Sixth Grade
Lesson 72 - exponents. Remember, the little number doesn't tell you what to multiply the big number by, it tells you how many times to multiply the big number by itself. So, 4 to the 3rd power, would be 4 x 4 x 4 = 64, NOT 4 x 3.
Seventh Grade
Grammar - Action Verbs pp. 39-40. Exercise A and B and DWS. For A, just write mental or visible. For B, just write the action verb. Follow instructions for DWS, remembering to use each word as a VERB.
Writing - Write your outline for your research paper. This was begun in class and most students will just need to finish up tonight.
Spelling - Test tomorrow over Unit 22!
Vocabulary - Test tomorrow over Unit 11! Be sure to study. I noticed that several of you left your vocabulary books at school.
Math - Lesson 6-2. Rates and unit rates.
Remember, every rate (a comparision of two unlike things) can be written two ways:
That is all you are doing on #1-2.For #4-6, you are writing the unit rate. Remember, this is where you write how many in ONE. In the example above, you could reduce the first rate to 15 miles per gallon. That is a unit rate because it is per 1 gallon. For unit rates, you always write it with the single unit (1 ounce, 1 hour, 1 gallon, etc.) on the bottom.
To find the unit rate, divide the top number by the bottom number.
For 8-10, you are finding the unit rate of the items in the table. Round to the nearest cent, when necessary. So, if you were dividing and ending up with $1.45873...., you would round that to $1.46.
For #12-14 and #19, you are comparing two (or three) items to determine which is the better buy. First, you need to find the unit rate of each item by dividing. Then compare the unit rates.
Eighth Grade
Lesson 6-8. #2-26 evens. Parallel and perpendicular lines.
Remember these two things:
Parallel lines have the SAME SLOPE.
Perpendicular lines have OPPOSITE RECIPROCAL SLOPES.
For #2-4, you are just writing the equation of a line that is parallel to the line given. It does not specify that it has to go through a certain point, so just use the SAME slope as the line that is given, and change the y-intercept. For example:
Given line: y=5x-7
Equation of a line parallel to that line: y=5x+3
So, both lines have the same slope, 5, but different y-intercepts.
For #6-8, you are just writing the equation of a line that is perpendicular to the one given. Again, it does not specify that it has to go through a certain point, so just use the OPPOSITE RECIPROCAL slope and the same OR different y-intercept.
For example:
Given line: y=-2x+4
Perpendicular line: y= 1/2x+8
Since the first slope is -2, the second slope must first be opposite (so positive) and ALSO the reciprocal. The reciprocal of any whole number is one OVER that number. So the reciprocal of 2 is 1/2. I changed the y-intercept, but for these you didn't have to!
Now, for #10-14, you are determining whether the two lines are parallel, perpendicular, or neither. Remember, you must FIRST change the equation to y-intercept form by moving anything on the left side of the equation that ISN'T y, to the right side. For example:
y+3x=5 should change to y=-3x+5
I subtracted 3x from both sides. In the second equation, I put it after the equals sign so that it is in slope intercept form.
The above line would be parallel to y=-3x+7 and perpendicular to y=1/3x+3. It would be neither with the line y=3x+4 because while 3 is the opposite of -3 it is NOT the reciprocal.
Now, for #16-20, you are writing the equation of a line parallel to a given line when you DO have a certain point your line must pass through. This time, it will matter what your y-intercept is. First, determine what the slope is of the given line. (you will have to change the line into slope intercept form for #20)
Now, plug that slope into a new equation but use b for the y-intercept. For example:
Given line: y=-2x+4, passes through (-3,6)
Parallel line: y=-2x + b Remember, it didn't matter that the y-intercept in the given line was 4.
Now, use the coordinates for x and y given in the point above (-3,6) and plug those in for x and y in the equation. Now you have: 6=-2*-3 + b (I'm using a * for multiplication here.)
Solve the equation for b. First multiply -2 and -3 to get this: 6=6+b
Now, subtract 6 from both sides. You are left with b=0. So your y-intercept is 0. Now, write the equation of your line with the same slope and the new y-intercept: y=-2x+0 or just y=-2x.
For perpendicular lines, you will do the same thing except instead of using the same slope, you will use the opposite reciprocal slope. For example:
Given line: y=-4x+2 passes through (8,5)
Perpendicular line: y=1/4x + b
Now, plug in the x and y values from the point the new line will pass through:
5= 1/4 * 8 + b
This would simplify to 5=2+b
Now subtract 2 from both sides to get: 3=b
Now write the equation with the new slope and y-intercept: y=1/4x + 3
That's it!
See you tomorrow!
Mrs. Swickey
