Assignment Prompt & Instructions
[>Algebra homework help](https://www.sweetstudy.com/fields/mathematics-algebra)
Please see attached.
– a month ago
**files (5)**
– ## GradePitchandSlipperySlopes.pdf
– ## WK4UsingtheEquationEditorinMyClassroom.pdf
– ## MATH110WK345DiscussionsHelp.docx
– ## WK4ReadThisFirst.pdf
– WK4MATH110SystemsofEquationswithAnswers.pdf
**## GradePitchandSlipperySlopes.pdf**
When you answer these, please incorporate enough of the question so
that we all can tell what you’re talking about without having to open
this file.
Simply saying “#40 All of them” is not very informative!
GRADE
1) What is meant by the grade of a highway?
2) How might the grade of a highway influence the prices set by
trucking companies to haul freight over the route?
3) What is a runaway truck ramp?
4) Why are residential roads higher in the middle than at the curb?
5) What is the generally accepted maximum grade for wheelchair
ramps?
6) What is an adhesion railroad?
7) What is the maximum grade that an adhesion railroad can
climb?
8) What are some of the steepest adhesion railroads in the world
and where are they located? (just give us one and leave the
others for classmates!)
9) What is a cog railway?
10)Where is the world’s highest cog railway?
11)Where is the world’s steepest cog railway?
12)How does a “rack-and-adhesion” railway work?
13)What is a funicular and how does it relate to slope?
14)What was the motivation for the invention of the San Francisco
cable cars?
15)How do the San Francisco cable cars work?
16)How can canals be used to help boat climb hills?
17)How does a canal lock work?
18)How high above sea level is Lake Gatun in the Panama Canal?
19)What are "jake brakes" and why are they prohibited in some
locations?
PITCH
20)How steep does a roof have to be to be considered “pitched”?
21)What distinguishes a “salt box” house?
22)What distinguishes an A-frame house?
23)You may have read The House of the Seven Gables – what’s a
gable?
24)Why are gable end roofs among the worst roof designs for
hurricane regions?
25)What are some advantages & disadvantages of a Dutch Hip Roof
Style?
26)Why are roof lines different in New England and the Southwest?
27)About how steep is the average residential staircase?
SLIPPERY SLOPES
28)About how steep is the angle of the slope for “Extreme Skiers”?
29)In the US, about how steep is a green, beginners’ slope?
30)In the US, about how steep is a blue, intermediate slope?
31)In the US, about how steep is a black, expert slope?
32)I can ski a double black diamond slope at home in Indiana. I
can’t wait to ski one in Colorado! Is this wise? Why?
**## WK4UsingtheEquationEditorinMyClassroom.pdf**
Using the Equation Editor …
… to make math problems
look like math problems!
Math on the keyboard:
x = [-b +/- sqrt(b^2 – 4ac)]/(2a)
Huh?
Math with the equation editor!
2 4
2
b b ac
x
a
− −
=
That’s better!
Let’s say that you want to show an algebraic fraction like
Trying to do this with just the keyboard looks “weird” …
x / (x + 3)
… and it invites mistakes (like not using the parentheses).
x / x + 3 means
𝑥
𝑥
+ 3 which is something completely different!
3
x
x +
The next time you go to post a discussion click the three
extra dots at the end.
You will see more options show up.
Right below the Bold button
you will see the Greek letter sigma.
This is the button to open the equation editor.
Select Graphical Equation
The Equation Editor has lots of tools, so let’s look at a few of the basics.
Good news: most things look like what they do.
For example, if you need a fraction, you will click the button that looks
like an empty fraction.
You will see a fraction appear – you just need to fill it in.
Use the arrows to navigate to the bottom of the fraction.
Be sure to use the right arrow to navigate
out of the fraction before continuing with your equation.
You will notice that the cursor is tall in this picture. That is how you
know that you are out of the fraction.
Another commonly used symbol is the exponent.
This time let’s try to create the expression:
To do this you will start by creating a fraction.
2
6
5
2
x
y
−
+
Once you are in the fraction, you type the x
and then click the exponent
button and then the 2.
Use the right arrow button to get out of the exponent
before typing the – 5.
Then, use the down arrow to move to the denominator.
In this picture you can see the cursor.
Note that the cursor will show you if
you are still in the exponent or not, so watch carefully!
Once you have the top of the fraction done …
… just rinse and repeat for the bottom!
Once done click insert.
We did it!
If you want to add words to your equations,
just type them in,
select them, and then click on the text font.
Experiment with it until
you can get the desired results.
The math may still be a challenge …
… but now writing the answers shouldn’t be!
**## MATH110WK345DiscussionsHelp.docx**
**W3: Grade Pitch and Slippery Slopes**
This is an opportunity to investigate the many ways that the concept of "slope"This is an opportunity to investigate the many ways that the concept of "slope" touches our daily lives.
Open the file called Grade Pitch and Slippery Slopes. Pick ONE of the questions that has not already been answered by a classmate. Click on Post New Thread and make the problem number and the topic (#1 Highway Grade) the subject of your post so that people can tell at a glance which problems have already been answered.
Give a full and complete answer to the question. I would like you to find out about the material and describe the answer in your own words. Most of these topics require some research. Don't forget that you must give attribution to your source. Be sure to cut and paste the URL of the site from which you got the information. Sometimes other students decide that a topic is interesting and would like to learn more about it. Your source will provide them with a good starting point. This initial post is worth 6 points.
You must also give a substantive response to two classmate's posts (worth 2 points each). You may ask questions to elicit a more in-depth explanation, add additional information to your own posting in response to questions, share additional knowledge on another posting or share an example from your own life related to the topic. Simply saying "Good post!" will not earn any points.
It's always fun when people add pictures to their Discussions. This is not required but, if you'd like to, feel free to add one.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
**Initial Post Due:** Thursday, by 11:55 p.m., ET
**Other Posts Due:** Sunday, by 11:55 p.m., ET
[**W4: If Only I Had a System …**](https://myclassroom.apus.edu/d2l/le/1457714/discussions/topics/1636546/View)
It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week's test, FOLLOW THESE
INSTRUCTIONS
It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week's test, FOLLOW THESE
INSTRUCTIONS!
Step 1: Read the file entitled "Read This First"
Step 2: Open the file "MATH110 Systems of Equations with Answers".
Step 3: Go through ALL the story problems provided and try to solve them. Pretend it's a Practice Test. Check your answers with the key provided.
Step 4: Pick ONE of the problems that you got right (that has not already been solved by a classmate) and demonstrate its solution for the rest of us.
Step 5: Study how your classmates solved the problems that you missed. Remember that these may be on the test!
Note: Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
1) To demonstrate your problem, select Start a New Conversation and make the subject of your post ONLY the problem number and topic (#10 Jarod and the Bunnies).
2) Begin your post with a statement of the problem so that we can understand what you are doing.
3) The answers are at the end of the file, so don't just give an answer — we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!
Your goal should be to explain this problem so well that a classmate who "just doesn't get it" will be able to understand it completely!
This is a moderated discussion. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit.
I will indicate in the grading feedback if corrections need to be made. If you haven't received credit, first double-check my comments. If everything looks OK, then email me asking me to check on it. You must make the necessary corrections and have your work posted in order to receive credit.
For this particular Discussion,
**no responses are required** – your initial post is worth the full points. Should you choose to respond to a classmate, a request for clarification on the procedure used, a suggestion for an alternate method of solving the problem or a general comment about the technique would all be appropriate. I'm sure that a "thank you" for an exceptionally clear explanation would also be welcome!
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
[**W5: Midterm Reflection**](https://myclassroom.apus.edu/d2l/le/1457714/discussions/topics/1636547/View)
Select Start a New Conversation using your name as the Subject.
Now that we have passed the half-way mark of the class, tell us what you think about learning math online?
Name at least one thing that you really enjoy about the class (come on, there must be something!) and at least one improvement that could make this class even better. Feel free to editorialize!
Also, this is a good time to make a "keep-quit-start" resolution.
• What are you doing to help yourself learn in this class that you are going to keep doing because it's working?
• What are you doing that is hindering you from learning in this class that you are going to quit doing?
• What do you think will help you improve your learning in this class that you are going to start doing?
Then, respond to 2 of your classmates in substantive postings.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
**## WK4ReadThisFirst.pdf**
Forum: If Only I Had a System…
Applications of Systems of Linear Equalities
The Problem:
When students are surveyed about what makes a good math Forum, at least half of the
responses involve
"discussing how to work problems"
"seeing how this math applies to real-life situations"
This Forum on applications of systems of equations addresses both of these concerns.
Unfortunately, the typical postings are far from ideal.
This is an attempt to rectify the situation. Please read this in its entirety before you
post your answer!
Pick-up games in the park vs. the NBA:
Shooting hoops in the park may be lots of fun, but it scarcely qualifies as the precision
play of a well-coached team. On the one hand, you have individuals with different
approaches and different skill levels, "doing their own thing" within the general rules of
the game. On the other hand you have trained individuals, using proven strategies and
basing their moves on fundamentals that have been practiced until they are second
nature.
The purpose of learning algebra is to change a natural, undisciplined approach to
individual problem solving into an organized, well-rehearsed system that will work on
many different problems. Just like early morning practice, this might not always be
pleasant; just like Michael Jordan, if you put in the time learning how to do it correctly,
you will score big-time in the end.
But my brain just doesn't work that way. . .
Nonsense! This has nothing to do with how your brain works. This is a matter of
learning to read carefully, to extract data from the given situation and to apply a
mathematical system to the data in order to obtain a desired answer. Anyone can learn
to do this. It is just a matter of following the system; much like making cookies is a
matter of following a recipe.
"Pick-up Game" Math
It is appalling how many responses involve plugging in numbers until it works.
"My birthday is the eleventh, so I always start with 11 and work from there."
"The story involved both cats and dogs so I took one of the numbers, divided by
2 and then I experimented."
"First I fire up Excel…"
"I know in real-life that hot dogs cost more than Coke, so I crossed my fingers
and started with $0.50 for the Coke…"
The reason these "problem-solving" boards are moderated is so that these creative
souls don’t get everyone else confused!
NBA Math
In more involved problems, where the answer might come out to be something
irrational, like the square root of three, you are not likely to just randomly guess the
correct answer to plug it in. To find that kind of answer by an iterative process (plugging
and adjusting; plugging and adjusting; …) would take lots of tedious work or a computer.
Algebra gives you a relative painless way of achieving your objective without wearing
your pencil to the nub.
The reason that all of the homework has involved x's and y's and two equations, is that
we are going to solve these problems that way. Each of these problems is a story about
two things, so every one of these is going to have an x and a y.
In some problems, it’s helpful to use different letters, to help keep straight what the
variables stand for. For example, let L = the length of the rectangle and W = the width.
The biggest advantage to this method is that when you have found that w = 3 you are
more likely to notice that you still haven’t answered the question, “What is the length of
the rectangle?”
Here are the steps to the solution process:
Figure out from the story what those two things are.
o one of these will be x
o the other will be y
The first sentence of your solution will be "Let x = " (or “Let L = ” )
o Unless it is your express purpose to drive your instructor right over the
edge, make sure that your very first word is "Let"
The second sentence of your solution will be "Let y = " (or “Let W = ” )
Each story gives two different relationships between the two things.
o Use one of those relationships to write your first equation.
o Use the second relationship to write the second equation.
Now demonstrate how to solve the system of two equations. You will be using
either
o substitution
o or elimination – just like in the homework.
More examples…
For this problem, I'd use substitution to solve the system of equations:
The length of a rectangle blah, blah, blah…
Let L = the length of the rectangle
… blah, blah, blah twice the width
Let W = the width of the rectangle
The length is 6 inches less than twice the width
L = 2W – 6
The perimeter of the rectangle is 56
2L + 2W =56
For this one, I'd use elimination to solve the system of equations:
Blah, blah, blah bought 2 cokes…
Let x = the price of a coke
.. blah, blah, blah 4 hot dogs
Let y = the price of a hot dog
2 cokes plus 4 hot dogs cost 8.00
2x + 4y = 8.00
3 cokes plus 2 hot dogs cost 8.00
3x + 2y = 8.00
For this one, I'd use substitution to solve the system of equations:
One number is blah, blah, blah…
Let x = the first number
…blah, blah, blah triple the second number
Let y = the second number
The first number is triple the second
x = 3y
The sum of the numbers is 24
x + y = 24
Checking your answers vs. Solving the problem
The problem: Two numbers add to give 4 and subtract to give 2. Find the numbers.
Solving the problem:
Let x = the first number
Let y = the second number
Two numbers add to give 4: x + y = 4
Two numbers subtract to give 2: x – y = 2
Our two equations are: x + y = 4
x – y = 2 Adding the equations we get
2x = 6
x = 3 The first number is 3.
x + y = 4 Substituting that answer into equation 1
3 + y = 4
y = 1 The second number is 1.
Checking the answers:
Two numbers add to give 4: 3 + 1 = 4
The two numbers subtract to give 2: 3 – 1 = 2
Do NOT demonstrate how to check the answers that are provided and call that
demonstrating how to solve the problem!
Formulas vs. Solving equations
Formulas express standard relationships between measurements of things in the real
world and are probably the mathematical tools that are used most frequently in real-life
situations.
Solving equations involves getting an answer to a specific problem, sometimes based
on real-world data, and sometimes not. In the process of solving a problem, you may
need to apply a formula. As a member of modern society, it is assumed that you know
certain common formulas such as the area of a square or the perimeter of a rectangle. If
you are unsure about a formula, just Google it. Chances are excellent it will be in one of
the first few hits.
If you are still baffled:
Check out all the examples worked out in the PowerPoints in the Other
Resources section of the Handy Helpers for Section 4.3.
Message me if you are still confused.
**WK4MATH110SystemsofEquationswithAnswers.pdf**
This file is too large to display. [View in new window](https://www.sweetstudy.com/files/wk4math110systemsofequationswithanswers-pdf)
**WK4MATH110SystemsofEquationswithAnswers.pdf**
This file is too large to display. [View in new window](https://www.sweetstudy.com/files/wk4math110systemsofequationswithanswers-pdf)
**## GradePitchandSlipperySlopes.pdf**
When you answer these, please incorporate enough of the question so
that we all can tell what you’re talking about without having to open
this file.
Simply saying “#40 All of them” is not very informative!
GRADE
1) What is meant by the grade of a highway?
2) How might the grade of a highway influence the prices set by
trucking companies to haul freight over the route?
3) What is a runaway truck ramp?
4) Why are residential roads higher in the middle than at the curb?
5) What is the generally accepted maximum grade for wheelchair
ramps?
6) What is an adhesion railroad?
7) What is the maximum grade that an adhesion railroad can
climb?
8) What are some of the steepest adhesion railroads in the world
and where are they located? (just give us one and leave the
others for classmates!)
9) What is a cog railway?
10)Where is the world’s highest cog railway?
11)Where is the world’s steepest cog railway?
12)How does a “rack-and-adhesion” railway work?
13)What is a funicular and how does it relate to slope?
14)What was the motivation for the invention of the San Francisco
cable cars?
15)How do the San Francisco cable cars work?
16)How can canals be used to help boat climb hills?
17)How does a canal lock work?
18)How high above sea level is Lake Gatun in the Panama Canal?
19)What are "jake brakes" and why are they prohibited in some
locations?
PITCH
20)How steep does a roof have to be to be considered “pitched”?
21)What distinguishes a “salt box” house?
22)What distinguishes an A-frame house?
23)You may have read The House of the Seven Gables – what’s a
gable?
24)Why are gable end roofs among the worst roof designs for
hurricane regions?
25)What are some advantages & disadvantages of a Dutch Hip Roof
Style?
26)Why are roof lines different in New England and the Southwest?
27)About how steep is the average residential staircase?
SLIPPERY SLOPES
28)About how steep is the angle of the slope for “Extreme Skiers”?
29)In the US, about how steep is a green, beginners’ slope?
30)In the US, about how steep is a blue, intermediate slope?
31)In the US, about how steep is a black, expert slope?
32)I can ski a double black diamond slope at home in Indiana. I
can’t wait to ski one in Colorado! Is this wise? Why?
**## WK4UsingtheEquationEditorinMyClassroom.pdf**
Using the Equation Editor …
… to make math problems
look like math problems!
Math on the keyboard:
x = [-b +/- sqrt(b^2 – 4ac)]/(2a)
Huh?
Math with the equation editor!
2 4
2
b b ac
x
a
− −
=
That’s better!
Let’s say that you want to show an algebraic fraction like
Trying to do this with just the keyboard looks “weird” …
x / (x + 3)
… and it invites mistakes (like not using the parentheses).
x / x + 3 means
𝑥
𝑥
+ 3 which is something completely different!
3
x
x +
The next time you go to post a discussion click the three
extra dots at the end.
You will see more options show up.
Right below the Bold button
you will see the Greek letter sigma.
This is the button to open the equation editor.
Select Graphical Equation
The Equation Editor has lots of tools, so let’s look at a few of the basics.
Good news: most things look like what they do.
For example, if you need a fraction, you will click the button that looks
like an empty fraction.
You will see a fraction appear – you just need to fill it in.
Use the arrows to navigate to the bottom of the fraction.
Be sure to use the right arrow to navigate
out of the fraction before continuing with your equation.
You will notice that the cursor is tall in this picture. That is how you
know that you are out of the fraction.
Another commonly used symbol is the exponent.
This time let’s try to create the expression:
To do this you will start by creating a fraction.
2
6
5
2
x
y
−
+
Once you are in the fraction, you type the x
and then click the exponent
button and then the 2.
Use the right arrow button to get out of the exponent
before typing the – 5.
Then, use the down arrow to move to the denominator.
In this picture you can see the cursor.
Note that the cursor will show you if
you are still in the exponent or not, so watch carefully!
Once you have the top of the fraction done …
… just rinse and repeat for the bottom!
Once done click insert.
We did it!
If you want to add words to your equations,
just type them in,
select them, and then click on the text font.
Experiment with it until
you can get the desired results.
The math may still be a challenge …
… but now writing the answers shouldn’t be!
**## MATH110WK345DiscussionsHelp.docx**
**W3: Grade Pitch and Slippery Slopes**
This is an opportunity to investigate the many ways that the concept of "slope"This is an opportunity to investigate the many ways that the concept of "slope" touches our daily lives.
Open the file called Grade Pitch and Slippery Slopes. Pick ONE of the questions that has not already been answered by a classmate. Click on Post New Thread and make the problem number and the topic (#1 Highway Grade) the subject of your post so that people can tell at a glance which problems have already been answered.
Give a full and complete answer to the question. I would like you to find out about the material and describe the answer in your own words. Most of these topics require some research. Don't forget that you must give attribution to your source. Be sure to cut and paste the URL of the site from which you got the information. Sometimes other students decide that a topic is interesting and would like to learn more about it. Your source will provide them with a good starting point. This initial post is worth 6 points.
You must also give a substantive response to two classmate's posts (worth 2 points each). You may ask questions to elicit a more in-depth explanation, add additional information to your own posting in response to questions, share additional knowledge on another posting or share an example from your own life related to the topic. Simply saying "Good post!" will not earn any points.
It's always fun when people add pictures to their Discussions. This is not required but, if you'd like to, feel free to add one.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
**Initial Post Due:** Thursday, by 11:55 p.m., ET
**Other Posts Due:** Sunday, by 11:55 p.m., ET
[**W4: If Only I Had a System …**](https://myclassroom.apus.edu/d2l/le/1457714/discussions/topics/1636546/View)
It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week's test, FOLLOW THESE
INSTRUCTIONS
It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week's test, FOLLOW THESE
INSTRUCTIONS!
Step 1: Read the file entitled "Read This First"
Step 2: Open the file "MATH110 Systems of Equations with Answers".
Step 3: Go through ALL the story problems provided and try to solve them. Pretend it's a Practice Test. Check your answers with the key provided.
Step 4: Pick ONE of the problems that you got right (that has not already been solved by a classmate) and demonstrate its solution for the rest of us.
Step 5: Study how your classmates solved the problems that you missed. Remember that these may be on the test!
Note: Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
1) To demonstrate your problem, select Start a New Conversation and make the subject of your post ONLY the problem number and topic (#10 Jarod and the Bunnies).
2) Begin your post with a statement of the problem so that we can understand what you are doing.
3) The answers are at the end of the file, so don't just give an answer — we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!
Your goal should be to explain this problem so well that a classmate who "just doesn't get it" will be able to understand it completely!
This is a moderated discussion. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit.
I will indicate in the grading feedback if corrections need to be made. If you haven't received credit, first double-check my comments. If everything looks OK, then email me asking me to check on it. You must make the necessary corrections and have your work posted in order to receive credit.
For this particular Discussion,
**no responses are required** – your initial post is worth the full points. Should you choose to respond to a classmate, a request for clarification on the procedure used, a suggestion for an alternate method of solving the problem or a general comment about the technique would all be appropriate. I'm sure that a "thank you" for an exceptionally clear explanation would also be welcome!
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
[**W5: Midterm Reflection**](https://myclassroom.apus.edu/d2l/le/1457714/discussions/topics/1636547/View)
Select Start a New Conversation using your name as the Subject.
Now that we have passed the half-way mark of the class, tell us what you think about learning math online?
Name at least one thing that you really enjoy about the class (come on, there must be something!) and at least one improvement that could make this class even better. Feel free to editorialize!
Also, this is a good time to make a "keep-quit-start" resolution.
• What are you doing to help yourself learn in this class that you are going to keep doing because it's working?
• What are you doing that is hindering you from learning in this class that you are going to quit doing?
• What do you think will help you improve your learning in this class that you are going to start doing?
Then, respond to 2 of your classmates in substantive postings.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
**## WK4ReadThisFirst.pdf**
Forum: If Only I Had a System…
Applications of Systems of Linear Equalities
The Problem:
When students are surveyed about what makes a good math Forum, at least half of the
responses involve
"discussing how to work problems"
"seeing how this math applies to real-life situations"
This Forum on applications of systems of equations addresses both of these concerns.
Unfortunately, the typical postings are far from ideal.
This is an attempt to rectify the situation. Please read this in its entirety before you
post your answer!
Pick-up games in the park vs. the NBA:
Shooting hoops in the park may be lots of fun, but it scarcely qualifies as the precision
play of a well-coached team. On the one hand, you have individuals with different
approaches and different skill levels, "doing their own thing" within the general rules of
the game. On the other hand you have trained individuals, using proven strategies and
basing their moves on fundamentals that have been practiced until they are second
nature.
The purpose of learning algebra is to change a natural, undisciplined approach to
individual problem solving into an organized, well-rehearsed system that will work on
many different problems. Just like early morning practice, this might not always be
pleasant; just like Michael Jordan, if you put in the time learning how to do it correctly,
you will score big-time in the end.
But my brain just doesn't work that way. . .
Nonsense! This has nothing to do with how your brain works. This is a matter of
learning to read carefully, to extract data from the given situation and to apply a
mathematical system to the data in order to obtain a desired answer. Anyone can learn
to do this. It is just a matter of following the system; much like making cookies is a
matter of following a recipe.
"Pick-up Game" Math
It is appalling how many responses involve plugging in numbers until it works.
"My birthday is the eleventh, so I always start with 11 and work from there."
"The story involved both cats and dogs so I took one of the numbers, divided by
2 and then I experimented."
"First I fire up Excel…"
"I know in real-life that hot dogs cost more than Coke, so I crossed my fingers
and started with $0.50 for the Coke…"
The reason these "problem-solving" boards are moderated is so that these creative
souls don’t get everyone else confused!
NBA Math
In more involved problems, where the answer might come out to be something
irrational, like the square root of three, you are not likely to just randomly guess the
correct answer to plug it in. To find that kind of answer by an iterative process (plugging
and adjusting; plugging and adjusting; …) would take lots of tedious work or a computer.
Algebra gives you a relative painless way of achieving your objective without wearing
your pencil to the nub.
The reason that all of the homework has involved x's and y's and two equations, is that
we are going to solve these problems that way. Each of these problems is a story about
two things, so every one of these is going to have an x and a y.
In some problems, it’s helpful to use different letters, to help keep straight what the
variables stand for. For example, let L = the length of the rectangle and W = the width.
The biggest advantage to this method is that when you have found that w = 3 you are
more likely to notice that you still haven’t answered the question, “What is the length of
the rectangle?”
Here are the steps to the solution process:
Figure out from the story what those two things are.
o one of these will be x
o the other will be y
The first sentence of your solution will be "Let x = " (or “Let L = ” )
o Unless it is your express purpose to drive your instructor right over the
edge, make sure that your very first word is "Let"
The second sentence of your solution will be "Let y = " (or “Let W = ” )
Each story gives two different relationships between the two things.
o Use one of those relationships to write your first equation.
o Use the second relationship to write the second equation.
Now demonstrate how to solve the system of two equations. You will be using
either
o substitution
o or elimination – just like in the homework.
More examples…
For this problem, I'd use substitution to solve the system of equations:
The length of a rectangle blah, blah, blah…
Let L = the length of the rectangle
… blah, blah, blah twice the width
Let W = the width of the rectangle
The length is 6 inches less than twice the width
L = 2W – 6
The perimeter of the rectangle is 56
2L + 2W =56
For this one, I'd use elimination to solve the system of equations:
Blah, blah, blah bought 2 cokes…
Let x = the price of a coke
.. blah, blah, blah 4 hot dogs
Let y = the price of a hot dog
2 cokes plus 4 hot dogs cost 8.00
2x + 4y = 8.00
3 cokes plus 2 hot dogs cost 8.00
3x + 2y = 8.00
For this one, I'd use substitution to solve the system of equations:
One number is blah, blah, blah…
Let x = the first number
…blah, blah, blah triple the second number
Let y = the second number
The first number is triple the second
x = 3y
The sum of the numbers is 24
x + y = 24
Checking your answers vs. Solving the problem
The problem: Two numbers add to give 4 and subtract to give 2. Find the numbers.
Solving the problem:
Let x = the first number
Let y = the second number
Two numbers add to give 4: x + y = 4
Two numbers subtract to give 2: x – y = 2
Our two equations are: x + y = 4
x – y = 2 Adding the equations we get
2x = 6
x = 3 The first number is 3.
x + y = 4 Substituting that answer into equation 1
3 + y = 4
y = 1 The second number is 1.
Checking the answers:
Two numbers add to give 4: 3 + 1 = 4
The two numbers subtract to give 2: 3 – 1 = 2
Do NOT demonstrate how to check the answers that are provided and call that
demonstrating how to solve the problem!
Formulas vs. Solving equations
Formulas express standard relationships between measurements of things in the real
world and are probably the mathematical tools that are used most frequently in real-life
situations.
Solving equations involves getting an answer to a specific problem, sometimes based
on real-world data, and sometimes not. In the process of solving a problem, you may
need to apply a formula. As a member of modern society, it is assumed that you know
certain common formulas such as the area of a square or the perimeter of a rectangle. If
you are unsure about a formula, just Google it. Chances are excellent it will be in one of
the first few hits.
If you are still baffled:
Check out all the examples worked out in the PowerPoints in the Other
Resources section of the Handy Helpers for Section 4.3.
Message me if you are still confused.
**WK4MATH110SystemsofEquationswithAnswers.pdf**
This file is too large to display. [View in new window](https://www.sweetstudy.com/files/wk4math110systemsofequationswithanswers-pdf)
**## GradePitchandSlipperySlopes.pdf**
When you answer these, please incorporate enough of the question so
that we all can tell what you’re talking about without having to open
this file.
Simply saying “#40 All of them” is not very informative!
GRADE
1) What is meant by the grade of a highway?
2) How might the grade of a highway influence the prices set by
trucking companies to haul freight over the route?
3) What is a runaway truck ramp?
4) Why are residential roads higher in the middle than at the curb?
5) What is the generally accepted maximum grade for wheelchair
ramps?
6) What is an adhesion railroad?
7) What is the maximum grade that an adhesion railroad can
climb?
8) What are some of the steepest adhesion railroads in the world
and where are they located? (just give us one and leave the
others for classmates!)
9) What is a cog railway?
10)Where is the world’s highest cog railway?
11)Where is the world’s steepest cog railway?
12)How does a “rack-and-adhesion” railway work?
13)What is a funicular and how does it relate to slope?
14)What was the motivation for the invention of the San Francisco
cable cars?
15)How do the San Francisco cable cars work?
16)How can canals be used to help boat climb hills?
17)How does a canal lock work?
18)How high above sea level is Lake Gatun in the Panama Canal?
19)What are "jake brakes" and why are they prohibited in some
locations?
PITCH
20)How steep does a roof have to be to be considered “pitched”?
21)What distinguishes a “salt box” house?
22)What distinguishes an A-frame house?
23)You may have read The House of the Seven Gables – what’s a
gable?
24)Why are gable end roofs among the worst roof designs for
hurricane regions?
25)What are some advantages & disadvantages of a Dutch Hip Roof
Style?
26)Why are roof lines different in New England and the Southwest?
27)About how steep is the average residential staircase?
SLIPPERY SLOPES
28)About how steep is the angle of the slope for “Extreme Skiers”?
29)In the US, about how steep is a green, beginners’ slope?
30)In the US, about how steep is a blue, intermediate slope?
31)In the US, about how steep is a black, expert slope?
32)I can ski a double black diamond slope at home in Indiana. I
can’t wait to ski one in Colorado! Is this wise? Why?
**## WK4UsingtheEquationEditorinMyClassroom.pdf**
Using the Equation Editor …
… to make math problems
look like math problems!
Math on the keyboard:
x = [-b +/- sqrt(b^2 – 4ac)]/(2a)
Huh?
Math with the equation editor!
2 4
2
b b ac
x
a
− −
=
That’s better!
Let’s say that you want to show an algebraic fraction like
Trying to do this with just the keyboard looks “weird” …
x / (x + 3)
… and it invites mistakes (like not using the parentheses).
x / x + 3 means
𝑥
𝑥
+ 3 which is something completely different!
3
x
x +
The next time you go to post a discussion click the three
extra dots at the end.
You will see more options show up.
Right below the Bold button
you will see the Greek letter sigma.
This is the button to open the equation editor.
Select Graphical Equation
The Equation Editor has lots of tools, so let’s look at a few of the basics.
Good news: most things look like what they do.
For example, if you need a fraction, you will click the button that looks
like an empty fraction.
You will see a fraction appear – you just need to fill it in.
Use the arrows to navigate to the bottom of the fraction.
Be sure to use the right arrow to navigate
out of the fraction before continuing with your equation.
You will notice that the cursor is tall in this picture. That is how you
know that you are out of the fraction.
Another commonly used symbol is the exponent.
This time let’s try to create the expression:
To do this you will start by creating a fraction.
2
6
5
2
x
y
−
+
Once you are in the fraction, you type the x
and then click the exponent
button and then the 2.
Use the right arrow button to get out of the exponent
before typing the – 5.
Then, use the down arrow to move to the denominator.
In this picture you can see the cursor.
Note that the cursor will show you if
you are still in the exponent or not, so watch carefully!
Once you have the top of the fraction done …
… just rinse and repeat for the bottom!
Once done click insert.
We did it!
If you want to add words to your equations,
just type them in,
select them, and then click on the text font.
Experiment with it until
you can get the desired results.
The math may still be a challenge …
… but now writing the answers shouldn’t be!
**## MATH110WK345DiscussionsHelp.docx**
**W3: Grade Pitch and Slippery Slopes**
This is an opportunity to investigate the many ways that the concept of "slope"This is an opportunity to investigate the many ways that the concept of "slope" touches our daily lives.
Open the file called Grade Pitch and Slippery Slopes. Pick ONE of the questions that has not already been answered by a classmate. Click on Post New Thread and make the problem number and the topic (#1 Highway Grade) the subject of your post so that people can tell at a glance which problems have already been answered.
Give a full and complete answer to the question. I would like you to find out about the material and describe the answer in your own words. Most of these topics require some research. Don't forget that you must give attribution to your source. Be sure to cut and paste the URL of the site from which you got the information. Sometimes other students decide that a topic is interesting and would like to learn more about it. Your source will provide them with a good starting point. This initial post is worth 6 points.
You must also give a substantive response to two classmate's posts (worth 2 points each). You may ask questions to elicit a more in-depth explanation, add additional information to your own posting in response to questions, share additional knowledge on another posting or share an example from your own life related to the topic. Simply saying "Good post!" will not earn any points.
It's always fun when people add pictures to their Discussions. This is not required but, if you'd like to, feel free to add one.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
**Initial Post Due:** Thursday, by 11:55 p.m., ET
**Other Posts Due:** Sunday, by 11:55 p.m., ET
[**W4: If Only I Had a System …**](https://myclassroom.apus.edu/d2l/le/1457714/discussions/topics/1636546/View)
It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week's test, FOLLOW THESE
INSTRUCTIONS
It is difficult to learn how to do story problems because there are so many
different types. If you want to do well on this week's test, FOLLOW THESE
INSTRUCTIONS!
Step 1: Read the file entitled "Read This First"
Step 2: Open the file "MATH110 Systems of Equations with Answers".
Step 3: Go through ALL the story problems provided and try to solve them. Pretend it's a Practice Test. Check your answers with the key provided.
Step 4: Pick ONE of the problems that you got right (that has not already been solved by a classmate) and demonstrate its solution for the rest of us.
Step 5: Study how your classmates solved the problems that you missed. Remember that these may be on the test!
Note: Problems are selected on a first-come basis. If a classmate has already chosen a problem you had wanted to answer, please select a different problem. Our goal is to answer and discuss as many different problems as possible.
1) To demonstrate your problem, select Start a New Conversation and make the subject of your post ONLY the problem number and topic (#10 Jarod and the Bunnies).
2) Begin your post with a statement of the problem so that we can understand what you are doing.
3) The answers are at the end of the file, so don't just give an answer — we can already see what the answers are. Don't post an explanation unless your answer matches the correct one!
Your goal should be to explain this problem so well that a classmate who "just doesn't get it" will be able to understand it completely!
This is a moderated discussion. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit.
I will indicate in the grading feedback if corrections need to be made. If you haven't received credit, first double-check my comments. If everything looks OK, then email me asking me to check on it. You must make the necessary corrections and have your work posted in order to receive credit.
For this particular Discussion,
**no responses are required** – your initial post is worth the full points. Should you choose to respond to a classmate, a request for clarification on the procedure used, a suggestion for an alternate method of solving the problem or a general comment about the technique would all be appropriate. I'm sure that a "thank you" for an exceptionally clear explanation would also be welcome!
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
[**W5: Midterm Reflection**](https://myclassroom.apus.edu/d2l/le/1457714/discussions/topics/1636547/View)
Select Start a New Conversation using your name as the Subject.
Now that we have passed the half-way mark of the class, tell us what you think about learning math online?
Name at least one thing that you really enjoy about the class (come on, there must be something!) and at least one improvement that could make this class even better. Feel free to editorialize!
Also, this is a good time to make a "keep-quit-start" resolution.
• What are you doing to help yourself learn in this class that you are going to keep doing because it's working?
• What are you doing that is hindering you from learning in this class that you are going to quit doing?
• What do you think will help you improve your learning in this class that you are going to start doing?
Then, respond to 2 of your classmates in substantive postings.
Please pay attention to spelling and grammar. These skills are most important in about 80% of college courses that require written papers. Good writing skills will also reflect more positively on your status as a college student and graduate.
Please
**sign** ALL your discussion posts with the name that you like to be called – it makes it so much easier for the rest of us to address you by your preferred name when we respond.
**## WK4ReadThisFirst.pdf**
Forum: If Only I Had a System…
Applications of Systems of Linear Equalities
The Problem:
When students are surveyed about what makes a good math Forum, at least half of the
responses involve
"discussing how to work problems"
"seeing how this math applies to real-life situations"
This Forum on applications of systems of equations addresses both of these concerns.
Unfortunately, the typical postings are far from ideal.
This is an attempt to rectify the situation. Please read this in its entirety before you
post your answer!
Pick-up games in the park vs. the NBA:
Shooting hoops in the park may be lots of fun, but it scarcely qualifies as the precision
play of a well-coached team. On the one hand, you have individuals with different
approaches and different skill levels, "doing their own thing" within the general rules of
the game. On the other hand you have trained individuals, using proven strategies and
basing their moves on fundamentals that have been practiced until they are second
nature.
The purpose of learning algebra is to change a natural, undisciplined approach to
individual problem solving into an organized, well-rehearsed system that will work on
many different problems. Just like early morning practice, this might not always be
pleasant; just like Michael Jordan, if you put in the time learning how to do it correctly,
you will score big-time in the end.
But my brain just doesn't work that way. . .
Nonsense! This has nothing to do with how your brain works. This is a matter of
learning to read carefully, to extract data from the given situation and to apply a
mathematical system to the data in order to obtain a desired answer. Anyone can learn
to do this. It is just a matter of following the system; much like making cookies is a
matter of following a recipe.
"Pick-up Game" Math
It is appalling how many responses involve plugging in numbers until it works.
"My birthday is the eleventh, so I always start with 11 and work from there."
"The story involved both cats and dogs so I took one of the numbers, divided by
2 and then I experimented."
"First I fire up Excel…"
"I know in real-life that hot dogs cost more than Coke, so I crossed my fingers
and started with $0.50 for the Coke…"
The reason these "problem-solving" boards are moderated is so that these creative
souls don’t get everyone else confused!
NBA Math
In more involved problems, where the answer might come out to be something
irrational, like the square root of three, you are not likely to just randomly guess the
correct answer to plug it in. To find that kind of answer by an iterative process (plugging
and adjusting; plugging and adjusting; …) would take lots of tedious work or a computer.
Algebra gives you a relative painless way of achieving your objective without wearing
your pencil to the nub.
The reason that all of the homework has involved x's and y's and two equations, is that
we are going to solve these problems that way. Each of these problems is a story about
two things, so every one of these is going to have an x and a y.
In some problems, it’s helpful to use different letters, to help keep straight what the
variables stand for. For example, let L = the length of the rectangle and W = the width.
The biggest advantage to this method is that when you have found that w = 3 you are
more likely to notice that you still haven’t answered the question, “What is the length of
the rectangle?”
Here are the steps to the solution process:
Figure out from the story what those two things are.
o one of these will be x
o the other will be y
The first sentence of your solution will be "Let x = " (or “Let L = ” )
o Unless it is your express purpose to drive your instructor right over the
edge, make sure that your very first word is "Let"
The second sentence of your solution will be "Let y = " (or “Let W = ” )
Each story gives two different relationships between the two things.
o Use one of those relationships to write your first equation.
o Use the second relationship to write the second equation.
Now demonstrate how to solve the system of two equations. You will be using
either
o substitution
o or elimination – just like in the homework.
More examples…
For this problem, I'd use substitution to solve the system of equations:
The length of a rectangle blah, blah, blah…
Let L = the length of the rectangle
… blah, blah, blah twice the width
Let W = the width of the rectangle
The length is 6 inches less than twice the width
L = 2W – 6
The perimeter of the rectangle is 56
2L + 2W =56
For this one, I'd use elimination to solve the system of equations:
Blah, blah, blah bought 2 cokes…
Let x = the price of a coke
.. blah, blah, blah 4 hot dogs
Let y = the price of a hot dog
2 cokes plus 4 hot dogs cost 8.00
2x + 4y = 8.00
3 cokes plus 2 hot dogs cost 8.00
3x + 2y = 8.00
For this one, I'd use substitution to solve the system of equations:
One number is blah, blah, blah…
Let x = the first number
…blah, blah, blah triple the second number
Let y = the second number
The first number is triple the second
x = 3y
The sum of the numbers is 24
x + y = 24
Checking your answers vs. Solving the problem
The problem: Two numbers add to give 4 and subtract to give 2. Find the numbers.
Solving the problem:
Let x = the first number
Let y = the second number
Two numbers add to give 4: x + y = 4
Two numbers subtract to give 2: x – y = 2
Our two equations are: x + y = 4
x – y = 2 Adding the equations we get
2x = 6
x = 3 The first number is 3.
x + y = 4 Substituting that answer into equation 1
3 + y = 4
y = 1 The second number is 1.
Checking the answers:
Two numbers add to give 4: 3 + 1 = 4
The two numbers subtract to give 2: 3 – 1 = 2
Do NOT demonstrate how to check the answers that are provided and call that
demonstrating how to solve the problem!
Formulas vs. Solving equations
Formulas express standard relationships between measurements of things in the real
world and are probably the mathematical tools that are used most frequently in real-life
situations.
Solving equations involves getting an answer to a specific problem, sometimes based
on real-world data, and sometimes not. In the process of solving a problem, you may
need to apply a formula. As a member of modern society, it is assumed that you know
certain common formulas such as the area of a square or the perimeter of a rectangle. If
you are unsure about a formula, just Google it. Chances are excellent it will be in one of
the first few hits.
If you are still baffled:
Check out all the examples worked out in the PowerPoints in the Other
Resources section of the Handy Helpers for Section 4.3.
Message me if you are still confused.
**WK4MATH110SystemsofEquationswithAnswers.pdf**
This file is too large to display. [View in new window](https://www.sweetstudy.com/files/wk4math110systemsofequationswithanswers-pdf)