Thursday, April 29, 2010
Monday, April 26, 2010
Today in class, we focused on maintaining equality. That means keeping the numbers that you are working on balanced. For example: 85=70+15. If you add 5 to 85, then you have to maintain equality by adding 5 to 70+5, and the numbers will stay equal.
We also worked on problem 3.2, which was about coins and pouches. What we had to do was keep the number of coins per pouch equal, which was maintaining equality. If there were 3 pouches and 2 coins on one side, then you would cross out 3 pouches and 2 coins on the other side too, to keep the number of coins per pouch equal. That is what we worked on today in math class.
We also worked on problem 3.2, which was about coins and pouches. What we had to do was keep the number of coins per pouch equal, which was maintaining equality. If there were 3 pouches and 2 coins on one side, then you would cross out 3 pouches and 2 coins on the other side too, to keep the number of coins per pouch equal. That is what we worked on today in math class.
Friday, April 16, 2010
Math Relfection p. 23
1. The dependent variable changes at steady rate, as the independent also changes at a steady rate. For example, the independent variable may go up at 1, and the dependant variable may go up by 3. Also the dependent variable may go down by steady rate also, like the independent variable goes up by 1, and the dependent variable goes down by 5.
2. A pattern for a linear relationship shows up in a graph through a straight line. It could be any straight line, horizontal, vertical, or diagonal. As long as its a straight line, its a linear relationship. A linear relationship shows up i a table by the numbers increasing, decreasing, or staying the same in a steady rate. Like, x starts at 1, y starts at 2. Then, as x increases by 1, y stays the same. A linear relationship is shown in a equation by as x increases or decreases, y increases or decreases by a steady rate, not jumping around to random numbers.
2. A pattern for a linear relationship shows up in a graph through a straight line. It could be any straight line, horizontal, vertical, or diagonal. As long as its a straight line, its a linear relationship. A linear relationship shows up i a table by the numbers increasing, decreasing, or staying the same in a steady rate. Like, x starts at 1, y starts at 2. Then, as x increases by 1, y stays the same. A linear relationship is shown in a equation by as x increases or decreases, y increases or decreases by a steady rate, not jumping around to random numbers.
Thursday, April 15, 2010
1. As the independent variable increases at a steady rate so does the dependent variable. For example if x increases by 1 and does that the entire time and y increases by 3 and does that every time then the relationship is linear. So if i was to raise money for a bike ride and I got $100 no matter how far i rode. Therefore the relationship is linear because it does nothing at a steady rate. However if I was a shopper and I had $100 to start and spent $10 per week for 10 weeks then the relationship is linear because it decreases at a steady rate.
2. A relationship shows up in a graph, a table, and an equation. It shows up in a graph because if the line is straight then the relationship is linear. It shows up in a table because you can see the numbers increasing at a steady rate. It shows up in the equation because you can see how the x and y increase.
2. A relationship shows up in a graph, a table, and an equation. It shows up in a graph because if the line is straight then the relationship is linear. It shows up in a table because you can see the numbers increasing at a steady rate. It shows up in the equation because you can see how the x and y increase.
Math Reflection
1. In a linear relationship the dependent variable (the y axis on a graph) changes along with the independent variable (the x axis) but not at the same rate usually. If Steve is selling T-shirts at a concert for $3.00 per T-shirt you could make a table that looked like this..
X Y
1 3
2 6
3 9
4 12
5 15
6 18
7 21
8 24
9 27
10 30
As X (the independent variable) increases by one Y (the dependent variable) goes up by 3. If you put it in an equation it would be X * 3 = Y.
2. In a linear relationship the pattern of change can show up in a graph, table and an equation. In a graph you can tell if it's linear because the graph will be in a straight line and always is going at the same rate. An example of this is Steve selling his T-shirts since he has a linear equation it automatically makes him have a linear graph. You can tell if a tables linear because the numbers in the table increase or decrease in a steady rate. For example in Steve's table for every T-shirt he sells he makes $3.00 and as the table goes on Steve's money increases by a steady rate of $3.00. If you look at an equation you tell its linear because all of the numbers are compatible with each other and don't increase and decrease in the same graph or table. An example of this would be for each T-shirt Steve sells he makes $3.00 and to get how much money he makes for selling X amount of T-shirts you would do X * 3 = Y. X being the number of T-shirts bought and Y being the total money he makes off selling them.
Wednesday, April 14, 2010
MSR Math Reflection 1
1. In a linear relationship, as the indipendent variable changes, the dependent variable can change as well. Since it is linear, the independent variable changes by a steady rate while a dependent variable does as well. An example is that as the independent variable increases by 1, the dependent variable incrreases by 5. They will both always increase or decrease at the same rate.
2. The pattern of change in a linear relationship shows up in a table by X increasing or decreasing by the same number every-time and then Y increasing or decreasing by the same number everytime. It shows up in a graph because the line will be a straight line. You will be able to see that every data point incereases or decreases on the X axis by a consistent rate while the the data point increases or decreases by another number every-time on the Y axis. It shows up in an equation because it will say Y equals a certain number times X which shows that it will alwyas be a steady rate.
Math Reflection
1. In a linear relationship the dependent variable changes as the independent variable changes, but they often don't change at the same rate. A linear relationship is one that changes at a constant rate and shows up as a straight line when graphed. The dependent variable is the one that depends on the other variable, and is the y that belongs on the y axis. The independent variable is the one that keeps going no matter what. It is the x that belongs on the x axis. The independent variable often goes up by 1. As the x goes up by 1, y goes up at a constant rate as well. An example of this in an equation is: y=5x or y=x+3 or y=7 (which would create a horizontal line on a graph), or y=60-5x (a decreasing linear relationship).
2. The pattern of change (or rate) in a linear relationship shows up in the table, graph, and the equation. The rate shows up in the table in the numbers. The x variable often increases by 1 and the rate will be in the numbers, which often takes some searching to find. You must look at the relationship between the y and x variable to find the pattern of change. You can tell whether the linear relationship is increasing, decreasing or not changing by observing the y or dependent variable. The pattern of change shows up in the graph on the line. As the x is steadily increasing, the y will be changing at a constant rate, and that is where the rate is to be found. In an equation, the rate is found in the numbers surrounding the y and x variables. The rate can be found in the equations above. In the equation y=5x, the rate is 5 times the independent variable. In the equation y=x+3, the rate is 1 plus a constant of 3.
2. The pattern of change (or rate) in a linear relationship shows up in the table, graph, and the equation. The rate shows up in the table in the numbers. The x variable often increases by 1 and the rate will be in the numbers, which often takes some searching to find. You must look at the relationship between the y and x variable to find the pattern of change. You can tell whether the linear relationship is increasing, decreasing or not changing by observing the y or dependent variable. The pattern of change shows up in the graph on the line. As the x is steadily increasing, the y will be changing at a constant rate, and that is where the rate is to be found. In an equation, the rate is found in the numbers surrounding the y and x variables. The rate can be found in the equations above. In the equation y=5x, the rate is 5 times the independent variable. In the equation y=x+3, the rate is 1 plus a constant of 3.
Math Reflections MSA 1
1. As the independent variable increases or decreases so does the dependant variable. For example if an equation was Y=3X than every time X increases by 1 the Y increases by 3. Or if it was M=50-2W than every time W increases by 1 M decreases by 2.
2. In a graph you can tell if it’s linear if the line is straight. In table you can tell if it’s linear if the independent variable and the dependent variable both go up at a constant rate. In an equation you can tell if it’s linear if the equation has an independent variable a dependant variable and a rate.
2. In a graph you can tell if it’s linear if the line is straight. In table you can tell if it’s linear if the independent variable and the dependent variable both go up at a constant rate. In an equation you can tell if it’s linear if the equation has an independent variable a dependant variable and a rate.
MSA Mathematical Reflection 1
1. The dependent variable changes as the independent variable changes in a linear relationship by having the x variable ( independent variable) increase or decrease, the y variable (dependent variable) increases or decreases too. For example if a person named Kate buys two kittens every week she would have more kittens increasing by two every week that goes by.
Kate's Kittens
X Y
0 0
1 2
2 4
3 6
4 8
5 10
2. The pattern of change for a linear relationship shows up in a table, a graph, and an equation. The pattern of change for a linear relationship shows up in a table by having a repeated pattern increasing or decreasing at a constant rate. For example if the rate for Kate and her kittens is 2 kittens per week, then her table shown in number one would have the weeks(x) go up by one, and the kittens(y) go up by two's. The pattern of change for a linear relationship shows up in a graph by having the graph plots from the table go in a straight line. The line can go either way, in a straight line going up in a diagonal, in a straight line going down in a diagonal line, and or sideways in a straight line, parallel to the x axis. For example since Kate and her kittens is linear, then on a graph for every week two would go up in a diagnol by two on the y axis ( # of kittens), and would go in a straight line. The pattern of change for linear relationship shows up in an equation by having the equation work for all the numers in a constant rate. An example is also using Kates kittens by having the equation be, y=x2. These are some things to look for a linear relationship in tables, graphs, and equations.
Kate's Kittens
X Y
0 0
1 2
2 4
3 6
4 8
5 10
2. The pattern of change for a linear relationship shows up in a table, a graph, and an equation. The pattern of change for a linear relationship shows up in a table by having a repeated pattern increasing or decreasing at a constant rate. For example if the rate for Kate and her kittens is 2 kittens per week, then her table shown in number one would have the weeks(x) go up by one, and the kittens(y) go up by two's. The pattern of change for a linear relationship shows up in a graph by having the graph plots from the table go in a straight line. The line can go either way, in a straight line going up in a diagonal, in a straight line going down in a diagonal line, and or sideways in a straight line, parallel to the x axis. For example since Kate and her kittens is linear, then on a graph for every week two would go up in a diagnol by two on the y axis ( # of kittens), and would go in a straight line. The pattern of change for linear relationship shows up in an equation by having the equation work for all the numers in a constant rate. An example is also using Kates kittens by having the equation be, y=x2. These are some things to look for a linear relationship in tables, graphs, and equations.
1) In a linear relationship, the dependent variable changes as the independent variable changes. As the x variable (independent variable) increases or decreases, so does the y variable. That is a linear relationship. Example- This is a linear relationship because as x increases by 1, y increases by 2. They both increase at a steady rate, which makes it linear.
x y
0 0
1 2
2 4
3 6
4 8
5 10
2) The pattern of change for a linear relationship shows up in a table, a graph, and an equation.
Table- The pattern shows up when y goes up or down at a constant rate while x does also.
Graph- The pattern shows up when the line is straight.
Equation- The pattern shows up in an equation when the equation works for all numbers and they come out in a constant rate.
x y
0 0
1 2
2 4
3 6
4 8
5 10
2) The pattern of change for a linear relationship shows up in a table, a graph, and an equation.
Table- The pattern shows up when y goes up or down at a constant rate while x does also.
Graph- The pattern shows up when the line is straight.
Equation- The pattern shows up in an equation when the equation works for all numbers and they come out in a constant rate.
MSA Math Reflections 1
1. How the dependent variable in a linear relationship changes depends on how the independent variable changes. For example, if in the bike-athon, Mr. Murphy's class generated $200.00 to give to charity. Each week they donate $20.00 to the local Children's hospital. The independent variable is weeks and the dependent variable is the money left in the account. As the weeks increase by one, $20 is deducted from the class account. Another example of this is Joey works for his neighbor. For every hour that he works, he gets paid $10.75. The independent variable is hours while the dependent variable is how much Joey gets paid. As the hours increase by one, Joey earns $10.75 more.
2. The pattern of change in a linear relationship shows up as:
Graph, A straight line going either up or down.
Table, Increases or decreases with the same rate as time moves on.
Equation, A steady rate, if the same amount is added or taken away as time moves on.
2. The pattern of change in a linear relationship shows up as:
Graph, A straight line going either up or down.
Table, Increases or decreases with the same rate as time moves on.
Equation, A steady rate, if the same amount is added or taken away as time moves on.
1. The dependant variable changes as the independent variable changes in a linear relationship, because if the independent variable increases, so does the dependant variable, and if the independent variable decreases, so does the dependant variable. For example, in problem 4 on page 13, as the time increases by 1 hour, the distance increases by 6.5 miles.
2. The pattern of change for linear relationship shows up in a table, because if there is a steady increase in the numbers, then there will be a linear relationship, but if the numbers have no pattern, there will not be a linear relationship. The pattern of change shows up in a graph, because if there is a straight line on the graph, that shows a linear relationship between the numbers, and if the data in the graph doesn't make a straight line, then there will not be a linear relationship. The pattern of change for linear relationships show up in an equation, because if the equation does not work for all numbers, then there will not be a linear relationship. If the equation woks for every number that you try and it makes a linear relationship, then the equation and data are linear.
2. The pattern of change for linear relationship shows up in a table, because if there is a steady increase in the numbers, then there will be a linear relationship, but if the numbers have no pattern, there will not be a linear relationship. The pattern of change shows up in a graph, because if there is a straight line on the graph, that shows a linear relationship between the numbers, and if the data in the graph doesn't make a straight line, then there will not be a linear relationship. The pattern of change for linear relationships show up in an equation, because if the equation does not work for all numbers, then there will not be a linear relationship. If the equation woks for every number that you try and it makes a linear relationship, then the equation and data are linear.
Math Reflection
1. The dependent variable changes as the independent variable changes in a linear relationship. If the independent variable increases by 1, and the dependent increases by 5 each time, it is changing in a linear relationship. It is changing in a linear relationship because it is going up by 5 each time, and it doesn't change. If you sketched a graph the line would come out straight because it is evenly going up by 5 each everytime the independent variable increases by 1. For example, if the independent variable increases by 2 each time, and the dependent variable is increasing by 4 each time, it is changing in a linear relationship.
2. The pattern of change for a linear relationship shows up in a table, graph, and an equation of the relationship. It shows up in a table, if X shows up as 2,4,6,8,10 and Y shows up as 10,20,30,40,50, then it is linear because it is increasing by the same number (10) every time it increases by 2. In a graph a pattern of change in a linear relationship would show up by showing a straight line on the graph. For example, if X was increasing by 5 on the X axis, and Y was increasing by 20 on the Y axis, then a straight line would come out when you graphed it. The pattern of change for a linear relationship shows up in a equation of the relationship because the equation stays the same with the same numbers. For example, if X was 1 and Y was 5 the equation would stay as 5y=x.
2. The pattern of change for a linear relationship shows up in a table, graph, and an equation of the relationship. It shows up in a table, if X shows up as 2,4,6,8,10 and Y shows up as 10,20,30,40,50, then it is linear because it is increasing by the same number (10) every time it increases by 2. In a graph a pattern of change in a linear relationship would show up by showing a straight line on the graph. For example, if X was increasing by 5 on the X axis, and Y was increasing by 20 on the Y axis, then a straight line would come out when you graphed it. The pattern of change for a linear relationship shows up in a equation of the relationship because the equation stays the same with the same numbers. For example, if X was 1 and Y was 5 the equation would stay as 5y=x.
MSA Math Reflection 1
1. As the independent variable changes, the dependent variable does too. It either increases, decreases, or stays the same. For example, if the independent variable is weeks and the dependent variable is money, the dependent variable will increase if you receive money, decrease if you spend it, or stay the same if you don't spend or get any.
2. You can see patterns and linear relationships in tables, graphs, and equations. In a table, you can see the relationship if the data increases at a steady rate. For example, if money increases by $5 every week. In a graph, you can see the relationship if there is a straight line of data points, increasing, decreasing, or staying the same at a constant rate. In an equation, there must be a number that can be multiplied, divided, added, or subtracted by the independent variable to equal the dependent variable. For example; m=5w. M= amount of money W=weeks. There are many ways to figure out if there is a linear relationship of data.
2. You can see patterns and linear relationships in tables, graphs, and equations. In a table, you can see the relationship if the data increases at a steady rate. For example, if money increases by $5 every week. In a graph, you can see the relationship if there is a straight line of data points, increasing, decreasing, or staying the same at a constant rate. In an equation, there must be a number that can be multiplied, divided, added, or subtracted by the independent variable to equal the dependent variable. For example; m=5w. M= amount of money W=weeks. There are many ways to figure out if there is a linear relationship of data.
Math reflection
1. If the graph is linear than the dependent variable goes down at a steady rate. So as the independent variable goes up or down the dependent variable will go up or down by the same number every time. For example on p. 11 problem 1.4 part B has a graph that is linear because the dependent variable goes down by 10 every time the independent goes up by 1.
2. Graph: If the line is a straight line than it is a linear relationship. Table: If it is miles per hour the miles should go up or down at a steady rate as the hours go up than it is a linear relationship. Equation: If the equation is like y=x with an exponent over the x it is not linear but if the equation is like y=2x+73 it is linear. Or even if it is like y=53 it is linear.
1) A dependent variable changes as the independent variable
changes in a linear relationship when a number or a unit is
changed and the line that will be put on the graph when it is
graphed will not be straight it will have bumps.
2) The pattern of change shows up on the graph wjen the line
isnt straight, it shows up on the table when the pattern of
numbers suddenly change from going up by a certain ammount
and changes to going up by a different ammount that the other
numbers are not and the pattern shows up in the equation when
the equation doesnt work for a certain number.
changes in a linear relationship when a number or a unit is
changed and the line that will be put on the graph when it is
graphed will not be straight it will have bumps.
2) The pattern of change shows up on the graph wjen the line
isnt straight, it shows up on the table when the pattern of
numbers suddenly change from going up by a certain ammount
and changes to going up by a different ammount that the other
numbers are not and the pattern shows up in the equation when
the equation doesnt work for a certain number.
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Moving Straight Ahead
Today in math class, we did some more with linear relationship. First we did a do now that consisted of two tables and we had to figure out if they were linear. We were asked to look at both tables and find out which ones were linear. To find these out we needed to know if these were a straight line on a graph because if it is, then we know that it is linear relationship. We could have found out if it was linear by seeing if the table did not change, but that it was consistent. This brings me to my other description on what we learned to day. We learned what a steady rate is and how and where to use them. For example in one of the boxes, there was a five in one column and a 18 in the one next to it. This graph was linear because as each went up if you multiplied it by five column then used the steady rate which is 3. So 5x5+3= 18. the next two numbers were 10 and 33. So 10x5+3=33.
-Dan
-Dan
Tuesday, April 13, 2010
Monday, April 12, 2010
Sunday, April 11, 2010
Friday in class we learned about different types of linear relationships. When I say this I mean that we learned about decreasing and non - moving linear relationships.
For example one of the problems we did in class was problem 1.4. One part of the problem told us to make a graph of the class who took $12 out each week to buy books. The graph decreased by 12 each week and because it is a steady rate it qualifies as linear. Another problem we did was for homework. The problem was to graph 3 people who were raising money for a walkathon. One of the kids was earning $10 no matter how far she walked so her graph was a straight line from 0 meters to x meters. Since her graph steadly doesn't go anywhere it is linear. In short if the rate is steady the relationship is linear.
For example one of the problems we did in class was problem 1.4. One part of the problem told us to make a graph of the class who took $12 out each week to buy books. The graph decreased by 12 each week and because it is a steady rate it qualifies as linear. Another problem we did was for homework. The problem was to graph 3 people who were raising money for a walkathon. One of the kids was earning $10 no matter how far she walked so her graph was a straight line from 0 meters to x meters. Since her graph steadly doesn't go anywhere it is linear. In short if the rate is steady the relationship is linear.
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