Thursday, August 27, 2009
A Middle School Coin Puzzle To Start The Year
I have an equal number of pennies, nickels and dimes. I also have some quarters which have the same value as the pennies, nickels and dimes combined. If I have no other coins, what is the fewest possible total number of coins I could have? What is the value of all the coins?
Comments
(1) An opening day problem?
(2) Would you have students working alone or in small groups?
(3) Would you allow the calculator?
(4) Appropriate for prealgebra students? Students below grade 6?
(5) Is zero a possible answer?
(6) Wording too confusing for most students? Is it ambiguous or clear?
(7) Do you feel there are important underlying concepts and ideas embedded here or is it just a fun puzzle to engage students?
(8) Do students have difficulty in separating number of coins from their value?
REMINDER!
MathNotations' Third Online Math Contest is tentatively scheduled for the week of Oct 12-16, a 5-day window to administer the 45-min contest and email the results. As with the previous contest, it will be FREE, up to two teams from a school may register and the focus will be on Geometry, Algebra II and Precalculus. If any public, charter, prep, parochial or homeschool (including international school) is interested, send me an email ASAP to receive registration materials: "dmarain 'at' gmail dot com."
Read Update (4) below!
Updates:
(1) The first draft of the contest is now complete.
(2) As with the precious two contests there will be one or two questions which require demonstration, that is, the students will have to derive, explain or prove a statement. This is best done freehand and then scanned as a jpeg image which can be emailed as an attachment along with the official answer sheet. In fact, the entire answer sheet can be scanned but there is information on it that I need to have.
(3) Some of the questions are multipart with the last part requiring more generalization.
(4) Even if you have previously indicated that you wish to participate, please send me another email using the title: THIRD MATHNOTATIONS CONTEST. Please copy and paste that into the title. Also, when sending the email pls include your full name and title (advisor, teacher, supervisor, etc.), the name of your school (indicate if HS or Middle School) and the complete school address. I have accumulated a database of most of the schools which have expressed interest or previously participated but searching through thousands of emails is much easier when the title is the same! If you have already sent me an email this summer or previously participated, pls send me one more if interested in participating again.
(5) Finally, pls let your colleagues from other schools in your area know about this. Spread the word! If you have a blog, pls mention the contest. If you're connected to your local or state math teachers association, pls let them know about this and ask them to post this info on their website if possible.
Note: Sending me the email is not a commitment! It simply means you are interested and will receive a registration form.
Posted by Dave Marain at 8:01 AM 6 comments
Labels: coin problem, middle school, puzzle, starting the year, warmup