A hands-on prime vs. composite numbers investigation

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

The setup is easy: students cut out 100 squares to use as their algebra tiles. You can get the free 100 squares template here.


free 100 squares prime numbers investigation template

After cutting out their squares, students investigate different numbers to see if they make rectangles. 

Since a prime number is cool in that the only numbers that divide into it are 1 and itself, if a number is prime we won't be able to make a rectangle from its number of squares manipulatives.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

Let's start with 24. I counted our 24 squares to use in this investigation. At first it may seem that we can't make a rectangle... but we have to try more than one configuration.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

And since we can make a rectangle from 24 squares, 24 is composite. 

There only needs to be one way to make a rectangle to prove that a number is composite, but some numbers will of course make more than one rectangle. Some students may find 24's 2x12 configuration. If there's even one configuration that makes a rectangle, we have a composite number!

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

Is 23 prime? This configuration doesn't make a rectangle.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

Neither does this one.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

After a bunch of tries, we find that it is impossible to make a rectangle from 23 squares, so 23 must be prime. 

The more students working on each number the better. This helps make sure no configurations are left out so that students can be sure a number is prime.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

Let's try one more... 27. This isn't a rectangle.

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

Neither is this, but we're almost there....

If your students struggle with the idea of prime vs. composite numbers, this hands-on investigation activity into prime numbers may be helpful, especially to the kinesthetic learners in your classroom.

24 squares makes a rectangle so 27 is composite. 


Additional resources:

If you'd like to learn more about ways to use algebra tiles, I have put together an algebra tiles tutorial video that covers ways to use algebra tiles in middle school math.


Using Algebra Tiles in Middle School Math:



watch video





Scaffolded Math and Science blog


15 comments:

  1. How do you address 2 and 3? They are both prime and can make rectangles. Would we need to specify that if the only way to make a rectangle is one long line, then that number is prime?

    ReplyDelete
    Replies
    1. Great question. Yes, a side of 1 can't count because it would show a factor of 1.

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  2. Love this activity! Thank you for sharing

    ReplyDelete
    Replies
    1. My pleasure! I hope you have a wonderful winter break!

      Delete
  3. I love this activity for prime numbers and use it all the time with decks of cards.

    ReplyDelete
    Replies
    1. That's neat that you use cards! I hadn't thought to do that.

      Delete
  4. How does this transfer to other higher numbers? My students do not know their multiplication/division factors. They are in Resource Room for math in 6th grade.

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  5. Can we use for this for greater numbers more than 100

    ReplyDelete
    Replies
    1. Definitely! I just kept it under 100 so the pieces would be manageable for my daughter to count. You could use any number of pieces.

      Delete
  6. How do you address 9? 9 is a composite number but it forms only square instead of rectangle. What will do?

    ReplyDelete
    Replies
    1. Since a square is a rectangle, arranging the pieces into a square would mean that the number is composite and not prime.

      Delete

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