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January's Problem
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What is the missing number?


6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = ? x 3

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A solution to this problem will appear along with next month’s problem.
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December's Problem
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Emma rides her bike for 20 minutes at an average rate of 45 kilometers per hour. She then travels twice as far as before for the rest of the trip, which takes another 30 minutes. What is her average rate of speed for the entire trip?

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METHOD 1: Find the Totals:
The entire solution should use consistent units of measurement: km, hours, and km/h. At 45 km/h Emma travels 15 km in 1/3 h. The rest of the trip is therefore 30 km and takes 1/2 h. Her total distance is 45 km and her total time is 1/3 + 1/2 = 5/6 h. Thus, her average rate of speed for the entire trip is 45 ÷ 5/6 = 54 km/h.

METHOD 2: Make a table:
A good way to see this is to set up a table as shown below, using the formula Rate × Time = Distance. The shaded boxes contain the results of the computations, multiplying across and adding down. We see that the rate for the entire trip is 54 km/h.

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November's Problem
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Megan has four discount coupons that she can use. Their values are $8, $13, $17, and $22. How many different amounts can she save by using one or more of these four coupons?

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METHOD 1: Make a table:
Prepare four lists, according to the number of coupons selected and see that there are 14 different amounts.


(Note: Each time you choose three coupons, you omit the fourth coupon. There are only four ways that one coupon can be omitted. Using this gives you a faster way to find the number of 3-coupon amounts.)

METHOD 2: Use the Counting Principle:
Megan must use either zero or one $8-coupon. That is 2 possibilities. Similarly, there are 2 possible amounts using the $13-coupon ($0 or $13), 2 possible amounts using the $17-coupon ($0 or $17), and 2 possible amounts using the $22-coupon ($0 or $22). Together, there are 2 × 2 × 2 × 2 = 16 different sums that can be made. However, this includes both $0 and the two ways to make $30. Thus, there are 14 different sums that can be made using at least one coupon.

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For many additional problems we highly recommend the following books:

Math Olympiad Contest Problems for Elementary and Middle Schools by Dr. G. Lenchner
and
Math Olympiad Contest Problems Volume 2 edited by Richard Kalman
and
MOEMS® Contest Problems Volume 3
edited by Richard Kalman & Nicholas J. Restivo.
are sources of many such problems.

Creative Problem Solving in School Mathematics 2nd Edition by Dr. George Lenchner
can help you to teach solving these types of problems