The Great Mathematical Scavenger HuntAuthor(s): Sharyn EvansSource: The Mathematics Teacher, Vol. 73, No. 7 (October 1980), pp. 513-514Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27962132 .

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sharing teaching ideas

The Great Mathematical Scavenger Hunt It is often difficult to find a mathematics

project that motivates a student. I came up with the idea of having the students answer

a list of mathematics-related questions, then substitute their answers into an in

volved equation to find the unknown. This

assignment gave the students an opportu

nity to use library sources, calculators,

computers, and mathematical textbooks.

Many staff members participated in this

project as well. The students became very enthusiastic

and worked until the value of was deter

mined (table 1). Many said it was difficult

TABLE 1

fs

= ? \(t + m)l

+ k ij(a-b)(y-u<y nc

h-r (y + x-p)

g e-(d+v + rf) f-g

a ? a speed of 60 mph that corresponds to how many km/h?

b = normal body temperature in centi

grade. c = the length of a side of a cube whose

volume is 125 cm3.

d = the number of nanograms in one

microgram.

e ? the value of: s

m

f ? the value of this Mayan symbol: =

g ? the value of 239twelve in base ten.

h ? the value of 5736cight in base ten.

i = Ikumi, the Lamba word for what

number?

j ? .076923, the same as what fraction?

k ? birth year of Mikolaj Kopernik. / = the sum of the fifth row of Pascal's

triangle. m = the number of pounds sterling that

the Irish Sweepstakes Derby ticket

cost in 1972.

=

o =

P =

q =

r =

s ?

t ?

u =

?

w ?

X =

y =

the zip code of Annette, Alaska, minus the zip eode of Kotlik, Alaska.

the number of blue stripes in the

Cuban flag. the year Phineas Barnum was born,

the number of subsets in a set with

five elements.

13(mod 7) - ? the value of 3P2 the density of water in g/cm3 (at

3.98?C). the number of letters in the name

of the artist who created the lith

ograph Reptiles. th? number of the computer Hal in

2001?a Space Odyssey, divided by 10.

the number of letters in the animal name for 1980 according to the

Chinese lunar calendar,

population of Hallettsville, Texas, in 1950. the number of times greater the di

ameter of Jupiter is than the diam

eter of Earth is when rounded to

the nearest whole number.

October 1980 513

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and a challenge, but most of all it was just plain fun! The answers appear below. You

may want to change some of the questions to fit your own resources.

Sharyn Evans Middletown High School South

Middletown, NJ 07748

Answers

a ? 97, b = 37, c = 5, d ? 1000, e = 3164, /= 12, g = 333, A = 3038, / = 10, j

= 1/13, k = 1473, / = 32, m = 1, = 300, o = 3,/?

=

1810, 4 = 32, r = 6, s = 6, / = 1, u = 6, =

900, w = 6, = 2000, y=\\,z

= 75.

A Different Way of Finding Fractional Equivalents

Do your _

asked to add students groan when they are rl

3 1 3 1 0 ?I-h-h?? 8 6 14 7

While teaching mathematics in prison, I have found that many students find the

process of finding a common denominator and then writing equivalent fractions to be laborious and time-consuming, especially

when large numbers are involved. My stu dents have successfully used the prime fac tor method for finding the lowest common

denominator, eliminating trial and error and finding the lowest common denomina tor on the first try. The method seems com

plex at first, but students have been excited to learn that the prime factors extracted

while using the prime factor method can be used again to find equivalent fractions without having to divide the lowest com mon denominator by the original denomi nator.

This second use of the factors extracted

during the use of the prime factor method is what this article discusses. Before de

scribing this new method of finding frac tional equivalents, I will give an example of the prime factor method for those who are not familiar with it. The prime factor method works by finding the prime factors of all the denominators and multiplying each prime factor extracted together with

any number not reduced to 1. The method

can be traced back to 1788. It was demon strated in the January 1980 Arithmetic

Teacher, pages 34-37, "A Look at the Past."

Prime Factor Example

Problem:

3 13 1 8 + 6 + 4+7

Write down all the denominators. Then examine them to see if there are two or

more that can be divided by the same

prime number.

8, 6, 14, 7

In this case 8, 6, and 14 can all be divided

by 2. Write the 2 to the left of the denomi nators. Next divide each denominator by 2 and put the quotient directly beneath the number being divided. If a number cannot

be divided without having a remainder, list the number itself.

2)M, 14,7 4,3, 7,7

Examine the new set of numbers to see if there are two or more numbers that may be divided again by a prime number. In this case the two sevens can be divided by 7.

2)8, 6, 14, 7

7)4, 3, 7, 7

4, 3, 1, 1

514 Mathematics Teacher

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