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Math Help - Your favorite problems?

  1. #1
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    Your favorite problems?

    Hello,

    I'm looking to make a database of some math problems. I'm a secondary teacher and LOVE interesting problems to add to my bank. I'm looking for all kinds of problems, not just Algebra. Anything 6-12.

    Here are some of my favorites:
    Wine/water mixing problem - Wikipedia, the free encyclopedia
    The String Around the Earth Problem .........
    Connected Mathematics 2

    Basically, problems that have interesting/surprising results, multiple ways to solve them, etc.

    What are some of your favorites?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Your favorite problems?

    Quote Originally Posted by paupsers View Post
    Hello,

    I'm looking to make a database of some math problems. I'm a secondary teacher and LOVE interesting problems to add to my bank. I'm looking for all kinds of problems, not just Algebra. Anything 6-12.

    Here are some of my favorites:
    Wine/water mixing problem - Wikipedia, the free encyclopedia
    The String Around the Earth Problem .........
    Connected Mathematics 2

    Basically, problems that have interesting/surprising results, multiple ways to solve them, etc.

    What are some of your favorites?


    On any great circle around the world, the temperature, pressure, elevation, carbon dioxide concentration, or any other similar quantity which varies continuously, there will always exist two antipodal points that share the same value for that variable.
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  3. #3
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    Re: Your favorite problems?

    Math problems can be on fractions, for 6th grade math for example; two numbers add to 13/14 and one of them is 3/5, find the other number.
    2. 5/7 and its half added together, what do you get.
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  4. #4
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    Re: Your favorite problems?

    Try this.

    Find two sets, P and Q, such that:
    1) P and Q are both subset of the rectangle in [itex]R^2[/itex] with vertices (-1, -1), (1, -1), (1, 1),and (-1, 1).

    2) P contains the diagonally opposite points (-1, -1) and (1, 1) and Q contains the diagonally opposite points (-1, 1) and (1, -1).

    3) P and Q are both connected sets.

    4) P and Q are disjoint.
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  5. #5
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    Re: Your favorite problems?

    1) A kid and his father are 11 years apart, the kid is 9 years old the father is 36, in how many years will the age of the father be equal to 3 times the age of the kid. ( I'm not sure about these values but you get the logic that's to be used here )

    2) The perimeter of a rectangle is 200 meters long, its width is 4 times smaller than its length. Give the value of width/length. Find from the reasoning you may have used ( without resorting to an equation ) Thales' Theorem.

    3 ) On day 1 a farmer sells 15 chickens and 20 potatoes for 500 $, on day 2 he sells 5 chickens and 40 potatoes for 650 $. Prices of chickens and potatoes ?

    4) 3 persons just got paid. The sum of the income of the 1st and 2nd is 34 $, the sum of the 2nd and 3rd is 22 $, the sum of the 1st and 3rd is 28 $. How much did each received ?

    5) 3 persons share a sum of 5000 $, the first takes 1/3 plus 300 $, the second takes 3/5 plus 700 $, the third one gets the remaining part.Value ?
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