Modeling Approximate Square Roots of Nonperfect Squares

Approximating the decimal of nonperfect square roots was dreamy using modeling with tiles. This is by far my favorite way to introduce and teach it! After learning about perfect square roots, I challenged my students to find the square root of 11 without a calculator. They racked their brains and went through their multiplication tables 47 times before saying they didn't think they could. I gave them algebra tiles and graph paper and told them to use eleven tiles and make a square. Group by group started saying it wasn't possible.

I then had them remove tiles to make a perfect square and count how many that was. We talked about how the square root of eleven had to come after the square root of nine. Next, we replaced the extra tiles with a different color and wrote that number as our numerator.

Tiles were added until they had a perfect square. They counted and we discussed where on the number line it would fall. The number of tiles for the next perfect square was used as our denominator.

Include the perfect square and approximate the decimal. I had them check to see how close we came using the calculator and it was all "oooohhhs, ahhhhhs" around the classroom! It was exciting and my students felt like mathletes!

I gave them graph paper and they begged for more! I have used the number line with fractions of the distance between perfect squares but modeling the fractions took this to the next level. Students understood why they needed to use the perfect square before and after and where it fit on the number line.