A complete unit with direct instruction to the student, ample practice problems and word problems. Common Core aligned. Great for independent practice/homework.
The topics in the unit Factors, Factoring, GCF, and LCM belong to a branch of mathematics known as number theory. Number theory has to do with the study of whole numbers and their special properties. In this unit, we study divisibility, primes, prime factorization, the greatest common factor (GCF), and the least common multiple (LCM).
In the first lesson, we present the concept of divisibility, which is followed by a lesson that puts into practice the common divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10.
Next, we study prime numbers. Primes are fascinating “creatures,” and you can let students read more about them by accessing the Internet resources listed below. The really important but far more advanced application of prime numbers is in cryptography. Some students might be interested in reading additional material on that subject—please see the list below for Internet resources.
Later, in the lesson Finding Factors, we learn how to find all factors of a given two-digit number. This is followed by the lesson Prime Factorization, in which we use factor trees.
The main application of factoring and the greatest common factor in arithmetic is in simplifying fractions,so that is why I have included a lesson on that topic. However, it is not absolutely necessary to use the GCF when simplifying fractions, and the lesson emphasizes that fact.
The concepts of factoring and the GCF are important to understand because they will be carried over to algebra, where students will factor polynomials. In this unit, we lay the groundwork for that by using the GCF to factor simple sums, such as 27 + 45. For example, a sum like 27 + 45 factors into 9(3 + 5).
Similarly, the main use for the least common multiple in arithmetic is with finding the smallest common denominator for adding fractions, and we study that topic in this unit in connection with the LCM.