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 square manipulatives. 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. 

If you try this activity, I'd love to hear how it goes! 


Related ideas:

 Finding GCF and LCM with the Upside-down Cake Method
Finding GCF and LCM with the cake method

GCF, LCM and Prime Factors Math Pennant Activity
GCF, LCM and Prime Factors Math Pennant

free prime factorization math word wall reference
free prime factors math word wall references

Scaffolded Math and Science blog


4 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?

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

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