4.OA.4 TSWBAT recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.

Students will learn that multiples are only a matter of skip counting and be able to use factors to help find muliples with ease.

20 minutes

*I want my students to really focus on the difference between and factor and an multiple. Throughout the lesson I will gradually release different concepts to see where the students go with it.*

I begin this lesson by explaining that multiples are the product of two factors. For example 12 is a multiple of 3 because 3 times 4 is 12. 12 is also a multiple of 4 because 3 times 4 is 12. 6 is a multiple of 2 because 2 times 3 is 6. 6 is also a multiple of 3 because 3 times 2 is 6. It is easy to find the multiples of numbers when using a multiplication chart. I display a large chart on the board for the students to see. I explain that is I want to know the multiples of 3, I look at the 3 and continue skip counting of going down the line. I model 3,6,9,12,15,18,21., etc. I ask students to give me the multiples of 5. **5,10,15,20,25,30,35,40. **

In other words, a multiple is the product of any given number and any other whole number. I go on to explain that we are going to find the lowest common multiple in a given set of numbers. I model Let's look at 6 and 12. I am going to write the multiples for these numbers on the board

6: 6 12 18 **24 ** 30

12: 12 ** 24** 36

I explain that the least common multiple for those two numbers are 24.

To help struggling students determine the difference between a multiple and a factor, I use a multiplication chart. We use the chart to help us fill out the T-chart of what is the factor and what is the multiple. Multiplication chart.ppt T Chart explanation.ppt

**In this lesson we will focus on the following Mathematical Practices:**

MP.2. Reason abstractly and quantitatively.

**MP.7. Look for and make use of structure. **

15 minutes

**Resources: WorksheetWorks_Multiples_and_Factors_1.pdf**

I break students into pairs and give them t-charts to list their multiples under each side. I give them numbers such as 2 and 12... 5 and 6..... 9 and 12, and so on. I explain to students that I want them to place one number on the left side of the t-chart and the other number on the right side. They will continue to find the multiples of those numbers until they find a common multiple. I ask students to explain again what a multiple is. **A number that can be made by multiplying a number by another number. **What is a common multiple? **Numbers that are multiples of both pairs.** **It is the lowest number that both numbers have in common. **The students worked well with finding the common multiples. I ask students how they determine which number is a factor/multiple.

**Student Response:**

*Students noted that writing the multiplication expression for numbers with several factors and for numbers with a few factors help them make conjectures about the numbers. Basically they say the repeated pattern in some of the numbers they explored.*

15 minutes

I pose word problems for students such as Mark goes swimming every 3 days. Tammy goes swimming every 4 days. What days will they both be at the pool?

We write the multiple for 2 and the multiples for 3

2,4,6,8,10,12,14,16,18,20

3,6,9,12,15,18,21

What are the multiples that these two have in common? **6, 12, and 18**

Ok, so they will meet at the pool on days 6, 12, and 18. What is the soonest day that they will meet? **Day 6.**

I change up the numbers to see if students grasp the concept. We continue this until I am sure that this lesson is mastered. After that students completed a multiple assessment on their own. As they were working, I circle the room to see what they are thinking.** For instance, I ask students to think of another way to determine the multiple ; how do you know? can you illustrate it? **