You+can+never+escape+the+potential+problems!

Students can always get confused, even when you don't expect it. Here are some helpful hints to accomplish a smooth trip along the choppy seas of the Pythagorean theorem.
 * It is not that easy...is it? **

We suspect there are a few potential problems that //most// students will probably struggle with. While there will be other problems, these are the three we find most prevalent.

**__Potential Problem 1:__**

Students will usually use any two numbers you give them, without checking which numbers are the legs or hypotenuse (basically, they forget to ask, "what is a, b, and c?"). They get the wrong answers and more importantly reinforce misconceptions about the theorem each time they do not check for the hypotenuse. Remind them that the hypotenuse is the side of the triangle that is opposite the right angle.  TIP-- Make the students circle the hypotenuse on each triangle for each problem, so that it stands alone and they do not confuse a leg with the hypotenuse.

**__Potential Problem 2:__**

Students often do not know how to properly reduce a square root. But in geometry, it is important that students have the skills to both reduce square roots properly (exactly) and to decimals because there are times the exact answer is important, but other times that a decimal answer is helpful (measurement). For example, once you change (root) 5 to a decimal, you are approximating because square roots are irrational numbers that don’t end or repeat so a decimal is not completely exact (Think of 3.14 to represent irrational number, pi). TIP-- Have students practice, practice, //practice// reducing square roots! This is an invaluable skill they should develop.

**__Potential Problem 3:__**

Square roots in general are tricky for students, especially when they are part of problem solving. If students know they have the length of one side and the hypotenuse, they may be able to set up the equation as 5 2 + b 2 13 2, but they may not know how to solve for b once they know b 2 = 144. Reinforcing the relationship between squaring a number and taking the square root of a number is essential for students, especially when working with the Pythagorean Theorem! Make sure they know that squaring a number means multiplying the number by itself, so it is another way of showing the relationship between multiplication and division. Help students see that 5 2 is the same as 5x5 which equals 25, so the way to "undo" that, or take the square root, would be to divide 25 by 5.  *Think what number multiplied by itself will equal 25? TIP--Give students practice problems that show the relationship between squares and square roots, such as 5 2 and √25.


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