Additional Model: Which of the following are all factors of 24.docx
In this lesson, I want students to understand that factoring is like breaking a number apart or decomposing it. I explain what factors are and the difference between a factor and a multiple. I also explain that factors can be prime or composite(except 0 and 1 are neither prime or composite). I have a list of reminders to assist students in finding the factors of all numbers.
To determine if a number is a multiple of a given one-digit number remember that
1. all even numbers are multiples of two.
2. all even numbers that can be halved twice are multiples of four.
3. all numbers ending in 0 or 5 are multiples of 5.
I write the number 8 on the board and explain that I am going to find all of the factors of 8. I write 1 on the far left with a comma behind it and 8 on the far right. I explain that all of the factors must fall within those numbers. I ask a volunteer if they can remember why I wrote 1 and 8 on the board. Because 1 and 8 can be multiplied together to get 8. That's right, any two numbers that can be multiplied to get 8 are factors of 8.
I go on to explain that I am going use my reminders to help me find the factors of 8. Hmmm. 8 is an even number, therefore, two is a factor. 8 can be halved into four, therefore 4 is a factor. Why did I write 2 and 4? Because 2 times 4 equals 8; therefore they are factors of 8. Can I multiply 3 by any number to get 8? No. What about 5? No. 6? No. 7? No. I think that I have found all of the factors of 8.
This lesson focus on the following Mathematical Practices:
MP.2. Reason abstractly and quantitatively.
MP.7. Look for and make use of structure.
Students are divided into groups and given cubes to assist in finding factors of numbers. I give students the number 24 and ask them to find the factors for 24. we begin by writing 1 on the far left and 24 on the far right. I ask them to make arrays using 24 cubes, however, all cubes have to be used when finding the arrays. I transition throughout to classroom to watch students work. I ask one student, what were you asked to do? Find factors for the number 24. What is a factor? Its like taking a number apart. What numbers are you going to list first? 1 and 24. Why? Because 1 and the number can always be multiplied to get that number. I continue to watch students put the cubes together to find the arrays. I see the following examples:
2 and 12
3 and 8
4 and 6
After all students are finished, we share the factors for the number 24, which are 1, 2, 3, 4, 6, 8, 12 and 24.
Printable Multiplication Chart: multiplication chart.gif
All students are given a multiplication chart that we are using to find factors of numbers. multiplication chart.gif
I give the students a number such as 30 and explain that we have to find all of the factors that when multiplied together give us the product 30. The students were very excited and anxious and began yelling out the factors before I could write them on the board. We agreed that all of the factors in 30 are 1, 2, 3, 5, 6, 10, 15, and 30. I gave them the number 45 which we concluded the factors were 1, 3, 5, 9, 15, and 45. I asked students to look at the factors for the number 30 and 45.
We then found the common factors for those numbers which were 1, 3, 5, and 15. I explained that if we want to find the greatest common factor in the two numbers, we would have to look at the largest number that both numbers have in common which is 15. We continue to go through this concept finding the greatest common factor and the least common factor in numbers. I continue to ask students, how do you know, and can you explain. Most students could respond as to way numbers are considered factors.
The students will independently complete an exit ticket where they are asked to find the factors for numbers, the greatest common factors, and the least common factors. This lesson was outstanding and the multiplication chart was a plus. For instances, the chart provided support for all students to quickly locate factors and multiples.