# Prime and Composite

### Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

My favorite way to teach is to not teach at all.  So, I’m done with this post.

Oh, you’re still here!  So is this just the rambling of an eccentric math coach?  No.  What I mean is that it’s so much richer when kids learn on their own without being “taught”.  A case in point is one of my favorite lessons on prime and composite numbers.

The lesson starts out by having kiddos work in pairs using graph paper to find all the different arrays for 24.  Come together as a class and share all the ways they found.  Take them as the kids offer them, without organizing them in any way.  After the students have offered all their suggestions, ask if there is any way to determine if we’ve found all the combinations.  If nobody offers it, suggest that maybe we organize our number sentences.

Then is looks something like this:

1 x 24
2 x 12
3 x 8
4 x 6
6 x 4
8 x 3
12 x 2
24 x 1

It’s always fun to ask the kiddos what patterns they notice.  Next, I like to show the kids how to create a t-chart for factors and how to organize the factors in a list (see the picture below).

Now for the fun!  Pair the students and assign them numbers to represent three ways–with arrays, a t-chart, and an organized factor list.  Your goal is to get as many numbers done as possible.  So initially assign the numbers sequentially to each pair, but as pairs finish, just give them the next number in the sequence.  See the pictures below to visualize what they are creating.

Once they’ve finished, take the posters to a large open space (my 5th-grade teachers use the hallway) and lay the posters out to make a number line.  Again, ask what the kids notice (some numbers have more factors than others, some only have 2 factors, etc.).  Bingo!  Now it’s time to introduce the vocabulary–prime and composite.  Prime numbers have only two factors, 1 and itself (for example, 7 has only 2 factors–1 and 7).  Composite numbers have more than two factors.  The kids then go back and add to the bottom of their posters if their number is prime or composite.  With the posters complete, put them up on the wall for a great visual.  Things to discuss:

• 2 is the only EVEN prime number.  All other even numbers are composite.
• Odd numbers CAN be composite (big misconception with kiddos).  Point out examples–9, 15, 21, etc.
• What about 1?  It has only one factor–1.  I love how one of my sweet 5th-grade teacher’s kiddos put it–instead of prime or composite, they put weird on their poster!  Mathematically, 1 is neither prime nor composite.

So now do you see what I mean about not teaching?  In this lesson, the kids make their own discoveries and then you just put the words to it.  Learning without teaching. 🙂

1. Perfect timing! I’m just getting ready to start this. Love this activity!

• Gotta love great timing! Thanks for the comment. 🙂

2. Just writing multiples & factors, prime & composite lesson plans for next week. This is perfect!

• Yea! Glad to hear it was right on time!

3. Donna:
I saw this on Facebook when you first posted it and immediately printed it out. Last Thursday I did this activity with my fourth graders. They LOVED this activity! Instead of graph paper, I got out my counters and they made arrays out of them. We called the number one “Special” because it is not prime or composite. I have to admit I was skeptical, because sometimes I feel that my students sit back and expect me to discover things for them. Because of this, I planned a second day of teaching to actually teach them about prime and composite numbers. Surprise, surprise. . . I didn’t have to! My students really understood the concept! We then moved on to the Sieve of Eratosthenes and I showed them how the Greek mathmetician figured out how to determine prime numbers. Any how, I just wanted to let you know how much I enjoy your blog and how successful this activity was for me. I look forward to many more activities (and I’m sure my students do as well!)

• Jean, thank you SO much for coming back and updating me on how this lesson turned out with your class. My heart is so happy!! 🙂