Prime and Composite Numbers

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.

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The lesson starts out by having kiddos work in pairs using square tiles to find all the different arrays for 24. The students record their arrays on graph paper. 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.

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.

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:

• 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.
• 2 is the only EVEN prime number. All other even numbers are composite, because 2 will always be a factor.
• Odd numbers CAN be composite (big misconception with kiddos). Point out examples—9, 15, 21, etc.

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.