Math Puzzles and Brainteasers, Grades 3-5
Over 300 Puzzles that Teach Math and Problem-Solving Skills
By Terry Stickels
John Wiley & Sons
Copyright © 2009
John Wiley & Sons, Ltd.
All right reserved.
ISBN: 978-0-470-22719-0
Chapter One
Part I
NUMBERS
and
OPERATIONS
Whole Numbers
1. What is the next number in the sequence below?
1 4 9 16 25 36 ?
2. Place the numbers 1-12 in the twelve circles below so the sum of
each side of the triangle is 36. I will give you a head start by placing
some of the numbers for you. (The numbers may be used once only.)
[ILLUSTRATION OMITTED]
3. My brother has a summer job and earns $5 an hour. He is going to
work 5 hours a day for 5 days a week, and will do this for 5 total
weeks.
a. How much money will he make in 1 week?
b. What is the total amount of money that he will earn?
4. Brenda bought a new catcher's mitt for $75. Her mom saw another
mitt that was a better quality glove and cost less, so she bought it
for $60. Brenda sold her first mitt for $65. A week later, Brenda's
mom accidentally threw her new glove in the trash. Brenda found
her first mitt for sale a month later for $50. She bought it back.
How much money did Brenda and her mom end up losing on these
transactions?
5. Two shapes are each given a value. Each value is a whole number.
This whole number is at least 0 and at the most 10.
[ILLUSTRATION OMITTED]
Write the value for the following shape.
[ILLUSTRATION OMITTED]
Once you know the value, do the following exercises by replacing the
shape with its value.
[ILLUSTRATION OMITTED]
6. Mrs. Johnson was going to purchase an iPod on sale for $250. At
the checkout counter she received an additional 10% discount. How
much did Mrs. Johnson pay for the iPod after the discount?
7. In the addition problem below, the digits B and C represent a
number different from any of the other numbers shown (that is,
not 1, 4, 5, 6, or 9).
B5
+C9
______
164
What are the only two possible values for B and C?
8. What is the missing number in the pie below?
[ILLUSTRATION OMITTED]
9. The grid below has a certain pattern to it that holds true for each
row. Can you determine that pattern and find the missing number?
[ILLUSTRATION OMITTED]
10. Can you determine the missing number in the box? The same rule of
logic applies to all three boxes.
[ILLUSTRATION OMITTED]
11. The three numbers in each box have a relationship that is the same
in all six boxes. Knowing this, can you find the missing number
where the question mark is? What is the relationship?
[ILLUSTRATION OMITTED]
12. In the addition problem below, the letters AB represent a two-digit
number. If you know that the letter B is not a zero (0), can you tell
me which numbers represent A and B?
AB
AB
+AB
_____
19B
13. Below is a fun puzzle called an alphametic. Each letter stands for a
different digit. Zero (0) is sometimes used for alphametics, but it
can never start a word. You may use any of the digits 0-9.
TWO
+TWO
______
FOUR
This puzzle has only one solution if we let the letter W 5 2 and
R = 6. Can you find the other numbers that fit the addition
problem?
Just for Fun:
Frame Game
14. Find the hidden phrase or title.
FRAME
K
C
YEARLY
H
C
GAMES
15. Analogy puzzles ask you to think about the relationships between two
things. The symbol : : means "is the same as" or "is analogous to."
Example: 5 : 25 : : 6 : ? would be read as "5 is to 25 as 6 is to what?"
The answer is 36 because 5 times itself is 25 and 6 times itself is 36.
Use the example above to answer these analogy puzzles.
a. 4 : 16 : : 10 : ?
Choose from: 12 32 25 100
b. Triangle : Hexagon : : Rectangle : ?
Choose from: Square Pentagon Line Octagon
16. By looking at the first three circles, can
you see a pattern or relationship that is
the same in all four circles? This pattern or
relationship will help you determine the
missing number in the last circle. What is
that number?
[ILLUSTRATION OMITTED]
17. Roman numerals are written as combinations of the seven letters
below. They usually are written as capital letters because they are
easier and less confusing to read.
Roman Numerals
I = 1 C = 100
V = 5 D = 500
X = 10 M = 1,000
L = 50
If smaller numbers follow larger numbers, the numbers are
added. If a smaller number precedes a larger number, the smaller
number is subtracted from the larger number. For example:
VIII = 5 + 3 = 8
IX = 10 - 1 = 9
XL5 50 2 10 5 40
XC = 100 - 10 - 90
MCMLXXXIV = 1,000 + (1,000 - 100) + 50 + 30 + (5 - 1) = 1,984
Change the following from Arabic to Roman and from Roman to
Arabic numerals:
a. 59 = ? e. LXIX = ?
b. 88 = ? f. MCD = ?
c. 449 = ? g. 2,919 = ?
d. MXLVII = ? h. CMXCIX = ?
18. Joan's sister scored 17 points in her school's basketball game. She
had an even number of 2-point shots and an odd number of 3-point
shots for her points. She attempted no freethrows. How many baskets
of each type did Joan's sister make?
19. You can have lots of fun creating your own puzzles. Here's an
example to get you started:
Write the numbers 1 through 9 in a straight line.
1 2 3 4 5 6 7 8 9
Now, depending upon what your goal is, you can insert the basic
math operation symbols between the numbers and arrive at
different totals.
1 + 2 + 3 + 4 - 5 + 6 + 7 - 8 + 9 = 19
12 - 3 + 45 - 67 + 89 = 76
123 + 45 - 67 + 8 - 9 = 100
Now try to get the answer 100 in different ways. Then try to
create some problems of your own. (Don't forget-you can use
multiplication and division, too.)
20. Which of the values below is the same as 7?
a. (6 x 5) ÷ 2
b. (3 + 14) ÷ 5
c. (10 - 4) + 1/1
d. (12 - 25) + 2
21. Below is a pyramid of numbers where the number on each brick is
the sum of two bricks below it. The numbers given will help you fill
in the entire pyramid.
[ILLUSTRATION OMITTED]
22. Use the clues to find these mystery numbers that include decimals.
"My hundredths number is one half my tenths number. My ones
digit number is twice my tenths number. There is no number 1 in
any of the three places."
What number am I?
--.-- --
23. In the addition problem below, A, B, C, and D each stand for a
different one-digit number.
None of the letters represents zero.
A
+B
___
DC
If C is 5 and A is 7, then B is ?.
24. The numbers 1 through 6 are placed in the triangle below so that each
of the three sides totals 12. Using the same numbers, can they be placed
around the triangle so that each side totals 9?
[ILLUSTRATION OMITTED]
25. Solve the puzzle by putting back the parts that are missing. Equations
are formed horizontally from left to right and vertically from top to
bottom. Use both numbers and math operations (1, 2, and 5 signs).
[ILLUSTRATION OMITTED]
26. On one of my math travel excursions, I ended up in the far-off land
of Footfree. The entire country of Footfree liked shoes, and all the
residents had some of the neatest and strangest shoes I've ever seen.
Everything they did had to do with shoes. Even their schools were
built like army boots. All the problems in their math books used
shoes as examples-like this problem.
Three fourth-graders had shoes sizes of 6 1/3, 8 1/2, and
5 2/3 (yes, they had all kinds of fractional sizes).
Three fifth-graders had shoe sizes that added up to the same total as
the sum of the fourth-graders' shoes.
Two of the fifth-graders' sizes were 7 1/4 and 6 1/2. What size
was the third fifth-grader's shoe?
27. Also, in Footfree, the residents liked to combine adding and
multiplication. They had a math operation called a "shoebox" that
looked like this:
5 [|??] 3 -> 23
The shoebox between the 5 and the 3 meant that you had to add 5 + 3,
then multiply 5 x 3, and then add those two sums together:
5 + 3 = 8
5 + 3 = 15
__________
23
What does this shoebox puzzle equal?
4 [??] 2 + 3 [??] 6 = ?
28. Before I left Footfree, the kids in all the math classes had "Footfree
Puzzle Day" and asked me to be their guest. It was great fun with lots
of food. Here is the puzzle they gave me to remember my time in
their wonderful school:
Tennis shoes -> $4.00 (Footfree dollars)
Snow boots -> $3.00
Slippers -> $2.00
Flip-flops -> $2.00
All of the above prices are based on a simple math concept. Based
on these prices, what would a pair of loafers cost?
a. $1.00
b. $3.00
c. $4.00
d. $8.00
29. Here's a fun puzzle game called Circle Squeeze. Each circle has two
numbers. For each pair of circles, the sum of their two numbers is the
same, like this:
[ILLUSTRATION OMITTED]
But the circles are like magnets. They crash into each other, and one
number from each circle is added to one number from the other circle.
[ILLUSTRATION OMITTED]
You can see here that the 3 from the circle on the left has been added
to the 6 from the second circle to form the sum of 9. Now here's the
puzzle:
[ILLUSTRATION OMITTED]
What are the two numbers that go back into circle #1 and circle #2?
In other words, what did these two circles look like before they were
"squeezed" into each other? Is there an easy way to solve this?
30. What if there are three circles? What did these three circles look like
before they were squeezed into each other?
[ILLUSTRATION OMITTED]
31. The boxes on the left fit together in such a way that their numbers
help to build the box on the right. See if you can determine how the
numbers in the two rows on the left make the numbers on the right,
then fill in the missing numbers.
[ILLUSTRATION OMITTED]
32. My friend Billy needs some help. His math teacher told him to take a
look at the addition problem below.
16
+69
____
85
The teacher then asked him what are the fewest number of single
digits that would have to be changed for the sum to be 160 instead
of 85. Can you help Billy? Here are the choices:
a. 1 digit-the 1
b. 2 digits-the 1 and the 6 in "69"
c. 3 digits-the 9 and the 1 and 6 in "16"
d. 2 digits-the 1 and the 9
33. The numbers in the corners of the boxes below fit together in such a
way that they determine the number in the middle of each box. The
rule for finding that middle number is the same in each box.
[ILLUSTRATION OMITTED]
Once you find that rule, see if you can put the correct number
in this box:
[ILLUSTRATION OMITTED]
34. What number or numbers comes next in this series?
1 22 333 4444 55555 666666 ?
35. Here's a fun puzzle game called FTN (Find This Number). It works
like this:
I'll give you some instruction, and you put the clues together and
write down the answer. Here's an example:
7 < this="" number="" />< 12.="" this="" number="" is="" often="" used="" when="" speaking="" about="" cats.="" ftn!="" />
Answer: The number is 9. Because 9 is more than 7 and less than 12,
and cats are said to have 9 lives. Now try these:
a. 3 < this="" number="" />< 7.="" this="" number="" is="" between="" two="" other="" numbers="" that="" total="" 10.="" ftn!="" />
b. 15 > this number > 9 and exactly in the middle of the two numbers
mentioned here. FTN!
c. This number is (5 x 2) 1 3 + 7 - 6. Take that result and divide by
7 and multiply by 3. FTN!
36. In this puzzle, each of the letters has a whole-number value from 1
to 9. (No two letters can share the same value.) Your job is to find the
value of the letters so the sum at the end of each row and column
comes out correctly. To get you started: A = 3.
[ILLUSTRATION OMITTED]
37. In this arithmetic puzzle you have to fill in the question marks in the
equations with numbers or one of the three operation symbols:
+, -, x. (This puzzle has no division.)
[ILLUSTRATION OMITTED]
38. Can you place the numbers 1, 4, 5, 6, 7, and 0 in the boxes below?
Each number can be used once and only once. There is more than
one correct answer.
[ILLUSTRATION OMITTED]
39. The numbers 1-9 can be placed in the nine circles below in such
a way that both sets of crossed circles can add up to 26. From the
numbers already given, where would the number 1 go? It can be
placed in either one of two circles.
[ILLUSTRATION OMITTED]
40. In a group of 28 junior high school students, 7 take French, 10 take
Spanish, and 4 take both languages. The students taking both
French and Spanish are not counted with the 7 taking French or
the 10 taking Spanish. How many students are not taking either
French or Spanish?
41. A fruit dealer packages pears in two different box sizes. One size
holds 5 pears and the other size holds 12 pears. The dealer sold 68
pears in one of the stores in one hour. He said to his assistant, "You
don't see that very often. We sold the same number of boxes of each
type of packaging." How many boxes of each size did they sell in one
hour?
Just for Fun:
Frame Game
42. Find the hidden phrase or title.
[ILLUSTRATION OMITTED]
43. Suppose all numbers from 1 to 1,000 are arranged in columns like
they are below.
A B C D E F G
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 - - - -
- - - - - - -
- - - - - - -
Under what letter will 50 appear? What about 100?
44. A person was born on May 14, 40 b.c. and died on May 14, 30 a.d.
How many years did this person live?
45. Below is a fun type of puzzle called a Number Scramble or an
Equation Scramble. The numbers and operations are scrambled, so
you'll have to move things around so the equation will make
sense. You must use all the parts in the boxes on the left-hand side
of the equation to arrive at the solution on the right-hand side of the
equation.
Here is an example:
[3] [5] [x] [7] [1] [()] [=] [56]
One solution is:
(3 + 5) x 7 = 56
Now try these:
a. [6] [4] [()] [+] [2] [x] [=] [32]
b. [x] [4] [+] [5] [()] [5] [1] + [=] [50] [()]
c. [x] [÷] [2] [()] [3] [x] [4] [6] = [4]
d. [1] [+] [+] [2] [3] [÷] [6] [=] [()] [1]
46. Complete the table using the pattern already created by the numbers
you see. Fill in the last three boxes.
[ILLUSTRATION OMITTED]
47. A certain whole number is evenly divisible by 3. It is also divisible by
5 and 4. What is the smallest number that fits these conditions? Can
you find a number larger than 100 that is divisible by 3, 4, and 5?
48. One of the following numbers does not belong with the others in
each of the three puzzles. The other numbers have a similarity the
"odd one out" does not have. Which one does not belong?
(Continues...)
Excerpted from Math Puzzles and Brainteasers, Grades 3-5
by Terry Stickels
Copyright © 2009 by John Wiley & Sons, Ltd..
Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.