Tuesday, April 23, 2013
Equations v. Inequalities
Answer the following about equations and inequalities.
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
2) How is graphing linear inequalities different? What does it help us understand?
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
This post is worth 8 points (2 per problem). You will be graded based upon the completeness and thoughtfulness of your answers.
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1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteGraphing linear equations are used in real world applications. We used graphing linear equations in our Marketplace Project to determine our break even point. We do this by finding the intersection point of our revenue and the fixed cost. We think that also businesses around the world uses break even graphs to determine their profit for selling a certain amount of products. Graphing helps us understand where two points intersect with each other.
2) How is graphing linear inequalities different? What does it help us understand?
Linear inequalities are all the possible numbers and points on the graph. Shading it symbolizes all the possibilities in that region. Graphing these linear inequalities helps us understand the vast amount of probability of the number that is less than or at least less than.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Conjunctions are simply a section on a number line where two inequalities meet. You can tell if two inequalities are conjunctions if they are connected by and. In order to graph it, you need to find the intersections between the two inequalities and shade it in on the number line. A disjunction is all the possibilities of two inequalities of a number line. The two inequalities are usually connected with an or. You shade in all the solutions for each inequality.
You can remember this by relating to its English definition. Conjunctions are connecting sentences using a word such as and. On the other hand, the prefix dis in disjunctions means away or apart. These English definitions are similar in math; conjunctions are intersecting and disjunctions are all possible solutions and are usually depicted as not intersecting on a number line.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
For example, Alex only have $5 in your pocket. Alex can buy a certain number of cookies ($1) and ice cream ($1.5) and the total cost needs to be less than or equal to $5. But he needs to buy less than 2 cookies because his mom doesn’t want him to eat too much sugar. How many ice creams and cookies can he buy?
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteWe think that the point of graphing linear equations is so that we can easily see the possible solutions of a problem. It helps us understand the relationship between the two variables. It also helps us understand where the lines intersect, which is basically the answer.
2) How is graphing linear inequalities different? What does it help us understand?
When graphing linear equations, you always need to remember to shade in the correct sides, unlike when graphing linear equations. You also have to make sure to check if the point needs to be colored in or not colored in. Also, when you graph linear equations with two variables, you need to check if your line is dotted or solid.
It helps us understand the pattern between the possible answers. Such as when one goes up the other goes down and so on. We think it helps us understand the possible answers, the pattern between them, and least and most that the variable could possibly be.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
The basic concept with conjunctions and disjunctions is the difference between the words “and” or “or”.
Think of railroads. When there is a conjunction, there are two railroads that meet therefore there are two railroads(the two different shaded regions) and one section where they meet(overlap). Only one train can move on these tracks so there will only be one “section” of an answer unlike in disjunctions where there are two parts. So, in your answer, you want the overlapping shaded region to be your answer because that’s the conjunction of the two railroads and where the train travels on.
However, let’s go back to the disjunctions. In a disjuncted railroad, there are two railroads that are not connected so there will be two seperate trains that run on these railroads. Therefore your answer will(most of the time) be the two seperate railroads(two seperate shaded regions).
You can make sure that you don’t forget them by, because in conjunctions there are two trains, you must think one train AND another train. In disjunctions, because there are two seperate railroads, you must pick either this train track OR the other one. So, when you see the word “AND” you should think of a train that travels on OVERLAPPING tracks. Also, when you see the word “OR”, you should think of two different trains, so two different “parts” of an answer.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
y > x + 2
y > 5
y = Tom
x = Jack
Jack has at most 2 less cookies than the number of cookies Tom has. Tom has at least 5 cookies. (When solving, use the variables x and y each representing the number of cookies Tom and Jack have.)
Wrong one!
Delete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
DeleteWe think that the point of graphing linear equations is so that we can easily see the possible solutions of a problem. It helps us understand the relationship between the two variables. It also helps us understand where the lines intersect, which is basically the answer.
2) How is graphing linear inequalities different? What does it help us understand?
When graphing linear equations, you always need to remember to shade in the correct sides, unlike when graphing linear equations. You also have to make sure to check if the point needs to be colored in or not colored in. Also, when you graph linear equations with two variables, you need to check if your line is dotted or solid.
It helps us understand the pattern between the possible answers. Such as when one goes up the other goes down and so on. We think it helps us understand the possible answers, the pattern between them, and least and most that the variable could possibly be.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
The basic concept with conjunctions and disjunctions is the difference between the words “and” or “or”.
Think of railroads. When there is a conjunction, there are two railroads that meet therefore there are two railroads(the two different shaded regions) and one section where they meet(overlap). Only one train can move on these tracks so there will only be one “section” of an answer unlike in disjunctions where there are two parts. So, in your answer, you want the overlapping shaded region to be your answer because that’s the conjunction of the two railroads and where the train travels on.
However, let’s go back to the disjunctions. In a disjuncted/disconnected railroad, there are two railroads that are not connected so there will be two separate trains that run on these railroads. Therefore your answer will(most of the time) be the two separate railroads(two separate shaded regions).
You can make sure that you don’t forget them by, because in conjunctions there are two trains, you must think one train AND another train. In disjunctions, because there are two separate railroads, you must pick either this train track OR the other one. So, when you see the word “AND” you should think of a train that travels on OVERLAPPING tracks. Also, when you see the word “OR”, you should think of two different trains, so two different “parts” of an answer.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
y > x + 2
y > 5
y = Tom
x = Jack
Jack has at most 2 less cookies than the number of cookies Tom has. Tom has at least 5 cookies. (When solving, use the variables x and y each representing the number of cookies Tom and Jack have.)
1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteThere are some people who understands better when something is visualized. Rather than explaining in words, or when speaking, it may be easier for majority of people to understand when something is picturized. When the relation between the input and output are shown visually, we can easily see the slope, wether it's a positive slope, or a negative slope. In our opinion, graphing linear equations helps us understand the relation of two variables
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities and linear equations are somewhat similar, but there are some minor differences when graphing them. When graphing, they both use the y-intercept and the slope. After drawing the points, for linear inequalities, there are two ways that the line can be depending on the equation. For linear inequalities, there can be a solid line, and dotted line, also we have to shade the side where the solutions can be in. We believe that graphing linear inequalities help us understand that the solutions lining in the line can be the solution for the equation and sometimes can't be the solution for the equation.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Conjunctions are when two inequalities are joined by the word AND. When there are two numbers with two inequality signs in both sides of the variable, it's always conjunction because they are connected. You can memorize it by the first three letters of conjunction, "con". To graph the conjunctions, the solutions are where they are connected, or joined.
Disjunction are when two inequalities are joined by the word OR. Disjunction dislike each other so they don't care of each other. You also can memorize this by the first three letters "dis". You can just graph this and that can be the solution.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
Alex and Kimberly together have $400. To celebrate 2013 Eight grade graduation, they want to buy some one cupcakes and one poptarts to each of their friends. If cupcakes are $4 each and poptarts are $1.50 each, how many friends can they give?
The last example is not a system of inequalities. 4c +1.5p is less than or equal to 400....but that's only one equation.
DeleteAnswer the following about equations and inequalities.
ReplyDelete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
The point of graphing linear equations is so that we can understand linear equations visually. Linear equations are important because they are used not only in Algebra math, but in real life situations too. Many jobs use linear equations like economics. However, sometimes linear equations could be hard to understand if you only see the numbers and variables. On the other hand, if you graph the line and actually see the line, it helps to understand the equation more easily. Not only does it help in understanding, but if there are two lines that intersect, we can find the intersection coordinate easily.
2) How is graphing linear inequalities different? What does it help us understand?
When you graph linear inequalities, you have to shade above or below the graph when in graphing linear equations you only draw the line with no shading. Also, for linear equations you just draw a solid line, but for linear inequalities, some lines are dotted lines and others are solid. It helps us understand where the two lines(equations) intersect. It also helps us understand the possible solution of the graph and the relationship between the two variables.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
A plane crashed into an island. Person S is a survivor(disjunction), and he doesn’t care if the other people survived or not. Person T is caring guy and he cares for the others too and so he tries to build a team to survive throughout the wilderness.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
If you have a maximum amount of money you’re allowed to use to buy a number of items, then you will be able to know the maximum number of items you can buy.
Ex: x < 10
If you’re trying to buy flowers, you’ll be able to know that the maximum number of flowers you can buy is 9.
This post is worth 8 points (2 per problem). You will be graded based upon the completeness and thoughtfulness of your answers.
- Joy, Kevin
This last example is not a system of inequalities. You only gave one inequality. A system would be two inequalities with two variables.
Delete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteThe point of graphing linear equations is to help us find the intersecting point visually. You can find the intersecting point with equations and other methods but using the graphing method can help you visually see it and understand it better. Plus, it helps us understand the process of two equations intersecting.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities are different because there are other things you have to add on to from what you learned from graphing systems of equations. When you graph a system of inequalities, you have to use different types of lines to identify the different symbols:closed or open circles. Also for systems of inequalities, you have to shade in the side of the solution sets and the area where both systems are shaded is like the intersection point. So, there is a lot more happening in a inequality compared to a linear equation.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
There was a plane that was about to land on the ground in a certain area. The flight attendant would only allow this. However, another plane just landed on the ground in a random place outside of the certain area which was okay to the pilot, but not the flight attendant. The flight attendant would only be satisfied if the planes landed on the specified area which is called a conjunction, but the pilot is okay with landing anywhere on the ground which is call a disjunction.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
Jadyn was craving sweet treats so she decided to go buy some chocolate bars and skittles packs. She could buy as many packs of these foods as she wanted as long as she spent $20 or less. Then, Jadyn went back to buy one more item of junk food that was less than $5.
x + y ≤ 20 (y ≤ -x + 20)
y < 5
The first inequality only works if each item costs $1. The second inequality is completely unrelated to the first.
Delete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteIn my opinion, the point of graphing linear equations is to practice for situations that can happen in real life. It helps us apply to situations like how far you could go on a certain amount of gas. Also if you graph linear equations you can explore most of the possible solutions and if you can see the solutions you can solve the problem you have at hand such as not knowing how much gas you’ll need for a trip.
2) How is graphing linear inequalities different? What does it help us understand?
It helps us understand how much we can have in the maximum and how much we must have minimum. Linear equalities are different in that we focus on the limits of what we can have while linear equations sheerly focus on only the solution set. Also, the linear inequalities are a little bit more difficult because
you have to think where to shade and where the solution set is located either above or below.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
A mnemonic device is probably most effective in this situation. Dis the latin root means against or the opposite so you can see that it can fill the purpose of or so when you see the word disjunction immediately think of “or”. When you see conjunction think of the conjunction song from grammar and immediately think of the word “and.”
4) Name one original real-world application for graphing a SYSTEM of inequalities.
When you want to take math lessons and science lessons so that you can do well in school, and when you only have $1,000, you can choose who many classes you want to take. However, you don’t want to spend less than $500 because then you won’t learn enough. Then you can create a graph with SYSTEM of inequalities to show how many classes you can take for each of them.
You did not mention how to remember to graph #3.
Delete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
ReplyDeleteThe point of graphing is to have a better idea of the solution. It visually shows how the slope is steep/low. We can also view the many possible solutions in the graph. It helps us understand where it can intercept with each other.
2) How is graphing linear inequalities different? What does it help us understand?
Conjunction - “con” means positive “friendly”
- where they meet and cross each other
- shade in the place the two lines meet
Disjunction - “dis” is kind of like negative “disrespectful” etc)
- all possible answers
- shade in the place where there is a possibility of being the answer
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
Graphing linear inequalities shows the possible solution sets. It helps us understand the basic range of solution sets. To graph it, conjunctions only require what each equation both have in common. To graph disjunctions, You must shade every part of the equation, in other words, all possible answers. If you’re still having a difficult time, remember the “con” in conjunction is positive, so it likes to be with others. Disjunctions on the other hand sounds negative and doesn’t want to be with others. It wants to be alone.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
You had 10 dollars to spend on junk foods. One candy costs 50 cents and one chocolate costs a dollar. Your parents told you the maximum amount of chocolate you can buy is 5. If you wanted to buy 5 chocolates, what’s the maximum amount of candy you can buy with 10 dollars.
“0.5x + 1y ≦ 10”
y = 5
0.5x ≦ 5
x ≦10
#3 is weak, and you answered #2 inside of #3. Also, the last example is not quite a system, since you should have TWO inequalities, not one inequality and one equation.
DeleteAnswer the following about equations and inequalities.
ReplyDelete1) In your opinion, what is the point of graphing linear equations? What does it help us understand?
In my opinion, the point of graphing linear equations is to help people easily understand them. It helps us understand how the output comes out after a number is input, clearly defining which is which. Viewing linear equations as numerical variables is quite complex to understand compared to a graphed one.
2) How is graphing linear inequalities different? What does it help us understand?
Graphing linear inequalities are different from graphing linear equations, because you have to determine if the boundaries are solid or dotted. Also, you have to determine to shade above the line or below the line. It helps us understand how to find out the intersection of two or more inequalities.
3) You are tutoring a student that is having a difficult time understanding conjunctions and disjunctions. Come up with a unique, original way of remembering what each term means and how to graph it.
First, a conjunction uses the word ‘and’ to connect two inequalities. When you graph a conjunction on a number line, you have to find a region that both inequalities overlap and you only shade that region. Since a conjunction uses the word ‘and’ I hope a student can remember this by referring to his/her English class. A conjunction connects two words or a group of words using the word ‘and’ or ‘like’. Conjunctions in math are ‘and’ problems, ad you graph the a-like region. For disjunctions, you “dis” a conjunction by using a word that is the opposite of ‘and’. So, a disjunction uses the word ‘or’ to connect two inequalities. When you graph a disjunction, you can graph everything on the number line, and I hope a student can remember this by also dissing the way you graph a conjunction.
4) Name one original real-world application for graphing a SYSTEM of inequalities.
Jennifer wants to spend $70 at most to buy red velvet and vanilla butter cupcakes for her brothers birthday party. The red velvet cupcakes were $5, and the vanilla butter was $6. Jennifer’s brother wanted 5 more red velvet cupcakes than vanilla butter cupcakes.
This last problem is not quite a system of inequalities, since the second one is an equation.
ReplyDelete