?
4. Express 1�
431
++
as a mixed number.
1 1 1 1 2 11 3 3 1
Sum Fun Sum Fun
42 2009–2010 MATHCOUNTS Club Resource Guide
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.
A total of 4 rounds are conducted with rotations and shuffles between each round. After the last round, the scorecards are collected and students are ranked by point total. (The sample scorecard to the right shows Pythagoras’ score after completing six rounds.) Ties can be 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.
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.
CONSIDERATIONSEnlisting 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 www.mathcounts.org) 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 (1) encourage students to meet students from other schools, (2) allow students of various ability levels to work together and (3) keep an “all-star” school from dominating the event.Though the scorecards have room for 8 rounds (which would take approximately 1 hour, 30 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.
Remember: There are Rotate and Shuffle Rules, Student Scorecards and multiple sets of problems/answer keys available for download from www.mathcounts.org on the MCP Members Only page of the Club Program section.
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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.
Round Number
Table Number
Question Round Total1 2 3 4
1
2
3
4
5
�
7
8
Total All Rounds
NAME: Scorecard
PythagorasSmith
241213
342133
16
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Rounds 1-8
Problem Sheets andAnswer Key
This material was originally used at the Sum Fun 12 Event
in Terre Haute, IN in November 1998.
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What is the value of 2x2 – 3x + 1 when x = 2?
2. What number can be subtracted from both the numerator and
denominator of 1924
so that the resulting fraction will be equivalent to 34
?
3. Your job is to number the pages of a book beginning with page 1. You have twenty of each of 0s, 1s, 2s, 3s, 4s, 6s, 7s, 8s and 9s. You only have four 5s. Under these conditions, what is the last page you can number?
4. What is the value of 5 .0386 to the nearest millionth?
Sum Fun Round 1
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What is the units digit when 217 – 3 is expressed as an integer?
2. Jim took a ride in a taxi that charges $1.75 for the first mile and 30 cents for each additional quarter mile. Jim rode for 6 miles, paid the driver $10.00 and told him to keep the change as a tip. How much was the tip?
3. A student had an average of 88% after 6 tests. The next test counts as two tests (the score is counted twice). If 85% 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.
Sum Fun Round 2
1. Two concentric circles (having the same center) have radii of 2 units and 3 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.
2. The total surface area of a closed right circular cylinder that is 5 inches tall and 4 inches in diameter is q� square inches. What is the value of q?
3. If one marble is to be chosen from a bag that contains 10 red marbles, 5 blue marbles and 15 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 37, 68 and 73 lies between?
32
Sum Fun Round 3
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What percent of 12.875 is 1287.5?
2. If Zach had twice as many dollars as he has now and added half as many dollars as he has now, he would have $100. How many dollars does Zach have now?
3. Express 16% of 4 as a decimal.
4. How many different size squares can be formed by connecting 4 dots as vertices of the squares?
Sum Fun Round 4
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. If a ♣ b = a2 + b, what is the value of 4 ♣ 3?
2. 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.
3. 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?
4. What is the positive difference between the product of 14.3 and 9.4 and the sum of 114.3 and 119.4? Express your answer as a decimal to the nearest hundredth.
20
14
3
75
7
11
H
B C
E D
FG
A
Sum Fun Round 5
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. 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?
2. Express the following expression in simplest radical form:
5 9 9 9 92 2 2 2+ + +
3. What is the value of n if 4–3 • 24 = 2n?
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
Sum Fun Round 6
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What is the value of q for the equation 23 5− =q ?
2. What is the maximum number of equilateral triangles that can be made from 6 equal-length line segments if only the endpoints can coincide?
3. The numbers a and b are consecutive, even, positive integers. If a < 300 < b, what is the product ab?
4. What is the value of the expression 5
5 5
555 +
++
when written as a mixed number?
Sum Fun Round 7
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What is the value of the sum 50 .29
+ ? Express your answer as a common fraction.
2. What is the simplified value of the following expression: 1 + 2 – 3 + 4 + 5 – 6 + 7 + 8 – 9 + 10 + 11 – 12 + ... + 97 + 98 – 99?
3. What is the area, in square meters, of a triangle whose base is 2000 cm and whose corresponding height is 12,000 mm?
4. What is the degree measure of angle ABC in this figure?
B
50
60
55
63
CA
?
Sum Fun Round 8
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
These problems were originally used at the November 1998 Terre Haute, IN Sum Fun 12 Event. We thank them for sharing these problems/answers with the rest of the MATHCOUNTS community!
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Round Number
Table Number
Question Round Total1 2 3 4
1
2
3
4
5
6
7
8
Total All Rounds
NAME:
Scorecard
Round Number
Table Number
Question Round Total1 2 3 4
1
2
3
4
5
6
7
8
Total All Rounds
NAME:
Scorecard
Round Number
Table Number
Question Round Total1 2 3 4
1
2
3
4
5
6
7
8
Total All Rounds
NAME:
Scorecard
Round Number
Table Number
Question Round Total1 2 3 4
1
2
3
4
5
6
7
8
Total All Rounds
NAME:
Scorecard
Sum Fun Sample Rotate & Shuffle Rules
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Round Position A Position B Position C Shuffle
1 Forward 1 table Forward 2 tables Forward 3 tables Alphabetically by first name
2 Forward 2 tables Forward 3 tables Forward 1 table Alphabetically by last name
7 Forward 2 tables Forward 1 table Forward 3 tables Ascending order by height
8 Forward 3 tables Forward 2 tables Forward 1 table Ascending order by foot length
Sum Fun Rounds 1-8
Problem Sheets andAnswer Key
This material was originally used at the Sum Fun Event
in Bartlesville, OK in September 1994.
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What is the value of xy + xyz – z if x = 24, y = 1/4 and z = 2?
2. 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.
3. If a ♫ b = ab, what is the value of (5 ♫ 3) ♫ 2?
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 45 miles per hour and arrived one minute early. How far, in miles, does Ms. Baylor drive to work?
Sum Fun Round 1
25 2920
18
65
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. How many cubic centimeters (cm3) are equivalent to 40 cubic meters (m3)?
2. The length of a rectangle is increased by 50%. By what percentage would the width have to be decreased to keep the same area? Express your answer as a mixed number.
3. How long, in centimeters, is the slanted line in the figure shown? Express your answer as a decimal to the nearest tenth.
4. The width of a particular rectangle is 4/5 of its length. The perimeter is 216 cm. What is the area of the rectangle, in cm2?
Sum Fun Round 2
4 cm
16 cm
8 cm
1. An airplane has a wingspan of 47 feet. Suppose you decide to make a model of this airplane that is 1/30 the real size. What should the wingspan of the model be, in feet? Express your answer as a mixed number.
2. What is the area of the shaded region, in units2? Use � = 3.14. Express your answer as a decimal to the nearest hundredth.
3. What is 90% of 10% of 500?
4. A formula for the circumference of a circle is C = 2�r, and the formula for the area of a circle is A = �r 2, where r is the radius in each equation. If the area of circle P is 36� square inches, what is the circumference of circle P, in inches? Express your answer in terms of �.
Sum Fun Round 3
6
12
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What is the value of (–1)3 + (3)–1? Express your answer as a common fraction.
2. Joe tossed 4 splugs into an empty pot. Their average weight was 6 pounds each. Then he tossed in 5 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?
3. The first five rows of Pascal’s Triangle are listed here. What are the numbers in the seventh row?
4. What is the value of 67
431
++
when expressed as a mixed number?
Sum Fun Round 4
1 1 1 1 2 1 1 3 3 11 4 6 4 1
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. What percent of 32 is 160?
2. What is the total area, in square units, of the shaded regions in this 1-by-1 unit square? All angles that appear to be right angles are right angles. Express your answer as a common fraction.
3. N is the number of buttons in a sewing box. N is more than 40 and less than 80. When N is divided by 5, the remainder is 2. When N is divided by 7, the remainder is 4. What is the value of N ?
4. What is the ones digit when 71863 + 52106 is simplified?
Sum Fun Round 5
1
1
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. There are three parks (A, B and C) in which boys and girls are playing. The areas of parks A, B and C are 500 m2, 500 m2 and 300 m2, respectively. The numbers of children playing in these parks are 60, 30 and 40, respectively. Which park is the most crowded with respect to children per m2?
2. What is the simplified value of [4 • 2–3 + (7 – 4)2 • (18)–1]10?
3. A one-foot-square tile costs $0.87. How much will it cost to cover a family room floor that measures 18 feet by 12 feet with this type of tile?
4. How many triangles are created by the segments in this figure?
Sum Fun Round 6
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. Jim scored 11 fewer points than Danny scored. Together they scored 37 points. How many points did Danny score?
2. The product of two positive numbers is 128 and one of their quotients is 8. What is the sum of the numbers?
3. A dealer has 30 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 5600 cm2, what is the total length of the table top, in cm? Use � = 22/7.
Sum Fun Round 7
Length
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
1. 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.
2. What is the greatest common factor (GCF) of 420 and 546?
3. Marshmallows cost $0.06 each. A marshmallow weighs 5 grams. What would be the price of a 0.45-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?
Sum Fun Round 8
5 13
9 7
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
These problems were originally used at the September 1994 Sum Fun Event in Bartlesville, OK. We thank them for sharing these problems/answers with the rest of the MATHCOUNTS community!
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
