4th Grade SLIP Problems
1 After
Another
A Certain Set
A Money
Matter
A Prime
Example
A Purse Full of
Coin
Combinations
A Terminal
Case of Zeros
In the following sequence of numbers, each
number has one more 1 than the preceding
number: 1, 11, 111, 1111, 11111, … What is the
tens digit of the sum of the first 30 numbers of
the sequence?
In a set of natural numbers, all have different
values. Their sum is 350. Their average is 50.
One of the numbers is 100. What is the largest
number that can be in the set?
I spent 2/3 of my money is store A. I then
spent 1/3 of what remained in store B. When I
left store B, I had $4. How much money did I
have when I entered store A?
A prime number is a whole number, greater than
1, that is divisible only by itself and 1. Some
examples of prime numbers are 2, 3, 5, 7, 11 and
13. What is the largest prime number, P, such
that 9 times P is less than 400?
A purse contains 4 pennies, 2 nickels, 1 dime, and
1 quarter. Different values (amounts of money)
can be obtained by using one or more coins in the
purse. How many different values can be
obtained?
If a number ends in zeros, the zeros are called
terminal zeros. For example, 520,000 has four
terminal zeros, but 502,000 has just three
terminal zeros. Let N equal the product of a
natural numbers from 1 to 20:
N = 1 x 2 x 3 x 4 x … x 20.
How many terminal zeros will the product N
have?
4th Grade SLIP Problems
Add „Em Up
What is the largest possible sum that can result
from
BAD + MAD + DAM
If different letters represent different digits,
chosen from 1, 3, 8 and 9.
Alternating
Each of eight traffic lights on Main Street
Lights
shows green for 2 minutes, then switch to other
colors. The traffic lights turn green 10 seconds
apart, from the first light to the eighth light.
From the time that the first light turns green
until it switches to another color, for how many
seconds will all eight lights show green at the
same time?
Amy‟s Lost Coin Amy had a nickel, a dime, a quarter, a half-dollar,
and a silver dollar. After she lost one coin, she
had exactly seven times as much money as her
bother had. Which coin did she lose?
An Average
A motorist made a 60-mile trip averaging 20
Round Trip
miles per hour. On the return trip, he averaged
30 miles per hour. What was the motorist‟s
average speed for the entire trip?
An Odd
If the pattern shown is continued, what is the
Pattern
sum of the terms in row 12?
Row 1…1
Row 2…1 + 3
Row 3…1 + 3 + 5
Row 4…1 + 3 + 5 + 7
Row 5…1 + 3 + 5 + 7 + 9
Binding Books
In any one complete day, a man can bid 100 books
and his helper can bind one-quarter as many
books. If they take turns working complete
days, how many days would it take them to bind
500 books?
4th Grade SLIP Problems
Bowling
In three bowling games, Alice scores 139, 143,
and 144. What score will Alice need in a fourth
game to have an average score of 145 for all four
games?
Can You “C” the If the digits A, B and C are added, the sum is
Answer?
the two-digit number AB as shown. What is the
A
value of C?
B
+C
AB
Can You Figure In the figure, each number represents the
Out This
length of the segment which is nearest it. How
Figure‟s Area? many square units are in the area of the figure if
there is a right angle at each corner of the
figure?
Combined
Paul has half as many pieces of candy as
Pieces of Candy Jennifer. Jennifer has half as many as Charles.
Charles as 12 times as many as Susan. Susan has
4 pieces. How many pieces do Charles and Paul
have altogether?
Count the Code Using the letters A and B, the following twoletter code words can be formed: AA, AB, BB,
and BA. Using the letters A, B, and C, how many
different three-letter code words can be
formed?
Counting 2s
Suppose Sandy writes every whole number from
1 to 100 properly and without skipping any
numbers. How many times will Sandy write the
digit “2”?
4th Grade SLIP Problems
Counting Seats
Counting
Square
Numbers
Counting
Triangles
Differing
Differences
Digit Fidget
Divisible by 6
or 9
Do You Know
Your ABC‟s?
6, B 5 2
9C4
+A,3 7 D
1 1, 1 1 1
One seat in an auditorium is broken. It is in the
3rd row from the front of the auditorium and in
the 18th row from the back of the auditorium.
There are 12 seats to its left and 17 seats to its
right. If every row has the same number of
seats, what is the total number of seats in that
auditorium?
When a natural number is multiplied by itself,
the result is a square number. Since 1 X 1 = 1,
2 X 2 = 4, 3 X 3 = 9, 4 X 4 = 16. 1, 4, 9, 16 … are
square numbers. How many natural numbers less
than 500 are square numbers?
If every vertex of a regular pentagon is
connected to every other vertex, how many
triangles are formed?
Each of AB and BA represent a two-digit number
having the same digits, but in reverse order. If
the difference of the two numbers is 54 and
A + B = 10, find both number, AB and BA.
How many two-digit numbers are there in which
the tens digit is greater then the ones digit?
How many different natural numbers less than
200 are exactly divisible by wither 6 or 9 or by
both?
In this addition problem, different letters
represent different digits. What digits do A, B,
C and D represent?
4th Grade SLIP Problems
Equal Areas,
Different
Lengths
Exclusive Area
Figure It Out!
Find A and B
Find the
Largest Area
Find the Lost
Value
Mary‟s rectangular garden and Kevin‟s
rectangular garden each have the same area, 36
square meters. Each side is measured in whole
meters. Mary‟s garden is 1 m wider than Kevin‟s
garden, but Kevin‟s garden is 3 m longer than
Mary‟s garden. How wide is Mary‟s garden, in
meters?
The length of each segment in the overlapping
rectangles, as shown, is given in cm. Find the
sum of the areas of the shaded regions, in sq.
cm.
Compute: 26(64) – 24(64)
In the multiplication example shown, different
letters represent different digits. Find the
values of A and B.
A8
X3B
____
2730
The perimeter of a rectangle is 26 units. Each
of the length and width of the rectangle is
measured in natural numbers. What is the
largest area in square units that the rectangle
could have?
The average of five numbers is 6. If one of the
five numbers is removed, the average of the
four remaining numbers is 7. What is the value
of the number that was removed?
4th Grade SLIP Problems
Find the
Perimeter
The figure shown consists of 6 congruent
squares. The area of the figure is 96 sq. cm.
What is the perimeter of the figure, in cm?
Fire Fighting
on a Ladder
A firefighter stood on the middle rung of a
ladder, went up 3 rungs, was forced down 5
rungs, and then went up 7 rungs to extinguish
the fire. Then the firefighter climbed the
remaining 6 rungs to the top of the ladder. How
many rungs are there on the entire ladder?
A clock is set correctly at 1:00 PM. If it loses 3
minutes every hour, what will the clock show
when the correct time is 10:00 AM the next
day?
Exactly 10 disks are in a bowl. Each is marked
with a different natural number selected from 1
through 10. Gina and Monique each select 5
disks. Two of Gina‟s disks are marked 2 and 8.
Two of Monique‟s disks are marked 7 and 9.
What is the largest sum that Gina‟s disks can
have?
A group of 21 people went to the county fair
with 9 people on a stagecoach and 3 people in
each buggy. On the return trip, 4 people rode in
each buggy. How many people returned on the
stagecoach?
Fix That Clock!
Gina‟s Disks
Goin‟ to the
Fair
4th Grade SLIP Problems
How About the
Kids?
Increasing
Inaccuracy
Largest
Possible
Product
Marked
Measuring
Stick
Maximize the
Area
Missing Links
Some parents and children added up all of their
ages and got 100. Then they decided to average
their ages, and they got 20. Three of them, the
parents, were 25, 30 and 35 years old, and no
one in the group was the same age. List all the
sets of possible ages of the children in the
group.
A” fast” clock gains time at the same rate every
hour. It is set to the correct time at 10 AM.
When the fast clock shows 3:30 PM that day,
what is the correct time?
Each of PQ and RS represent a 2-digit number.
Different letters represent different digits,
chosen from 6, 7, 8 and 9. What is the largest
product that PQ x RS can have?
On a 100 cm measuring stick, marks are made a
19, N, and 99 cm, from left to right. The
distance between the marks at N and 99 cm is
three times the distance between the marks at
N and 19 cm. What is number N?
A single story house is to be built on a
rectangular lot 70 feet wide by 100 feet deep.
The shorter side of the lot is along the street.
The house must be set back 30 feet from the
street. It also must be 20 feet from the back
lot line and 10 feet from each side lot line.
What is the largest are that the house can have,
in sq. ft?
Find the missing value of
1 + 5 + 9 + … + 41.
4th Grade SLIP Problems
Money
Exchange
Kelly made two purchases. She gave one cashier
$20 for a compact disc and received $6 change.
Then she gave another cashier $15 for a
bracelet and received $4 change. After these
purchases she had $28. How many dollars did
she have before buying the compact disc and
bracelet?
Multiple
Consider all pairs of natural numbers whose sum
Products
is less than 11. The two members of a pair could
be either the same as each other or different.
How many different products are possible if the
two numbers are multiplied?
Name This
In a four-digit number, the sum of the thousands
Number
and hundreds digit is 3. The tens digit is 4 times
the hundreds digit. The ones digit is seven more
than the thousands digit. No two digits are
equal. What is the four-digit number?
Natalie‟s Radio The number of two-dollar bills Natalie needs to
pay for a clock-radio is 9 more that the number
of five-dollar bills she needs to pay for the same
radio. How much does the radio cost?
Naturally, They The sum of two natural numbers is less than 7.
Are Counting
The two numbers can be either the same as each
Numbers!
other or different. How many different
products are possible if the two numbers are
multiplied?
(HINT (if you want one): This is a two-part
problem, isn‟t it? First, make an organized list or
table of all the possible pairs of numbers that
will work. How many different pairs are there?
Then, find the products for each of the pairs.
How many different products are there? That is
your answer!)
4th Grade SLIP Problems
Newton and His On his birthday, Newton was 14 years old and his
Dad
father was 41. Newton noticed that his age was
his father‟s age with the digits reversed. How
many years later will their ages next have their
digits reversed?
On the Road?
Joseph‟s car can travel 1 mile in 1 minute 12
seconds. How many miles will his car travel in 1
hour at the given rate?
Pattern Hunt
All counting numbers are arranged in the
triangular pattern as shown by the first four
rows. What is the first number in the 13th row?
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
…and so on.
Perplexing
How many different natural numbers between 10
Natural
and 200 have the sum of their digits equal to 6,
Numbers
if zero is not a digit of any of the numbers?
Pith Possum‟s
The weather during Pith Possum‟s vacation was
Vacation
strange. It rained on 15 different days, but it
never rained for a whole day. Rainy mornings
were followed by clear afternoons. Rainy
afternoons were preceded by clear mornings.
There were 12 clear mornings and 13 clear
afternoons in all. How long was the vacation?
Placement and A 14-digit number N is created by writing 8 as
Division
both the first and last digits and then placing
the 3-digit number 793 between the two 8s four
times. What is the remainder when N is divided
by 7?
4th Grade SLIP Problems
Playing with
Plastic
The 14 digits of a credit card number are
written in the boxes. If the sum of any three
consecutive digits is 20, find the value of A.
Price the
Widget
For every two widgets I buy at the regular price,
I can buy a third widget for $4. I bought nine
widgets for a total of $90. Find, in dollars, the
regular price of a widget.
A cube has 6 faces: top, bottom and all four
sides. The object shown is made of six
congruent cubes. Not all faces are visible. All
outer faces of the object including the bottom
are painted blue. How many faces of the cubes
are painted blue?
Find the smallest natural which when divided by
6 gives a remainder of 1, and when divided by 11
give a remainder of 6.
The first fifteen multiples of 6 are: 6, 12, 18,
24… 84, 90. What is the sum of these multiples?
Most pizzas are cut through the center like this.
Notice that 5 cuts are shown, resulting in 10
pieces. Bill claims that he can get more pieces
by still using only 5 cuts. If each cut must be a
straight line and must go from edge to edge,
what is the maximum number of pieces possible
with 5 cuts? Show how you would cut the pizza
to get that many.
Mark has 42 identical cubes, each with 1-cm
edges. He glues them together to form a
rectangular solid. If the perimeter of the base
is 18 cm, find the height of the rectangular solid
centimeters.
Sea of Faces
See What
Remains
Sequence of
Sixes
Slice the Pizza
Solid
Construction
4th Grade SLIP Problems
Stringy
Multiplication
Summing Up
Evens and
Odds
The Baseball
League
The Bottom of
the Box
The Clock‟s
Face
The Dart
Throw
The Folded
Square
3 x 3, 3 x 3 x 3, and 3 x 3 x 3 x 3 are
“multiplying strings” of two 3‟s, three 3‟s and
four 3‟s respectively. When each string
multiplication is done, 3 x 3 ends in a 9,
3 x 3 x 3 ends in a 7, and 3 x 3 x 3 x 3 ends in a
1. In what digit will a multiplication string of
thirty-five 3‟s end?
D is the sum of the odd numbers from 1 through
99 inclusive, and N is the sum of the even
numbers from 2 through 98 inclusive.
D = 1 + 3 + 5 + … + 99 and
N = 2 + 4 + 6 + … + 98.
Which is greater, D or N, and by how much?
A baseball league had nine teams. During the
season, each of the nine teams plays exactly
three games with each of the other teams.
What is the total number of games played?
It takes 125 identical wooden cubes to fill a
cubical box. How many of these cubes does it
take to cover the bottom of the box?
Divide the face of the clock into three parts
with two lines so that the sum of the numbers in
the three parts are equal. (a standard clock with
numbers 1 – 12; not a digital clock)
Roberta throws five darts at the target shown.
Each dart lands in a region of the target, scoring
the points shown. Of the following total scores,
list all that are NOT possible:
6, 14, 17, 38, 42, 58
A square piece of paper is folded in half to form
a rectangle. This rectangle has a perimeter of
4th Grade SLIP Problems
The Four-Digit
Numeral
Mystery
The Grocer‟s
Profit
The Husband‟s
Age Puzzle
The Ice Cream
Stand
24 cm. Find the area of the original square, in
sq. cm.
The four-digit numeral 3AA1 is divisible by 9.
What digit does A represent?
A grocer bought 15 dozen oranges at $1.00 a
dozen. She threw away 20 rotten oranges, and
then sold the rest at 8 oranges for 85 cents.
How much profit did the grocer make, in dollars
and cents?
The age of a man is the same age as his wife‟s
age with the digits reversed. The sum of their
ages is 99 and the man is 9 years older than his
wife. How old is the man?
An ice cream stand has nine different flavors. A
group of children come to the stand and each
buys a double scoop cone with two flavors of ice
cream. If none of the children choose the same
combination of flavors, but all possible
combinations of flavors are used, how many
children are there?
FLAVORS:
1. Vanilla
2. Maple
3. Chocolate
4. Tiger
5. Raspberry
6. Strawberry
7. Coffee
8. Moon Mist
9. Cherry Vanilla
4th Grade SLIP Problems
The Ping Pong
Tournament
The
Rectangular
Parts
The Twins,
Some Candy
and Some
Cents
Thelma and
Doug‟s Bicycle
Thinking
Outside the
Box(es)
Nine people signed up for the ping pong
tournament. Each of the nine people played one
game with each of the other people. What is the
total number of games played?
A square has an area of 144 square inches.
Suppose the square is partitioned into six
congruent rectangles as shown. How many inches
are there in the perimeter of one of the six
rectangles?
Twins Joanie and Tony each start with the same
number of cents. Joanie buys 1 candy bar and
has 70 cents left. Tony buys 3 candy bars at the
same price and has 20 cents left. How many
cents did Joanie start with?
Thelma wants to purchase a bicycle but is $23
short. Doug wants to purchase the same bicycle
but is $25 short. They decide to combine their
money, and they discover that they will have
exactly enough money to buy the bicycle! How
much does the bicycle cost?
Each of the small boxes in the figure is a square
and the area of the figure is 52 square units.
How many units are there in the outer perimeter
of the figure?
4th Grade SLIP Problems
This Is So Odd Consider the set of consecutive odd numbers, {1,
3, 5, 7, 9 …}. 1 is the first odd number, 3 is the
second odd number, and 5 is the third odd
number, and so on.
a. What is the 40th odd number?
b. What is the 100th odd number?
c. What is the 501st odd number?
This One‟s Plum Thirteen plums weigh as much as two apples and
Crazy
one pear. Four plums and one apple have the
same weight as one pear. How many plums have
the weight of one pear?
Top Forty
A and B are two different numbers selected
from the first forty counting numbers, 1 through
40 inclusive. What is the largest value that
A X B can have?
A-B
Tower Power
The tower shown below is made of horizontal
layers of unit cubes. Not all of the cubes are
visible in the diagram. How many unit cubes are
contained in the tower?
Two Tired
Watch the
Ones
Each wheel on Thomas‟s bicycle has a radius of
14 inches. Thomas rode his bike 22 yards. How
many times did each wheel turn?
(5273)² means 5273 x 5273; (5273)³means
5273 x 5273 x 5273; and so forth. Suppose
(5273) is completely multiplied out. What ill the
units (or ones) digit be in the resulting product?
4th Grade SLIP Problems
Wave as We Go Boston is 295 miles from New York City along a
By!
certain route. A car starts from Boston at 1:00
PM and travels along this route toward New York
at a steady rate of 50 mph. Another car starts
from New York at 1:30 PM and travels along this
route toward Boston at a steady rate of 40 mph.
At what time do the cars pass?
What Can‟t Be Assume that a post office issues only 3¢ and 8¢
Done?
stamps and all postage is in whole numbers of
cents. What is the largest amount of postage in
cents which CANNOT be make using only 3¢ and
8¢ stamps?