Students will be able to understand the difference between a factor and a multiple.

Students explore a factory of factors and multiples to build number sense and conceptual understanding.

5 minutes

In today's Curriculum Reinforcer, I want my students to review their division skills with decimals. I also want to take them back to a previous grade level, when they learned to add and subtract with fractions. My reason for this is that when teaching today's lesson, I want to be able to make the connection between factors and multiples and something that they are already be familiar with, adding and subtracting fractions.

5 minutes

To introduce today's primary topic, we will follow a two-step protocol for brainstorming ideas about factors and multiples. I will pose and opening discussion question and ask students to discuss it with a partner for two minutes:

**What is the difference between a factor and a multiple?**

After students brainstorm ideas for two minutes, I will give students the opportunity to call out ideas about the difference between a factor and a multiple for one minute. As students volunteer ideas and comparisons, I will record the call outs as a bulleted list on the board. Here are some items that I anticipate my students might contribute:

10 minutes

Using the Bulleted List, we will now work as a class to create a thorough, clear, and concise explanation of the difference between factors and multiples. In order to accomplish this, we will start with the ideas that we generated on the List. We will work through points of agreement and disagreement. I expect that students will offer a lot of examples as we talk about these ideas. We will use these ideas to clarify the concept of a factor of a number and a multiple of a number in students minds. As needed, I will model explanations, revoice strong contributions, and ask questions to help highlight and address misconceptions. In Factors & Multiples I discuss some of the ways that I scaffold my students understanding of these ideas.

As a final product, my students will create a graphic organizer that highlights the unique characteristics of both factors and multiples. This organizer will also highlight the most common way each are presented in real-world problems. The Factors Multiples Foldable resource is an example of the types of ideas that I will ask my students to create. They will work on this during the next section of the class.

10 minutes

Today's Try It Out challenges students to create an informative, fold-able organizer that displays their understanding of the characteristics of factors and multiples. As an added challenge, the resource should include an example of a real world situation in which factors and/or multiples might be used to solve the problems.

I give students the following tasks to think about as they begin this work:

1. Find all the factors of the following quantities:

**18 56 144**

2. Provide the first 12 multiples of the following quantities:

**8 12 20**

Once students complete their organizers, we will employ them in today's guided practice.

20 minutes

As students complete their organizers, I will give them the Secret Number task to work on. In this task, they attempt to guess Juanita's secret number using clues the she provides in the task description. In order to successfully identify her number, they need to apply their knowledge of factors and multiples, as well as prime numbers.

As they work, I encourage my students to explain their thinking. It may take some of my students up to 20 minutes to complete the task. In order to promote reasoning and explanation, I will allow students to work with a partner. While with their partner, I encourage students to compare and discuss methods. As I listen in on students' progress with the task, I am trying to identify students whom I would like to explain their problem solving process at the conclusion of the activity.

20 minutes

After selected student partners present their work on the Secret Number task, I will give my student the following prompt for a Ticket Out The Door:

**What is the difference between a factor and a multiple?**