## Skills & Strategies #4 - Visualizing and Understanding Square Roots Using a Multiplication Table4/10/2017 Square roots can be a confusing concept. They can be especially tricky for younger students (e.g., middle schoolers) who may not be developmentally ready for the concept, for students who have difficulty making connections between concrete and abstract concepts, and for students who have difficulty visualizing information. I've found that a multiplication table can be a great tool to help students visualize the relationship between squares, their sides and areas, square numbers, and square roots. Here are some activities to consider: - As an instructional lesson, demonstrate how to draw a square on a blank multiplication table. Articulate and show the relationships between the sides and area of the square, how those values can be represented on the multiplication table, and then how that visual information can be used to find the square root of the square number. Use this visual representation to show the relationship between the square root of the number and the answer (e.g., "the square root of 16" and "4"; the square root of the area of a square gives you the length of the side...). There are lots of ways to play with this -- have fun!
- Have students create their own square root multiplication tables using a blank multiplication table (these are available to download on my
). Several of my students have really enjoyed doing this, both because they can be creative, and because it makes the concepts super concrete and accessible, which makes them feel knowledgeable and in charge.**website**
- For students who have a very significant difficulty processing visual information and may become overwhelmed by too much visual information, consider having them use separate multiplication tables for each square root instead of drawing them all on one page.
- Once students can see the basic relationship, this table can also be used to approximate and visualize square roots of non-square numbers (e.g., the square root of 20 is between 4 and 5) by creating or visualizing squares in between the perfect squares and/or using the line created by the perfect square (roots) as a diagonal number line. Note that some students may want to find the square root of 20 by finding the number 20 on the multiplication table. This becomes a great teaching opportunity -- if the numbers on the multiplication table can be used to find the exact square root of 25, why isn't the same true for finding the square root of 20?
- Give students time to practice using their multiplication table to find square roots as an independent exercise to build skill and understanding, then have them practice using their tables while completing math problems that require them to find square roots (applications!).
- Consider allowing students to use their visual aid during subsequent assignments and assessments pertaining to square roots, especially if they have known difficulties processing visual information. Some of my students have put their square root tables in their math notebooks in addition to a regular multiplication table for easy access during assignments and assessments.
Enjoy!
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