Here’s a fun way to teach square roots and exponents in a hands-on way with LEGO bricks!

Lately, I’ve been working on hands-on math activities for pre-algebra and algebra 1. If you’ve taught these levels, you’ve probably realized that the concepts quickly become more difficult in a different way than elementary math.

Algebra requires symbolic notation and understanding abstract concepts. To make things worse, abstract thinking has to do with physical development and not necessarily intelligence. Have you ever tried teaching negative numbers to someone who isn’t quite ready? Everyone cries, everyone is frustrated, and no one learns math! An otherwise intelligent student may still struggle with abstract concepts if their body has not caught up yet.

During the elementary years, we can use math counters or blocks or cookies to show that 12 + 7 = 19. But how do you picture 7 – 12 = -5? You can’t exactly show -5 cookies! (This is where a good number line activity comes in, but that’s not my point for now. It’s still hard for some students!)

And yet the math book moves on…

As homeschoolers, we can choose to wait on a concept and come back to it a month or two later. We can even choose to change books mid-year, or do a second year of pre-algebra or algebra 1 if we want. But I know that not all of you have that luxury.

And so, to help your students and mine, here is the first post in a series on hands-on math for pre algebra and algebra 1. We CAN make math concepts more concrete to help our kids!

Teach Square Root with LEGO Bricks

Calculating square root is a complex process. Students in pre-algebra and algebra 1 can memorize the common square roots, or can use a scientific calculator to calculate them. However, it’s important to understand the concept.

We started by building a square out of LEGO bricks that is 8 studs by 8 studs. It’s easy to see that this square has 64 total LEGO studs in it.

The square root of a number is the number that can be multiplied by itself to get that number. So, the square root of 64 is 8.

Does every number have a square root? Yes. But, it won’t always be a WHOLE number!

Actually, every positive number has TWO square roots, one positive and one negative. -8 x -8 would also equal 64. But we can’t show that with LEGO bricks as well…

We built a fun series of the whole number squares up through 10. It looks so cool!

Teach Exponents with LEGO Bricks

When my current 8th grader started learning about exponents, he had a hard time remembering that exponents mean multiplication and not addition. For example, he would go back and forth between understanding that 33 means 3 x 3 x 3 and thinking that it means 3 + 3 + 3. There’s a BIG difference!

Here’s a way to build exponents with LEGO bricks!

The first row is 3.

Then, we build 32, which is 9.

Deciding how to build 33 took a little thinking.

This was my first thought – to do a cube that is 3 x 3 x 3. And this definitely works! But then, you might get stuck on how to represent 34.

So here’s another way to approach it.

You can think of 33 as three 32‘s. In other words, three 9’s.

Then when you move on to 34, you can build it as three 33‘s or three 27’s.

This really is a great way to show exponential growth!

3, 9, 27, 81.

If you keep going, 35 would be 324! It would be 3 of what you see there for 34.

Pull out the LEGO bricks, and math can be FUN!

Soon, I’ll be linking more hands-on algebra ideas here.

For now, here’s a collection of elementary math activities with LEGO bricks!


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  1. Katrina Feb 20, 2023

    I’m excited to share these with my 8th grader in pre-algebra. Thank you, and please keep the algebra lessons coming. 🙂. They’re helping ME visualize what these concepts actually mean, after a lifetime of “plugging and chugging” numbers into formulas.


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