The ideas in this lesson are taken from Multiplication Division 3 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Factoring and prime numbers
Free lesson plan from HomeschoolMath.net

This 'lesson' should actually be divided into several lessons for the student.

Example problems

1.  Express each number as a product of two factors.  Sometimes there are several ways of doing this and you can choose which way you like, but don't use 1 × the number itself.  Look at the example.  This process is called factoring.

2.  Express each number as a product of two factors and then make division facts and state by which numbers it is divisible.  Look at the examples.  Sometimes there are many ways that you can express a number as a product of two factors.

3.  Use the previous exercise as a help and make a divisibility list of  numbers between 1 and 20.  Circle every number that is divisible only by 1 and the number itself.  Such numbers are called  prime numbers.  (Usually 1 is excluded and is not counted as a prime number.)

Example problems

1.  Fill the table and circle each prime number between 20 and 30. 

2.  Factor the following numbers so the factors are prime numbers.

We can do the factoring process backwards, too.  Let's start with the building blocks and build numbers:   2 × 5 × 2 × 2 \ /         \ / 10 × 4 \         / 40   2 × 3  ×  2 × 3  ×  2 \ / \ /  | 6 × × 2 |       \      / ×   \             /                 72     2 × 7  ×  2 × 3 \ / \   / ×     \          /

 
3.  Build numbers from primes.

Sieve of Eratosthenes

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