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# Using LEGO to Build Math Concepts

By Alycia Zimmerman on December 27, 2013

I was not one of those LEGO® kids growing up. Sure, my brothers had LEGO bricks, and every so often I’d kidnap some tiny LEGO men for a make-believe game. But I didn’t truly appreciate the engineering capacity of those studded plastic bricks. They were just so rigidly rectangular!

As an adult, I’ve come to appreciate LEGO, both for its rectilinear aesthetic, and even more so, for its mathematical might. In the classroom, the tiny bricks are now my favorite possibility-packed math manipulative! Read on for a sampling of math activities that use LEGO pieces to build and reinforce key math concepts.

## LEGO – Not Just for Playtime

Chances are that if you are a parent or teacher, you already know, at least in theory, that these sturdy plastic blocks have huge intrinsic educational value. Along with the obvious creative implications, while children play with LEGO blocks, they are also building their spatial and proportional awareness. Advanced LEGO kits are even used on the high school and college level for computer programming, robotics, and more.

Let’s face it though – many elementary school teachers are women who, like me, did not grow up as LEGO experts. And until you’ve had some firsthand experience playing around with the blocks, you may not be comfortable using it as a teaching tool. So, here is my plea: Find some LEGO bricks in a storage closet or basement, and take some time exploring how they work. Count the studs, explore the dimensions, build some towers. And I guarantee, you’ll now be thinking … MATH!

You'll undoubtedly find mathematical inspiration in a pile of LEGO bricks.

## LEGO for Building Part-Part-Total Thinking

For younger mathematicians, composing and decomposing numbers is a key component of building the number sense needed for arithmetic operations. Students begin with small landmark numbers such as five (one hand) or six (a standard die,) and build towards the all-important ten.

LEGO bricks are awesome for part-part-total explorations! As with other popular part-part-total math manipulatives such as dominoes or dice, these bricks have clearly marked chits (on LEGO we call them studs) for students to count. The studs are often grouped in twos, which facilitate counting by twos rather than counting the studs individually. With practice, students will recognize arrangements of studs, and will not need to count them at all (subitizing).

Students can group combinations of two or more LEGO bricks and find the total number of studs, or students can start with a larger brick, cover part of it with a smaller brick, and figure out the amount of remaining uncovered studs.

As a third grade teacher, I’ve spent hours and hours drawing arrays, modeling how to skip count with arrays, deconstructing arrays, and building arrays with a myriad of tiny things. (Raisins, pennies, grains of rice …) After all, internalizing why and how arrays work is a cornerstone of building multiplicative thinking among my budding mathematicians. (For more ideas about building multiplication concepts, see my blog post Total Recall: Helping Our Students Memorize Multiplication Facts.)

Having a collection of LEGO pieces on hand during multiplication lessons is so useful. I whip a few out to reinforce the area model, to demonstrate square numbers, and to remind my students about the commutative property of multiplication. Here’s a photo tour of some of the possibilities for using Lego to teach multiplication, and of course, its twin sibling, division.

Students can combine LEGO bricks to make a wide range of arrays.

Exploring the factors of 48 using the area model and Lego bricks.

Download my Multiplication and Division Exploration with LEGO for students to complete independently or with a partner.

## Tackling Fractions with LEGO

Fractions always seem to trip up my students. Things get murky when we’re talking about different size “wholes” or when we switch from thinking about the fractions of one whole to fractions of a set. The only way to combat fraction-mayhem is to provide students with a LOT of opportunities to experience fractions with tangible objects. Pattern blocks are a popular fraction manipulative, but I like LEGO even more. (Pattern blocks can only be broken down into sixths when using the hexagon as one-whole. LEGO blocks have many more possibilities!)

With guided inquiry packets, students can work independently on exploring new math concepts.

## Exploring Mean, Median, Mode, and Range with LEGO

When analyzing data, upper elementary students explore various ways to express the “central tendency” of their data set; that is, various ways to express the average. When finding the mean (arithmetic average), students quickly learn to add all of the data and then divide the total by the number of data points. But very few students fully understand why they do this add-then-divide dance to find the mean. While evening out LEGO towers of varying heights, students have a first-hand experience of what “mean” means.

Students "add" and then "evenly divide" four LEGO towers to discover the mean value.

## Two Tips for Teaching with LEGO

### “Explore” Not “Play”

Let’s be honest, the first time you put out a bunch of LEGO pieces during a math lesson, the students are going to be itching to build towers, stage battles, and trade bricks. Don’t fight the tide – embrace it, for a bit.

Give your students a predetermined amount of time to “explore the mathematical possibilities of their bricks.” Really, this is just a fancy way of permitting the students to play around, but it will go much smoother later on if you get this sanctioned playtime out of the way. (For more ideas about managing the use of math manipulatives, check out Meghan Everette’s fabulous blog post Math Manipulatives: Learning to Control the Chaos.)

### Bag your LEGO into Kits

When preparing for a LEGO lesson, I rarely give students access to the full range of LEGO pieces. Ahead of time, I prepare Ziploc bags with a careful selection of the pieces I know my students will need to complete the assignment.

I also make sure my students understand how to return their bags of bricks. Bags are to be sealed and bricks are separated, unless they received a bag of “towers.” I often use LEGO-math as a math center activity, and the students are remarkably independent when they are provided with clearly labeled bags of specific bricks.

What are your favorite math manipulatives? Do you use LEGO in the classroom? Share your suggestions, questions, and comments in the Comments section below!

Hey guys this is an amazing way of math play. We love it!!

Check out the amazing wooden math blocks from SumBlox they also are an extremely inventive way of introducing children to Mathematics and the basic fundamentals behind Addition, Subtraction, Multiplication, Fractions and Even Adding Fractions. We are here in Australia to help at www.sumblox.com.au Be sure to check this out as they are truly revolutionary teaching resource.

I am putting together a presenter's idea packet for a grant I wrote on using LEGOs in math and would like permission to use the download pages available in this article. I will certainly reference the downloaded worksheets and the article in my bibliography. The idea packet is written to inform other teachers about the grant I wrote regarding the LEGOs MoreToMath Curriculum Pack and how to adapt my grant within their classroom and grade level.

Hope to hear from you soon,

Zeny Ulloa

Just been reading about Lego being taught in education for Robotics bit.ly/1oTYWXc

a few months ago i got a Lego set and have produced a webpage called
Math with Legos
http://ldecola.net/projects/legos/
Lee De Cola.

Awsome

I have been trying to find ideas for teaching my third-graders fractions using Lego bricks. So glad I found your blog. Thank you for the activities and insight. Now, I just need to find some Legos.

Thanks,
L. Jones

I would like to publish one of your pictures along with a link to this blog post in an elementary school newsletter--is it possible to get permission to republish?

Hi Julie, message me on Facebook (www.facebook.com/TeacherAlycia) and I'll share whatever files you want to use. All the best - Alycia

Could someone recommend a great kit that would be enough for the students to use for all of these ideas? I would like to ask a grant for them to use this program in my learning support math group. THank you!

Hi Pam - I just use a collection of hand-me-down LEGO odds and ends to make my math kits, and I restock from time to time with donations from families. That being said, all you need is a basic bricks kit - you don't need the fancy wheels, windows, and other construction pieces. If you look online, you'll see Lego sells basic brick kits - something like the "Lego Education Brick Set 779384" would be more than enough to get you going. (It costs about \$50.) Good luck! ~ Alycia

Thank you for sharing this. I was really blown away by this, I NEVER noticed math in LEGOs I always saw it as art. I struggled with math my entire life and to be truthful hated it. If more teachers looked outside the norms and taught in this manner maybe they would be able to save a few more kids like me.

This concept seems like it would work to teach basic music rhythmic notation as well. As a music teacher it is always a challenge to get younger students to understand "how many in what" such as a whole note equals four quarter notes, etc. Thank you!

Great point, Robin, thanks for sharing. Coming from the opposite perspective, I often ask my students to apply their musical knowledge to understanding fractions. They are usually intrigued that a notation system they are familiar with relates directly to the fractions work we are doing in class. Cheers! Alycia

Hi,
Thank you for sharing this information. Seems to be very interesting and educational. I plan to try it whenever I teach the topics of multiplication, division and fractions. I know children will have fun learning using Lego. Plan to buy some to use in my class.

Thank you so much for sharing such a great idea, Alycia. Thanks also for the templates - I can hardly wait to try them out with my students!

This is great stuff, and you're absolutely right about the wonderful versatility of Legos in the classroom. I teach college chemistry, and use Legos when we're first talking about chemical reactions. Legos stand in wonderfully well for atoms, and it really drives home the point of how atoms combine to make molecules.

I have had a similar idea lately. I have about 5-6 ideas of things to teach with Legos. The first 2 I have completed short, 10-minute videos for, and they use Legos as props more than manipulatives. I am planning a few more on LCD and GCF and other topics using the Legos directly. I love your ideas!

Adding and subtracting positive and negative numbers:

Intro to percentage problems:

There is a new Netflix like service for Legos called Pleygo. You can create a wish list and get tons of different Lego sets. I use them and I think they are great.

My son is in Lego heaven. He has even lost some pieces and was not charged. I love it!

I love this concept. I plan to write a grant for Legos.

Hello Alycia, I love these worksheets and looking forward to incorporate into my LEGO Club that I run after school... Learning can be FUN!

Thank you for sharing your ideas. I plan to try it this week

Thanks, Miriam! I hope the lessons work for you and your students.

We used fraction strips in hand, and manipulative pieces for exploring equivalents. But when it came to doing the math on paper, I lost about half of them. Besides starting later in the year next year, when more of their abstract thinking ability will kick in, I will try your Lego bags. Maybe using something many of them know will help the ideas stick, so when we get to simplifying a fraction they can still picture it. Thanks for the templates.

Hi Cindy, I totally hear what you're saying when it comes to the blank stares over fractions. I use a LOT of different hands on activities to build the students' understanding of fractions and how they work. Just last week I had a group of students "playing" with fractions towers in an open-exploration (mind you that this is a month after beginning learning about equivalent fractions, which they can all do on paper,) and one of my students excitedly called me over. What did she have to show me? That four of the eighths blocks was the same height as two of the quarter blocks. This was a BIG discovery to her, even though she had already seen equivalent fractions in so many different ways and could ostensibly calculate equivalent fractions. Sometimes kids just need to see it in yet another way to have their a-ha moment, especially for fractions, it seems. So, LEGO may be the catalyst for some of your students - I hope it works for you! I'd love to know how it goes next year.

All the best,
Alycia

Can you provide us with the makeup of the bags you provide the students with?

These are amazing resources! My school wrote a grant for engineering and technology and was able to get a lot of Legos. I can't wait to do this with students.

Hi Kristina - Wow, a "Lego engineering" grant sounds fabulous - how fortunate for your school. Lego lessons always go over really well in my classroom, no matter the concept I'm trying to teach. The students are just so much more engaged when they get to "play" with Legos while learning math or science. Best of luck putting this into action in your classroom! ~ Alycia

Incredible article - - thanks !!!!!!!!!!!

Thanks so much for sharing. I can't wait to use lego to teach fractions!
Mariam

Mariam, thanks for your comment! Lego-Fractions was my first Lego lesson, and it made a huge difference in terms of clearing up the confusion over equivalent fractions. It's a lot of prep bagging all of the sorted Lego bricks into ziploc bags for the lesson, but I felt the investment in time was worth it! Make sure to read the exploration activity carefully to get all the groups of Lego you'll need. I'd love to know how you lesson goes after you teach it!
All the best - Alycia

Awesome lesson to solidify often difficult concepts such as fractions! Thank you for letting me have an access to this lesson.