Tiered Problems for a Variety of Middle School ... - WordPress.com

7th Grade Unit: Factors Fractions and Exponents
Lesson: Prime Factorization, Greatest Common Factor and Simplifying Fractions
! Goals: Students learn to find the prime factorization of a number, the greatest common factor
(GCF) of two or more numbers, to find equivalent fractions and to write fractions in simplest form.
Green level problems:
1. Use prime factorization to find the GCF of
2 3 2
27 x y ,46x y
2. Write in simplest form:
2
x y
3yz
Blue Level Problems:
3. What is the sum of the three distinct prime factors of 47,432?
4. In a certain code, each of the 26 letters of the English alphabet is represented by a number
(A=1, B=2, C=3,... Z=26). A word is then encoded by multiplying the numbers that represent its
letters. For example, CAT is encoded by 3* 1* 20 = 60, MATH is encoded by 13*1*20*8 = 2080.
Find a word that would be encoded as 7560 and explain how you found it. Could there be other
words? Explain why or why not.
Black Level Problems:
5. What is the least whole number value of x such that f(x) = x 2 + x + 11 is not prime?
6. A natural number n, such that n > 1, can’t be written as the sum of two more consecutive odd
numbers if and only if n is prime or n is twice an odd number. Of the ten natural numbers 20 through
29, how many can’t be written as the sum of two or more consecutive odd numbers?
5