This week in Pre-Algebra we are reviewing square and introducing cube roots. Many of the kids have a tough time visualizing why a number is squared (it really makes a square!) and why they are cubed (3-D cube!). I wanted to spend some time really linking exponents to roots.. squaring is opposite of square root, cubing is opposite of a cube root..

I started the lesson with a square root video from BrainPop (requires login) and had the kids fill in an organizer with their own definitions of words from the video.

Then I played the song “It’s Hip To Be Square” by Huey Lewis and the News while they created a circle map of everything they knew already about squares.

Then with their shoulder partners, they had to draw the first three smallest squares and talk about their dimensions (1×1, 2,×2, and 3×3) in relation to the total squares.

After some discussion, they had to draw the first 15 (or as many as they could fit – then follow the pattern) perfect squares on a sheet of graph paper that they glued into their interactive notebooks. They used the information from their graph paper to fill in this chart:

We then discussed the relationship between length, width, and area of a square. We discovered that the side lengths will always be the same in a perfect square so we can say side x side = side squared.

After more discussion we filled in this organizer:

I really think the “if…. equals….. then…. is….” helped a lot of my students to understand the relationship between the two. I made sure to use the sentence framing for each of the examples.

I have a 90 minute block A/B schedule, so we then continued on to cube roots and approximations of square roots. For a shorter class this is a great ending point before practice/homework.

Cube Roots: I first had the students independently answer these two questions based on the diagram:

A lot of students didn’t understand how there were only 27 cubes, they wanted to count faces and answered 54. I had to show them layer by layer why there are only 27.

Then we discussed how cube roots are similar and different from square roots here:

Then I gave them the rest of the chart for independent practice:

We quickly talked about approximating square roots to what two whole numbers a non-perfect square lies between.

They all seemed to get this part fairly quickly:

Then I gave them a homework page with word problems and practice placing roots on a number line.

The file is available (for free) in my TPT store!!

Enjoy!

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