You are here:Home > Olympiad Program > Contests > Samples > Problem of the Month > Awards > Enrollment > What They Wrote > MOEMS Board of Directors

 

Copyright © 2017 by MOEMS® (Mathematical Olympiads for
Elementary and Middle Schools). All rights reserved.

 

a

a
a
February's Problem
a

A large cube 2 meters along each edge is cut into small cubes that are 2 centimeters along each edge. How many small cubes are there?

a
A solution to this problem will appear along with next month’s problem.
a
a
a
a

 

 

a

a
a
January's Problem
a

What is the missing number?


6+6+6+6+6+6+6+6 = ?x3

a

METHOD 1: Find the sum:
The sum of the eight 6's is 48. 48 ÷ 3 = 16. The missing number is 16.

METHOD 1: Relate 3's to 6's:
Since 3 is half of 6, adding eight 6's is equal to adding sixteen 3's. The missing number is 16.

a
a
a
a

 

 

 

a

a
a
December's Problem
a

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?

a

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.

a
a
a
a

 

 

 

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