# Factor Pairs, Arrays, Patterns and Fun! Building factor pairs to 50

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## Objective

SWBAT list factor pairs and create arrays to discover prime, composite, and square numbers 1-50.

#### Big Idea

A hands-on lesson where students learn how to create factor pairs, arrays, and find prime, square and composite numbers by discovery.

## Finding Factor Pairs: Review Warm Up

10 minutes

Prepare Materials the Day Before: Note cards with numbers 18, 20, 24, 36, 19,  and all the factor pairs associated with those products (I created just enough to fit the amount of students in my class.)

Each of my students found a card face down on their desk when they enter the classroom. It got their curiosity going and engaged them right away. I asked them to leave them there and not peek at them just yet. Some students peeked. They thought they got away with something sneeky.

Quick Review of Factor Pair Listing Strategy: I opened the lesson with discussion about what strategies we had learned from the day before ( http://betterlesson.com/my/lesson/520758/how-to-easily-find-all-those-factor-pairs), about listing factor pairs. Students easily and quickly remembered how to list factor pairs to the "turn around" or commutative pair. They mastered it well.  I could see they were ready to do our next activity.

Milling to Music and Finding All the Factor Pairs: I was trying to think of something fun to get their brains going and came up with this fun activity. Students use the factor pair/product note cards to mill about to music and match the product with the factor pairs.

When a group found all of their factor pairs, they rang the bell on my desk and we stopped to look. They had to order themselves in a line from 1 x _  and talk about their factor pairs and product. The first group to ring the bell and have them all right, won the game.

Even after a team won, we continued  until all had matched and all had shared. It was a blast! They loved it. It was great organized chaos. Just enough to settle them into their new task.

*I picked a funky jazz  tune called "Moanin" that had a lot of bari sax. I thought it was a fun piece to set the mood.

Students clearly showed me that they could figure out the factor pair pattern, find the "turn around"  and they appeared completely ready to move onto the core lesson. My goal for getting their minds set for working with more factor pairs up to 50 was reached! We were ready!

## Step by Step: Creating the Factor Pair Cards

15 minutes

Prepared a Day Ahead of Time:

Materials:  Large construction paper cut in half to create: 1 pink, 28 Green, 15 Red and 6 Blue sheets. Write in black marker ( vertically) all prime numbers on the red. The number 1 is the pink sheet, all composite numbers are green, and finally, all the blue sheets are for the square numbers in a set of numbers 1-50.

You will need: 1 pack of 1/4 square graph paper, Colored pencils, glue sticks.

Prepare the number "48 card" by creating all the factor pair arrays from graph paper,  and glue only the 1x48 array on it. (It will hang over the edge a little.) Keep the other arrays aside for later. I hung my card with a magnet on the whiteboard.

I partnered students the day before the lesson telling them that something special was planned for partner work.  I partnered them up by pairing students who struggle, with higher level thinkers. I did this because in this activity, lower achieving students needed the support even though they have practiced making factor pairs in prior lessons.

The Lesson Begins:

It's important to model the steps of creating the factor pair card because I have learned from the past that students can sometimes have difficulty switching to the physical graph paper, posting on the construction paper and listing the factor pairs in a row x column manner. So, this next section is step by step. After they are clear, I know I will have freedom to rove and stimulate thinking skills without being hung up on the "how to".

I chose the card with the product of 48 on it that I had prepared earlier. I returned to the Smart Board Factorize! webpage and typed 48 in start of factor pairs listed for 48 so that students had a visual direction and understanding before they started. I have found that this visual step is essential, even though we have practiced making arrays on graph paper in prior lessons. Student's used divisibility rules they had learned in the past lessons and other strategies to complete the factor pairs. I emphasized using strategies to solve. This helps support some foundational principals that revolve around CCSS. "Well, how do we figure it out? What strategy can we use?"  was continually being asked to students throughout the lesson to support and encourage independent thinking. The Factorize ap supported their learning when they were unsure. They continually checked whether the "turn around" "double factor pairs" or ( commutative pair) had been found.

When students were ready to advance to the actual gluing of the factor pairs on the cards,  I asked them to join me nearer to the board for explicit instruction. I saved the last cut out array (6x8) to demonstrate the row and column idea and how it relates to the Commutative Property of Multiplication.

I wanted them to fully Understand how to demonstrate the Commutative Property using their cut aray: I posed the question: What happens if 6 rows of 8 are flipped to 8 rows of 6? How is it different? How is it the same? If I am listing 6 rows of 8, which direction should it be? Do I need to keep going to show 8 rows of 6? Why or why not? They could easily see the Commutative Property and we rehearsed 6 rows of 8 and then 8 rows of 6.  I hung it up for a visual example to refer to as they began their independent work.

I explained in detail what materials they needed to have. I explained exactly what they needed to do. I would give them their card after they paired up, and got their work area settled.

It was time to start making cards!

## On Their Own!

30 minutes

Students got busy pairing up and coming to me to get their cards as soon as their work area was settled.  I passed out cards to partners, considering their levels. I encouraged them to keep the flow going by shifting the jobs back and forth between them, of listing and or drawing the arrays on the graph paper.

I roved about checking progress, stopping and showing the class good work as I saw it. One student figured out that in Educreations, you can make a graph background and use it as we did the Factorize! graph to find the missing factor.

As students approached me, there were a lot of "high fives" as they were excited about their completing of cards. I told them as they finished to go get another one and keep creating cards. They kept it going. They were engaged and the talk was constructive, hard work was going on. I loved it! We were satisfying the part of the standard that asks us to find the factor pairs and we were having fun!

Some students were able to complete as many as 5 cards in 30 minutes because either they were so good at their factor pairs, or there were a small amount of factor pairs for arrays.

As they chose their cards. I roved around asking questions about what they noticed. I didn't say anything about the colors of the construction paper because I wanted them to notice the patterns after they are laid out. I had a wonderful teaching moment about accuracy and cutting the arrays. One girl had made the factor arrays for 25 and 5x5 was not square. I counted the squares and she saw that it wasn't accurate. I explained how important that accuracy was in mathematics and that these needed to be precise. I made her go back to her work area and create an accurately cut 5x5 array. She returned to me with it  done well.

After 30 minutes I stopped them. I asked what they had learned so far. One girl mentioned that working with partners helped her find all the factor pairs more easily. Another student talked about how it was a fun way to learn their factor pairs. I asked about the importance of accuracy and the girl I had corrected raised her hand and smiled. I asked if she would share her experience.

It was time to pick up and gather together to place our cards and examine them.

## Looking for Patterns

10 minutes

I gathered students in the center of the room asking them to bring all the cards they had finished.

I asked for cards in numerical order as I laid them down in wide spot of floor in my classroom. I asked students to keep laying the cards down in numerical order in arrays. I stopped around the number 32 because it was enough for us to look at for patterns.

I asked them to all take a good look at them and see if they notice some kind of pattern. I got various answers as they tried to pick out some pattern with the colors. They weren't linking the amount of factor pairs with the colors yet. They weren't seeing it. I finally guided their thinking by drawing their attention to the red cards. And then it all started to fall in line. They noticed the red had one factor pair and it was a beautiful transition to talk about prime numbers. I did not list the vocabulary word on the board at this point because I wanted them to continue focusing on the cards.We continued by looking at the green cards and they saw the amount of factors as I introduced the concept of composite verbally. After that, they focused on the blue cards. They quickly saw the square arrays on these cards. I told them that the next lesson would be about learning to how to identify prime, composite and square numbers and we would focus on the vocabulary and meaning using these cards. This was a great way to wrap up and introduce tomorrow's lesson!