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?

Problems for summer time - Part 1

1. 5 friends and handshakes

5 friends exchanged 4 handshakes with each other. How many handshakes they did?

Answer: 40

2. Fake coin

There are 9 coins and one of them is fake. We know that the fake coin is lighter than others. How to determine which coin is fake with 2 attempts?

Answer: Divide 9 coins into 3 sets with 3 coins in each set. Compare 2 sets. If one set is lighter than the other then it means that the fake coin in the lighter set. If those two sets weight is the same then the fake coin in the third set. Now we know that the fake coin among 3 coins. Select 2 coins from those 3 coins and compare them. If one is lighter then that would be the fake coin. If they are equal then the third coin is fake.

3. Continue the sequence

Here is the sequence: 2, 20, 40, 400, 800. Could you please continue it?

Answer: The second number is 10 times more then the first. The third number is twice as much as second, the fourth is 10 times more than the third, the fifth is twice as much as the fourth
2, 20, 40, 400, 800, 8000, 16000, ...

4. Interesting square

Imagine the square 3 x 3 (9 cells all together). Put numbers from 1 to 9 in such a way that one number should be in one cell, a number is not repeated, sum of the numbers that reside on the same level horizontally, vertically, and diagonally is the same.

Answer:
One of the answers
2 7 6
9 5 1
4 3 8

5. Cleaning windows

6 workers clean 6 windows within 6 minutes. What is the minimal number of workers needed to clean 100 windows within 100 minutes?

Answer: 6

6. Treasure hunters

2 treasure hunters found treasure. They don't have any means to measure that. How to divide the treasure between those two treasure hunters in most fair fashion?

Answer:
One treasure hunter divides treasure in the way he/she thinks fair and the other one chooses the part he/she likes.

7. Saturday

September 1 2001 was Saturday. What day of the week was October 1 2001?

Answer: Monday

8. Kids in circle

There is some number of kids stay in circle. We know that the third person on the left from James is the same person who is 11th on the left from James. How many are in the circle?

Answer: 8 or 4 or 2

9. Third grade

On Tuesday there are 4 classes in the third grade: Math, Writing, Reading, and Arts. How many different combinations (in what order they go) exist?

Answer: 24

10. Cats competition

2 cats participate in running competition. They need to run first from point A to point B and then back from point B to point A. The first cat is running with the same speed the whole distance. The second cat is running twice as fast than the first one from point A to point B , but from point B to point A the first cat is running twice as fast as the second cat.
Who will finish first?

Answer: First cat

Proposal for Math lesson on May 21 2010

1. How many apples were on the table?

3 brothers asked their mother to leave apples on the dinner table and went to sleep. The eldest brother woke up, found apples on the table, ate 1/3 of them and went back to bed. The middle brother woke up, found apples on the table, ate 1/3 of them and went back to bed. The youngest brother woke up, found apples on the table, ate 1/3 of them. Then he woke up two brothers and offered them to finish eating 24 apples that were at the table.
How many apples were on the table originally?

2. Magic quadrant
Imagine a quadrant 5x5 (5 columns & 5 rows). Each number 1, 2, 3, 4, 5 is repeated 5 times. In each row has only one occurrence of each number and in each column has one occurrence of each number. Draw this quadrant.

3. Stamps
Jane purchased 3 stamps: one from the USA, second from France, and third from Italy.
The sum of the stamps without USA stamp is $13. The sum of the stamps without Italian stamp is $11. The sum of all stamps without French stamp is $12.
How much does each stamp cost?

4. Garages
This problem is similar to the 'shelves' problem we had a couple of months ago.
There are two huge garages. The number of cars in both garages is equal to 22. First garage has 8 cars less than the second garage.
How many cars are in each garage?

Proposal for Math class on May 14, 2010

1. How many are three digit numbers where all digits are odd and no digit repeats in the same number?

2. Where the elevators stops more?
There is a 10 stories building. The entrance to the building on the first floor. 1 person lives on the first floor, 2 people on the second, ..., 10 people live on the 10th floor.
Where (on what floor) the elevators stops more?

3. What was the day of the week, March 1 1996?
We know that February 1 1996 was Thursday. What day of the week was March 1 1996?

4. How many black cats who like salmon?
There are 15 cats, 8 of them are black and 8 of them like to eat salmon. How many cats are black and like to eat salmon.

5. What is the sum of all numbers from 101 to 200?

Treasure chests

The gnome separated his treasure into 3 different chests, each different
color, each standing by the wall. One chest had precious stones, one chest
had gold coins, and one chest had magic books. He remembers that red chest
is to the right of the one with the stone. And books are to the right of
the red chest. What chest contains books, if green chest is to the left of
the blue chest?

This is a problem on logic and the kids did it very successfully.
There were 9 kids in my class, so I divided them in 3 groups. Each group chose what they represent. One group was Precious stones, another was Gold coins, and the third was Magic books.
We all decided to put the 'Precious stones' team next to the wall. Kids realized that two other teams should stay on the right side from 'Precious stones'. They also found that one of those teams is red. Because 'Magic books' team on the right from red team it meant that 'Gold coins' team is red. Because green chest is to the left from blue chest it meant that 'Magic books' is blue and 'Precious stones' is green.
The problem is solved!

How many trucks and cars in the garage?

There are 17 trucks and cars in the garage.
Trucks have 6 wheels and
cars have 4 wheels. How many of each are in the garage if the total number
of wheels is 82?

This problem is very similar to the farm problem we did a couple of months ago. Surprisingly (again) all kids solved this problem very quickly :)
The answer is 10 cars and 7 trucks

What are the number in the following pattern

I gave this type of problem to the kids before.
The sequence I chose was 720, 360, 180, 90

It was a challenge for kids to determine the pattern. When I wrote those numbers on the board I made a mistake. Instead of 180, I wrote 120. So it didn't help them to find the pattern. But I could see how hard the kids were thinking :) When I gave a hint that each following number is a half from previous number. The kids were paid attention to minor details of may explanation. So when I said that 120 is a half from 360. They noticed this right away and corrected me on the spot.
I started asking what is a half of 90:45.
A half from 45: 22 1/2
A half from 22 1/2: 11/1/4
But then it was very difficult for them to get a half from 11 1/4. So I draw 11 circles and additional circle where I marked 1/4. Together we derived a half from 11: 5 1/2. Then we get a half from 1/4: 1/8. The next step was to add
5 1/2 and 1/8. It was not a trivial exercise for kids, so I posed a question: How many 1/8th in 1/2. They solved: 4/8. Then the kids realized that all they need to do next is to add 5 + 4/8 +1/8 = 5 5/8
As the next step I asked them: What is a half from 5 5/8.
We did a similar exercises as before. We got a half from 5: 2 1/2. Then we needed to make a half from 5/8. Together they got it that 5/8 is the same as 10/16 and a half from this would be 5/16.
So the result was 2 1/2 + 5/16. The next step was to add 1/2 and 5/16. I asked : how many 1/16th is 1/2. They answered 8/16. So the final answer was 2 + 8/16 + 5/16 = 2 13/16