Enrichment problem
Once there lived a farmer, his wife, and their three sons. When the farmer died, his will said that the eldest son was to receive one-half of what he owned, the middle son was to receive one-third, and the youngest son was to receive one-ninth. All the farmer owned, however was seventeen horses. And try as they might, the three sons could not figure out any way to divide the seventeen horses by their father’s wishes.
Their mother however, went to the neighboring farm and borrowed a horse. Then with a total of eighteen horses, she gave the eldest son one-half, or nine horses. She gave the middle son one-third or six of the horses. And she gave the youngest son one-ninth, or two of the horses. She returned the last horse to their neighbor.
Nine plus six plus two makes the seventeen horses their father left them. How did she do it?
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Educational media
Friday, April 28, 2006
Numbers and Operators & Distance of two towns
Enrichment problem
(1) Numbers and Operators
Use digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 once and insert simple arithmetic symbols to add up to 1.
(2) Distance of two towns
Two boats go up and down the river between two towns. They have the same two constant speeds: a high speed going down-stream and a low speed going upstream.
The first boat leaves town A as the second boat leaves town N. They pass each other 7 miles from town A; they stop 4 minutes each at their destinations; they start back and pass each other the second time at 9 miles from town A.
What is the distance between the towns?
Source:
(1) Numbers and Operators
Use digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 once and insert simple arithmetic symbols to add up to 1.
(2) Distance of two towns
Two boats go up and down the river between two towns. They have the same two constant speeds: a high speed going down-stream and a low speed going upstream.
The first boat leaves town A as the second boat leaves town N. They pass each other 7 miles from town A; they stop 4 minutes each at their destinations; they start back and pass each other the second time at 9 miles from town A.
What is the distance between the towns?
Source:
Grade 6 Word Problem – Sequences & Numbers and Operators
Enrichment problem
(1)
12, 1, 1, 1, 2, 1, 3, __ , __ , __ , __ ,
Continue the sequences above.
(2)
Rearrange the above numbers so that the four propositions pictured are correct. (There are 3 horizontal equations and one vertical equation)
Source:
(1)
12, 1, 1, 1, 2, 1, 3, __ , __ , __ , __ ,
Continue the sequences above.
(2)
Rearrange the above numbers so that the four propositions pictured are correct. (There are 3 horizontal equations and one vertical equation)
Source:
Find the number & Profit and Loss
Enrichment problem
(1) Find the number
What number, between 1 and 10, when divided by 4, yields the same answer as when you subtract 4 from it?
(Hint: This strange number is not a whole number)
(2) Profit and Loss
When Calvin Collectible opened his Antiques Shoppe some 20 years ago, these two statuettes were proudly displayed in the front window. Up until last week, they were still there. Then in two days, he sold the first one for $198 and made a 10 percent profit on it, and then sold the second one for $198 and took a 10 percent loss on it. Taken together, did Calvin make profit on the two sales or did he sustain a loss?
Source:
(1) Find the number
What number, between 1 and 10, when divided by 4, yields the same answer as when you subtract 4 from it?
(Hint: This strange number is not a whole number)
(2) Profit and Loss
When Calvin Collectible opened his Antiques Shoppe some 20 years ago, these two statuettes were proudly displayed in the front window. Up until last week, they were still there. Then in two days, he sold the first one for $198 and made a 10 percent profit on it, and then sold the second one for $198 and took a 10 percent loss on it. Taken together, did Calvin make profit on the two sales or did he sustain a loss?
Source:
Find the shortcut & As easy as a pi
Enrichment problem
(1) Find the shortcut
We know that 5³ = 125 and 6³ = 216.
With this in mind, suppose you were told that the number 148,877 is the cube of some other whole number. What would that other number be? (Don’t use a calculator to do this problem: Once you find the right track, it’s simpler that it first appears. It doesn’t look simple, though, does it?)
(2) As easy as a pi
In the diagram bellow, which shaded region is bigger? (The side of the other square on the left is the same with the square on the left)
Source:
(1) Find the shortcut
We know that 5³ = 125 and 6³ = 216.
With this in mind, suppose you were told that the number 148,877 is the cube of some other whole number. What would that other number be? (Don’t use a calculator to do this problem: Once you find the right track, it’s simpler that it first appears. It doesn’t look simple, though, does it?)
(2) As easy as a pi
In the diagram bellow, which shaded region is bigger? (The side of the other square on the left is the same with the square on the left)
Source:
At a Cattle Market
Enrichment problem
Three countrymen met at a cattle market. “Look here,” said Hodge to jakes. “I’ll give you six of my pigs for one of your horses, and then you’ll have twice as many animals here as I’ve got.” “If that’s your way of doing business,” said Durrant to Hodge, “I’ll give you fourteen of my sheep for a horse, and then you’ll have three times as many animals as I.” “Well, I’ll go better than that,” said Jakes to Durrant; “I’ll give you four cows for a horse, and then you’ll have six times as many animals as I’ve got here.
No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge and Durrant must have taken to the cattle market.
Source:
Three countrymen met at a cattle market. “Look here,” said Hodge to jakes. “I’ll give you six of my pigs for one of your horses, and then you’ll have twice as many animals here as I’ve got.” “If that’s your way of doing business,” said Durrant to Hodge, “I’ll give you fourteen of my sheep for a horse, and then you’ll have three times as many animals as I.” “Well, I’ll go better than that,” said Jakes to Durrant; “I’ll give you four cows for a horse, and then you’ll have six times as many animals as I’ve got here.
No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge and Durrant must have taken to the cattle market.
Source:
Moving 3 piles of matches
Enrichment problem
Place three piles of matches on a table, one with 11 matches, the second with 7, and the third with 6. You are to move matches so that each pile holds 8 matches. You may add to any pile only as many matches as it already contains, and all the matches must come from one other pile. For example, if a pile holds 6 matches, you may add 6 to it, no more or less. You have 3 moves.
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Place three piles of matches on a table, one with 11 matches, the second with 7, and the third with 6. You are to move matches so that each pile holds 8 matches. You may add to any pile only as many matches as it already contains, and all the matches must come from one other pile. For example, if a pile holds 6 matches, you may add 6 to it, no more or less. You have 3 moves.
Source:
A tricky river crossing
Enrichment problem
This is a very old puzzle. It tells of a showman traveling the countryside on tour with a wolf, a goat and a cabbage. He comes to a river bank and the only means of getting accosts is a small boat which can hold him with only one of the wolf, the goat or the cabbage. Unfortunately he dare not leave the wolf alone with the goat or the goat alone with the cabbage for the wolf would eat the goat and goat would eat the cabbage. After some thought the showman realized that he could use the boat to transport himself and all his belongings safely across the river. How did he do it?
Source:
This is a very old puzzle. It tells of a showman traveling the countryside on tour with a wolf, a goat and a cabbage. He comes to a river bank and the only means of getting accosts is a small boat which can hold him with only one of the wolf, the goat or the cabbage. Unfortunately he dare not leave the wolf alone with the goat or the goat alone with the cabbage for the wolf would eat the goat and goat would eat the cabbage. After some thought the showman realized that he could use the boat to transport himself and all his belongings safely across the river. How did he do it?
Source:
Going to Coney Island
Ian and Adam wanted to go to Coney Island and were trying to figure out the fastest way to get there. Ian wanted to take the subway, but Adam noted that the subway only gets halfway to Coney Island and then you have to walk the rest of the way. Adam said that the fastest way to get there would be by bicycle, but Ian still felt the subway would be faster. So Adam hopped on his bicycle and Ian took the subway.
The Subway was four times as fast as Adam on his bicycle, but Adam was twice as fast as Ian’s walking speed.
Who got to Coney Island first?
Source:
The Subway was four times as fast as Adam on his bicycle, but Adam was twice as fast as Ian’s walking speed.
Who got to Coney Island first?
Source:
Multiplying whole numbers
Enrichment problem
Place the digits 1 through 9 in the space bellow to complete the equation. (Hint: the digits 1 through 9 appear on each side of the equal sign)
_ 2 _ 4 _ 8 _ _ x 6 = _ _ _ 2 8 _ _ 4 6
Source:
Place the digits 1 through 9 in the space bellow to complete the equation. (Hint: the digits 1 through 9 appear on each side of the equal sign)
_ 2 _ 4 _ 8 _ _ x 6 = _ _ _ 2 8 _ _ 4 6
Source:
Numbers, Multiplications and Percentages
(1)
If a man weight 75% of his own weight plus 39 lbs, how much does he weight?
(2)
Multiply by 5 the number of times that an even numbers is immediately followed by an odd number in the list below.
38592768954173421978
What is the answer?
Source:
If a man weight 75% of his own weight plus 39 lbs, how much does he weight?
(2)
Multiply by 5 the number of times that an even numbers is immediately followed by an odd number in the list below.
38592768954173421978
What is the answer?
Source:
Thursday, April 27, 2006
Estimating Sums & Differences
(1)
When two whole numbers are each rounded to the nearest ten, the sum is 80. One of the addends is the greatest number that rounds to 30. The second addend is the least number it can be.
What is the sum of the two numbers?
(2)
Rounded to the nearest hundred, the sum of two numbers is 11,000. Each addend is the greatest number it can be. One addend has 4 digits and the other has 3 digits.
What are the numbers?
Source:
When two whole numbers are each rounded to the nearest ten, the sum is 80. One of the addends is the greatest number that rounds to 30. The second addend is the least number it can be.
What is the sum of the two numbers?
(2)
Rounded to the nearest hundred, the sum of two numbers is 11,000. Each addend is the greatest number it can be. One addend has 4 digits and the other has 3 digits.
What are the numbers?
Source:
Factors, fractions and percentages
(1)
My house number is the lowest on the street that when divided by 2, 3, 4, 5, or 6, will always leave a remainder of 1. However, when divided by 11 there is no remainder. What is my house number?
(2)
The average of three numbers is 17. The average of two of these numbers is 25. What is the third number?
(3)
A statue is being carved by a sculptor. The original piece of marble weights 140 lb. On the first week 35% is cut away. On the second week the sculptor chips off 26 lb and on the third week he chips off two-fifth of the remainder, which complete statue. What is the weight of the final statue?
Source:
My house number is the lowest on the street that when divided by 2, 3, 4, 5, or 6, will always leave a remainder of 1. However, when divided by 11 there is no remainder. What is my house number?
(2)
The average of three numbers is 17. The average of two of these numbers is 25. What is the third number?
(3)
A statue is being carved by a sculptor. The original piece of marble weights 140 lb. On the first week 35% is cut away. On the second week the sculptor chips off 26 lb and on the third week he chips off two-fifth of the remainder, which complete statue. What is the weight of the final statue?
Source:
Additions and subtractions
(1)
Shawn has 440 basketball cards so far. By the end of the months, he wants to own a total of 500.
The cards come in packs of 5. The first week of the month, he bought 4 packs of cards. The second week, he bought 3 packs. He bought 2 packs during the third week and 2 packs during the fourth week.
Did he reach his goal of 500 cards?
(2)
Alexa, Barker, and Crystal entered a charity walkathon. Their sponsors agreed to give $1.00 for each mile they walked.
Alexa had 10 sponsors, and she walked 4 miles. Barker had 12 sponsors, and he walked the same distance as Alexa. Crystal had 20 sponsors, and she walked 1 more mile than Alexa.How much money did the 3 walkers raise all together?
Source:
Shawn has 440 basketball cards so far. By the end of the months, he wants to own a total of 500.
The cards come in packs of 5. The first week of the month, he bought 4 packs of cards. The second week, he bought 3 packs. He bought 2 packs during the third week and 2 packs during the fourth week.
Did he reach his goal of 500 cards?
(2)
Alexa, Barker, and Crystal entered a charity walkathon. Their sponsors agreed to give $1.00 for each mile they walked.
Alexa had 10 sponsors, and she walked 4 miles. Barker had 12 sponsors, and he walked the same distance as Alexa. Crystal had 20 sponsors, and she walked 1 more mile than Alexa.How much money did the 3 walkers raise all together?
Source:
Peppy Pizza Parlor - Multiplication
The Peppy Pizza Parlor baked 15 pizzas for the New Town School Picnic. Each pizza was cut into eight slices. Each person at the picnic ate one slice of pizza, and none was left over. How many people were at the picnic?
Source:
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Hoppy’s Climb
Hoppy the frog is hopping up a tilted log that is 13 feet long.On each jump, she moves 5 feet forward. Then she slides back 2 feet before jumping again.
How many jumps will it take for Hoppy to jump off the end of the log?
Source:
How many jumps will it take for Hoppy to jump off the end of the log?
Source:
One Bee in Our Classroom
Complete the poem by filling in the missing numbers.
(Hint: Look for a pattern)
1 bee in our classroom, and then there were 3.
Soon there were 5, straight from the hive.
Next there were ____________. That wasn’t so fine.
And when the days ended, the total was ______.
Source:
(Hint: Look for a pattern)
1 bee in our classroom, and then there were 3.
Soon there were 5, straight from the hive.
Next there were ____________. That wasn’t so fine.
And when the days ended, the total was ______.
Source:
Monday, April 24, 2006
Fibonacci poems multiply on the Web
Blogs
spread
gossip
and rumor
But how about a
Rare, geeky form of poetry?
That's exactly what happened after Gregory K. Pincus, a screenwriter and aspiring children's book author in Los Angeles, wrote a post on his GottaBook blog several weeks ago inviting readers to write "Fibs," six-line poems that used a mathematical progression known as the Fibonacci sequence to dictate the number of syllables in each line. (Number of syllables in line: 1, 1, 2, 3, 5, 8, 13, ...)
Within a few days, Pincus, 41, had received about 30 responses, a large portion of them Fibonacci poems. Most of them were from friends or relatives or people who regularly read his blog, which focuses on children's literature.
Then, on April 7, a subscriber to the popular Web site Slashdot.org--which runs over a tagline that reads "News for nerds. Stuff that matters"--linked to Pincus' original post, and suddenly, it seemed, Fibs were sprouting all over the Internet.
The allure of the form is that it is simple, yet restricted. The number of syllables in each line must equal the sum of the syllables in the two previous lines. So, start with 0 and 1, add them together to get your next number, which is also 1; 2 comes next; then add 2 and 1 to get 3; and so on. Pincus structured the Fibs to top out at line six, with eight syllables.
More info…
spread
gossip
and rumor
But how about a
Rare, geeky form of poetry?
That's exactly what happened after Gregory K. Pincus, a screenwriter and aspiring children's book author in Los Angeles, wrote a post on his GottaBook blog several weeks ago inviting readers to write "Fibs," six-line poems that used a mathematical progression known as the Fibonacci sequence to dictate the number of syllables in each line. (Number of syllables in line: 1, 1, 2, 3, 5, 8, 13, ...)
Within a few days, Pincus, 41, had received about 30 responses, a large portion of them Fibonacci poems. Most of them were from friends or relatives or people who regularly read his blog, which focuses on children's literature.
Then, on April 7, a subscriber to the popular Web site Slashdot.org--which runs over a tagline that reads "News for nerds. Stuff that matters"--linked to Pincus' original post, and suddenly, it seemed, Fibs were sprouting all over the Internet.
The allure of the form is that it is simple, yet restricted. The number of syllables in each line must equal the sum of the syllables in the two previous lines. So, start with 0 and 1, add them together to get your next number, which is also 1; 2 comes next; then add 2 and 1 to get 3; and so on. Pincus structured the Fibs to top out at line six, with eight syllables.
More info…
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