3rd grade: Optional homework for March 1 2011 class

Problem #1

Julius Caesar wrote the Roman Numerals I, II, III, IV, and V in a certain order from left to right. He wrote I before III but after IV. He wrote II after IV but before I. He wrote V after II but before III. If V was not the third numeral, in what order did Caesar write the five numerals from left to right?

Problem #2
In the multiplication problem below, each blank space represents a missing digit.
Find the product.















Problem #3
Thirteen plums weigh as much as two apples and one pear. Four plums and one apple have the same weight as one pear.
How many plums have the weight of one pear?

Problem #4
During a school year, a student was given an award of 25 cents for each math test he passed and was fined 50 cents for each math test he failed. At the end of the school year, the student had passed 7 times as many tests as he had failed, and received $3.75.

How many tests did he fail?

3rd grade: Math problems for March 1 2011

Problem #1

If 24 gallons of water are poured into an empty tank, then 3/4 of the tank is filled.

How many gallons does a full tank hold?

To see solution click here




Problem #2

A train can hold 78 passengers. The train starts out empty and picks up 1 passenger at the first stop, 2 passengers at the second stop, 3 passengers at the third stop, and so forth.

After how many stops will the train be full?

To see solution click here



Problem #3
The number of two-dollar bills I need to pay for a purchase is 9 more than the number of five-dollar bills I need to pay for the same purchase.

What is the cost of the purchase?

To see solution click here



Problem #4
The last Friday of a particular month is on the 25th day of the month.
What day of the week is the first day of the month?

Here is the video with almost correct solution. Please find the error.
See here



Problem #5

The age of a man is the same 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?

To see solution click here




Problem #6

D is the sum of the odd numbers from 1 through 99 inclusive, and N is the sum of the evn 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?

Optional homework for February vacation

Problem #1
You have a red bag (where you can put 600 gram of sugar), a napkin, a box( which contains 1 kilogram and 100 gram of sugar), and a blue bag,(where you can put as much sugar as you want).
How to fill the blue bag with 1 kilogram of sugar.

Hints:
1 kilogram = 1000 grams
You can put any amount of sugar on the napkin and use it inside of any bag or the box

See solution here


Problem #2
The apartment building has 5 floors. 4 people live in this building. Each of them live on separate floor (from second to fifth). These people are entering elevator on the first floor at the same time. Elevator needs to stop on only one floor (from which all these people will go home). If a person walks down 1 floor he/she gets 1 point. If a person walks up 1 floor he/she gets 2 points. What floor elevator should stop so total number of points for all 4 people is minimal?

Problem #3
We know that 51/A - 12 is the whole number and greater than 0. What value is A?

3rd grade: Math problems for February 15 2011

Problem #1

Suppose five days before the day after tomorrow was Wednesday.
What day of the week was yesterday?

Problem #2

X and Y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive.

What is the largest value that

(X+Y)/(X-Y) can have?

Problem #3

If 20 is added to one-third of a number, the result is the double of the number.
What is the number?

Problem #4

The counting numbers are arranged in four columns as shown below. Under which column letter will 101 appear?

A...B...C...D

1....2...3...4

8....7...6...5

9..10.11.12

..........14.13

Problem #5

In the 'magic square' below, the four numbers in each column, in each row, and in each of the two diagonals, have the same sum. What value should N have?

? ? 7 12

N 4 9 ?

? 5 16 3

8 11 ? ?

Problem #6
In the addition problem below, each letter stands for a digit and different letters stand for different digits.
What digits do the letters H, E, and A each represents.

HE
HE
HE
HE
+
HE
___
AH

The same written in different way: HE + HE +HE+HE=AH

Optional homework for Math class Feb. 8 2011

Problem #1
In the multiplication problem below, A and B stand for different digits. Find A and B.

  AB
 X
  BA
_____
 114
304
_____
3154

Problem #2
100 pounds of chocolate is packaged into boxes each containing 1 1/4 pounds of chocolate. Each box is then sold for $1.75. What is the total selling price for all of the boxes of chocolate?

Problem #3
P and Q represents numbers, and
P * Q means (P + Q)/2.
What is the value of 3 * (6 * 8)?

3rd grade: Math problems for February 8 2011

Problem #1
The four-digit numeral 3AA1 is divisible by 9.
What digit does A represents?
Rule: A number is divisible by 9 if sum of its digits
is divisible by 9.
Examples:
9 has one digit 9 is divisible by 9
18 has two digits, 1 and 8 => 1 + 8 = 9 is divisible by 9
900 has three digits, 9, 0, 0. 9 + 0 + 0 = 9 is divisible by 9

Problem #2
Suppose all the counting numbers are arranged in columns as
shown below.
Under what column-letter will 100 appear?
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 _ _ _

Problem #3
A boy has the following seven coins in his pocket: 2 pennies,
2 nickels, 2 dimes, and 1 quarter. He takes out two coins, records
the sum of their values, and then puts them back with the other
coins. He continues to take out two coins, record the sum of their
values, and then put them back.
How many different sums can he record at most.

Problem #4
In a group of 30 students, 8 take French, 12 take Spanish and
3 take both languages.
How many students of the group take neither French nor Spanish?

Problem #5
Glen, Harry, and Kim each have a different favorite sport among
tennis, baseball, and soccer. Glen doe not like baseball or soccer.
Harry does not like baseball. Name the favorite sport of each person.


Problem #6
In the 'magic-square' below, five more numbers can be placed in the
boxes so that the sum of the three numbers in each row, in each
column, and in each diagonal is always the same.
What value should X have?

15	__	35
50	__	__
25	X	__

Math Problems for 3rd grade - Part 1

1. How many digits are all together in all numbers from 1 to 100

2. One wheel of the cart is 3 times larger than the other. The big wheel has made over 1000 rotations on the path. How many rotations has the smaller wheel made?

3. A person answers questions with "yes" or "no". He has the right not to say truth only once. With how many questions you can guess what number he/she thinks of, if that number is from 1 to 4?

4. There are 8 coins. One of them is fake and it is lighter. There are pan scales. In how many weighings you can find fake coin?

5. There are two cans of water: large and small. The large can has 5 times more water than the small can. The small can has 8 oz less water than the large can. How much water is in each can?

6. The length of the room is 20 ft. The snail moves from one side of the room to another. During the day the snail moves 2 ft towards the end of the room, but during the night the snail moves back 1 ft. In how many days will the snail reach the end of the room?

7. What is the missing number? (587 + 213 + 111) x ? = 0

8. How many rooks can be arranged on a chessboard such that none of them threaten the other?
Examples of correct answers:


















9. Two tourists were making sandwiches. Third tourist came, and the first two tourists gave him something to eat: the first gave him 3 sandwiches, and the second 2 sandwiches. The third tourist paid them $10. How do the first two tourists need to divide money among themselves?

10. Grandfather is 56 years old and his granddaughter is 14. In how many years grandfather's age will be twice as much as his granddaughter's?