S
Fun
um
Sum Fun Tournament Meeting
(Multiple Topics)
Sum Fu
n
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
Round 1
team then works together to solve the problems
1. Simplify (–1)3 + 3 –1. Express your answer
and to agree on a single answer for each problem.
as a common fraction.
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
2. Joe tossed 4 splugs into an empty pot.
Their average weight was 6 pounds. Then
will be accepted. When time is up, the teacher
he tossed in 5 more splugs whose average
will credit each student at a table with the number
weight was 7 pounds each. Then he threw
of questions their team collectively answered
in a big splug. The overall average weight
correctly. These points are recorded on each
of the splugs in the pot was 7 pounds. What
was the weight, in pounds, of the big splug?
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
2009–2010 MATHCOUNTS Club Resource Guide
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 3 +
1
1
1
1 2 1
1 3 3 1
4
as a mixed number.
1 + 1
41
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.
Scorecard
NAME:
Pythagoras Smith
Question
Round
Number
Table
Number
1
2
3
2
4
4
3
1
2
4
2
1
1
2
3
4
Round
Total
A total of 4 rounds are conducted
1
3
5
with rotations and shuffles between
3
3
6
each round. After the last round,
7
the scorecards are collected and
8
students are ranked by point total.
Total All Rounds
16
(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.
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 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.
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.
42 2009–2010 MATHCOUNTS Club Resource Guide
Sum Fun Rounds 1-8
Problem Sheets and
Answer 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
Sum Fun Round 1
1. What is the value of 2x2 – 3x + 1 when x = 2?
2. What number can be subtracted from both the numerator and
3
denominator of 1 9 so that the resulting fraction will be equivalent to ?
24
4
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 .0 38 6 to the nearest millionth?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 2
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.
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 3
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
3
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?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 4
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?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 5
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.
14
B
A
C
H
7
11
G
20
7
F
5
E 3 D
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.
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 6
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
29 + 29 + 29 + 29
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
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 7
1. What is the value of q for the equation 3 −
2
q
=5 ?
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 < 3 0 0 < b, what is the product ab?
5
4. What is the value of the expression 5 +
when written as a mixed
5
5
+
5 +5
number?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 8
5
1. What is the value of the sum 0 .2 + ? Express your answer as a
9
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?
50
55
60
?
B
A
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
63
C
Answers to Sum Fun Rounds 1-8
Round 1 Round 2 Round 3
Round 4
Round 5
Round 6
Round 7
Round 8
Question
#1
3
9
40
81
10,000%
19
144
–1
7
9
Question
#2
4
$2.25
28
$40
115
45 2
4
1584
Question
#3
page
44
76%
1
2
0.64
12
–2
228
120
Question
#4
5.038687
125
2
119
8
99.28
15
5 1101
48°
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
Scorecard
Scorecard
NAME:
Round
Number
NAME:
Table
Number
Question
1
2
3
4
Round
Total
Round
Number
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
Total All Rounds
Table
Number
Question
1
3
4
Round
Total
4
Round
Total
Total All Rounds
Scorecard
Scorecard
NAME:
Round
Number
2
NAME:
Table
Number
Question
1
2
3
4
Round
Total
Round
Number
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
Total All Rounds
Table
Number
Question
1
Total All Rounds
2
3
Sum Fun Sample Rotate & Shuffle Rules
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
3
Forward 3 tables
Forward 1 table
Forward 2 tables
Numerically by
birth month
Forward 5 tables
Numerically by
day of the month
of birthday
Forward 3 tables
Ascending order
according to the
last letter of last
name
4
5
Forward 1 table
Forward 5 tables
Forward 3 tables
Forward 1 table
6
Forward 1 table
Forward 3 tables
Forward 2 tables
Descending
order according
to first 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
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Rounds 1-8
Problem Sheets and
Answer 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
Sum Fun Round 1
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 25
the figure, in square feet? Express your
answer as a decimal to the nearest tenth.
20
29
18
65
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?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 2
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 cm
8 cm
16 cm
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?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 3
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.
12
6
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 �.
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 4
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?
1
1
1
1
2 1
1 3 3 1
1 4 6 4 1
4. What is the value of 3 +
4
1+
6
7
when expressed as a mixed number?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 5
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
1
as a common fraction.
1
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?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 6
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?
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 7
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.
Length
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Sum Fun Round 8
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?
5
9
13
7
Copyright MATHCOUNTS, Inc. 2009. MATHCOUNTS Club Resource Guide Problem Set
Answers to Sum Fun Rounds 1-8
Round 1
Round 2
Round 3
Round 4
Round 5
Round 6
Round 7
Round 8
Question
#1
16
40,000,000
1 13 70
− 32
500
C
24
1 0 0 DX
Y
Question
#2
1127.5
3 3 31
84.78
11
7
32
1
36
42
67
$187.92
8
$5.40
8
35
112
11
Question
#3
15,625
14.4
45
1, 6, 15,
20, 15,
6, 1
Question
#4
12
2880
12�
5 123
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