Another week has come and gone, and I'm sure you all enjoyed this past week, if for nothing else because it was a SHORT one! To recap, last week, we got more into our study of squares and square roots. I taught you all the following points: every positive number has two square roots, a positive one and a negative one. Secondly, I taught you three situations that you would see which would require you to simplify square roots. We also continued to work on and study exponents, scientific notation, and all the standards in probability which we studied before we got into square roots. The week culminated with Test-takin' Thursday (I didn't know that all of my colleagues had also scheduled tests for that day, but I'm sure you all did fine).
This week, we will learn how to add, subtract, multiply and divide expressions which have square roots, and then we will get into our next GPS Task for this nine weeks, exploring what we have learned about exponential powers of 10. See ya in the Red Hallway, Knights! 801, SECOND TO NONE!
Saturday, October 24, 2009
Friday, October 16, 2009
We're Baaaaack!
Hey guys, sorry it's been a minute since I last posted. I get home and my weekends get so busy that I sometimes run out of time to recap and preview on the weekends. That's why I am doing this posting now, before I even leave the school!
This past week, we left our study of scientific notation and turned our attention to square roots. To recap, scientific notation is a shorter way of writing very LARGE or very small numbers. You do so by writing a factor (a number) that is greater than or equal to 1 but less than ten, and then multiplying it by power of 10. The key thing to remember is that the exponent of that power of 10 does NOT signify how many zeroes are in front of or behind the numbers. The exponent ONLY means how many times you have to MOVE THE DECIMAL. Remember also that you DO have to move the decimal, or you have not truly rendered the number in scientific notation. If you need to review this a little more, come see me after school on Wednesday of next week.
From scientific notation, we moved into the beginning of our study of radicals and square roots. Again, let me clear up a common mistake: the square root of a number is NOT just taking it and trying to cut it in half. You have to ask yourself, "What number can I multiply BY ITSELF to get the number under the radical?" For example, the square roots of 25 are 5 and -5, because 5 x 5 = 25 and (-5) x (-5) = 25. Remember that when you see the radicand sign, you are only supposed to name the POSITIVE square root of the number. We spent a little time having you all make a chart of your perfect squares and square roots all the way out to the number 25. Make sure you don't lose that chart! You will need it for some time to come! One last review point I want to make here: remember that the square root of a perfect square is the length of one side of the square. This information will come in handy for you later on in the year.
Next week, we will pick up where we left off. We'll learn how to find radicals on a number line, how to simplify expressions that have radicals, and how to add and subtract radical expressions. This is where the school year gets REALLY interesting, so make sure you are here to get in on all the fun! See ya in the Red Hallway, Knights! 801, SECOND TO NONE!!!
This past week, we left our study of scientific notation and turned our attention to square roots. To recap, scientific notation is a shorter way of writing very LARGE or very small numbers. You do so by writing a factor (a number) that is greater than or equal to 1 but less than ten, and then multiplying it by power of 10. The key thing to remember is that the exponent of that power of 10 does NOT signify how many zeroes are in front of or behind the numbers. The exponent ONLY means how many times you have to MOVE THE DECIMAL. Remember also that you DO have to move the decimal, or you have not truly rendered the number in scientific notation. If you need to review this a little more, come see me after school on Wednesday of next week.
From scientific notation, we moved into the beginning of our study of radicals and square roots. Again, let me clear up a common mistake: the square root of a number is NOT just taking it and trying to cut it in half. You have to ask yourself, "What number can I multiply BY ITSELF to get the number under the radical?" For example, the square roots of 25 are 5 and -5, because 5 x 5 = 25 and (-5) x (-5) = 25. Remember that when you see the radicand sign, you are only supposed to name the POSITIVE square root of the number. We spent a little time having you all make a chart of your perfect squares and square roots all the way out to the number 25. Make sure you don't lose that chart! You will need it for some time to come! One last review point I want to make here: remember that the square root of a perfect square is the length of one side of the square. This information will come in handy for you later on in the year.
Next week, we will pick up where we left off. We'll learn how to find radicals on a number line, how to simplify expressions that have radicals, and how to add and subtract radical expressions. This is where the school year gets REALLY interesting, so make sure you are here to get in on all the fun! See ya in the Red Hallway, Knights! 801, SECOND TO NONE!!!
Saturday, October 3, 2009
Wow, What a Week...
This past week was very hectic! We learned many things about exponents, but a lot of other stuff was going on as well. Nonetheless, I'm just going to review what we taught in my classroom. Exponents are a shorter way of showing repeated multiplication. When an expression is written in exponential form, it is shown with a base and an exponent. The exponent tells you how many times to multiply the base by itself. So, if you saw "four to the third power", the base would be four (that's the big number) and the exponent would be three (that's the small number above the base and to the right). That would tell you to multiply four by itself three times, as in 4 x 4 x 4, which would be 64. Get it?
After we got a good understanding of how exponents work, we taught on the properties of exponents. There are several that we covered. Whenever the exponent is 0, the answer is always 1, regardless of what the base is. If the exponent is negative, you have to take the reciprocal of the base before you evaluate it. When you are multiplying expressions that have exponents, if the bases are the same, you keep the base and add the exponents. Conversely, if you are dividing expressions which have exponents and the bases are the same, you keep the base and subtract the exponents. When you are raising a power to a power (we call that "power power"), you will see one base with two exponents, one exponent will be in the parentheses with the base and the other will be outside the parentheses. In this case, you keep the base and multiply the exponents. And if you see a product (or more than one thing) in the parentheses and an exponent outside the parentheses, you distribute the exponent among everything inside the parentheses. Whew! That's a lot of stuff we covered last week, isn't it? At any rate, all that stuff we covered is setting us up for what we will do next week, which will be....
... covered when I do my next post tomorrow! See you then!
After we got a good understanding of how exponents work, we taught on the properties of exponents. There are several that we covered. Whenever the exponent is 0, the answer is always 1, regardless of what the base is. If the exponent is negative, you have to take the reciprocal of the base before you evaluate it. When you are multiplying expressions that have exponents, if the bases are the same, you keep the base and add the exponents. Conversely, if you are dividing expressions which have exponents and the bases are the same, you keep the base and subtract the exponents. When you are raising a power to a power (we call that "power power"), you will see one base with two exponents, one exponent will be in the parentheses with the base and the other will be outside the parentheses. In this case, you keep the base and multiply the exponents. And if you see a product (or more than one thing) in the parentheses and an exponent outside the parentheses, you distribute the exponent among everything inside the parentheses. Whew! That's a lot of stuff we covered last week, isn't it? At any rate, all that stuff we covered is setting us up for what we will do next week, which will be....
... covered when I do my next post tomorrow! See you then!
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