Download Math Games and Puzzles

Math Games and Puzzles
(Level III Math Teacher Resource)
Draft
(NSSAL)
C. David Pilmer
©2011
(Last Updated: December 2013)
This resource is the intellectual property of the Adult Education Division of the Nova Scotia
Department of Labour and Advanced Education.
The following are permitted to use and reproduce this resource for classroom purposes.
 Nova Scotia instructors delivering the Nova Scotia Adult Learning Program
 Canadian public school teachers delivering public school curriculum
 Canadian nonprofit tuition-free adult basic education programs
The following are not permitted to use or reproduce this resource without the written
authorization of the Adult Education Division of the Nova Scotia Department of Labour and
Advanced Education.
 Upgrading programs at post-secondary institutions (exception: NSCC)
 Core programs at post-secondary institutions (exception: NSCC)
 Public or private schools outside of Canada
 Basic adult education programs outside of Canada
Individuals, not including teachers or instructors, are permitted to use this resource for their own
learning. They are not permitted to make multiple copies of the resource for distribution. Nor
are they permitted to use this resource under the direction of a teacher or instructor at a learning
institution.
Table of Contents
Introduction (for Instructors) ……………………………………………………………… ii
3 by 3 KenKen Puzzles (A to D) …………………………………………………………. 1
4 by 4 KenKen Puzzles (A and B)………………………………………………………… 5
5 by 5 KenKen Puzzles ……………………………………………………………………. 8
KenKen Puzzles: Signed Numbers ……………………………………………………… 9
Magic Squares ……………………………………………………………………………. 12
Addition Pyramids: Whole Numbers …………………………………………………….. 13
Addition Pyramids: Decimal Numbers …………………………………………………… 15
Addition Pyramids: Signed Numbers …………………………………………………….. 16
Row Factors and Column Factors ………………………………………………………… 17
Whole Number Cross Word Puzzles (A to D) …………………………………………… 18
Signed Numbers Cross Word Puzzles (A and B) ………………………………………… 22
RAD Puzzles: Whole Numbers …………………………………………………………... 24
RAD Puzzles: Signed Numbers ………………………………………………………….. 27
Connect Four Whole Number Addition Game (A and B) ……………………………….. 30
Connect Four Whole Number Subtraction Game (A and B) …………………………….. 32
Connect Four Whole Number Multiplication Game (A to D) …………………………… 34
Connect Four Whole Number Division Game …………………………………………… 38
Divisibility or Prime Connect Four Game ……………………………………………….. 39
Connect Four Fraction Decimal Equivalency Game …………………………………….. 40
Connect Four Adding Decimal Numbers Game (A and B) ……………………………… 41
Connect Four Subtracting Decimal Numbers Game (A and B) …………………………. 43
Connect Four Fraction Percent Equivalency Game ……………………………………… 45
Connect Four Percentage Game …………………………………………………………. 46
Connect Four Adding Signed Numbers Game …………………………………………… 47
Connect Four Subtracting Signed Numbers Game ………………………………………. 48
Connect Four Multiplying Signed Numbers Game ……………………………………… 49
Connect Four Dividing Signed Numbers Game …………………………………………. 50
Connect Four Squaring and Cubing of Signed Numbers Game …………………………. 51
Connect Four Time Ahead Game (A and B) …………………………………………….. 52
Connector ………………………………………………………………………………… 54
Fraction Fury Puzzles (A and B) …………………………………………………………. 55
Math Logic Puzzles ………………………………………………………………………. 59
Answers ………………………………………………………………………………….. 60
NSSAL
©2011
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C. D. Pilmer
Introduction (for Instructors)
One of the ongoing concerns for teachers, instructors, and professors, who teach secondary and
post-secondary mathematics courses, is poor arithmetic skills (and related estimation skills)
displayed by some learners. These educators are attempting to teach higher level mathematical
concepts to their learners but, in some cases, these efforts are impeded when learners have poor
arithmetic and estimation skills. These learners waste valuable time and effort and/or fail to
understand underlying concepts because of deficiencies in this area. For example, how can a
learner factor a trinomial by inspection, if one does not know their whole number math facts?
Similarly, how can a learner simplify a rational expression, if they have difficulty working with
fractions?
In the past, the approach to fostering strong arithmetic skills was to have learners complete a
variety of "drill-and-kill" questions, usually in a timed situation. Examples of such questions are
shown below.
Complete the following questions within the next ten minutes.
3 2
7
(a) 39  85
(b) 6  1
(c) Convert 2
to a decimal.
8 3
16
(d) 2945  8
(e) 45.8 + 682.3
4 1
(f) 2  1
5 6
(g) 563  28  6137
6  15  12 
(h)
31  4  7
(i) 6   5  7    8   1
2
3
2
Learners who were unable to correctly answer 80% of the questions during the allotted time
would often be expected to return at lunch time or after school to make the necessary corrections.
For those adults schooled during the 1960s and 1970s, this was a common practice.
Although this practice did result in stronger arithmetic skills and in some cases stronger
estimation skills, they were two shortcomings associated with it.
1. The focus was primarily on the mastery of specific algorithms. Instead of thinking flexibly
about mathematics, learners were largely expected to follow the same rules to answer
questions. Therefore this feeds the misconception that mathematics is a rule-driven noncreative discipline.
2. A timed test, with lunch hour or afterschool corrections, was not fun anyone. Who enjoys
math when the only reward is avoiding a correction session (i.e. detention). Also, learner
perception was that the only thing valued by the math teacher was the right answer; all the
work that preceded it was moot if the learner made a careless mistake in their last step. The
"all-that-counts-is-the-final-answer" misconception is fostered by this practice.
Does that mean that we never expose our learners to these types of "drill and kill" questions?
No, but we must recognize that these questions are only one tool for improving arithmetic skill
and that they must be used judiciously.
NSSAL
©2011
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C. D. Pilmer
Are there non-threatening and engaging means of improving arithmetic skills that also foster
more flexible thinking? Yes, and this can be accomplished using mathematical games and
puzzles. Hence we have created the following outcome for our Level III Math course.
Learners will be expected to develop efficient strategies, high levels of automaticity, and
flexible thinking skills as they pertain to arithmetic skills in the context of whole numbers,
decimal numbers, fractions, and signed numbers through the ongoing use of games and
puzzles.
In this accompanying Level III Math resource, instructors can find a variety of games and
puzzles that range from Level I to Level III. This being said, not all puzzles and games are
appropriate for all learners. Therefore the material in this resource should not be viewed as a
unit that a learner completes from "stem-to-stern" within an allotted time; rather, this is an
instructor resource where activities are gradually, yet regularly, distributed based on the
instructor's professional judgment.
NSSAL
©2011
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C. D. Pilmer
3 by 3 KenKen Puzzles (A)
Insert the numbers 1, 2, and 3 into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
2  : find two numbers when multiplied give you 2).
(a)
2
4+
5+
(b) 9 
6
3+
3+
6
(c)
6
4+
(d) 12 
5+
4+
3
(e)
3+
6
4+
(f) 6 
3+
2
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©2011
3
3+
5+
3
3
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3 by 3 KenKen Puzzles (B)
Instructions: Insert the numbers 3, 4, and 5 into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
12  : find two numbers when multiplied give you 12).
(a)
12 
(b) 15 
8+
4
12 
9+
15 
(c)
5
15 
7+
4
(d) 8+
12+
7+
12+
12 
8+
20 
(e)
20 
9+
(f) 12 
11+
15 
8+
14+
12 
5
NSSAL
©2011
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3 by 3 KenKen Puzzles (C)
Instructions: Insert the numbers 5, 6, and 7 into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
35  : find two numbers when multiplied give you 35).
(a)
35 
(b) 42 
13+
5
11+
12+
42 
(c)
30 
11+
30 
19+
(d) 17+
7
35 
11+
18+
13+
(e)
7
42 
11+
5
13+
13+
35 
NSSAL
©2011
42 
(f) 17+
30 
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3 by 3 KenKen Puzzles (D)
Instructions: Insert the numbers 7, 8, and 9 into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
72  : find two numbers when multiplied give you 72).
(a)
72 
16+
8
(b) 9
15+
63 
15+
63 
(c)
56 
17+
56 
24+
(d) 17+
72 
56 
23+
72 
16+
(e)
72 
15+
(f) 63 
25+
17+
72 
22+
56 
NSSAL
©2011
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C. D. Pilmer
4 by 4 KenKen Puzzles (A)
Insert the numbers 1, 2, 3, and 4 into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
8  : find two numbers when multiplied give you 8).
(a)
8
12 
4+
1
(b) 3 
6+
6+
4
6
6
12 
(d) 6+
1
2
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©2011
3
7+
3
9+
8+
4+
8
1
12 
4
7+
6
6+
(c)
2
4
3+
24 
1
2
5
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4 by 4 KenKen Puzzles (B)
Insert the indicated numbers into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
8  : find two numbers when multiplied give you 8).
(a) 1, 2, 3, 4 Puzzle
3
(b) 1, 2, 3, 4 Puzzle
8
6
6
12 
5+
5+
12 
4
3+
8+
12 
15 
5+
9+
2
12+
6+
6+
10 
8
6+
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©2011
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(d) 2, 3, 4, 5 Puzzle
20 
15 
3+
5+
(c) 2, 3, 4, 5 Puzzle
8
5+
6
8+
5
6
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C. D. Pilmer
(e) 3, 4, 5, 6 Puzzle
24 
(f) 3, 4, 5, 6 Puzzle
7+
8+
11+
30 
18 
10+
15 
15 
(g) 4, 5, 6, 7 Puzzle
11+
30 
42 
4
28 
20 
4
17+
20 
15+
13+
35 
11+
(i) 5, 6, 7, 8 Puzzle
48 
NSSAL
©2011
42 
4
(j) 6, 7, 8, 9 Puzzle
15+
30 
13+
56 
72 
15+
14+
35 
12+
10+
(h) 4, 5, 6, 7 Puzzle
11+
12+
11+
8+
30 
11+
12 
11+
56 
42 
17+
63 
14+
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5 by 5 KenKen Puzzles
Insert the numbers the appropriate numbers into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
8  : find the numbers when multiplied give you 8).
(a) 1, 2, 3, 4, 5 Puzzle
8
20 
4+
(b) 2, 3, 4, 5, 6 Puzzle
6
15 
5
18 
4
4
2
5+
42 
4
35 
6+
9+
11+
5+
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©2011
24 
(d) 5, 6, 7, 8, 9 Puzzle
30 
9
40 
40 
48 
13+
9+
7
30 
3
19+
48 
6+
14+
8+
15+
11+
6
9+
(c) 4, 5, 6, 7, 8 Puzzle
32 
8
3+
5
12+
54 
63 
45 
20+
10+
42 
6
72 
13+
8
Draft
C. D. Pilmer
KenKen Puzzles: Signed Numbers
Insert the numbers the appropriate numbers into the grid such that:
 no number is repeated in the same row or column, and
 the numbers in the cages produce the target number using the indicated operation (e.g.
-8  : find the numbers when multiplied give you -8).
(a) 1, -2, 3 Puzzle
-2 
(b) -1, 2, -3 Puzzle
4+
3
-1+
-1+
-6 
-20 
-4+
-1+
-12 
3
-6 
-3
4
48 
-20 
14+
-1+
-1+
-30 
-5+
-12 
8+
24 
1+
(h) 7, -8, 9 Puzzle
-7
1+
(f) -4, 5, -6 Puzzle
5
(g) 6, -7, 8 Puzzle
NSSAL
©2011
8
(e) 3, -4, 5 Puzzle
15 
-56 
1+
-2 
(d) -3, 4, -5 Puzzle
(c) 2, -3, 4 Puzzle
(i) -7, 8, -9 Puzzle
63 
-7+
-72 
16+
-56 
-25+
-56 
1+
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(j) 1, -2, 3, -4 Puzzle
-4 
8
4+
-2
(k) 2, -3, 4, -5 Puzzle
-6 
-1+
-5
-20 
-3+
-1+
-18 
(m) 4, -5, 6, -7 Puzzle
-30 
15 
-42 
-5
-12 
48 
7
-1+
-1+
-72 
-1+
35 
-7
-42 
-1+
-1+
5+
-40 
NSSAL
©2011
-20 
(o) 6, -7, 8, -9 Puzzle
6+
-56 
6
24 
(n) 5, -6, 7, -8 Puzzle
-30 
-1+
-28 
-10+
-20 
-1+
-1+
15 
2
(l) 3, -4, 5, -6 Puzzle
-1+
-12 
-1+
1
8
63 
48 
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(p) 1, -2, 3, -4, 5 Puzzle
-6 
-20 
15 
(q) 2, -3, 4, -5, 6 Puzzle
-18 
-5+
-12 
-1+
-3+
-1+
-10 
-8
-14+
-8+
3
-10 
-12 
NSSAL
©2011
-42 
8
-30 
-30 
45 
-1+
-54 
-42 
-4
8+
(s) -5, 6, -7, 8, -9 Puzzle
-7+
3+
5+
4
-28 
12+
8
3+
3+
(r) -4, 5, -6, 7, -8 Puzzle
48 
6+
12 
5
1
1+
15 
-5
63 
-72 
-42 
9+
-40 
-40 
8
-16+
-12+
11
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C. D. Pilmer
Magic Squares
In a magic square, the numbers in each column, row, and diagonal all
add up to the same number. For example, with the magic square on the
right, the numbers in each column, row, and diagonal all add up to 30.
7
14
9
12
10
8
11
6
13
Complete each of the magic squares below.
(a)
(b)
3
5
(c)
6
3
7
2
7
6
7
(d)
5
(e)
5
(f)
4
4
10
8
6
1
8
(g)
5
(i)
4
12
7
NSSAL
©2011
7
8
7
(h)
2
3
12
5
9
4
10
3
12
9
8
6
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C. D. Pilmer
Addition Pyramids: Whole Numbers
With addition pyramids, the two numbers in adjoining boxes add to give the number in the box
immediately above.
8
18
3
5
7
34
11
5
2
14
9
5
4
20
9
11
1
8
3
Insert the missing numbers in each of the following addition pyramids.
1.
2.
4
6
13
5
3.
10
4.
8
3.
9
6.
14
2
9
9
7.
8
8.
9.
9
7
2
10.
9
10
3
6
11.
18
2
12.
4
19
11
3
8
13.
14.
7
21
12
3
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©2011
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1
7
15.
9
2
14
4
13
6
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C. D. Pilmer
16.
17.
18.
30
16
10
7
6
0
5
8
19.
2
7
1
5
20.
13
21.
12
7
12
3
8
9
22.
2
23.
9
11
14
6
22
12
6
2
40
20
10
NSSAL
©2011
3
24.
17
3
7
10
5
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C. D. Pilmer
Addition Pyramids: Decimal Numbers
Complete the following addition pyramids. With addition pyramids, the two numbers in
adjoining boxes add to give the number in the box immediately above.
1.
2.
3.
3.8
1.2
0.4
2.1
1.7
2
0.8
4.
5.
1.4
6.
3.4
1.4
1.1
0.9
7.
0.2
0.3
0.9
0.7
8.
3.1
0.6
9.
4.3
2.3
1.3
0.4
1.4
10.
1.4
1.8
0.8
1.1
11.
12.
2.7
1.2
0.3
1.4
0.9
13.
0.9
2.1
0.3
14.
3.4
2.6
3.2
0.2
2.7
1.7
1.8
0.4
0.3
17.
9.7
0.1
15.
1.8
16.
0.8
0.6
5.7
1.6
18.
4.3
5.3
4.6
2.4
2.5
0.9
NSSAL
©2011
1.3
0.7
1.1
15
1.6
0.9
0.4
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C. D. Pilmer
Addition Pyramids: Signed Numbers
Complete the following addition pyramids. With addition pyramids, the two numbers in
adjoining boxes add to give the number in the box immediately above.
1.
2.
3.
2
-6
-5
4.
2
-6
-4
5.
4
-2
-4
6.
-2
-3
-6
-1
7.
-4
-5
9.
-2
-6
-6
6
3
-3
10.
-1
11.
-2
12.
-2
-5
-1
3
-3
7
-2
4
-4
13.
-8
-2
14.
15.
-8
1
-4
-5
16.
6
3
-4
18.
-3
-1
2
2
-6
-1
-5
NSSAL
©2011
-5
-3
17.
-4
-3
3
-6
-2
5
4
8.
3
-3
-6
16
-1
2
4
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C. D. Pilmer
Row Factors and Column Factors
In each question you have been provided with a chart that is missing four numbers. These
numbers are the factors of the numbers found to the right of each row, and factors of the numbers
found at the bottom of each column. Find the missing numbers.
Example:
35
Answer:
15
5
3
15
28
7
4
28
35
12
12
Questions:
(a)
10
(b)
18
12
8
6
27
(e)
60
24
18
(h)
(k)
NSSAL
©2011
30
35
(l)
14
32
28
(n)
28
56
40
72
7
8
20
30
54
40
42
16
(m)
21
(i)
54
18
27
3
4
18
15
24
28
45
10
(j)
30
(f)
20
20
36
8
8
9
(g)
12
6
7
21
20
2
15
(d)
(c)
16
(o)
35
6
21
16
17
27
15
63
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Whole Number Crossword Puzzle (A)
A
B
C
F
H
D
E
G
I
J
K
L
M
O
R
N
P
S
Q
T
V
U
W
Across:
Down:
A. Next even number after 384
B. 8  10
C. 22 + 10 + 10
D. 2000 + 100 + 30 + 9
G. one thousand, four hundred twenty
E.
337 - 10
I. 5 more than 228
F.
8  90
J. Double 25
H. 7 less than 470
L. The product of 4 and 8
K. Next number in the following sequence.
70, 74, 78, 82, ____
O. 196 + 231
Q. 143 - 87
R. 5 times 7
T. The number of minutes in 1 hour and 34
minutes
M. 3 sets of 9
N. increase 734 by 20
P.
11 + 5 + 3 + 9
S.
Next number in the following sequence.
63, 60, 57, 54, ____
V. 42
W. A number between 10 and 20 that is
divisible by both 5 and 3
NSSAL
©2011
U. The number of cents in 2 quarters, 1 dime,
and 1 nickel
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Whole Number Crossword Puzzle (B)
A
B
C
F
H
D
E
G
I
J
K
L
M
O
R
N
P
S
Q
T
V
U
W
Across:
Down:
A. 50  9
B. The next odd number after 51
C. 5 more than 81
D. six thousand, four hundred thirty-nine
G. 4000 + 800 + 10 + 5
E.
213 rounded to the nearest tens
I. increase 153 by 30
F.
Next number in the following sequence
394, 399, 404, 409, ____
J. 63 - 29
L. ____  7 = 4
O. The number of minutes in 6 hours and 4
minutes
Q. A number between 10 and 20 that is
divisible by 2, 3, 6, and 9
R. decrease 70 by 7
T. The product of 2 and 7
V. 5 + 10 + 2 + 30
H. 156 + 316
K. 72
M. Double 12
N. 1542  3
P.
6 sets of 11
S.
6 less than double 20
U. Next number in the following sequence
60, 54, 48, 42, ____
W. The even number before 88
NSSAL
©2011
19
Draft
C. D. Pilmer
Whole Number Crossword Puzzle (C)
A
B
C
F
H
D
E
G
I
J
K
L
M
O
R
N
P
S
Q
T
V
U
W
Across:
Down:
A. 70  8
B. 6 + 20 + 2 + 40
C. Triple 6 plus 1
D. nine thousand, seven hundred twelve
G. 7558 rounded to the nearest hundreds
E.
Next number in the following sequence
886, 890, 894, 898, 902, ____
F.
15  23
I. increase 361 by 40
J. Number of cents in 3 quarters and 2 dimes
L. 9 times 6
O. 800 + 70 + 4
Q. 37 + 56
R. 581  7
T. Double 13
H. The next multiple of 5 that follows 130
K. 8 sets of 4
M. 82
N. Number of minutes in 3 hours and 16
minutes
P.
161 - 87
V. Next number in the following sequence
50, 47, 44, 41, ____
S.
39 decreased by 6
W. ____  6 = 8
U. A number between 20 and 30 that is
divisible by 2, 4, 7, and 14
NSSAL
©2011
20
Draft
C. D. Pilmer
Whole Number Crossword Puzzle (D)
A
B
C
F
H
D
E
G
I
J
K
L
M
O
R
N
P
S
Q
T
V
U
W
Across:
Down:
A. The next odd number after 769
B. 87 decreased by 9
C. 6 sets of 3
D. 8000 + 600 + 20 + 9
G. six thousand, three hundred seven
E.
746 increased by 60
I. Next number in the following sequence
338, 344, 350, 356, ____
F.
50 less than 784
J. 444  6
H. Number of minutes in 2 hours and 37
minutes
L. 25+47
K. triple 8 plus 4
O. 1 + 30 + 4 + 100 + 50
M. Next number in the following sequence
107, 104, 101, 98, ____
Q. 6 times 7
R. ____  9 = 4
T. Number of cents in 2 quarters and 3 dimes
V. A number between 40 and 50 that is a
multiple of 3, 5, 9, and 15
N. 24  35
P.
92
S.
Double 32
U. 119 - 37
W. The product of 8 and 9
NSSAL
©2011
21
Draft
C. D. Pilmer
Signed Number Crossword Puzzle (A)
A
B
C
F
H
D
E
G
I
J
K
L
M
O
R
S
V
N
P
Q
T
U
W
Across:
Down:
A. -6  7
B. -5  (-8)
C. 24 + (-3)
D. -90  (-20)
G.
 90 
2
I. -20 + 650
E.
300 - (-100)
F.
Next number in the following sequence
-44, -49, -54, -59, ____
J. (-3) + 3  9
H. Decrease -46 by 2.
L. 78 - 2  (-1)
K. 12 less than double 5
O. 8 sets of -2
M. 6 + (-5)  (-4)
Q. -10 + 40 + (-20)
N. -22 + 3
R. 8 - 15
P.
 2 
S.
40  2 + (-8)
T. 10 less than -1
V. 30 more than -10.
W. 3 + 5  (-2)
NSSAL
©2011
2
 10
U. -5  (-3) - 4  (-3)
22
Draft
C. D. Pilmer
Signed Number Crossword Puzzle (B)
A
B
C
F
H
D
E
G
I
J
K
L
M
O
R
N
P
S
Q
T
V
U
W
Across:
Down:
A. -3  8
B. -40  (-7)
C. 15 - 18
D. 3400 + (-200)
G. Double 120 plus -5
E.
8 sets of -7
H. 40 more than -10
F.
5 + (-50)
I. -70  (-6)
K. The number between 0 and 20 that is
divisible by both -6 and -9.
J. 2 decreased by 7
L. Find the next number in the sequence.
16, 10, 4, -2, ____, …
M.
 4   5  9
N.
56   7    1
P.
-5 times -5
S.
4   9    1  2
T.
How many times does -4 go into -120?
O. -24 - (-3)
Q.
 10 
2
 10
R. -18 - (-5)  3
V.
 3  4 
2
W. 2   4 
NSSAL
©2011
U. (-3)  4 + 8
2
23
Draft
C. D. Pilmer
RAD Puzzles: Whole Numbers
Using the numbers in the table below, correctly complete each puzzle.
(a)
11
(b)
-
+
=
=

-

+

+
-
=
+
10

=
-
+
-
12
=
=

=
=
=
=
16
=
=
=
+
0
=
=

6
=
=
8
=
=
=
+
=
=
=
=
=
=
=
=


-


+
-
-
0

+

1 2
4 4
30 32
=
2
4
2
6
=
2
7
3
8
+
3
8
1
+
3
=
3 4
10 21
0 1
4 4
48 60
1
5
2
5
(c)
=
2
5
2
6
+
2
6
3
9
3
24
(d)


=
=

+
+

28
+


=

=

-
+
-
=
=
=
=
7
=
40
=
-
=
=
=
=
6
=
=

=
=
=
=

=
=
=
=
36

=
=
=
4
=
9

2

=
+
=
1

+
+
-
2 2 3 3 4 4 4 4 5
7 10 10 21 30 31 34 36 41
42 80
NSSAL
©2011
-
0 1
6 6
45 54
24

-
5
=
1
9
1
9
2
9
+
=
+
3
9
3 4 5
11 40 42
Draft
C. D. Pilmer
(e)
(f)


=
-
=
72
-

-
+

+
=

-
-
6
=
=
+
=
=
=
40
2
+
+
+
1 2
7 7
60 70
=
63
3
7
=
9
=
=

=
=
24
=
=

=
=
=
=
=
=
=
=

+


-
+

+

=
3
8
+
4 5 6 6
10 20 21 49
0 1
6 6
36 48
(g)
32
+
3
=

8
=
=
3
7
=

=
2
8

=
20
=
2
8
3 4 4 6 6
10 12 19 23 30
(h)
+

=

-
=
=

=
=
1
21
+


1 2
7 7
24 56
NSSAL
©2011
28
=

=


=
=
=
=
+
+
4
2
=
=
2
-
=
=
=
=
=
-



=
=
=
18

=
=
=
=
-

36
+
=
2
8

=
=

=
3
8
3
8
+

-
=
+
3
9
4 4 6
14 17 19

-

=
=
-
9
2 2 3 3 4 5 6 7 8
9 10 11 13 15 24 27 28 30
50 81
25
Draft
C. D. Pilmer
(i)
(j)
-

+
=
6
=
+
=

=
=
=
=

=
30
+

53
1
=
=

=
=
+
=
+


+
=
=
=
2
=

=
=
+
=

=
=
=
48
=
-
1
=
=
=
=
-
+
-

36

7

+
1 2
5 7
42 60
=
2
7
2
8


-

=

3 3 3 4 5
10 14 16 18 30
0 1
6 7
49 85
(k)
=
2
7
2
8

=
2
2 3 4 6 6
10 12 18 30 36
(l)
-

=

+

=

5
3
+
+

=


=

-
+
7
=
10
=
-
=
=
=
=
64
=
=
=
4
=
=

=
=

=
=
=
=
=
32
=
=

=
=
=
=
48

+

7
+
=

=


1 1 2 6 8 8 8 8 8
9 10 11 12 16 22 40 42 72
84 88
NSSAL
©2011

-
1 2
6 6
64 72
26

=
2
8
8

=
+

2 3 3 4 4 6
12 13 16 24 36 61
Draft
C. D. Pilmer
RAD Puzzles: Signed Numbers
Using the numbers in the table below, correctly complete each puzzle.
(a)
(b)
+

=
=

-
-

8

+
=

-
-
13
=
=

=
=
=
=
20
-1
-
+
+
=
-9 -7 -6
-2 -2 -1
19 24
-6
2
-8
=
=
=
+
=
+
25
=

1

=
=
=
-6
=
=
=
+
-2
=
=
=
=
=
=
=
=
+

+

+
-

+
=
-5
6
-4
8

+
-4
9
-4 -3
10 11
-8 -8
-2 -1
42 48
(c)
=
-7
1
-6
2

=
-4
2
-4
3
-3
4
-1
-2 -2
14 21
(d)
+

=


=



+

=

=

+
22
=
=
-
52
=

+
=
=
=
-4
=
=
=
-6
3
=
=
=
=
=
=
=

-

-
-
+


=
=
=

=
=
-9
=
=

=
28

2

+
+
=
-9 -9 -8
2 3 4
36 44
-7
8
NSSAL
©2011
=
-6
9
-
+
-6 -2 -1 1
11 15 24 30
=
16
=

-4
-8 -5 -4 -3 -3 -1 -1 2 3
5 7 15 16 19 20 25 33 45
72 76
27
Draft
C. D. Pilmer
(e)
(f)
+

=


=



+

=

-

=

-
-1
=
-3
=
-
=
=
=
=
25
=

=
=
=
=
=
3
28
=
=
=

=
=
=
-7
=
-8

+
=
=
=
-6 -5 -5
1 2 5
60 75
-4
6
-3
9
=
21

=

=
15

=

+
+
14
-3 -3 -1 -1
10 15 24 50
+

-9 -7
3 3
21 63
(g)
=
-5
4

+
-5
4
=
-4
7
-2
7
+
+
-1
9
2 3
13 14
(h)


=
-

=
+
-
10
-4
+

+
=

-

=

+
9
=
-6
=

=
=
=
=
48
=
=
=
+

=
-8 -8 -7
4 4 5
40 50
-6
8
=
=
=
=
0

NSSAL
©2011
=

=
64
+
=

=
=
=
12
=
=
=
-
-1
=
=
=

+
-
8
+
+

+

-5 -3 -2 -1 2
10 12 22 25 33
-9 -6
0 1
30 36
28
=
-5
2
-4
2

=
-3
2
-3
3
-3
6
-2 -2
11 14
Draft
C. D. Pilmer
(i)
(j)
+

=
=

-
+


1

+
=
-
=

-
-9
=
=

-2
=
=
18
16

-5
=
=
=

=
-
40
=

=
=
8
=
=

=
=
=
=
=
=
=
=
=
=
=
+

+

+
+
-
+
-


=
-9 -6 -6
-2 -1 0
16 36
-6
1
=
-5
1
-4
2
-4
2

-3

-5
=
-3
5
-2
9
-8 -8
0 2
20 35
-7
3
-7
4
(k)

=
-5
5
-4
5
-2
7
-2 -1
12 15
(l)

=

=

3
=
=
+
+

-

-
+
-

-

=
=
=
=
=
=
=
=
=
=
-7
45
=
=
+
=
=
=
14

=
=
=
-5

=
=

+

-1
=
-9 -8 -8
-2 2 4
18 28
-4
5
NSSAL
©2011

=
-3
6

+
+
-3 -2 -2 -2
10 10 13 16
-9 -6
6 6
30 43
29
=
=


7

+

=
=
3

-5
=
-6
9
=

2
-4 -3 -2 -1 2 5
10 12 14 15 19 20
Draft
C. D. Pilmer
Connect Four Whole Number Addition Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Addend Strip whose sum is that desired square.
Once they have chosen the two numbers, they can capture one square with that appropriate
sum. They either mark the square with an X or place a colored counter on the square. There
may be other squares with that same sum but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Addend Strip. They then mark the square with that sum using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the addend strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
10
12
7
13
8
11
9
11
10
12
6
13
6
14
9
11
10
9
8
11
12
7
14
11
13
10
8
6
9
10
9
7
14
10
12
8
6
7
Addend Strip:
3
NSSAL
©2011
4
5
30
Draft
C. D. Pilmer
Connect Four Whole Number Addition Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Addend Strip whose sum is that desired square.
Once they have chosen the two numbers, they can capture one square with that appropriate
sum. They either mark the square with an X or place a colored counter on the square. There
may be other squares with that same sum but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Addend Strip. They then mark the square with that sum using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the addend strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
12
11
18
14
16
14
15
14
13
16
12
13
16
12
15
10
14
17
15
17
14
18
15
13
13
10
13
16
11
18
15
12
11
17
14
10
Addend Strip:
5
NSSAL
©2011
6
7
8
9
31
Draft
C. D. Pilmer
Connect Four Whole Number Subtraction Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate difference
(i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same difference but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that difference using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
3
2
5
4
6
4
7
4
6
2
3
5
6
0
1
0
5
6
3
5
3
7
2
4
4
3
2
4
1
0
1
7
0
5
3
6
Value 1:
13
NSSAL
©2011
Value 2:
12
11
10
9
6
32
7
8
9
Draft
C. D. Pilmer
Connect Four Whole Number Subtraction Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate difference
(i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same difference but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that difference using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
3
5
4
5
6
5
6
8
7
9
10
7
9
7
6
3
5
9
7
10
5
7
8
4
8
6
9
4
9
3
4
7
8
10
5
6
Value 1:
15
NSSAL
©2011
Value 2:
14
13
12
5
33
6
7
8
9
Draft
C. D. Pilmer
Connect Four Whole Number Multiplication Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Factor Strip whose product is that desired
square. Once they have chosen the two numbers, they can capture one square with that
appropriate product. They either mark the square with an X or place a colored counter on the
square. There may be other squares with that same product but only one square can be
captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Factor Strip. They then mark the square with that product using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the fraction strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
6
45
27
5
45
8
10
0
36
18
20
15
36
8
12
4
0
36
2
18
45
27
6
12
20
4
15
0
10
9
27
12
3
6
36
20
Factor Strip:
0
NSSAL
©2011
1
2
3
4
34
5
9
Draft
C. D. Pilmer
Connect Four Whole Number Multiplication Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Factor Strip whose product is that desired
square. Once they have chosen the two numbers, they can capture one square with that
appropriate product. They either mark the square with an X or place a colored counter on the
square. There may be other squares with that same product but only one square can be
captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Factor Strip. They then mark the square with that product using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the fraction strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
18
2
30
8
12
24
9
54
12
18
10
6
24
5
8
6
54
20
10
30
18
5
24
3
24
4
20
12
2
18
12
54
9
30
5
8
Factor Strip:
1
NSSAL
©2011
2
3
4
5
35
6
9
Draft
C. D. Pilmer
Connect Four Whole Number Multiplication Game (C)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Factor Strip whose product is that desired
square. Once they have chosen the two numbers, they can capture one square with that
appropriate product. They either mark the square with an X or place a colored counter on the
square. There may be other squares with that same product but only one square can be
captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Factor Strip. They then mark the square with that product using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the fraction strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
14
63
6
28
15
30
42
12
30
63
14
10
8
21
54
18
54
21
35
15
8
28
42
12
18
54
14
63
6
35
10
28
42
12
21
18
Factor Strip:
2
NSSAL
©2011
3
4
5
6
36
7
9
Draft
C. D. Pilmer
Connect Four Whole Number Multiplication Game (D)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Factor Strip whose product is that desired
square. Once they have chosen the two numbers, they can capture one square with that
appropriate product. They either mark the square with an X or place a colored counter on the
square. There may be other squares with that same product but only one square can be
captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Factor Strip. They then mark the square with that product using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the fraction strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
42
12
16
8
24
48
6
72
45
54
15
18
56
24
21
16
56
20
14
30
10
40
6
27
54
18
36
12
42
21
15
72
27
14
35
10
5
6
Factor Strip:
2
NSSAL
©2011
3
4
37
7
8
9
Draft
C. D. Pilmer
Connect Four Whole Number Division Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate quotient (i.e.
Value 1 divided by Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same quotient but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that quotient using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
6
24
12
15
12
2
8
3
6
30
4
15
18
12
10
9
8
12
6
8
2
24
6
9
30
4
15
12
4
3
6
18
9
2
10
18
Value 1:
30
NSSAL
©2011
Value 2:
24
18
12
6
1
38
2
3
Draft
C. D. Pilmer
Divisibility or Prime Connect Four Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place one paperclip on the Tens strip and one paperclip on the Ones strip. They have now
generated a two digit number. That two digit number is either divisible by a single digit
whole number greater than 1 (i.e. 2, 3, 4, 5, 6, 7, 8, 9), or the number is a prime. The player
captures a single square that describes the number. For example if the two digit number is
14, it is divisible by 2 or 7 (of the choices we are given), then the player can capture either a
square with a 2 on it, or a square with a 7 on it. If the number is prime, then a square marked
P can be captured.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on either the Tens or Ones strip. They then mark the square that describes that
number using an O or a different colored marker. If a player cannot move a single paperclip
to capture a square, a paperclip must still be moved in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
6
4
7
2
6
3
P
9
6
8
P
2
5
3
P
5
4
9
4
8
9
7
3
2
7
2
4
6
8
P
6
P
9
3
2
5
Tens Strip:
1
NSSAL
©2011
Ones Strip
2
3
1
2
39
4
5
6
8
Draft
C. D. Pilmer
Connect Four Fraction Decimal Equivalency Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. The
square with a specified decimal is captured by creating the equivalent fraction using the
numerator and denominator strips at the bottom of the page. One paperclip is placed on each
strip to do so. For example, if one chooses 3 on the numerator strip and 4 on the
3
denominator, then they can capture one square labeled 0.75 ( is equivalent to 0.75). They
4
either mark the square with an X or place a colored counter on the square. Only one square
can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with the equivalent decimal using an O or a different
colored marker. If a player cannot move a single paperclip to capture a square, a paperclip
must still be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
0.4
1
0.2
0.4
1
0.5
0.6
0.2
0.3 0.25 0.3
0.4
0.25 0.1 0.75 0.8
0.3
0.6
0.75 0.2
0.4
0.8
0.2
1
0.2
0.8 0.25 0.1
0.5
0.4
0.1
0.5
0.3 0.75
0.6
1
Numerator (Top) Strip:
1
NSSAL
©2011
2
3
Denominator (Bottom) Strip:
4
4
40
5
10
Draft
C. D. Pilmer
Connect Four Adding Decimal Numbers Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Addend Strip whose sum is that desired square.
Once they have chosen the two numbers, they can capture one square with that appropriate
sum. They either mark the square with an X or place a colored counter on the square. There
may be other squares with that same sum but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Addend Strip. They then mark the square with that sum using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the addend strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
0.8
1.4
1.3
2
0.8
1.1
1.1
0.5
0.9
1.5
1.2
0.9
1.4
1.6
0.8
1.1
0.5
2
1.2
0.7
1.4
1.7
1.6
0.8
0.8
1.3
2
0.5
1.3
1.4
1.4
1.7
1.1
0.9
1.5
0.7
Addend Strip:
0.2
NSSAL
©2011
0.3
0.5
0.6
41
0.9
1.1
Draft
C. D. Pilmer
Connect Four Adding Decimal Numbers Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Addend Strip whose sum is that desired square.
Once they have chosen the two numbers, they can capture one square with that appropriate
sum. They either mark the square with an X or place a colored counter on the square. There
may be other squares with that same sum but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Addend Strip. They then mark the square with that sum using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the addend strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
3.8
3
4.8
2
1.6
3.4
2.2
2
2.6
4.8
0.8
3
2.6
4.2
5.2
3.8
4.4
5.2
0.8
3.4
4.4
3
1.6
4.2
2
2.6
3.8
2.2
3.4
2.6
4.4
1.6
3
5.2
4.8
2.2
2
2.4
Addend Strip:
0.2
NSSAL
©2011
0.6
1.4
42
2.8
Draft
C. D. Pilmer
Connect Four Subtracting Decimal Numbers Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate difference
(i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same difference but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that difference using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
2.5
0.6
1.8
0.1
1.9
0.9
0.1
2
1.2
2.5
0.8
2.7
1.9
2.6
2.8
1.4
2.3
1.7
1.6
0.9
1.7
1.8
2
1.6
2
2.7
1.4
2.6
0.9
2.5
1.7
0.8
2.3
1.2
2.8
0.6
Value 1:
3
NSSAL
©2011
Value 2:
2.8 2.2 1.9 1.1
0.2 0.3 0.5
43
1
Draft
C. D. Pilmer
Connect Four Subtracting Decimal Numbers Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate difference
(i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same difference but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that difference using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
2.4
1
1.4
1.2
3.2
0.8
0.4
2.2
0.8
2.6
1.4
1
2
3.2
1.6
1.8
2
2.4
1.8
0.6
3
2.8
1.2
0.4
0
1.2
1.4
0.8
0.6
2.6
2.8
1.6
2.2
0
3
1.8
Value 1:
3.6
NSSAL
©2011
Value 2:
3
2.4 2.2 1.6
0.4 0.8 1.2 1.6
44
Draft
C. D. Pilmer
Connect Four Fraction Percent Equivalency Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. The
square with a specified percent is captured by creating the equivalent fraction using the
numerator and denominator strips at the bottom of the page. One paper clip is placed on
each strip to do so. For example, if one chooses 3 on the numerator strip and 4 on the
3
denominator, then they can capture one square labeled 75% ( is equivalent to 75%). They
4
either mark the square with an X or place a colored counter on the square. There may be
other squares with that same difference but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with the equivalent decimal using an O or a different
colored marker. If a player cannot move a single paperclip to capture a square, a paperclip
must still be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one player clip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
40%
10%
20% 100% 40%
50%
25% 100% 25%
80%
60%
20%
30%
60%
40%
50%
30%
40%
75%
20%
30%
25%
80% 100%
20%
80%
75%
10%
20%
40%
10%
50% 100% 60%
30%
75%
Numerator (Top) Strip:
1
NSSAL
©2011
2
3
Denominator (Bottom) Strip:
4
4
45
5
10
Draft
C. D. Pilmer
Connect Four Percentage Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two strips below; one on the "Percentage" strip and one on the "Of"
strip. Take the percentage of that number and capture the appropriate square (e.g. 20% of 40
allows one to capture an "8" square). They either mark the square with an X or place a
colored counter on the square. There may be other squares with that same value but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that value using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
10
16
10
12
8
20
30
8
3
24
15
10
2
5
18
4
25
30
25
20
10
6
16
8
6
4
12
2
3
5
18
24
15
20
12
4
Percentage:
Of:
10% 15% 20% 25%
NSSAL
©2011
20
46
40
80 100 120
Draft
C. D. Pilmer
Connect Four Adding Signed Numbers Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Addend Strip whose sum is that desired square.
Once they have chosen the two numbers, they can capture one square with that appropriate
sum. They either mark the square with an X or place a colored counter on the square. There
may be other squares with that same sum but only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Addend Strip. They then mark the square with that sum using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the addend strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
-6
-14
7
-10
-2
-8
0
3
-8
-4
-6
16
-12
16
-2
-14
2
1
2
1
-10
9
-4
0
-4
7
-6
0
-12
-8
1
-14
9
3
-6
-2
1
8
Addend Strip:
-7
NSSAL
©2011
-5
-1
47
Draft
C. D. Pilmer
Connect Four Subtracting Signed Numbers Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate difference
(i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same difference but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that difference using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
-1
1
2
-4
-1
-7
12
-4
7
-10
9
12
-7
2
6
-2
-1
15
-1
4
-10
-7
1
7
15
7
-2
12
-4
6
-4
9
-7
-10
4
-1
Value 1:
10
NSSAL
©2011
Value 2:
2
-3
-6
4
48
1
-2
-5
Draft
C. D. Pilmer
Connect Four Multiplying Signed Numbers Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers on the Factor Strip whose product is that desired
square. Once they have chosen the two numbers, they can capture one square with that
appropriate product. They either mark the square with an X or place a colored counter on the
square. There may be other squares with that same product but only one square can be
captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips on the Factor Strip. They then mark the square with that product using an O or a
different colored marker. If a player cannot move a single paperclip to capture a square, a
paperclip must still be moved on the factor strip in order to ensure that the game can
continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
18
-30
-54
36
25
-12
9
10
4
-15
18
-54
4
-6
81
9
-12
-54
45
-15
25
-30
-27
25
-12
-27
4
45
10
18
-30
18
-15
36
-6
81
Factor Strip:
-9
NSSAL
©2011
-5
-2
3
6
49
Draft
C. D. Pilmer
Connect Four Dividing Signed Numbers Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on two numbers; one from Value 1 and one from Value 2. Once they
have chosen the two numbers, they can capture one square with that appropriate quotient (i.e.
Value 1 divided by Value 2). They either mark the square with an X or place a colored
counter on the square. There may be other squares with that same quotient but only one
square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that quotient using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
-8
-12
9
-5
2
4
-9
15
-4
6
10
-3
-15
2
6
-8
9
12
-6
-3
10
-9
-4
-5
12
-4
-8
-5
15
6
9
-15
-6
4
6
-12
Value 1:
Value 2:
-30 24 -18 12
NSSAL
©2011
-3
50
-2
2
6
Draft
C. D. Pilmer
Connect Four Squaring and Cubing of Signed Numbers Game
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place two paperclips on the two strips; one on the Base Strip and one on the Exponent Strip.
Once they have chosen the values, they can capture one square with that appropriate value.
For example, if the base value is -3, and the exponent is 2, then the player can capture a 9
square
 3  9 . They either mark the square with an X or place a colored counter on the
2
square. Only one square can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that value using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one paperclip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
4
125
25
-64
27
-1
-27
-8
4
-1
9
125
9
27
16
-27
-64
-8
-64
25
125
4
8
1
8
9
-1
27
25
4
4
-27
1
-8
16
9
Base Strip:
-4
NSSAL
©2011
Exponent Strip:
-3
-2
-1
2
3
51
5
2
3
(square)
(cube)
Draft
C. D. Pilmer
Connect Four Time Ahead Game (A)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place paper clips on the strips below; one on the Start Time Strip and one on the Minutes
Ahead Strip. If the player chose 3:30 (start time) and 45 (minutes ahead), then they could
capture a square labelled 4:15. They either mark the square with an X or place a colored
counter on the square. There may be other squares with this same time but only one square
can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that time using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one player clip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
5:00
4:30
6:00
4:15
3:30
5:45
3:45
5:15
4:00
4:45
3:45
4:30
4:45
5:45
3:15
5:00
4:00
5:15
3:15
4:00
5:30
4:15
6:00
3:45
4:15
5:00
4:45
5:15
3:15
5:30
5:30
3:30
4:30
3:45
5:00
4:15
Start Time Strip
Minutes Ahead Strip
3:00 3:30 4:00 4:30 5:00
NSSAL
©2011
52
15
30
45
60
Draft
C. D. Pilmer
Connect Four Time Ahead Game (B)
Number of Players: Two
Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically
or diagonally.
Instructions:
1. Roll a die to see which player will go first.
2. The first player looks at the board and decides which square he/she wishes to capture. They
place paper clips on the strips below; one on the Start Time Strip and one on the Minutes
Ahead Strip. If the player chose 2:45 (start time) and 30 (minutes ahead), then they could
capture a square labelled 3:15. They either mark the square with an X or place a colored
counter on the square. There may be other squares with this same time but only one square
can be captured at a time.
3. Now the second player is ready to capture a square but he/she can only move one of the
paperclips. They then mark the square with that time using an O or a different colored
marker. If a player cannot move a single paperclip to capture a square, a paperclip must still
be moved in order to ensure that the game can continue.
4. Play alternates until one player connects four squares. Remember that only one player clip is
moved at a time. If none of the players is able to connect four, then the winner is the
individual who has captured the most squares.
Game Board:
3:45
3:00
4:15
3:15
4:00
3:30
3:15
4:30
2:30
3:30
2:45
3:45
2:45
4:00
3:15
3:45
3:30
4:15
3:45
3:30
4:15
3:00
4:00
3:15
4:30
3:00
3:45
3:15
2:30
3:30
3:15
2:45
3:30
4:00
3:45
3:00
Start Time Strip
Minutes Ahead Strip
2:15 2:30 2:45 3:00 3:15 3:30
NSSAL
©2011
53
15 30 45 60
Draft
C. D. Pilmer
Connector
In this two or three player game, your objective is to obtain as many points as possible by
connecting numbers in straight lines vertically, horizontally, or diagonally on the playing board
below. The point values are shown below. (The points are calculated at the end of the game.)
2 points for 2 in a row
4 points for 3 in a row
7 points for 4 in a row
10 points for 5 in a row
14 points for 6 in a row
How do you capture a number? It involves rolling three six-sided dice. You use the three
numbers rolled and the operations of addition, subtraction, multiplication, division, and
exponentiation to capture one desired number. For example, if you rolled the numbers 2, 5, and
6, here are some of the possible numbers you could capture.
 1 because 2  5  6  1
 3 because 2  6  5  3
 7 because 2  6  5  7
 15 because 6  2  5  15
 28 because 6  5  2  28
 31 because 52  6  31
The first player rolls and captures a single number that they desire. That number should be
marked with a symbol or color specific to that player. Then the next player rolls, captures, and
marks their desired number. This process continues until it becomes difficult to complete the
remaining numbers on the board. Tally the points at the end to determine the winner.
1
8
2
3
9
4
5
6
10
7
11
12 13 14 15 16 17 18
19
20
21
22
23 24 25 26 27 28 29
30
31
32
33
34 35 36 37 38 39 40
NSSAL
©2011
54
Draft
C. D. Pilmer
Fraction Fury Puzzles (A)
With the fraction fury puzzle, your mission is to use the six
4
6
1
indicated numbers to create the desired nine fractions. However,
5
3
2
you are not permitted to repeat a number in a row or column
(They can be repeated in a diagonal.). Hints are provided so that
1
5
4
you can figure out which fraction (proper or improper) belongs in
each of the nine squares. If we look at the completed puzzle on
3
2
6
the right, the hint for the first square (top left) could have been
" 1  0.2 ." There is only one possible solution based on this hint
2
1
5
4
6
4
3
and it is . For the second square (top center), the hint could
5
6 4
2
4
have been "Simplifies to 2." The possibilities are , , or . The can be eliminated
3 2
1
2
because we already used the 4 in the previous square (Can't repeat the same number in a row or
6
2
column.) At this point, you are unable to determine whether or belongs in square two.
3
1
You will have to look at the hints provided for the other squares before determining which of the
two possible answers is appropriate for square two. Please note that you must be comfortable
with fractions, decimals and percentages to complete these puzzles.
(a) 1, 2, 3, 4, 5, 6 Puzzle
Whole
Number
60%
2 - 0.75
300%
(b) 2, 3, 4, 5, 6, 7 Puzzle
Equal to
6
NSSAL
©2011
of 3
9
1.2
14
3
2
5
1
2
1
16

3

6
Little >
1
2
5
2.5
150%
16
55

5
3.5 - 2.75
14
Between 1
and 2
Equal to
Between 0.5
and 1
Double
1
3
7
10
Draft
C. D. Pilmer
(c) 3, 4, 5, 6, 7, 8 Puzzle
1

3
1
1.5
(d) 4, 5, 6, 7, 8, 9 Puzzle
1
Little >
2
7
Little < 1
Equal to 2
2 1
1
1
8
2
Between 1.5
and 2
of 150%
6
of
3.5
8
Little <
1
2
NSSAL
©2011
Equal to
9
14
2
Equal to
3
8
2 - 0.2
3
1
1
7
175%
Little < 2
1
3
14
8


1
Equal to
3
8
12
(f) 2, 4, 5, 6, 8, 9 Puzzle
1
1
3
5
450%
2
Little > 1
10
3
Little > 1
4
(e) 1, 2, 3, 5, 7, 9 Puzzle
1
1
Little <
9
1
Between 0.5
and 1
2
5
1
1
4

8
Between 1
and 2
9
of 300%
3 sets of
2
Equal to
4
Little >
2
1
4
56
3
Equal to 2
0.8
1
2
Equal to
2
3
Draft
C. D. Pilmer
(g) 1, 3, 4, 5, 8, 9 Puzzle
(h) 1, 2, 5, 6, 7, 8 Puzzle
2
5
1
6
2
Between 1
and 1.5
Close to 0
160%
2.25
Whole
Number
50% of 1.2
Equal to 2
7

18
5
3

4
1

3
Little >

1
11
12
Equal to 1
1
Equal to 2
1.5
7
3
20

5
1
3

7
3
Whole
Number
Little > 1
Between 0.5
and 1
Equal to 4
Equal to
1
4
125%
250%
3
2
Between 1
and 1.5
(j) 2, 5, 6, 7, 8, 9 Puzzle
2
8
Equal to
1
12
Between 2
and 3
NSSAL
©2011
Close to 1
18
(i) 3, 4, 5, 6, 7, 8 Puzzle
1
of 0.8
Little > 1
1
20
3
16
57

5
16
Between 1
and 1.5
Little < 1
Between 1
and 1.5
Equal to
75%
50% of
4
9
Draft
C. D. Pilmer
Fraction Fury Puzzles (B)
All of the puzzles on this page use the numbers 1 through 8.
1.
2

3
11
3
5

21
7
8
1
21
Equal to 2
3 7
1 
8 8
2.
2
1
3
4
1
4
Double
2
3
1
3
1
Little >
6
2
1
Equal to
7
2 sets of
2

5
1
5
4
Whole
Number >4
2 - 1.6
Between 2.5
and 3
2
Equal to
5
1
6
3
7
6
3
Equal to
16
120%
Between 2.7
and 3.6
600%
3 - 1.25
21

8
21
Whole
Number >4
Equal to
1
2
NSSAL
©2011
58
1
1 3
8
Equal to
1 - 0.6
1
Triple
2
1
5
14

1
6
9
1
14
4
of
1
1
6
1
3
1.75
1
of
3
4
1
Between 1.5
and 2
3.
Equal to 4
2
160%
Double
2
1
3.5
4
80%
8 sets of
Equal to
75%
2
4
of
Equal to
1 - 0.75
Equal to
3
Whole
Number <6
18
10
One part of
six
1
9
16

11
16
Equal to 2
2
Draft
C. D. Pilmer
Math Logic Puzzles
For each, find the numbers represented by the symbols , , and . Hint: For each of the
puzzles, one of the equations, not necessarily the first equation, allows you to solve for a symbol
very quickly.
Puzzle 1:
-=2
+1=6
+=8
Puzzle 4:
-=3
 +  +  = 10
 4 = 8
Puzzle 7:
-3=
 +  = 2 
14   = 2
Answers (in no particular order)
 = 4,  = 6,  = 2
 = 14,  = 6,  = 4
 = 2,  = 5,  = 3
NSSAL
©2011
Puzzle 2:
Puzzle 3:
+=8
+=6
+=7
Puzzle 5:
+=8
3  = 6
 +  = 10
Puzzle 6:
-2=7
 +  +  = 17
   = 18
Puzzle 8:
-=5
++=9
+=
Puzzle 9:
++2=
  3=4
-=6
24   = 
++1=9
 +  = 3 
 = 6,  = 4,  = 12
 = 11,  = 3,  = 8
 = 4,  = 2,  = 5
 = 6,  = 2,  = 9
 = 7,  = 5,  = 1
 = 1,  = 7,  = 4
59
Draft
C. D. Pilmer
Answers
3 by 3 KenKen Puzzles (A) (page 1)
(a)
(b)
2
1
3
3
1
2
1
3
2
2
3
1
3
2
1
1
2
3
(c)
(d)
1
2
3
2
3
1
3
1
2
1
2
3
2
3
1
3
1
2
(e)
NSSAL
©2011
(f)
3
1
2
3
2
1
1
2
3
2
1
3
2
3
1
1
3
2
60
Draft
C. D. Pilmer
3 by 3 KenKen Puzzles (B) (page 2)
(a)
(b)
4
5
3
3
5
4
3
4
5
4
3
5
5
3
4
5
4
3
(c)
(d)
5
3
4
3
4
5
4
5
3
5
3
4
3
4
5
4
5
3
(e)
NSSAL
©2011
(f)
5
4
3
4
3
5
3
5
4
3
5
4
4
3
5
5
4
3
61
Draft
C. D. Pilmer
3 by 3 KenKen Puzzles (C) (page 3)
(a)
(b)
5
6
7
7
5
6
7
5
6
6
7
5
6
7
5
5
6
7
(c)
(d)
6
5
7
6
7
5
5
7
6
5
6
7
7
6
5
7
5
6
(e)
NSSAL
©2011
(f)
7
6
5
5
7
6
5
7
6
6
5
7
6
5
7
7
6
5
62
Draft
C. D. Pilmer
3 by 3 KenKen Puzzles (D) (page 4)
(a)
(b)
8
7
9
9
7
8
9
8
7
7
8
9
7
9
8
8
9
7
(c)
(d)
7
9
8
9
8
7
9
8
7
8
7
9
8
7
9
7
9
8
(e)
NSSAL
©2011
(f)
8
7
9
7
9
8
7
9
8
8
7
9
9
8
7
9
8
7
63
Draft
C. D. Pilmer
4 by 4 KenKen Puzzles (A) (page 5)
(a)
(b)
2
3
1
4
3
1
2
4
4
1
2
3
2
4
3
1
3
2
4
1
4
2
1
3
1
4
3
2
1
3
4
2
(c)
NSSAL
©2011
(d)
1
2
4
3
2
1
3
4
3
4
2
1
4
3
1
2
4
1
3
2
3
4
2
1
2
3
1
4
1
2
4
3
64
Draft
C. D. Pilmer
4 by 4 KenKen Puzzles (B) (pages 6 and 7)
(a) 1, 2, 3, 4 Puzzle
(b) 1, 2, 3, 4 Puzzle
1
3
4
2
2
3
1
4
4
1
2
3
4
1
2
3
2
4
3
1
3
2
4
1
3
2
1
4
1
4
3
2
(c) 2, 3, 4, 5 Puzzle
NSSAL
©2011
(d) 2, 3, 4, 5 Puzzle
4
5
2
3
5
3
4
2
2
3
5
4
3
2
5
4
5
4
3
2
2
4
3
5
3
2
4
5
4
5
2
3
65
Draft
C. D. Pilmer
(e) 3, 4, 5, 6 Puzzle
(f) 3, 4, 5, 6 Puzzle
6
4
3
5
4
3
6
5
5
6
4
3
6
4
5
3
3
5
6
4
5
6
3
4
4
3
5
6
3
5
4
6
(g) 4, 5, 6, 7 Puzzle
NSSAL
©2011
(h) 4, 5, 6, 7 Puzzle
4
6
5
7
7
4
6
5
7
5
4
6
5
6
7
4
5
7
6
4
4
7
5
6
6
4
7
5
6
5
4
7
66
Draft
C. D. Pilmer
(i) 5, 6, 7, 8 Puzzle
(j) 6, 7, 8, 9 Puzzle
8
6
7
5
7
9
6
8
5
7
8
6
6
8
7
9
6
8
5
7
9
6
8
7
7
5
6
8
8
7
9
6
5 by 5 Ken Ken Puzzles (page 8)
(a) 1, 2, 3, 4, 5 Puzzle
(b) 2, 3, 4, 5, 6 Puzzle
2
5
4
1
3
6
3
5
4
2
4
3
5
2
1
4
2
3
6
5
5
1
3
4
2
2
4
6
5
3
1
4
2
3
5
3
5
4
2
6
3
2
1
5
4
5
6
2
3
4
NSSAL
©2011
67
Draft
C. D. Pilmer
(c) 4, 5, 6, 7, 8 Puzzle
(d) 5, 6, 7, 8, 9 Puzzle
4
7
6
8
5
9
5
8
7
6
8
4
5
7
6
6
8
9
5
7
6
5
8
4
7
8
7
6
9
5
7
6
4
5
8
5
9
7
6
8
5
8
7
6
4
7
6
5
8
9
KenKen Puzzles: Signed Numbers (pages 9 to 11)
(a) 1, -2, 3 Puzzle
(b) -1, 2, -3 Puzzle
(c) 2, -3, 4 Puzzle
-2
1
3
-3
-1
2
2
4
-3
1
3
-2
2
-3
-1
-3
2
4
3
-2
1
-1
2
-3
4
-3
2
(d) -3, 4, -5 Puzzle
(e) 3, -4, 5 Puzzle
(f) -4, 5, -6 Puzzle
-5
-3
4
3
5
-4
5
-4
-6
4
-5
-3
-4
3
5
-4
-6
5
-3
4
-5
5
-4
3
-6
5
-4
NSSAL
©2011
68
Draft
C. D. Pilmer
(g) 6, -7, 8 Puzzle
(h) 7, -8, 9 Puzzle
(i) -7, 8, -9 Puzzle
6
8
-7
-8
9
7
-9
-7
8
-7
6
8
7
-8
9
8
-9
-7
8
-7
6
9
7
-8
-7
8
-9
(j) 1, -2, 3, -4 Puzzle
(k) 2, -3, 4, -5 Puzzle
-4
3
1
-2
-3
2
-5
4
1
-2
3
-4
-5
-3
4
2
3
-4
-2
1
4
-5
2
-3
-2
1
-4
3
2
4
-3
-5
(l) 3, -4, 5, -6 Puzzle
(m) 4, -5, 6, -7 Puzzle
-4
3
-6
5
-7
-5
4
6
3
-6
5
-4
6
-7
-5
4
5
-4
3
-6
-5
4
6
-7
-6
5
-4
3
4
6
-7
-5
NSSAL
©2011
69
Draft
C. D. Pilmer
(n) 5, -6, 7, -8 Puzzle
(o) 6, -7, 8, -9 Puzzle
5
-8
-6
7
8
-9
-7
6
-6
7
-8
5
6
8
-9
-7
-8
5
7
-6
-7
6
8
-9
7
-6
5
-8
-9
-7
6
8
(p) 1, -2, 3, -4, 5 Puzzle
(q) 2, -3, 4, -5, 6 Puzzle
3
-4
5
1
-2
6
-3
-5
2
4
-2
5
1
-4
3
-5
4
2
6
-3
1
3
-2
5
-4
-3
2
6
4
-5
-4
1
3
-2
5
4
6
-3
-5
2
5
-2
-4
3
1
2
-5
4
-3
6
(r) -4, 5, -6, 7, -8 Puzzle
(s) -5, 6, -7, 8, -9 Puzzle
5
-6
-8
-4
7
8
-7
6
-9
-5
-4
-8
5
7
-6
-9
6
-7
-5
8
7
5
-6
-8
-4
-5
8
-9
-7
6
-8
-4
7
-6
5
6
-9
-5
8
-7
-6
7
-4
5
-8
-7
-5
8
6
-9
NSSAL
©2011
70
Draft
C. D. Pilmer
Magic Squares (page 12)
(a)
(b)
(c)
8
1
6
3
8
1
7
2
9
3
5
7
2
4
6
8
6
4
4
9
2
7
0
5
3
10
5
2
9
4
9
4
11
10
3
8
7
5
3
10
8
6
5
7
9
6
1
8
5
12
7
6
11
4
5
10
3
6
11
4
12
5
10
4
6
8
5
7
9
7
9
11
9
2
7
10
3
8
8
13
6
(d)
(e)
(g)
(f)
(h)
(i)
Addition Pyramids: Whole Numbers (pages 13 and 14)
1.
4
3.
6
9
5
4.
10
8
NSSAL
©2011
2.
10
2
3.
4
14
71
10
3
6.
9
5
13
9
8
1
Draft
C. D. Pilmer
7.
8.
21
9
7
10.
9
12
2
10
3
4
13.
8
8
14.
16.
11
6
6
0
19.
13
8
8
7
5
22.
2
12
5
17
3
NSSAL
©2011
4
6
10
11
5
72
3
2
6
22
18
6
10
8
40
12
2
13
5
24.
8
6
7
20
19
3
8
2
8
28
15
6
13
5
2
21.
39
9
1
20
7
3
23
9
3
19
10
7
10
3
8
6
30
9
15
23.
36
4
18.
6
27
14
10
50
12
3
5
1
20.
25
13
2
0
24
5
7
3
6
6
15.
16
10
5
7
26
18
5
13
1
7
17.
19
12
2
9
4
5
12.
11
9
29
2
21
12
3
4
6
10
9
7
29
18
19
7
3
11.
11
7
16
9
6
18
9.
18
1
10
12
5
7
3
Draft
C. D. Pilmer
Addition Pyramids: Decimal Numbers (page 15)
1.
6.3
2.5
0.4
2.
3.8
2.1
4.
0.4
1.7
0.5
7.
2.3
1.9
1.4
0.1
10.
0.4
1.4
9.3
4
1.7
0.3
13.
3
0.9
6
3.4
0
0.8
1.1
0.6
1.9
0.4
NSSAL
©2011
0.9
2.1
15.
1.7
0.7
0.5
1.2
73
0.6
2.5
2.1
1.4
1.6
0.7
0.9
0.3
5.3
4.6
1.1
2.7
1.8
18.
2.5
0.7
6.2
1.8
0.8
0.8
0.1
3.5
1
4.3
1.8
0.7
0.6
3.2
0.4
1.6
0.8
1.3
8.9
3
2.4
1.5
0.7
5.4
4.3
2.1
0.6
1.4
1.1
3.7
0.9
1.4
17.
9.7
0.7
12.
0.3
2.5
0.2
1.5
5.7
2.6
1.6
16.
1.2
14.
1.8
1.6
0
2.1
2.5
1.8
1.5
1.2
0.8
4.3
2.4
2.7
1.4
0.6
9.
5.1
5.3
1.4
0.3
2.3
11.
2.3
0.9
0.7
0.8
0.6
2.3
1.1
2.2
2
1.4
6.
4.5
1.7
1.3
0.4
0.2
0.4
8.
3.1
1.8
3.4
0.3
3.8
1
0.8
5.
0.8
1.4
3.
1.2
2.2
0.9
2.2
1.2
2.8
1.9
0.9
0.4
0.5
1.4
Draft
C. D. Pilmer
Addition Pyramids: Signed Numbers (page 16)
1.
-14
-11
-6
2.
-3
2
8
5
-2
-8
6
10.
9
4
13
-3
7
13.
-2
-6
-2
-14
-4
-3
-7
-8
-3
-8
-3
-10
NSSAL
©2011
-4
-4
2
74
6
13
-11
19
23
-4
-5
1
-6
3
-5
-2
-3
8
-7
2
5
-2
3
6
3
-5
4
18.
-1
-6
-11
-3
-6
-5
-1
-5
-3
-9
-5
8
-6
3
17.
2
7
-7
-7
-1
-5
15.
-3
-4
-5
0
-8
-7
-2
-1
-13
-10
1
16.
3
-9
-2
12.
-5
14.
-2
-2
0
-4
5
-1
-5
3
1
-6
3
-7
-1
5
4
9.
-3
-3
11.
5
-10
-4
-6
8
-6
-10
-3
-1
12
-5
8.
-4
6.
7
-4
3
2
-4
-9
-7
-2
-2
-2
-1
7.
6
5.
-3
-9
2
-6
4
7
3.
0
-5
4.
2
4
-1
-9
2
8
-6
Draft
C. D. Pilmer
Factor Rows and Factor Columns (page 17)
(a)
2
5
10
4
3
12
8
15
3
9
27
7
1
7
21
9
9
2
18
4
5
20
36
10
3
8
24
9
2
18
27
16
9
6
54
8
5
40
72
30
(d)
(g)
(j)
(m)
NSSAL
©2011
(b)
(e)
(h)
(k)
(n)
6
3
18
1
2
2
6
6
6
10
60
4
2
8
24
20
3
6
18
5
9
45
15
54
5
4
20
6
7
42
30
28
7
8
56
3
2
6
21
16
75
(c)
(f)
(i)
(l)
(o)
4
5
20
2
6
12
8
30
4
7
28
1
3
3
4
21
8
5
40
1
7
7
8
35
7
2
14
4
8
32
28
16
5
7
35
3
9
27
15
63
Draft
C. D. Pilmer
Whole Number Crossword Puzzle (A) (page 18)
3
8
6
0
7
4
2
6
3
5
5
1
2
2
1
3
0
2
4
3
4
3
4
3
2
7
9
8
2
7
7
5
8
9
0
6
6
4
6
6
1
5
Whole Number Crossword Puzzle (B) (page 19)
4
5
0
3
4
4
1
7
2
3
3
4
NSSAL
©2011
6
6
7
6
4
8
4
8
3
6
8
2
8
3
1
0
9
4
2
5
4
1
1
5
9
8
4
3
8
76
6
Draft
C. D. Pilmer
Whole Number Crossword Puzzle (C) (page 20)
5
6
0
8
3
1
4
3
5
9
3
3
7
9
7
0
5
4
8
8
1
9
6
1
0
6
2
3
6
1
4
9
4
2
0
2
3
6
8
2
4
8
Whole Number Crossword Puzzle (D) (page 21)
7
7
1
8
7
1
3
5
7
7
6
4
NSSAL
©2011
8
1
5
8
6
6
4
2
1
3
1
8
3
2
0
6
9
2
9
8
5
4
8
7
8
2
0
8
7
77
2
Draft
C. D. Pilmer
Signed Number Crossword Puzzle (A) (page 22)
-
4
2
0
-
-
6
4
8
2
7
2
1
1
8
3
4
0
-
-
2
4
1
0
0
0
0
-
2
-
6
1
4
-
0
2
0
9
0
2
-
7
Signed Number Crossword Puzzle (B) (page 23 )
-
3
2
4
8
-
0
4
-
-
3
4
NSSAL
©2011
2
5
9
3
2
2
5
8
-
-
-
3
0
5
6
0
1
-
-
1
9
8
0
3
0
1
78
4
Draft
C. D. Pilmer
RAD Puzzles: Whole Numbers (pages 24 to 26)
(a)
11
(b)
-
3
=
8
=
6
+
2
60

6
=
10
=
2

5
+
-

+

-
+
-
+
-
21
1
2
4
3
12
0
2
1
0
=
=
=
=
=
=
=
=
=
=
6
48
32

2
=
16
=
10
+

6
=
8
=
3
+
5
=
=
=
=
=
=
=
=
=
=
4
0
4
30
7
24
2
3
4
9

+


-


+
-
-
1
2
8

2
=
4
=
3
+
(c)
10
+
3
=
5
=
1
+
4
+
3
=
45
=
9

5
(d)

3
=
30
=
2
+
28
42

+





-
+
-
4
31
5
21
4
7
2
9
0
1
=
=
=
=
=
=
=
=
=
=
7
6
40
-
34
=
6
=
42


6
=
36
=
9

4
=
=
=
=
=
=
=
=
=
=
80
36
10
41
4
54
11
40
9
1

-
-
+
+

-
-

+
3
9
2

NSSAL
©2011
2
=
4
=
1
+
79
-
5
=
4
=
1
+
3
Draft
C. D. Pilmer
(e)
10
(f)

7
=
70
=
72
-
2
36
+
12
=
48
=

6
8

-
-

+

-

-
+
6
4
7
8
5
6
8
2
3
0
=
=
=
=
=
=
=
=
=
=
7
6
60
+
3
=
63
=
9


4
=
24
=

3
8
=
=
=
=
=
=
=
=
=
=
40
2
3
6
49
6
23
4
30
6
+
+

+


-
+

+
7
1
20
+
1
=
21
=
3

(g)
32
+
19
=
20
=
10

2

8
=
3
=
30
-
27
(h)
+
24
=
56
=
7

8
24

-



+
+



8
17
2
2
4
4
2
6
15
3
=
=
=
=
=
=
=
=
=
=
2
28
4

7
=
28
=
14

-
10
=
18
=

2
9
=
=
=
=
=
=
=
=
=
=
1
21
19
6
3
4
50
36
13
81
+

+
+
-



-

1
7
3

NSSAL
©2011
3
=
9
=
8
+
80
-
5
=
2
=
11
-
9
Draft
C. D. Pilmer
(i)
18
(j)
-
4
=
14
=
7

2
6
+
2
=
8
=
7
+
1

+
+
+


+


+
3
1
16
53
1
2
2
6
7
0
=
=
=
=
=
=
=
=
=
=
2
12
6

5
=
30
=
60


4
=
48
=
49
-
1
=
=
=
=
=
=
=
=
=
=
42
8
3
30
7
36
10
30
85
2

-


-

-
+
-

5
3
7
+
3
=
10
=
2

(k)
9

6
=
18
=
36

2

12
=
36
=
6

6
(l)
-
1
=
8
=
40

5
3

+


+
+

-

+
8
7
8
10
11
61
6
4
3
10
=
=
=
=
=
=
=
=
=
=
16
64
72
-
8
=
64
=
4


2
=
32
=

2
16
=
=
=
=
=
=
=
=
=
=
12
1
22
88
8
72
2
4
48
13

+
+
-

-



+
2
8
6

NSSAL
©2011
7
=
42
=
84

81

1
=
8
=
24

3
Draft
C. D. Pilmer
RAD Puzzles: Signed Numbers (pages 27 to 29)
(a)
-6
(b)
+
8
=
2
=
10
-
8
3

14
=
42
=
21

2

-

-
+

-

-
+
-4
11
-4
19
-7
-2
13
-7
25
-4
=
=
=
=
=
=
=
=
=
=
1
-6
24

-3
=
-8
=
-9
+

1
=
-6
=
-4
+
-2
=
=
=
=
=
=
=
=
=
=
20
-1
-2
9
6
48
-3
-8
-2
-1
-
+
+

+

+
-

+
-5
-8
-4
+
-2
=
-6
=
-1
+
(c)
-8

4
=
-2
=
2

-1

3
=
45
=
20
+
25
(d)
+
44
=
36
=
-6

-6
15



+




+
-
4
22
-9
30
1
5
-1
-5
52
33
=
=
=
=
=
=
=
=
=
=
-6
3
-2

2
=
-4
=
24


-3
=
-9
=
72

-8
=
=
=
=
=
=
=
=
=
=
-1
11
28
3
9
-1
16
7
76
2

+


-

-
-
+

15
-3
2
+
NSSAL
©2011
-9
=
-7
=
8
-
82
+
19
=
16
=
-4

-4
Draft
C. D. Pilmer
(e)
-6
(f)
+
1
=
-5
=
15

-3
7

9
=
63
=
21

3



+


-

-

-4
-1
-5
60
-1
4
13
-9
14
-3
=
=
=
=
=
=
=
=
=
=
3
28
24
-
-1
=
25
=
75


-4
=
-7
=

7
-1
=
=
=
=
=
=
=
=
=
=
-3
9
50
15
6
2
3
-5
21
4

-


+

+
+

+
-3
14
-8
+
10
=
2
=
5
+
(g)
2

-7
=
-2
=
3
+
-5
+
0
=
-4
=
2

-2
(h)

25
=
50
=
5

10
-4

-
+
-
+

-

+

-3
33
-2
-7
-6
-9
-3
-3
9
-2
=
=
=
=
=
=
=
=
=
=
4
36
-6

-8
=
48
=
12


3
=
12
=
11
-
-1
=
=
=
=
=
=
=
=
=
=
-1
64
8
22
0
6
8
-2
14
1
+

+
-
+
+
+

+
-
4
30
-5

NSSAL
©2011
-8
=
40
=
10

83

-5
=
-6
=
-3

2
Draft
C. D. Pilmer
(i)
-1
(j)
+
-2
=
-3
=
-4
+
1
-8

-2
=
4
=
20
-
16

-


+

-
-


9
0
-6
-9
1
-5
-7
12
-5
-8
=
=
=
=
=
=
=
=
=
=
2
40
-9

-2
=
18
=
36


5
=
8
=

-4
-2
=
=
=
=
=
=
=
=
=
=
-5
1
16
-6
5
5
0
15
3
2
+

+

+
+
-
+
-

-3
35
-4

-2
=
2
=
-6

(k)
-3

-5
=
-7
=
7

-1

10
=
20
=
14
+
6
(l)

-2
=
6
=
18

3
2
+

-

-
+
-

-

13
-2
-8
-9
10
43
19
-4
9
-6
=
=
=
=
=
=
=
=
=
=
-7
45
10
+
4
=
14
=
-2


-9
=
-5
=

5
-1
=
=
=
=
=
=
=
=
=
=
-5
5
28
16
-3
3
-6
7
30
-2

+


+

+
-


-4
15
-2

NSSAL
©2011
-1
=
2
=
-8

84
+
-3
=
12
=
6

2
Draft
C. D. Pilmer
Fraction Fury Puzzles (A) (pages 55 to 57)
(a) 1, 2, 3, 4, 5, 6 Puzzle
2
3
1
5
4
5
6
4
3
6
6
1
4
3
(c) 3, 4, 5, 6, 7, 8 Puzzle
7
6
3
5
7
6
8
4
5
9
2
3
7
NSSAL
©2011
5
4
8
8
9
6
7
6
9
2
2
2
5
2
4
8
85
4
6
4
1
5
9
5
5
9
9
(f) 2, 4, 5, 6, 8, 9 Puzzle
9
1
7
4
7
3
3
8
7
5
6
2
5
5
8
7
7
7
6
6
(e) 1, 2, 3, 5, 7, 9 Puzzle
1
6
6
9
4
3
4
4
3
5
2
(d) 4, 5, 6, 7, 8, 9 Puzzle
8
8
4
3
2
5
4
5
3
2
3
7
7
5
4
2
5
1
2
6
(b) 2, 3, 4, 5, 6, 7 Puzzle
8
6
5
9
Draft
C. D. Pilmer
(g) 1, 3, 4, 5, 8, 9 Puzzle
4
1
3
8
5
8
9
5
1
2
9
3
7
1
4
8
7
8
3
4
6
8
2
5
4
2
9
7
7
7
8
2
8
5
5
7
6
5
3
5
9
3
6
6
(j) 2, 5, 6, 7, 8, 9 Puzzle
6
7
7
1
6
(i) 3, 4, 5, 6, 7, 8 Puzzle
5
2
1
4
1
6
8
8
5
8
5
3
4
9
(h) 1, 2, 5, 6, 7, 8 Puzzle
6
7
5
8
5
8
2
6
9
Fraction Fury Puzzles (B) (page 58)
1.
2
8
5
1
7
5
7
6
6
1
4
8
4
4
8
2
5
6
6
2
7
2
8
3
1
3
3
NSSAL
©2011
4
5
7
3
1
86
Draft
C. D. Pilmer
2.
6
4
1
3
7
2
7
4
8
4
5
3
5
4
6
7
6
1
7
5
1
3
5
6
3
2
2
4
4
8
1
7
7
3
6
1
1
7
2
3
6
1
8
5
2
5
7
6
3
6
3
2
NSSAL
©2011
4
1
8
8
5
8
5
3.
2
8
4
8
2
87
Draft
C. D. Pilmer