Monthly Archives: May 2014

Checkerboard Squares

How many squares that do not contain the shaded cell can be formed on an 8 x 8 checkerboard? Source: NCTM Mathematics Teacher 2008 SOLUTION 1 x 1 squares Total number of squares = ; square contains the shaded cell … Continue reading

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Rational Approximation of Pi

A calculator gives us rational approximations of irrational numbers, so we can “see” that . Explain how a circle inscribed in a regular hexagon allows us to “see” that without any decimal approximations. Source: NCTM Mathematics Teacher 2008 SOLUTION Consider … Continue reading

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Rectangular Prism

Given the right rectangular prism shown, how many different planes can you find that contain point and also pass through another vertex of the prism? Source: NCTM Mathematics Teacher 2008 SOLUTION faces of the prism: diagonal planes: 3-point planes: Answer:

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ZIP Codes

So that ZIP codes may be machine readable, the Postal Service encodes them as a group of five bars, some tall, some short, in groups of five. In how many distinct ways can two tall and three short bars be … Continue reading

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Pythagorean Triples

The expressions , and , with and integers such that , generate Pythagorean triples. Given the triple , find the values for and that generate this triple. Source: NCTM Mathematics Teacher 2008 SOLUTION is even The hypotenuse has the largest … Continue reading

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