Approximating Square Roots Question Stack

Lately I've been using a lot of question stacks with my students.  I like that this practice structure is self-checking and helps students gain confidence.

My students have learned to approximate irrational square roots to the nearest whole number.  In past years, my students have always done well with determining the closest whole number; however when I asked them to plot an approximate point on a number line, many students put a point right on the whole number.  For example, my students would tell me that the square root of 46 is between 6 and 7 (closer to 7), but when they plotted a point on the number line, the point was right on the number 7 instead of somewhere between 6 and 7.

This year I wanted to give my students more practice with recognizing and plotting these irrational square roots on a number line.  I created two question stacks with different levels of difficulty.  Instead of writing the approximate answers in words (between 6 and 7), all of the answers were shown on a number line.

When it came time for a quiz, I found that my students this year did a much better job with approximating square roots on a number line.

Level 1

Level 2

View/Download: Approximating Square Roots Question Stacks