Wednesday, August 31, 2011
homework for 9-1
hw for 9-1: page 9, items 19, 20, 21
Don't forget that the feasible region is now smaller because we have introduced constraints, such as the maximum and minimum number of meals during the week, the maximum number of performances that Roy will buy tickets for, and the relationship between the number of tickets and the number of meals, m = 2(t)
Testing a point from a region means to plug the coordinates into the inequality to see if the statement is true for that point.
Don't forget that the feasible region is now smaller because we have introduced constraints, such as the maximum and minimum number of meals during the week, the maximum number of performances that Roy will buy tickets for, and the relationship between the number of tickets and the number of meals, m = 2(t)
Testing a point from a region means to plug the coordinates into the inequality to see if the statement is true for that point.
Tuesday, August 30, 2011
hw for 8-31 is page 8, items 17 and 18
hw for 8-31 is page 8, items 17 and 18
Be prepared to discuss the word constraint.
Be prepared to discuss the word constraint.
Feasible options 8-30, pages 6, 7, items 13, 16
Item 13: 100 (t) + 40 (m) < or = 1360
Try t = 0 to find easy point (0, m)
Then try m = 0 to find easy point (t, 0)
When t = 0, 40 (m) = 1360, so m = 34
When m = 0, 100 (t) = 1360, so t = 13.6
The easy points are (0, 34) and (13.6, 0)
Plot these point on the grid in item 16, and connect the dots with a line.
Try t = 0 to find easy point (0, m)
Then try m = 0 to find easy point (t, 0)
When t = 0, 40 (m) = 1360, so m = 34
When m = 0, 100 (t) = 1360, so t = 13.6
The easy points are (0, 34) and (13.6, 0)
Plot these point on the grid in item 16, and connect the dots with a line.
feasible region
Feasible means possible, possible, or reasonable. The feasible region is shown by graphing an inequality in two variables. Points (coordinates) in the feasible region make the inequality true. The feasible region is usually in quadrant I where the variables are positive. One boundary of the feasible region is the line that is the graph of the equation contained in or seggested by the inequality.
Monday, August 29, 2011
Math 11 homework for 8-30
We all need to make an adjustment to the Springboard textbook. In conventional textbooks, the homework problems are found gathered together on one or two pages after a section. In our Springboard book, homework problems are not found in a separate section. Homework problems can be assigned from the activity items in the text. It is important that you write down both the page and item numbers of homework assignments, and that you not get the two confused.
Homework for 8-30: page 6, items 11 and 12.
Notes on the previous homework that was due today 8-29, page 5, items 6 through 10:
6. -100 is the slope. 1360 is the y-intercept.
7a. This item is about the expense of meals. You need the information from pages 3 and 4 where you found that having a meal means your available money is reduced by $40.
Yesterday we wrote D(t) = 1360 -100(t) when we talked about tickets.
Today's equation has the same y-intercept but a different slope, a different rate at which money leaves.
Today for 7a we write D(m) = 1360 -40(m)
7b. Be careful to see that the horizontal axis is marked in five-meal increments, so the marks from L to R go 0, 5, 10, 15, 20, and so forth. The graph goes downhill and it drops $40 for each meal, which means it drops $200 for every five meals.
7b. IS A GOOD CANDIDATE FOR A HOMEWORK QUIZ.
8. Today's D(m) is a ___________ function. Hint: what is the shape of the graph?
9. What is the rate of change for D(m)? (Be sure to write the units)
A rate of change is a ratio, so it's some units over some other units, or some units per some other units, or some units divided by some other units. "Per" is a preposition which means "divided by".
In our example, the rate of change is -40 dollars per meal, or ($-40) / meal.
Homework for 8-30: page 6, items 11 and 12.
Notes on the previous homework that was due today 8-29, page 5, items 6 through 10:
6. -100 is the slope. 1360 is the y-intercept.
7a. This item is about the expense of meals. You need the information from pages 3 and 4 where you found that having a meal means your available money is reduced by $40.
Yesterday we wrote D(t) = 1360 -100(t) when we talked about tickets.
Today's equation has the same y-intercept but a different slope, a different rate at which money leaves.
Today for 7a we write D(m) = 1360 -40(m)
7b. Be careful to see that the horizontal axis is marked in five-meal increments, so the marks from L to R go 0, 5, 10, 15, 20, and so forth. The graph goes downhill and it drops $40 for each meal, which means it drops $200 for every five meals.
7b. IS A GOOD CANDIDATE FOR A HOMEWORK QUIZ.
8. Today's D(m) is a ___________ function. Hint: what is the shape of the graph?
9. What is the rate of change for D(m)? (Be sure to write the units)
A rate of change is a ratio, so it's some units over some other units, or some units per some other units, or some units divided by some other units. "Per" is a preposition which means "divided by".
In our example, the rate of change is -40 dollars per meal, or ($-40) / meal.
Math 11 8-29 bell ringer
Graph y = -2 + 1/4(x)
method 1: -2 is b, the y-intercept, so draw the first point at (0, -2). 1 over 4 is m, the slope, so from (0, -2) you go up 1 and over 4, since slope = rise over run. You arrive at (4, -1). Connect the two points with a line.
method 2: Use a table of values with easy points. Try x = 0, plug it in and you get y = -2, which you plot at (0, -2). Then try x = 4, simce when you plug it in the fraction 1/4 goes away. When x = 4, y = -2 + (1/4)(4) = -2 + 1 = -1, which you plot at (4, -1). Connect the two points with a line.
Graph the inequality y < -2 + (1/4)(x)
Pick a point in the blue region above the graph of y = -2 + (1/4)(x), such as (0, 0). Plug this point into the inequality y < -2 +(1/4)(x) and you get 0 < -2,which is false, so points in the blue region are not solutions.
Pick a point in the red region below the graph of y = -2 + (1/4)(x), such as (0, 0). Plug this point into the inequality y < -2 +(1/4)(x) and you get -3 < -2,which is true, so points in the red region are solutions.
To finish the graph, shade in the red region below the line.
Graph is a point on the number line: An equation in one variable.
Graph is a line or ray on the number line: An inequality in one variable.
Graph is a line on a plane: A linear equation in two variables.
Graph is an area or region on a plane: A linear inequality in two variables.
method 1: -2 is b, the y-intercept, so draw the first point at (0, -2). 1 over 4 is m, the slope, so from (0, -2) you go up 1 and over 4, since slope = rise over run. You arrive at (4, -1). Connect the two points with a line.
method 2: Use a table of values with easy points. Try x = 0, plug it in and you get y = -2, which you plot at (0, -2). Then try x = 4, simce when you plug it in the fraction 1/4 goes away. When x = 4, y = -2 + (1/4)(4) = -2 + 1 = -1, which you plot at (4, -1). Connect the two points with a line.
Graph the inequality y < -2 + (1/4)(x)
Pick a point in the blue region above the graph of y = -2 + (1/4)(x), such as (0, 0). Plug this point into the inequality y < -2 +(1/4)(x) and you get 0 < -2,which is false, so points in the blue region are not solutions.
Pick a point in the red region below the graph of y = -2 + (1/4)(x), such as (0, 0). Plug this point into the inequality y < -2 +(1/4)(x) and you get -3 < -2,which is true, so points in the red region are solutions.
To finish the graph, shade in the red region below the line.
Graph is a point on the number line: An equation in one variable.
Graph is a line or ray on the number line: An inequality in one variable.
Graph is a line on a plane: A linear equation in two variables.
Graph is an area or region on a plane: A linear inequality in two variables.
Friday, August 26, 2011
SBT hw for 8-29 is page 5, 6 through 10; explanation for item 2 on page 4
Homework for Monday: 6,7, 8, 9, 10 on page 5.
On page 4, the first colum in the table should say Total tickets. The 3rd row does not mean you buy 2 more tickets after you bought the 1st ticket in row 2; it means you bought 1 more ticket for a total of 2.
0 total tickets $1360 available
1 total tickets $1260 available
2 total tickets $1160 available
3 total tickets $1060 available
4 total tickets $960 available
5 total tickets $860 available
8 total tickets $560 available
10 total tickets $360 available
13 total tickets $60 available
On page 4, the first colum in the table should say Total tickets. The 3rd row does not mean you buy 2 more tickets after you bought the 1st ticket in row 2; it means you bought 1 more ticket for a total of 2.
0 total tickets $1360 available
1 total tickets $1260 available
2 total tickets $1160 available
3 total tickets $1060 available
4 total tickets $960 available
5 total tickets $860 available
8 total tickets $560 available
10 total tickets $360 available
13 total tickets $60 available
Thursday, August 25, 2011
Equation from a slope m and a point (x, y) alternate method
Draw x and y axes. Plot the point (-2, -3) in quadrant III. The given slope is m = 5 which is equivalent to m = 5/1 (five divided by one). So the rise is 5 and the run is 1. Put your pencil on the point (-2, -3) and go over one and up five spaces. You end up at (-1, 2). Again go over 1 (the run) and up 5 (the rise). You end up at (0, 7), intercepting the y-axis 7 spaces above the origin. So b, the y-intercept, is 7.
The equation of a line represents many combinations of x and y, so we keep the letters to show that the graph is not just one point. We use the information about m = 5 (given) and b = 7 (we found it) to write the slope-intercept form y = 5x + 7.
The equation of a line represents many combinations of x and y, so we keep the letters to show that the graph is not just one point. We use the information about m = 5 (given) and b = 7 (we found it) to write the slope-intercept form y = 5x + 7.
allocate, motherboard, pre-loaded pink slip
allocate - To purposefully assign work to different workers. To purposefully assign resources to different users. It's not like dealing cards or sharing a pizza because someone decides the best way to spread out or share the effort and materials.
motherboard - The largest plastic circuit board in a computer. Other things plug into it, such as components, power supplies, disc drives, and daughterboards.
pre-loaded pink slip - A demerit slip that already has your name on it, all it needs is a teacher's signature and it gets transferred directly from the bulletin board.
motherboard - The largest plastic circuit board in a computer. Other things plug into it, such as components, power supplies, disc drives, and daughterboards.
pre-loaded pink slip - A demerit slip that already has your name on it, all it needs is a teacher's signature and it gets transferred directly from the bulletin board.
Math 11 leadership opportunity
Reflect on our discussion of why we use a blog:
To save ________________ .
To actually use _______________ in the classroom and at home.
To build a study __________ that we can share.
So the teacher can include things we talked about that day in class for our ___________ .
Tell a ninth grader that there is a Math 9 blog that they can visit. Tell them the URL (web address) and have them write it down. http://www.ywlcsmath9.blogspot.com/
To save ________________ .
To actually use _______________ in the classroom and at home.
To build a study __________ that we can share.
So the teacher can include things we talked about that day in class for our ___________ .
Tell a ninth grader that there is a Math 9 blog that they can visit. Tell them the URL (web address) and have them write it down. http://www.ywlcsmath9.blogspot.com/
Write a linear equation when given a point (x, y) and a slope m
Write the equation of the line that passes through the point (-2,-3) and has a slope of 5.
We know that m = 5 because the slope is given, so y = 5x + b is a partial answer.
With the information (-2, -3) a common mistake is to try graphing two points at (-2,0) and (0, -3).
(-2, -3) represents only one point, and we don't have a graph that shows other points.
We use x = -2 and y = -3 to fill in the slope-intercept form equation to get -3 = 5 (-2) + b.
Now we have three out of four pieces, and we solve for the unknown b. -3 = -10 + b,
then add 10 to both sides.
b = 7
In college math we often use an intermediate answer to go back to the beginning of the problem to find the final answer. Here we use b = 7 in the y = mx + b that we started with.
y = mx + 7 and that becomes y = 5x + 7 when we pu in the slope.
The answer has the variables x and y in the equation, not the values -2 and -3, because the equation of a line represents the values of all possible points on the line.
We know that m = 5 because the slope is given, so y = 5x + b is a partial answer.
With the information (-2, -3) a common mistake is to try graphing two points at (-2,0) and (0, -3).
(-2, -3) represents only one point, and we don't have a graph that shows other points.
We use x = -2 and y = -3 to fill in the slope-intercept form equation to get -3 = 5 (-2) + b.
Now we have three out of four pieces, and we solve for the unknown b. -3 = -10 + b,
then add 10 to both sides.
b = 7
In college math we often use an intermediate answer to go back to the beginning of the problem to find the final answer. Here we use b = 7 in the y = mx + b that we started with.
y = mx + 7 and that becomes y = 5x + 7 when we pu in the slope.
The answer has the variables x and y in the equation, not the values -2 and -3, because the equation of a line represents the values of all possible points on the line.
Wednesday, August 24, 2011
Given the graph of a line, write the equation
Given the graph of a line, write the equation | The equation of a line has the form y = mx + b Where x is first/domain/horizontal/left in an ordered pair Where y is last/range/vertical/right in an ordered pair Where m is the slope Where b is the y-intercept |
m = slope means steepness | Rise over run, rise divided by run (Y1 minus y2) divided by (x1 minus x2) Slope measures steepness of the line |
Slope uphill | Look at the line and its points from left to right, they go up m is positive |
Slope downhill | Look at the line and its points from left to right, they go down m is negative |
Easiest points | Points which have x or y as zero (0, y) (x, 0) |
Easy points | Points on the corners of the grid squares |
Draw stairsteps | A way to see the rise and run |
Drop is a negative rise | If the graph goes downhill, the rise is negative |
(L, R) is alphabetical | x/domain/horizontal are earlier in the alphabet than y/range/vertical |
The meaning of y –intercept which equals b | How high or low the graph of the line is compared to the origin Where the graph crosses (intercepts) the y-axis (vertical axis) The number term added to the mx term The value of y when x = 0 (0, b) |
(picture) | y = 2x - 2 because the rise is 2 and the run is 1 because the graph crosses the y-axis at -2 |
Thursday, August 18, 2011
Parents Meet Teachers Night Micro-Lesson
A circle has a radius of 10 meters, and the length of the given chord PQ is 16 meters. If O marks the center of the circle, what is the length of segment OA?
A. 2(sqrt3)
B. 6
C. 12
D. 4(sqrt21)
E. 36
B. 6
C. 12
D. 4(sqrt21)
E. 36
Saturday, August 13, 2011
Mirth Math Inspire
Welcome to 11th grade math at YWLCS. I look forward to meeting parents on Thursday, August 18.
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