Triangles
If Y = 12 cm and X = 9 cm, what is the length of Z?
How would you solve this problem?
posted by Mrs. Kimball @ 4:45 PM
Sunday, March 4, 2007
If Y = 12 cm and X = 9 cm, what is the length of Z?
If Y = 12 cm and X = 9 cm, what is the length of Z?
6 Comments:
My students are very familiar with the Pythagorean Theorem. They would square both legs of the triangle and then take the square root of the sum of the squares. This would give them the hypotenuse of the triangle which is Z.
Pythagorean Theorem. MOst of my kids are not familiar with Pythagorean thm as we don't cover geometry until the end of the year. Most of my students are honors kids so i expect the'll get it easily. My 8th graders are very familiar with this and had no problems solving this problem. The biggest issue with pythagorean Theorem is when the students are given the hypotenuse and one of the legs and they have to realize that they aren't solving for c this time. I try to help them remember to identify the hyp. as the longest side and opposite the right angle.
I currently teach a replacement seventh grade math class with two students. We have not reached the geometry unit at this level. I gave the students the equation for the Pythagorean Theorem and they were able to work through the problems with guidance. The students were able to replace the variables, but had trouble with squaring the numbers and finding the square root of the answer.
I would instruct the students to look at the angles in the triangle. Since they know to use the Pythagorean Theorem when it is a right triangle that has two sides that are labeled and one side that is unknown we would write the equation on the board. This would help the students who have not memorized the formula. We could then substitute the variables for the numbers that we know. This would give us 12^2+9^2=c^2. The students are familiar with calculator functions and would square 12 and square 9 and add the two numbers giving them 225. Finally they will take the square root of c^2 and 225 which will leave them with c=15 cm.
Most of the 8th graders know to use the Pythagorean Theorem. The rest would need a reminder, but then could solve it. A few of the 7th graders are familiar with it, but once given the formula they can all solve problems like this.
My eighth graders are familiar with the Pythagorean Theorem and would be able to solve for the missing side given this problem. My sixth and seventh graders, while not familiar with the theorem, have worked on evaluating expressions and formulas. They would probably be able to solve this problem, given an explanation of the theorem. The biggest difficulty for most of them would be that as a final step they would have to take a square root, since they are solving for the length of one of the legs rather than the length of the hypotenuse.
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