Sixth Grade
Lesson 43 - Simplifying, comparing, and ordering decimals. To simplify decimals, if the decimal numbers ends with zeroes, you can remove the last zeroes. For example, if you added two numbers and the answer was 5.030, you could take off that final zero and have 5.03. If you multiplifed two numbers and ended up with 40.000, you can remove the three zeroes after the decimal point and have the whole number, 40. (You don't need to put a decimal point if it is a whole number.) To compare decimal numbers, you need to line up the numbers as if you were going to add them. Fill in any spaces with zeroes to make each number have the same number of decimal places. Then, compare the numbers after the decimal points. For example, if you were to compare 0.03 and 0.4, you would write them like this:
0.03
0.40
and compare the numbers after the decimal, in the first number, there is just a three, in the second number, it's a 40, so 0.4 is larger.
To order, you do the same thing, only with more numbers. For example, if you needed to order these: 0.051, 0.04, 0.15, and 0.405
Line them up like this:
0.051
0.040
0.150
0.405
Notice that on the 0.04 and 0.15, I added a zero after them so that all four numbers would have three digits after the decimal point. Now, just order the numbers after the decimal. Since 40 is the smallest, 0.04 is the smallest. Next is 51, so 0.051, then 150, so 0.15, and 405 is largest so 0.405 is the biggest. Don't forget to write them in order: 0.04, 0.051, 0.15, and 0.405
Seventh Grade
Spelling - Study for the test over Unit 13 tomorrow!
The class took a Vocabulary test today, so there is no vocabulary or Grammar homework. After the test, the class wrote about their study habits and we did a few memory activities to discuss the importance of paying attention! We will discuss in detail the reasoning for doing the activities in class tomorrow.
Math - The class continued with the memory activities during math and took the vision screening test.
Literature - Read up through chapter 17 by tomorrow!
Eighth Grade
Lesson 3-9, #2-15. Multi-step equations with variables on both sides.
For the first two equations, you will just need to get the variables on the same side of the equation. To do this, add or subtract the term with the variable from both sides. (Do whatever you need to do to eliminate it from one side.) For example:
3x + 5 = 2x -3
Here, you would subtract 2x from both sides. This would eliminate 2x from the right side. On the left side you would now have 1x (or just x) because 3x - 2x = 1x. So you would then have this:
x + 5 = -3
To solve this, you would subract 5 from both sides. -3 - 5 = -8, so x = -8
To solve #4, and any that have parentheses as part of the problem, you must first eliminate the parentheses by using the distributive property. For example:
-2(4x - 8) = 10x + 2
So, you would distribute the -2 across the parenthesis by multiplying it by both 4x and -8. You would have:
-8x + 16 = 10x +2
Notice that when I multiplied -2 x -8, it is now positive 16. Be careful and include the signs that are in front of the numbers.
Now, you would get the terms with the variables on the same side of the equation by subtracting 10x from both sides.
-8x + 16 = 10x + 2
-10x -10x
-18x + 16 = 2
This eliminates the 10x on the right side and -8x - 10x = -18x would be on the left side.
Now you solve like normal by subtracting 16 from both sides and since 2 - 16 = -14, you'd be left with this.
-18x = -14
Now, divide both sides by -18. You would have the fraction -14/-18. Simplify by dividing both by 2 and eliminating the negative signs. Your answer would be 7/9.
I used Mimio to make this problem to show you how to solve problems with fraction bars and numbers in the denominator. Step by step instructions are written below.
Step 1: First think of what number would make a common denominator. In this case, the common denominator is 4. Now, multiply both sides by that number. On the left side, you would cross off the 2 on the bottom and make it a 1 (or just nothing) and cross off the 4 and make it a 2. Just like regular multiplying fractions. Then, on the right side, you would cross off both 4's. Now you have eliminated the denominators.Step 2: On the left side, you are left with the 2, so you have to use distributive property to multiply it by x + 4. So it would be like doing this: 2(x+4) = 2x + 8, which it what it shows on the next line. Nothing happens on the right side, but if you had a number left on the top (instead of crossing it completely out like in this case) you would distribute there as well. You will have to do that on #6.
Step 3: Now you have an equation with variables on both sides. Subtract the x from both sides. This eliminates it on the right side and gives you just x on the left side. (2x - x = x)
Step 4: Now you have the equation, x + 8 = 9. Subtract 8 from both sides and you get your answer! x = 1
Remember, #9 is extra credit.
Also, be sure to show ALL the work. I will give you credit for both the answer and the work. (So, if you get the answer wrong but had some steps right, you will still get points.)
See you tomorrow!
Mrs. Swickey
