Multiply and Divide by Powers of Ten!

I have a bit of a love-hate relationship when it comes to teaching students the shift patterns of multiplying and dividing by powers of ten.  It's one of those underestimated concepts that you think will be so easy for them to learn.  You soon realize that it's not as simple to teach as you previously thought.

This pretty much sums up my early experiences after a lesson on multiplying and dividing by powers of ten:

My thoughts: "But, I just spent 45 minutes showing you this really SIMPLE and EASY way to multiply by powers of ten MENTALLY. Why are you still working this out on paper?!?

Obviously, the problem wasn't with my students; it was with my teaching.  This concept isn't as "simple" and "easy" as I naively thought.  Students not only need to have a sound understanding of place value, but they also need utilize some reasoning skills (which can sometimes be forgotten when they rely heavily on standard algorithms before they fully understand them).  After several "learning experiences" (AKA #fails) as a teacher, I found that there were 3 important elements that my lessons needed: 

1. Take it slow: There is no need to rush students through this concept.  Spend at least two days working on whole powers of ten (10; 100; 1,000) before introducing decimal powers of ten (0.1, 0.01,   0.001-- Speaking of decimal powers of ten, expect some confusion and reteaching when this is introduced)  This is really a worthwhile concept for students to fully understand, so you can justify spending more time on it.

2. Make it hands-on: Just like most math concepts, when students use models that they can actively engage with, they gain a deeper understanding.  They are also able to retain the concepts better.  Below are two of my favorite hands-on activities (acting it out and using number sliders) that I use when teaching powers of ten.

3. Avoid teaching rules: Number 2 will help take care of this one.  Students will construct their own rules the more hands-on experiences they have.  I remember being taught "Count the zeros, move the decimal."  Well, mathematically, the decimal point doesn't move; the numbers do.  And counting the zeros works great when you're working with whole powers of ten.  However, if students are only taught this rule, then they will definitely run into trouble when they are faced with decimal powers of ten.

Acting it Out:

I am all for getting kids up and out of their seats, and this little activity is a perfect way to do just that.  Using blue painters' tape, I make a "place value frame" on the floor of the classroom.  I use a playground ball (handball, basketball, soccer ball, etc.) to represent the decimal point.  Students are given a piece of paper with a digit on it and then they stand in the "place value frame."  I then call out an operation and a power of ten ("Multiply by 100" or " Divide by 1,000") and the students shift accordingly.  Have some "zeros" ready for when the students shift to the point that a place value is empty.  This activity not only provides a great visual for the students, but it also adds an active element for your more kinesthetic learners.  

Number Sliders:

These are a great way for your students to "play around" with shifting patterns.  Just print {Download HERE} the "frame" and the strips (legal size) and you're ready to go.  Students can do the cutting on their own; they may need to fold the frame in half to cut the slits.

Would love to hear more ideas and "tricks" for teaching powers of ten! Please comment below if you have anything to add:-)

Provide your students with more powers of ten practice with my 5th Grade 5-A-Day Review.


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