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Problem Solving June 2003 (v 27.4)
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Pick A Block Game GRADES K–2
This activity will help your students understand the tactics of a fair
game. In a fair game all players will have the same chance of winning.
To play the game place eight colored blocks (two
each of four colors) into a small paper bag. In partners, have the
students take turns guessing a color and then taking one block out of
the bag. The rule is if you take out the color block you guessed you
get to keep it. But, if you get any other color block you have to give
it to your partner. After a player wins a block they need to put that
block in front of them so it can be used for clues as the game
continues. Keep playing until all the blocks have been taken out of the
bag.
After the game has been repeated several times,
initiate a discussion to see if and why your students think this is a
fair game.
Probability and Dice GRADES 3–5
(Editor’s note: For this activity, the teacher needs a quiz—mathematics
vocabulary, basic facts, etc.—on an overhead and a die that has the
same number of faces as the number of questions on the quiz.)
Have the students pick the number of questions they
would like to answer on a quiz. If a ten-question quiz were to be
given, they could pick any number of questions to be answered from one
through ten and the die would have ten faces. They do not know in
advance which question will be asked or in what order.
Have the students create a table showing all the
possible outcomes (grades) for each number of questions attempted. For
example, if the student picks one question to attempt (the all or none
approach), the possible outcomes are either correct for 100% or
incorrect for 0%. Partial credit usually just confuses this activity.
If the student chooses 10 questions to answer, missing only one
question would leave them with a 90% correct rate (A-).
Have them write out a prediction of their
grade at the end of the quiz. What is the probability of getting the
easiest question available from all the questions on the quiz? Is only
choosing to do one question worth the risk?
Have the students write their opinion about the best
strategy to use when taking this quiz after their teacher rolls the die
to determine the question to be asked.
After the students have responded to the first
question, have them write about how the quiz is progressing: would they
like to revise their choice of the number of questions to be answered?
Please send examples of student work to the ComMuniCator.
Funky Fun Center Prizes GRADES 6–8
Jimmy played games at the Funky Fun Center for four hours and collected
5,000 tickets. These tickets can be redeemed for three types of prizes:
500 ticket prizes, 100 ticket prizes, and 10 ticket prizes. Jimmy used
all 5,000 tickets to get a combination of exactly 50 prizes. How many
of each type of prize did Jimmy get?
Students can use a variety of methods from
guess-and-check to algebraic equations to solve this problem. Make sure
students understand what is meant by combination— all three types of
prizes are included in the solution. After students have worked on this
problem ask them what key observations make it easier to solve (i.e.,
you can only purchase whole prizes; prizes that cost 10 tickets must be
redeemed in multiples of 10).
After students solve the Funky Fun Center problem
give them the Candy problem below. This problem is more challenging
because the costs are not all in the same units.
Fran had $80 to spend on candy. Three types of candy
were available: jelly beans at 5 cents each, candy bars at $1 each, and
large candy bars at $4 each. Fran spent exactly $80 buying a
combination of exactly 80 candies. How many of each type of candy did
Fran buy?
Have students explain in writing their key
observations and show their methods for solving these problems along
with their solutions.
Cutting Cake GRADES 9–12
Shireen Dadmehr wrote the following version of this issue’s problem
about cutting a square cake with equal volume and equal frosting. She
added the extension using a rectangular cake. Present the problem to
your students. Send their solutions to the ComMuniCator along with
their explanations of how they solved the problem.
Cutting Cake
All five finicky Finnegans favor frosting. Phranny Finnegan is turning
45 on Friday and wants to divide a square cake to share with her
family, Phred, Phrank, Phlorence, and Phil. Help Phranny determine how
to cut the square cake into 5 pieces, each of which has equal volume
and an equal amount of frosting.
- Yes, you must serve the whole cake.
- Yes, the cake is frosted on top and sides before you cut it.
- Yes, you may use whatever tools at your disposal.
Finished? Fantastic! Phil is turning 4 in February, and REALLY favors
frosted cake. The family has decided to bake a rectangular cake (not
square) and again divide it into 5 pieces, each with equal volume and
frosting. Please help them figure out how to finagle this.
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This Page was last updated: Wednesday, March 17, 2004 at 12:52:23 AM
This page was originally posted: 3/17/2004; 12:52:23 AM.
Copyright 2008 cmcmath
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