Math Problems of the
Day
140 Warm-Ups for 8th Graders
Problem # 1
How many ways can you
represent the number of
dots shown?
Problem # 2
The answer is 7.
What is the
question? (Make it a
good one! :)
Problem # 3
What is the BIGGEST 9-digit number you can make?
What is the SMALLEST 9-digit number you can
make? Put each of your answers in a place value
chart!
Problem # 4
Grown-ups round numbers all
the time in real life. Write down
as many examples as you can
think of when this might happen.
Problem # 5
Joni bought a pad of notebook
paper for $0.50. She bought two
pencils for $0.69 each. She
bought a used backpack for
$3.78. She lives in Oregon,
where there is no sales tax, and
she paid with a $10.00 bill. How
much change should she get
back?
Problem # 6
For lunch, Brady can choose
between two soups (minestrone
or chicken noodle) and three
drinks (water, milk, or chocolate
milk). What are all the possible
combinations he has to choose
from?
Problem # 7
Happy Hollow Elementary had a
canned food drive. 6th graders
donated 462 cans. 5th graders
donated 298 cans. 4th graders
donated 507 cans. About how
many cans did the school raise
altogether?
Problem # 8
Lucy danced for a total of one
hour, practicing jazz, tap, and
ballet. She practiced twice as
long on jazz as she did on ballet.
She practiced tap twice as many
minutes as ballet. For how many
minutes did she practice ballet?
Problem # 9
The table below shows the enrollment of
students at Schmappy Schmallow
Elementary:
Grade Level
Number of Students
Kindergarten
195
First
182
Second
207
Third
173
Fourth
148
Fifth
159
Sixth
196
What is the difference between the LARGEST
class and the SMALLEST one?
Problem # 10
A model kit has 100 pieces. The
kit has long beams, short beams,
and connectors. There are 20
long beams and 30 short beams.
Ann builds a bridge from 62
pieces. How many pieces does
she have left? Write an equation
to represent this problem!
Problem # 11
Patty is, right now, 3 times as
old as her brother Terry. In 10
years, the sum of their ages
will be 36. How old are they
right now?
Problem # 12
In June 2010, a fourth-grade class
planted a tree in the schoolyard.
The tree grew about 3 inches per
year. If the tree was 38 inches
high in June 2015, about how
high was the tree when it was
planted?
Problem # 13
Mrs. Fernandez has to run a few errands
before her TV show comes on at 7:00 pm.
She has to mow the lawn (45 minutes), go
grocery shopping (an hour), stop by the
post office (15 minutes), and walk her
dogs (45 minutes). What is the latest
time that she can leave the school to get
everything done and be ready for her TV
show at 7:00 pm?
Problem # 14
Joe made a frozen yogurt shake
with 10 ounces of milk and some
strawberry frozen yogurt. He used
the mixture to fill three 5-ounce
glasses, and had 2 ounces left over.
How much frozen yogurt did he
use?
Problem # 15
The difference between
two numbers is 3. Their
sum is 47. What are the
numbers?
Problem # 16
What is the thirteenth number in
this series?
1, 1, 2, 3, 5, 8, 13, 21, 34...
Problem # 17
The Boilermaker Special passes by
my house every 6 minutes. The
Lafayette City Bus passes by my
house every 15 minutes. The
trolley passes by my house every 10
minutes. All three passed by my
house at the same time at 6:00 pm.
When is the next time that will
happen?
Problem # 18
I am a number less than 100. Two of
my factors are 3 and 5. My digits are 1
apart. What number am I?
Problem # 19
A birthday present for Mrs. Psarros
costs $24. How much less will each
teacher pay if 4 teachers share the
cost equally than if 3 teachers share
the cost?
Problem # 20
Attendance at the National
Typewriter Show has been
decreasing each year. It was
2,000 in 2011; 1,750 in 2012;
1,500 in 2013; and 1,250 in 2014.
If the drop-off continues at the
same rate, in what year will NO
ONE attend anymore?
Problem # 21
The sum of two numbers is 27. The
difference of the same two numbers is
3. What are the two numbers?
Problem # 22
For Thanksgiving, a family of 9
is trying to share 4 storebought pies fairly. If each pie
is pre-cut into 8 slices, and
everyone gets the same
number of slices, how many
slices will be left over?
Problem # 23
Ashlyn and Brooke went to the
arcade with $12. They bought 4
bottles of water, which cost
$1.50 each. They each bought a
sticker book for $1.25 each.
Ashlyn put $0.50 in a fundraiser
jar. A game of pool cost $3 per
game. Did they have enough
money left to play?
Problem # 24
A single school bus has 15 rows,
with 2 seats in each row. Each seat
holds 3 children, or 2 adults, or 1
adult and 1 child. Four 4th-grade
classes are taking the bus on a field
trip. The classes each have 22
students, 1 teacher, and 2
chaperones. Will they have to take
one bus, or two?
Problem # 25
Students holding a Car
Wash Day washed 12 cars
in the first hour, 15 cars in
the next hour, and 10 cars
in each of the next 4 hours.
They earned $60 in the first
hour, and $50 in the third
hour. How much money did
they earn in all?
Problem # 26
If you triple a number, you
will have one-half the
number of hours in two days.
What is the number?
Problem # 27
At Nose for Clothes, Inez bought a T-shirt for $12.50
and a pair of jeans for $5 more than twice that price.
She paid with a $50 bill. What change should she
get back?
Problem # 28
In 1983 (the year Mrs. Fernandez was
born), the world’s lowest temperature
was recorded in Antarctica. In
degrees Fahrenheit, the thermometer
dropped to 160 degrees below
freezing (true story). What was the
temperature?
Problem # 29
The world’s longest foot race
took place in 1929. It took the
winner 11 weeks, 48 hours to
complete the 3,665-mile New
York-to-Los Angeles event
(true story). How many days
did it take him?
Problem # 30
What is the tenth number in the
series below?
1, 2, 4, 8, 16, 32...
Problem # 31
Which fraction is greater, 3 ¼ or
3 ⅙? PROVE IT with a picture!
Problem # 32
Bryce has 15 coins in his piggy
bank. All are nickels and dimes.
They total $1.35. How many of
each type of coin does he have?
Problem # 33
Charlie went to McDonald’s for a
Happy Meal. He could choose a
cheeseburger, hamburger, or chicken
nuggets as the main course. He could
choose between french fries and
apples as a side, and he could choose
between soda, juice, or chocolate milk
to drink. How many combinations of a
happy meal are possible?
Problem # 34
You want to plant a rectangular
garden that has an area of 12
square feet. To keep pests
away, you want to put up a
fence--but it’s expensive! So you
want to use the least amount of
fencing (ordered by the foot) as
possible. How much fencing will
you need?
Problem # 35
It is 1,518 miles from West Lafayette to Provo, UT
(where Mrs. Fernandez started in college). If I drive in
that direction 692 miles the first day and 674 miles the
second day, how many more miles will I have to drive
the third day until I reach my destination?
Problem # 36
If you double a number, you
will get the same as the
triple of one-fourth of 24.
What is the number?
Problem # 37
A rectangle is 7 inches by 11
inches (7” x 11”). A square has
the same perimeter. What is the
area of that square?
Problem # 38
Mandy had a box of chocolate malted milk balls. She ate 5 and gave her brother 3.
Then she passed around the remaining milk balls to her 8 friends. The first friend
took 1, the second friend took 3, the third friend took 5, and so on, with each team
member taking the next higher odd number of milk balls. There were just enough
milk balls in the box for the last team member to take her correct amount. What
was the original number of milk balls in Mandy’s box?
Problem # 39
Bill buys 4 boxes of candy, each
of which has 8 chocolates inside.
He has 5 sisters. If he is
generous and gives an equal
number of chocolates to each
sister (and the MOST number
each sister could receive), how
many chocolates will Bill have
left over for himself?
Problem # 40
How many seconds are
there in one day?
Problem # 41
Name a time where the two
“hands” of an analog clock
would form a right angle.
(BONUS: How many times
does a right angle form on the
clock face each day?)
Problem # 42
For his reading goal this nine weeks,
Jeonhee wants to read 1,000 pages.
The first week he read 10 pages per
day. The second week he read 15
pages per day. The third week he
read 20 pages per day. How many
more pages does he need to read to
reach his goal?
Problem # 43
After participating in the world’s biggest marble
hunt, you started a marble collection. You have 11
jars, and each jar can hold up to 28 marbles. You
have filled 7 ½ jars so far. How many marbles do
you have?
Problem # 44
The average school day in the U.S.
is 8 hours long, Monday-Friday.
Several small towns have toyed
with the idea of a four-day school
week, though, with extra hours
added on each day to make up the
time. How much longer would an
average school day be in this
case?
Problem # 45
Naomi caught half as
many fish as Jack did.
Together they caught
18 fish. How many fish
did Jack catch?
Problem # 46
Evan and Grant are brothers.
They earned an equal
allowance, and they pooled
their money to buy a
videogame that cost $22.00.
The cashier gave them $8.00
back. How much money did
each boy offer to begin with?
Problem # 47
Which is a better deal per
ounce--a 16-oz bag of
M&Ms that costs $3.20, or a
2-oz bag of M&Ms that costs
$0.50?
Problem # 48
A farmer raises chickens and
pigs. If he has twice as many
chickens as pigs, and there
are 160 feet out of all the
animals combined, how many
pigs does he have?
Problem # 49
Abby, BJ, and Coraline ran a relay
race. They finished the race in one
hour. Abby’s leg took ½ of the
time, and BJ’s leg took ⅓ of the
time. For how many minutes did
Coraline have to run?
Problem # 50
The answer is 0.01.
What is the question?
(Make it a good
one...or two!)
Problem # 51
If there were 25 questions on a
math test, and McKinstry got 22
of them correct, what grade did
she get?
Problem # 52
Michael had a great basketball
game the other day. He scored
35 of his team’s 62 points! If he
made 5 three-pointers and no
single-point foul shots, how
many baskets did he make in
all?
Problem # 53
The math team went out to eat
and ordered 7 eight-slice
pizzas. What fraction of the
total amount of pizza ordered
is left after 40 slices are
eaten? Express your answer
as a fraction in simplest form.
Problem # 54
A medium pizza from Pizza Hut
is cut into 8 slices and costs
$7.99. If there are 13 guests at
your party, and each person
needs at least two slices (it’s
okay to have leftovers), how
much money will you spend on
pizza?
Problem # 55
You’re making cookies for a bake sale, so you want to triple
the recipe you usually use. You estimate that you have about
7 cups of flour left. If the original recipe calls for 2 ¼ c. flour,
will you have enough flour to make the cookies, or will you
have to run to the store to buy more?
Problem # 56
I have some stickers in my collection.
My sister has 29 more than I do.
Together we have 773 stickers. How
many stickers are in my collection?
Problem # 57
One-half of one
number (let’s call it “x”),
added to one-fourth of
96, is 30. What is the
number “x”?
Problem # 58
A square has a perimeter of 28
inches. Another square has a
perimeter of 20 inches. What is
the difference of their areas?
Problem # 59
Jennifer and Pete are going to play Scrabble. The
number of tiles of each letter is in the chart above.
To determine who will go first, they will each
randomly select one letter, without replacement,
from the bag containing all of the letter tiles. The
person who selects a letter closest to A goes first (if
they both draw the same letter they will draw
again). Jennifer draws first and selects an E. What
is the probability that Pete’s selection will result in
Pete going first (without having to redraw)?
Problem # 60
Benson and Jenson are twins
born one minute apart. Benson
celebrated his 3rd birthday
anniversary on February 29,
2016, while Jenson has had 12
birthday anniversaries. What is
the month, day, year and time of
Jenson’s birth?
Problem # 61
Leap day happens every four
years. 2016 was a leap year, as
was 2012, etc. How many days
have you been alive?
Problem # 62
Emma and Uriah are going on a
camping trip. They scooped up
kernels of popcorn to roast over
the fire and put the kernels in
baggies. Emma used a ¼ c.
scoop three times, and Uriah
used a ⅓ c. scoop twice. Who
packed more popcorn kernels?
Problem # 63
Some ants can lift up to 50 times
their body weight. The current
world record (as of 2014) for a
105 kg man for lifting a barbell is
242 kg. If this man was as strong
as the strongest ant (relatively
speaking), by how many
kilograms could he exceed his
current world record?
Problem # 64
How many real-life jobs can you
list (in two minutes) that actually
use math?
Problem # 65
You wanted to earn a little
money, so you made a
lemonade stand over a long
weekend. The first day you sold
17 cups. The second day, you
sold 8 more than that. The third
day, you sold 3 cups less than
the second day. How many
cups did you sell in all?
Problem # 66
A salamander is sneaking
through the forest, trying to
avoid predators--but he does
spot several blue jays and
raccoons. Between the two
species, he counts 16 heads
and 42 legs. How many of
each animal did he see?
Problem # 67
Mrs. Fernandez and six of her
younger siblings have ages
that are consecutive. When
they moved from Battle
Ground to southern Lafayette,
their ages (all seven of them)
added up to 91. How old was
Mrs. Fernandez when they
moved?
Problem # 68
Quadra, a quirky pirate, has
100 gold coins to put into four
different bags. He puts them in
so that each bag has two
more coins than the one
before. How many coins are in
each bag?
Problem # 69
David is buying fish for his
aquarium. Clown fish cost
$12 each and angel fish cost
$7 each. If he has $100 to
spend, and he wants to
spend every dollar, how many
of each fish can he buy?
Problem # 70
Macy, Nawaar, and Orson
ran a relay race in one
hour. Macy took ⅖ of the
time. Nawaar ran ¼ of the
time. For how many
minutes did Orson have to
run?
Problem # 71
Aeryn spent 5 days building a
brick wall that had 100 bricks in
it. She got better each day and
managed to lay 4 more bricks
than the previous. How many
bricks did she lay her first day?
Problem # 72
Gage is training for a mini
marathon (13 miles). He wants
to run on Mondays,
Wednesdays, and Saturdays.
The first day (a Monday) he will
run 1 mile. If he adds a half mile
to his run each time that he
runs, in how many weeks will he
be trained to run 13 miles?
Problem # 73
I have a box of chocolates that is 9 chocolates high
by 5 chocolates wide. If I eat 2 rows of chocolates,
how many chocolates do I have left?
Problem # 74
The answer is 4/8. What
is the question?
Problem # 75
Insert symbols to make a true equation with the
numbers below:
1 2 3 4 = 5
Problem # 76
Solve the rectangle puzzle below so that
each side of the rectangle has a sum of
20.
4
5
9
1
3
Problem # 77
Newton made up a “code” where he
put letters in the place of numbers. He
only used the digits 1, 2, 3, and 4.
Here are the numbers in code:
#1) cabd
#2) bdca
#3) badd
#1 is the greatest and #2 is the least.
#3’s digits add up to 7. Which letters
stand for which numbers?
Problem # 78
Put the coins above in order so that:
●
●
●
●
The first three coins add up to 12 cents.
The last three coins add up to 16 cents.
The pennies are not next to each other.
The last coin is not a dime.
Problem # 79
Put the coins above in order so that:
● There is one coin between the two pennies.
● There are two coins between the two dimes.
● The first coin is not a penny.
Problem # 80
If you start with 3 ones and
12 tens, how many more
tens will you need to add to
get to the number 233?
Problem # 81
Find the missing number to
make the scale balance.
3
4
5
6
?
Problem # 82
Juan had 138 Lego bricks. He
also had two containers and
divided them equally between
the two. He had 14 bricks left
over. How many Lego bricks did
each container hold?
Problem # 83
Sam, Carla and Sarah spent on
afternoon collecting sea shells.
Sam collected 11 shells. Carla
collected three more than Sam.
In all, the three friends collected
34 shells. How many shells did
Sarah collect?
Problem # 84
Fill the the blanks to make a
pattern:
___, 2, 6, 24, ___, ___
Problem # 85
What is the tenth number in the
sequence below?
1, ½, ¼, ⅛, 1/16, ...
Problem # 86
There are 4 ponds and 22 frogs. No more
than 15 frogs can fit in a single pond. If each
pond is filled with a DIFFERENT odd number
of frogs, how many frogs are in each pond?
Problem # 87
There are five students in line:
● Ava is somewhere between Jude and Emmet.
● Katie and Ava are standing next to each other.
● Jude, who is last, and Maggie are not standing
next to each other.
● Emmet is not at either end of the line.
● There are two people between Katie and
Maggie.
What is the line order?
Problem # 88
A bicycle show featured some
bicycles and some tricycles.
There were 25 wheels in all. If
there were 5 bicycles shown,
how many tricycles were shown?
Problem # 89
I am a four-digit number.
●
●
●
●
The sum of all four digits is 15.
My tens digit is twice my thousands digit.
I am an odd number.
My ones digit is four less than my hundreds
digit.
● I am not divisible by 5.
What number am I?
Problem # 90
What is the next number in the sequence below? (In other
words, how many dots would there be in the next picture?)
Problem # 91
What is the difference
in the number of
factors between 24
and 50?
Problem # 92
Which is greater, 8/3 or 2 ½?
Prove it!
Problem # 93
Insert symbols to make a true
equation with the numbers
below:
50
6 7 8
Problem # 94
What is the eighth number in the
sequence below?
1, 4, 9, 16, 25, 36...
Problem # 95
Each shape below stands for a digit so
that the equations are true.
Which digit could each shape
represent?
Problem # 96
Fill in the blanks for this simple sudoku
so that each row, each column, and
each bolded box has each of the digits
1,2,3 and 4:
Problem # 97
Four people are in a Friendship
Club. Each week they make sure
they’ve talked on the phone oneon-one to the other three people
in the club. At least how many
conversations occur each week
between the four friends?
Problem # 98
What is a regular solid
shape that has half as
many vertices as a
pentagonal prism?
Problem # 99
Find the value of “x” to make the
scale balanced.
1
3
6
x
x
Problem # 100
I am a three digit number.
● My tens digit is twice as big as my
ones digit.
● My hundreds digit is half as big as
my ones digit.
● All three digits add up to 14.
What number am I?
Problem # 101
Is the number 5,287,734
divisible by 3? How can you
tell?
Problem # 102
Complete these sentences with
“odd” or “even.”
If you add two even numbers, you get an ______
number.
If you add an odd and an even number, you get
an ______ number.
If you add two odd numbers, you get an ______
number.
Problem # 103
How many triangles do you see
in this picture?
Problem # 104
The answer is 37.
What is the
question? (Make it a
good one...or two!)
Problem # 105
Here’s a cool math trick:
1) Write down any three-digit number where each digit
goes down by one each time (eg. 765, 321, 987,
etc.).
2) Reverse that number (so 567, 123, 789, etc.), and
then find the difference between the two numbers.
Write that difference down in a new place.
3) Take that new number and reverse it. Add the
difference and the reversed difference together.
Your answer is ... 1,089!
Problem # 106
Start at 4 on the number line below. Go +3, -8, +2, -6, +9.
Where do you end up?
Problem # 107
The sum of two prime
numbers, who are 10 apart on
a number line, is the product of
6 and 8. What are the two
prime numbers?
Problem # 108
What is the twelfth number in the
sequence below?
1, 1, 2, 4, 7, 11, 16, 22...
Problem # 109
Vivian is starting a simple savings
account. The first day she puts in 1
penny. The second day she doubles
it (puts in 2 pennies). The third day
she doubles it again (4 pennies),
and so on, doubling the amount
each day. How much money will she
have saved up after 10 days of this?
Problem # 110
You are drawing a giraffe next to
a tree. The actual giraffe is 16
feet, but in your picture it is only
8 inches tall. The tree next to it is
20 feet tall. How tall should the
tree be in your picture to keep it
to scale?
Problem # 111
Fill in the blanks for this simple sudoku
so that each row, each column, and
each bolded box has each of the digits
1,2,3 and 4:
Problem # 112
Here is a map you’ve drawn of Treasure Island. Pirate Pete is coming in on the ship for a treasure-hunting
vacation. He wants to find buried treasure for sure, but he doesn’t know what else to do. Can you (as his
travel agent) plan out a fun vacation for him, giving him at least 4 things to do IN ORDER so that he’s not
walking back and forth over the whole island, AND give him the coordinates or directions to each activity?
Problem # 113
Austin likes to watch squirrels find
and store acorns for the winter.
Brown Squirrels can carry two acorns
at a time. Gray Squirrels can carry
three acorns at a time, and Black
Squirrels can carry five acorns at a
time. There is a pile of 24 acorns.
How many more trips would a Gray
Squirrel need to make to store all of
the acorns in the pile than would a
Black Squirrel?
Problem # 114
If you start at a number and go +2, then -7, you end at -2. At
which number did you begin?
Problem # 115
Find the value of x to make the
scale balanced.
x
12
17
21
x
x
Problem # 116
What is a regular solid
shape that has half as
many faces as a
hexagonal prism?
Problem # 117
The answer is 45
degrees. What is the
question?
Problem # 118
You and your older sister want to
go see a dino exhibit at the
museum three times this month
(your parents would drop you
off). Which plan would be the
best use of your money and fit
your needs?
Problem # 119
What is the first time of the day
in which all the digits of the
time are different prime
numbers? What about the last
time of day in which that’s the
case?
Problem # 120
What is the ninth number in the
series below?
174, 164, 155, 147, 140...
Problem # 121
Put the coins above in order so that:
● The two quarters are not touching, but one of them is first.
● The dime and the penny are not touching, and have two
coins between them.
● The nickel and dime are right next to each other, and
neither are on the end.
Problem # 122
Emilie loves cats and she keeps
some as pets. All but two of
them are completely black. All
but two of them are completely
white. All but two of them are
completely ginger. How many
cats does Emilie have in all?
Problem # 123
Music is FILLED with math! In the example below, you have 4
beats in each of the first two measures and 2 beats in the third
measure. The notes are like fractions of a whole; a whole note
lasts the whole measure, or in these cases 4 beats, while a
half note only lasts 2. A quarter note would be one beat, then.
If we changed all the notes to sixteenth notes, how many
sixteenth notes would it take to fill these three measures?
Problem # 124
I am a fraction in simplest form
that is equivalent to a decimal
that is 15% less than 40%.
Problem # 125
If you subtract a number from
the square of 7, you will get onefourth the product of 9 and 8.
What is the number?
Problem # 126
Pascal’s triangle looks like this
(though it continues downward
infinitely):
Write down as many patterns
and observations as you can
about it in three minutes.
Problem # 127
Fill in the blanks for this simple sudoku
so that each row, each column, and
each bolded box has each of the digits
1,2,3 and 4:
Problem # 128
I am the seventh number in the
following sequence of numbers:
1, 3, 7, 15…
What number am I?
Problem # 129
Three consecutive numbers
have a sum of 135. What are the
numbers?
Problem # 130
I am a three-digit number that
is divisible by 7, but not by 2.
The sum of my digits is 4.
What number am I?
Problem # 131
If you start at a number and go +5, then -1, then +2, then -3,
then +5, you get to the number 1. At which number did you
begin?
Problem # 132
Find the value of x to make the
scale balanced.
x
40
60
x
70
x
Problem # 133
I am a fraction equivalent to ⅜.
My denominator is 20 greater
than my numerator. What
fraction am I?
Problem # 134
A triangle’s three angles add up to 180
degrees.
In triangle ABC, the degree measure
of angle A is 20° greater than the
degree measure of angle B. Angle C
is a right angle.
What is the measure of ∠B?
Problem # 135
Over a period of 6 hours, the temperature rose 4℉,
rose 3℉ more, dropped 2℉, rose 1℉, dropped 2℉,
and then dropped 3℉ more. The temperature at the
end of the 6-hour periods was -5℉. What was the
starting temperature?
Problem # 136
Put the coins above in order so that:
● The first three coins are equal in value to the 5th coin.
● The nickel does not touch any pennies.
● The sum of the 2nd and 3rd coins is 15 cents.
Problem # 137
When the square root of one
number is multiplied by the
square root of a second
number, the product is the
square root of 36. One of the
numbers is not 1. What are the
two numbers?
Problem # 138
The Washington Monument is 100
feet taller than the Great Pyramid of
Giza. If the Washington Monument
and the Great Pyramid each were 355
feet shorter, the Washington
Monument would be twice as tall as
the Great Pyramid. How many feet tall
is the Washington Monument?
Problem # 139
I am the fewest number of fish
that meets the following
conditions: When netted by
threes, by fours, or by fives,
there is always one left over.
What number am I?
Problem # 140
A huge frog ate 140 big bugs
in 5 days. Each day, it ate 8
more bugs than it did on the
previous day. How many bugs
did the frog eat on the first
day?