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?
Thursday, May 20, 2010
Thursday, May 13, 2010
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?
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?
Friday, May 7, 2010
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
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
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
Thursday, May 6, 2010
Proposal for Math lesson May 7
1. What are the next two numbers in the following pattern
720, 360, 120, 30
2. 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?
3. 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?
4. What is the sum of all the numbers from 101 to 200?
720, 360, 120, 30
2. 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?
3. 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?
4. What is the sum of all the numbers from 101 to 200?