brainteasers grade 4-5

Brainteasers
Grades 4–5
by Jillayne Prince Wallaker
illustrated by Vanessa Booth
Carson-Dellosa Publishing Company, Inc.
Greensboro, North Carolina
© 2004, Carson-Dellosa Publishing Co., Inc., Greensboro, NC 27425. All rights reserved. The purchase of
this material entitles the buyer to reproduce worksheets and activities for classroom use only—not for
commercial resale. Reproductions of these materials for an entire school or district is strictly prohibited.
No part of this book may be reproduced (except as noted above), stored in a retrieval system, or
transmitted in any form or by any means (mechanically, electronically, recording, etc.) without the prior
written consent of Carson-Dellosa Publishing Co., Inc.
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ISBN 978-1-60418-366-5Printed in the USA • All rights reserved.
Credits:
Author: Jillayne Prince Wallaker
Cover Artist: Peggy Jackson
Inside Illustrations: Vanessa Booth
Project Director: Sherrill B. Flora
Editors: Sharon Thompson and
Debra Olson Pressnall
Graphic Layout: Sharon Thompson
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Brainteasers
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Table of Contents
Introduction 4
Hitting the Target (problem solving and logical thinking) 5

Consecutive Number Add-Up (logic and problem solving) 6
Analyzing Consecutive Number Add-Up (logic and problem solving) 7
Could Be the Answer (order of operations, problem solving, and logic) 8
Finding the Answer (order of operations, problem solving, and logic) 9
Fill In the Digits (addition, subtraction, and problem solving) 10
Careful Placement (multiplication and puzzle logic) 11
Missing Digit (basic operations and problem solving) 12
Number Riddles (basic operations and logical thinking) 13
The Power of Zero through Nine (order of operations and problem solving) 14
Adding Words
(addition with positive and negative addends and problem solving) 15
Fact Triangles (problem solving and logic) 16
Find the Numbers (basic operations and problem solving) 17
Hidden Numbers (basic operations and problem solving) 18
Working with Digits (multiplication and problem solving) 19
Whose Answer? (multiplication, division, and matrix logic) 20
Place Value Riddles (place value and logic) 21
Missing Steps (addition, problem solving, and logic) 22
More Missing Steps (addition, problem solving, and logic). 23
Puzzle It Out (problem solving and logic) 24
Soil Stuff (problem solving and logic) 25
Ages (problem solving and logic) 26
Pick Apart (fractions, logic, and problem solving) 27
My Money (money, problem solving, and matrix logic) 28
Break the Bank
(money, problem solving, and logic) 29
Determining Money
(money, problem solving, and logic) 30
Probability Two Ways (probability and logic) 31
How Probable? (fractions, probability, and logic) 32

New Pet (data organization, logic, and problem solving) 33
Hide and Seek (matrix logic) 34
It's Buggy (algebraic thinking and problem solving) 35
Label the Venn Diagram (problem solving and logic) 36
Let’s Measure (problem solving and matrix logic) 37
Polygons (geometry and logic) 38
Polygon Matrix (geometry and matrix logic) 39
Got the Area (area, problem solving, and logical thinking) 40
Order Up (sequencing and problem solving) 41
Keep Ordering (sequencing and problem solving) 42
Ordering Again (sequencing and problem solving) 43
The Total (number sense and matrix logic) 44
Review Test 45
Answer Key 47
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Introduction
Provide fun math practice that goes beyond the facts! With Brainteasers, students use higher-
level thinking and processing skills to solve problems. Not only will students be expected
to make connections, analyze data, use deductive reasoning, and represent numbers in
alternate ways, they will have opportunities to utilize skills that are prerequisites to other
learning—skills such as addition, subtraction, multiplication, division, fractions, geometry,
measurement, and money. Students are encouraged to apply their understanding of those
concepts in a new, unusual, or atypical manner. Many students have memorized and
learned to use a skill in one or two given contexts. With Brainteasers, students explore their
understanding of grade level concepts and picture and apply their skills to different situations.
Remediation and Extension Suggestions and Alternatives
Remediations

1. Allow students to work with partners or complete the pages on their own and conference
with a partner to discuss problems on which they do not agree.
2. Let the student make a picture or sketch of the problem, or act it out.
3. Decrease the number of problems required for completion.
4. Represent the problems in a variety of ways.
5. Have students talk through or write their understanding of the process with partners. Often,
verbalizing assists understanding.
6. Many students cannot complete more than one or two higher-level thinking problems at
a time. Have the student cut the page up, gluing the parts onto folded paper to make a
booklet. Alternatively, assign one or two problems a day until the page is complete.
Extensions
1. Ask students to use the page as a model and write their own problems. The “write your
own” activities allow students to demonstrate mastery of the concept while providing an
avenue for self-expression and self-evaluation. Placed on index cards with the answers on
the back, the problems are great student-made additions to a math center.
2. Have students keep ongoing journals of where they encounter mathematics in real life.
A goal of adding one experience a day is reasonable.
3. Ask students to solve problems using a variety of strategies.
Have students evaluate which ones work best for them and
explain their preferences.
4. If appropriate, encourage students to do more than the
minimum requirements on the page. For example, if two
additional examples are required, the student would create
ve. Set up a point system where students can earn bonus
points for additional examples.
5. Have students write clear directions to explain the process
for solving a problem and then share them with classmates.
6. Direct students to write explanations with proof for the
methods used to solve the problems.
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Brainteasers
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Name _____________________________________
Choose 100 consecutive numbers. Write the numbers in order in the balloons below.
Write equations using the numbers in the table above. Include addition, subtraction,
multiplication, and division sentences. Use whole numbers, fractions, and decimals.
Include multistep problems. When a number is used as any part of a problem, shade
its balloon. Continue until each number has been used in an equation.
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
Trade papers with a partner. Check answers for accuracy.
Attribute checklist:

  Numbers in balloons are consecutive.
 Each number in a balloon is used in an accurate problem.
  Addition, subtraction, multiplication, and division problems are included.
  Whole numbers, fractions, and decimals are used.
  Multistep problems are used.
Hitting the Target
problem solving and logical thinking
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Brainteasers
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Name _____________________________________
Consecutive Number Add-Up
logic and problem solving
Place the numbers 1–9 in the rst grid so that the sum of the numbers in each row and
column are the same number. Write the sum on the line after each row and under
each column. Use grid paper to practice. Write your solution in the rst grid. Find other
solutions by comparing with classmates. Record them in the other 2 grids.
Look with a partner for patterns
in the above grids. Evaluate
how each number moves to
the next number.
Take any set of consecutive
numbers. Using the patterns
found above, place numbers
in the grids on the right. Use
a different set of numbers for
each grid.
Use multiples of 2, 3, and 4 in the grids. Does the pattern still work? ________
multiples of 2 multiples of 3 multiples of 4
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Brainteasers
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Name _____________________________________
Analyzing Consecutive Number Add-Up
Solve. Add the numbers in each column
and row. Write the answers in the blanks.
Evaluate how each number moves to the
next number. Numbers move 4 different
ways. Write those ways here.
40 47 24 31 38
46
27
33
34
28
29
35
41
30
36
42
48
37
43
44
25
39
45
26
32

1. _____________________________________
2. _____________________________________
3. _____________________________________
4. _____________________________________
Evaluate when each type of move is made. Write your observations here.
__________________________________________________________________________________
__________________________________________________________________________________
Place consecutive numbers in the grids so that the sum of each row and column is
equal. Start each grid with a different number. Share your results with a partner.
On a separate sheet of grid paper, use the patterns to write other sets of numbers in
a grid. Try numbers that are consecutive when counting by a number other than 1.
For example, write the multiples of 2, 3, 5, 10, or 100 in the grid.
logic and problem solving
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Name _____________________________________
Could Be the Answer
order of operations, problem solving, and logic
Use the order of operations to make each problem correct. Place parentheses to
arrive at the given answer.
A . 4 + 6 x 2 – 1 2 – 4 ÷ 2 = 6
B . 4 + 6 x 2 – 1 2 – 4 ÷ 2 = 0
C . 2 x 1 6 – 8 ÷ 2 x 6 = 2
D . 9 ÷ 3 + 6 x 4 + 8 – 5 = 3 0
E . 8 – 2 x 2 + 6 ÷ 3 = 6
F . 1 8 ÷ 3 x 3 – 2 + 8 ÷ 4 = 8
G . 5 + 5 x 5 ÷ 5 + 5 = 5
H . 2 1 ÷ 7 – 4 + 5 x 3 = 3 6
I . 2 x 9 ÷ 3 + 3 x 1 5 ÷ 5 = 9

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Finding the Answer
order of operations, problem solving, and logic
Think a bit harder about these problems. Place function symbols and parentheses in
each number sentence to arrive at the given answer.
A.
6 3 2 5 = 12
B. 5 3 12 3 = 1
C. 14 7 3 1 = 8
D. 13 8 4 5 = 3
E. 36 6 4 6 = 2
F. 2 7 4 2 = 9
G. 5 6 3 2 13 5 2 = 4
H. 4 8 2 11 3 7 4 = 2
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Brainteasers
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Name _____________________________________
Fill In the Digits
addition, subtraction, and problem solving
Add or subtract. Find the missing digits.


• Make your own problems.
• Check for accuracy with a calculator.
• Copy the problems into the boxes
on the right, but leave the shaded

boxes blank.
• Fold the paper back along the line.
• Trade problems with a partner.
• Add or subtract.
• Find the missing digits.
• When you are done,
unfold the page and
check your work.
+
5
9
2
1
1
5 2
8
+
1
5
8
7
6
5
7
0
–
9
4
2
7

2
7
6
3
+
2
4
5
4
4
3
3
4
1.
2.
3.
4.
+
3
2
5
2
5
8
7
3
+
3
5
4

3
5
6
4
1
–
7
1
3
8
8
3 4
9
–
8
5
5
4
3
4 8
2
9. 10. 11. 12.
–
2
4
2
5
1
8
4

7
–
3
1
2
7
5
5
6
8
+
4
2 9
5
7
5
8
5
+
2
6
2
6
9
0
5
8
5. 6.
7.
8.

fold
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Name _____________________________________
Careful Placement
multiplication and puzzle logic
Solve. Write the answers in the puzzle so that the vertical and horizontal numbers
interconnect. If an answer does not t in the puzzle, check your work.
4 3
x 9 1
9 4
x 9 1
4 4
x 3 5
4 6
x 7 5
Write your own multiplication problems, using only 2-digit or 3-digit factors.
Use another piece of paper to work the grid. Rewrite your nal answers here.
4 6
x 8 4
5 0
x 9 2
9 8
x 9 7
1 9 5
x 3 1

x

x

x

x

x

x

x

x
A.
C.
E.
G.
B.
D.
F.
H.
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Name _____________________________________
Missing Digit
basic operations and problem solving
Think carefully about each set of numbers. Look for relationships and explain them on
the lines below. Complete the grids.
4 6

8 2
9 7
1 3
5 8
3 4
2 5
4
6 2
3 4
4 9
6 6
2 4
8 1
9 2
3
9 5
1 4
1 9
1 0
7 8
1 5
6 5
1
9 7
2 5
6 5
1 4
8 6
2 4
5 3

2
Set B
Relationships: ____________________________________________________________________
Set C
Relationships:
____________________________________________________________________
Set D
Relationships:
____________________________________________________________________
Relationships: ____________________________________________________________________
Set A
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Brainteasers
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Name _____________________________________
Number Riddles
Read carefully to solve each number
riddle. Write your answer in the blank.
1. Divide me by 6 and add 3. Divide
this by 3, then multiply by 4 to get
12. What number am I? ________
2. Multiply me by 3, then add 3. Divide by 5,
then subtract 4. The nal answer is 2. What number am I? ________
3. Divide 24 by me, then multiply by 5.
Subtract 7 and multiply by 7. You get 56. What number am I? ________
4. Divide me by 5, subtract 9, then multiply by 6.
Subtract 2, then multiply by 4 to get 16. What number am I? ________
5. Add 2 to me, multiply by 3, then subtract 9.
Divide by 6, then add 4. You get 6. What number am I? ________
6. Divide 18 by me, then subtract 9 before

adding 1. Triple the answer. Add 6, then
divide by 9. You get 4. What number am I? ________
7. Multiply me by 9, then subtract 104. Divide this
by 5. Subtract 2, then divide by 8. Multiply this
by 7. You get 21. What number am I? ________
8. Add 34 to me, then divide by 4. Multiply this by 5.
Add 1 more. Multiply this by 2, then divide by 8.
The nal answer is 14. What number am I? ________
9. Divide me by 4, subtract 3, and then divide by 7.
Multiply by 8, then add 4. Divide by 4 to get 9. What number am I? ________
Think of 5 riddles of your own. Write them on another sheet of paper. Check your
problems for accuracy. Copy each problem onto an index card. Write the answer on
the back. Exchange your number riddles with a partner.
basic operations and logical thinking
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Name _____________________________________
The Power of Zero through Nine
Write 3 equations for each of the following answers. Each equation must include the
numbers 0–9. Use your knowledge of order of operations to help you. Compare your
answers with those of a partner. Check for accuracy.
example: 56
A. 9 – 8 + 0 – 1 + (6 x 7) + 4 + 5 + 3 + 2 = 56
B. 0 + (5 x 4) + (6 x 3) + (2 x 9) + 8 – (7 + 1) = 56
C. (8 + 4) x 0 + (5 x 6) + (9 – 1) x 2 + 3 + 7 = 56
41
A.
_____________________________________________________
B. _____________________________________________________

C. _____________________________________________________
100
A.
_____________________________________________________
B. _____________________________________________________
C. _____________________________________________________
125
A.
_____________________________________________________
B. _____________________________________________________
C. _____________________________________________________
36
A.
_____________________________________________________
B. _____________________________________________________
C. _____________________________________________________
Choose a number: __________
A.
_____________________________________________________
B. _____________________________________________________
C. _____________________________________________________
Choose a number: __________
A.
_____________________________________________________
B. _____________________________________________________
C. _____________________________________________________
order of operations and problem solving
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Name _____________________________________
Adding Words
addition with positive and negative addends
Use the table. Give each letter in the word a number value. Add the numbers to nd
the total value of the word.
Value Table

Find the value of these words.
1. sum ___________________________________
2. value _________________________________
3. digit __________________________________
4. fractions ______________________________
5. multiply _______________________________
6. divide _________________________________
Read and follow the directions.
7. How many words can you write with a value of 0? _____
8. Write 4 words with a value __________________ __________________
less than 0. __________________ __________________
9. Write 4 words with a value __________________ __________________
greater than 10. __________________ __________________
10. Find the value of this sentence: Math is fun. ____________________________________
11. Write a sentence. Find the total value of the words in your sentence. ____________
______________________________________________________________________________
12. Write a sentence with a value greater than 25. ________________________________
______________________________________________________________________________
13. Compare your sentence with the sentence of a partner.
Who has the sentence with the greatest value? ________________________________
14. Does the sentence with the most words have the greatest sum? ________________
Explain. ______________________________________________________________________
-5

2
3
4
5
a, e, i, o, u
b, g, l, q, v, z
c, h, m, r, w
d, j, n, s, x
f, p, t, y
example:
t + o + t + a + l = ?
5 + -5 + 5 + -5 + 2 = 2
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Brainteasers
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Name _____________________________________
Fact Triangles
problem solving and logic
Each letter in the addition/subtraction fact triangles represents a number 1–10. The
letter R equals 3. Find the value of each of the other letters. *Hint: The value of the
letter at the top of each triangle equals the sum of the other two addends.
S =
T =
W =
X =
Z =
A =
B =
C =
D =

R = 3
1.
*D
4.
*D
Z R
+/–
3.
*C
R T
+/–
2.
*A
W R
+/–
X C
+/–
5.
*B
8.
*R
W T
+/–
7.
*S
Z W
+/–
6.
*S
A C

+/–
T Z
+/–
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Brainteasers
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Name _____________________________________
Solve. Each letter stands for a digit. Substitute each letter with a number to make
each set of equations true.
Set A
M
M
M
M
+ T
TM
Set B
B
x B
JS
Set C
G
x G
ZK
Set D
U
x P
CP
Find the Numbers
basic operations and problem solving

T
x R
M
M
x M
RM
M =
R =
T =

J
+ S
B
B
+ B
SJ
B =
J =
S =
G
– K
K

Z + K + Z = G + G
G =
K =
Z =
C
x U
U

P – U = C + C
P
P
P
P
P
P
+ P
UP
C =
P =
U =
© Carson-Dellosa 18 CD-104006
Brainteasers
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Name _____________________________________
Hidden Numbers
basic operations and problem solving
Each puzzle contains multiple ways to make a given answer. Any squares that touch
can work together. Each number in the puzzle grid must be used at least once.
1. At least 10 threes can be found in this puzzle. Write 10 equations.
8 2 2 2
4 1 6 9
10 7 2 5
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________

_______________________
_______________________
_______________________
_______________________
2 4 11 8
1 6 3 2
7 2 10 1
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
6 2 3 1
2 7 5 4
1 8 3 9
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________

2. This puzzle contains at least 10 ves. Write 10 equations.
3. At least 10 tens can be found in this puzzle. Write 10 equations.
Compare your answers
with those of a partner.
Star those only you found.
( 8 ÷ 2 + 2 ) ÷ 2 = 3
© Carson-Dellosa 19 CD-104006
Brainteasers
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Name _____________________________________
Working with Digits
The following sets of digits have been used to write multiplication problems. Read the
clues and use the digits to solve them. Write the problems.
multiplication and problem solving
1 2 3 4
1. Ian used these digits to make
a 1-digit x 3-digit problem.
The answer to his problem is 1,236.
2. Brandon used these digits to
make a 1-digit x 3-digit problem
with a product of 924.
3. Madalen used the digits to
make a 2-digit x 2-digit problem
with a product of 714.
4. Judy took 1 digit out and used
the other 3 digits to make
a 1-digit x 2-digit problem
with a product of 124.
4 5 6 7
5. Paolo used the digits to make a

1-digit x 3-digit problem with a
product of 3,282.
6. Ruth used the digits to make a
2-digit x 2-digit number. The
answer to her problem is 3,450.
7. Ernest used the digits to make a
2-digit x 2-digit number. The
answer to his problem is 3,618.
8. Zoe used 1 digit twice. She made
a 1-digit x 4-digit problem with a
product of 33,292.
Choose a different set of digits. Write your own clues for someone else to solve.
© Carson-Dellosa 20 CD-104006
Brainteasers
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Name _____________________________________
Whose Answer?
multiplication, division, and matrix logic
Solve. Write each answer above a column in the matrix. Arrange the answers from
smallest to largest. Then use the clues and the matrix to identify the problem each
student wrote.
• Jade’s answer starts with an even digit.
• The answer to Luis’s problem is even.
• The sum of the digits in Will’s answer is 15.
• Eloy has a 4-digit answer.
• Gabe’s even answer has 3-odd digits.
• Jade’s answer has fewer digits than Will’s answer.
Eloy’s answer is
_________________________.
Gabe’s answer is ________________________ .

Jade’s answer is
________________________ .
Luis’s answer is
__________________________.
Sara’s answer is
_________________________.
Will’s answer is
__________________________.
572
x 30
341
x 21
6 61,386
3 63,948
20 72,480
643
x 7
Eloy
Gabe
Jade
Luis
Sara
Will
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Name _____________________________________
Place Value Riddles
place value and logic
Read each riddle. Write 4 possible answers on the lines.

1. I am a 4-digit number that is a multiple of 2. Take half of me and you get
a multiple of 3.
number: ___________ half is: ___________ number: ___________ half is: ___________
2. I am a 4-digit number whose digits add to 17. Each digit from left to right
is larger than the previous digit.
_____________ _____________ _____________ _____________
3. I am a 6-digit number with all odd digits. No more than 2 digits can be
the same. I am not a multiple of 3 or 5.
_____________ _____________ _____________ _____________
4. I am a 6-digit number. I am a multiple of 2, 3, and 5.
_____________ _____________ _____________ _____________
5. I am a 5-digit even number. Two digits are the same. The other 3 digits
are different from each other and larger than the 2 like digits.
_____________ _____________ _____________ _____________
6. I am a 4-digit odd number whose tens and hundreds digits are even.
The sum of my digits is 16.
_____________ _____________ _____________ _____________
Compare your numbers with those
of a partner. Check for accuracy.
Put a check mark next to each answer
that matches. Star those that only you
have. Make a group list of possible
answers for each riddle.
Write your own place value riddle on
another sheet of paper. Provide 4 possible
answers on the back. Share your riddles
with a partner.
I am
a . . .
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Brainteasers
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Name _____________________________________
Missing Steps
addition, problem solving, and logic
Add your way to the top. Add adjacent numbers and write the sum in the box above
them. Use the numbers given to ll in the rst row of steps.
84
A. 2, 4, 5, 6, 9
B. 1, 2, 3, 7, 8
88
C. 2, 4, 6, 8, 9
110 64
D. 1, 3, 5, 6, 7
© Carson-Dellosa 23 CD-104006
Brainteasers
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Name _____________________________________
More Missing Steps
A. 2, 2, 3, 3, 4, 5
110
B. 1, 2, 5, 7, 8, 9
157
Write your own. Check your answers.
Copy the nal sum on the top step of
the right pyramid. Leave the other boxes
blank. Write the numbers for the rst row
of steps, in order from least to greatest,
on the lines. Trade with a partner. _______
_______

_______
_______
_______
addition, problem solving, and logic
Add your way to the top.
Add adjacent numbers
and write the sum in the
box above them. Use the
numbers given to ll in the
rst row of steps.
Add your way to the top. Use the
numbers given to ll in the rst row.
When nished, unfold the paper and
check your work.
fold