Mary Dagani | April 2018

Building Musical Phrases Through Math

Hello and welcome back for more of Teaching with Creativity, season 2.

I’m Mary Dagani, and I’ll be your host for today’s show. I am a content specialist here at– your digital learning hub for arts integration and STEAM. I’m so excited that you are able to join me today, because I’d like to talk to you today about something very near and dear to my heart…music!

Yes, I’ve been playing the flute for over 40 years and am also an Orff Schulwerk music specialist.  Ironically, I don’t work as a music specialist though.  I am fortunate enough to be a STEAM Teacher on Special Assignment (TOSA), and I teach the arts in, and through, the STEM content areas.

Because of my extensive background in music, I do have an advantage when it comes to integrating anything having to do with music.  However, I’m very much aware that there are many of you out there who are more than a little apprehensive about integrating music into your content areas.  You know, music can be pretty intimidating.

I’m here to give you the support and hopefully provide you with a simple to use idea that you can integrate into your math content area when you are teaching addition, repeated addition, or multiplication at any grade level.

So, are you ready?  Here we go…


Building Math and Music through Phrases

We are going to start with some simple body percussion.

For those of you who have been fortunate enough to see the group Stomp, you know how complex and exciting body percussion really can be.  And it’s amazing how many timbres they get just by slapping, tapping, and stomping on the stage.  For those of you interested in learning more, I’ve included a link in the show notes to the website of one of the most influential musicians when it comes to body percussion.  A gentleman by the name of Keith Terry – I highly encourage you to check out his website when you get a chance!

For the sake of simplicity, we are going to use just 4 places on our body to create our sounds for out body percussion.  They are: our feet – we’re going to stomp, pat (thighs), clap, and a snap.  And by the way, if you’re working with your little ones and they ever say: “But teacher, I can’t snap.” You tell them to fake it till you make it!)

That’s all you have to know – stomp, pat, clap, snap.

We’re going to begin our lesson with direct imitation – with imitation, you are essentially just going to copy me, but not at the same time.  Often times, to clarify, I will say to the kids, “Please be my echo.”  Or sometimes I will use the terms:  my turn – your turn.  This way, they know that they don’t do what I’m doing, while I am doing it. Their job is to watch/listen, and then copy me when I’m done.

We are going to be using 4-beat phrases.  In music we have what we call common time or 4/4 time.  This is the simplest level to start at.  So basically is what it is, is 4 quarter notes.

I am going to play 4 beats and you’re going to play it right back to me.   I trust that you are doing it our there!

So here I go…1-2-echo-me…

You get the idea?  I play it – you play it.  This could go on forever with the little ones, trust me, in your primary classrooms.  Your students might even get so good at it, that they can take a turn being a leader, and the rest of the class could imitate them!  And actually that is a good sign, because that is when you know it’s time to move on to the next level.

One thing you can do to make it a lot more fun, is you can add music.  Any music in 4/4 time such as the – just a few suggestions – theme song from Rocky, Beverly Hills Cop, Star Wars, etc.  You get the idea.  Practice at home first, and any of those songs would work.

I would also suggest using pieces of music w/out words – this gives the students an opportunity to focus on the activity, and not on the lyrics of the song!

I know what you’re thinking about now –Hey Mary, where’s the math? Well, so far we’ve just been counting to 4.  That’s why this entry level is good with your little ones.  Think baby steps!

Let’s step up the process and have a musical conversation –  this is called question/answer

Just like a real conversation with your friends, a musical conversation needs to be interesting and exciting.  We don’t want to repeat each other’s words because that would get really boring – fast!

Once the students have gotten really good at stomping, patting, clapping, and snapping, it’s time to change it up!

In a musical question/answer or conversation, what happens is, the 4-beats belong to the first person, which would be the teacher in this case.  And the student answers back using 4 original beats.  So they’re no longer copy catting.  This takes a little longer because of that processing.  They have to think of what they are going to do AND they have to keep that steady beat going.  So, this might take a little while, but trust me, it is well worth it to push through that learning phase.

Don’t forget to point out that your 4-beats, plus their 4-beats is… 4 + 4 is…8.  So you’re actually creating 8 beats together.

So let’s do a little practice.  I am going to trust that you are giving me an answer back at home.  Question:  1-2-here I- go…

You get the idea.  So just back and forth with 4 and 4.

Imaging if we were writing this out, we could use a 1 by 4 array kind of like this…  And I’ve written out my: stomp/clap/pat/clap.  I would then ask the kids, “How could you take your own 4-beat answer and turn it into 8 beats?”

Well, in music we have something called a repeat – 2 parallel lines with 2 dots kind of like a colon.  And then at the end of the repeat, is the colon with the 2 parallel lines.  So everything within those two symbols gets repeated.  So what I’ve written down for you would go:  stomp/clap/pat/clap (repeat) stomp/clap/pat/clap.

Now what’s happening is the kids are playing 4 beats, but twice.  So, 2 x 4 is…?  Eight.  We are getting into multiplication here.

Now we could have a musical conversation where I’m going, okay, I’m going to repeat my pattern, and you repeat yours.  So I have:  stomp/clap/pat/clap (repeat) stomp/clap/pat/clap – your turn 3-4, (repeat) 2-3-4.  Got it?  So now we have 8 and 8.

It is very interesting.  Now we have many ways to make 8.  I could have 4 and your 4, or I could repeat my 4.  We are starting to get into repeated addition or multiplication here.

Image if the kids go and find a partner and have to write that out.  This would also be a good way for you to assess them.  You could see what they are doing and if they understand it, and they can write it out.  It’s kind of like the beginning steps of writing out their music in non-standard notation.

I just thought of a question:  Would it be okay for a student, if you are doing question/answer, to answer you with 4 of the same responses.  For instance, if you were doing 4-beats of a question and 4-beats of an answer, and the student answered you by just going: clap, clap, clap, clap.  Would that be okay?    Absolutely!  That’s where the student feels secure.  And our hopes would be that they would use all 4 levels of body percussion, however there are going to be some students that, maybe, just aren’t ready to move into that arena yet.  If they can just pat 4 times and keep that steady beat, you’re on the right track.

Reality Check!!!

If your district is anything like mine, our students have had little to no formal music training – other then what they have done at home and in private lessons.  So keeping a steady beat and body percussion is very new to all of our kids.  If I were starting this, I would have to use these basic, the imitation and the question/answer with my upper graders.  And I would need to teach them this and solidify it before I could start incorporating the math.  So think about that when you’re working with your kids.

So, let’s move on and assume that all of our students can confidently maintain a musical conversation with your, or with another student.  And create 8-beat phrases.

What if you asked them to work with a partner and turn your 8-beat phrase into a 16-beat phrase?  How would you do that?

Well, they could take their 8-beat phrase, for instance their phrase with a repeat, and add it to their partner’s phrase with a repeat.  And if I’m not mistaken, (2×4) + (2×4) is 16.

So if you ask them to work with their partner, they could start writing out equations to match up with their phrases.

One thing we could also look at, is taking partners writing an 8-beat phrase, putting repeat signs on the whole thing.  For instance 2 x 8 , what about, um,… if I wrote 8 and my partner wrote 8, we put them together – 8 + 8

There are so many different combinations they can use to make 16.

Here are just a few:



(2×4) + (2×4)


How about that one!  What would it look like on paper?  It would be 2×4, but I repeat it all 2 times.

Asking the students to write out their equations would help solidify how math is an essential part of creating musical phrasing in 4/4.  Don’t believe me?  Go check out that Star Wars theme again.  And you tell me if you don’t hear groups of 16.

I don’t know about you, but I can sincerely see spending a few minutes every day or every other day on this process – because there is more…

What would happen if you asked the students to now turn their 16 beats into 32?  Imagine all of the combinations they could have just starting with that 4 beats and a repeat sign:

They could have:

16 + 16


(2×4) + (2×4) + (2×4) + (2×4)


So, all of these ways to make 32 beats.  The complexity though, here, is remembering what the pattern is.

So using that repeat sign on a simple 4-beat phrase or 8-beat phrase is probably the most successful way to go.

I’d like to point out something – especially to those of you who may know a bit about music.  Please note that the rhythms we used today weren’t anything more than 4 quarter notes.  Since the objective of our lesson wasn’t fractions, we kept it really simple and we were able to focus on the use of addition, repeated addition, or multiplication to build a musical phrase.   And that was the whole point of my lesson.

I hope that I was able to share a simple music activity that you can integrate into your math lesson.

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And remember: you deserve to thrive as an educator.

Let your creativity shine through.

Thanks so much for watching – I’ll catch you next time on The Teaching with Creativity Show.

So long for now!!

About the Author

Mary is a STEAM TOSA, Project Lead the Way Launch Lead Teacher, and an Orff Schulwerk music specialist. Her eclectic background, along with her 28 years of elementary classroom teaching, gives her a unique perspective on Arts Integration.