Converting: Metric Style

Most of you probably know how to convert between metric units, but if not, this is how you do it with powers of ten.

Metric units all go up by powers of ten from the base unit (such as liters, meters, and grams). So 1m is equal 10²cm (100 cm), or 1m is equal 10⁻³ km (.001 km). Yes, the power can be positive or negative. It will be positive if the unit you are converting to a unit smaller than the original unit used (m→cm). While, the power will be negative if the unit being converted to is bigger than the original (m→km). The powers I keep mentioning refer to scientific notation. In math, you may have seen something such as 4.5•10². This really means 450. Since the power is 2, you move the decimal 2 places to the right. If the power was -2 (4.5 •10⁻²), you would move the decimal 2 places to the left (.045).

 

So positive = decimal moves right, and negative = decimal moves left

Tile Lab

 

This past class we white boarded yet another lab, the tile lab, from our “laborama” (see first post). In this lab we had to compare the area and the mass of VERY odd, annoying, and random cut pieces of carpet.

1)      Question

·        What is the relationship between area and mass?

2)      Prediction

·        Our group predicted a direct, linear graph with a small gradient. Also, area would be the independent variable(x) and mass would be the dependent variable(y).

3)      Set-Up

·        The set-up of this lab was pretty simple. Since we’re not allowed to “calculate” measurements (meaning we can’t use math to find our measurements), we had to trace the tiles on a piece of graph paper and count the number of squares to find the mass. Then to find mass, we used the triple beam balance.

4)      Data

·        Ok. So obviously if you looked at my group’s data table, you can see that a few of the measurements are really weird and completely off. I feel that some of the problems were due to the fact that we had multiple people trying to count the squares each using a different method.

5)      Graph (& Formula)

·        Our graph is probably really confusing because there are two formulas and one of them is quadratic even though the line is evidently linear. So our group was split between linear and quadratic. The half that thought it was quadratic only picked so because the points lined up well with that equation; while, my half went with linear because we knew that linear was the obvious chose and the linear equation lined up very well without the outliers.

6)      Conclusion

·        On the picture, the conclusion says, “For every cm² that area increases, mass increases by .006 grams”. That conclusion statement was for the other half of the group’s equation. So for our conclusion we got – For every cm² that area increases, mass increases by about 1.8 grams.

Indentifying Direct, Indirect, Proportional, and Inverse Relationships

Last class we had a very in depth conversation about the differences between these relationships. For each of them, we discovered a few unique traits that each must have.

1)      Direct

·        When x increases, so does y

Ø  This means the graph must have a positive slope. Whatever direction x moves, y must move in the same direction even if that means that they both move negatively.

·        Y-intercept

Ø  The graph can start anywhere on the y-axis.

·        Type of graph

Ø  Any type of education can represent a direct relationship as long as it follows the other traits.

2)      Indirect

·        “Not Direct”

Ø  Indirect literally breaks down into “not direct”. So whenever a graph does not follow all of the traits for direct it is indirect.

3)      Proportional

·    Δ x = Δ y   

Ø  In a proportional function, the change in x is equal to the change in y. So if x doubles, then y doubles also.

·        Y-intercept

Ø  In a proportional graph, the y-intercept must start at the origin. A y-intercept would not allow for the ratio between the change in x and y to remain proportional.

4)      Inverse

·        k/x (when k is a constant)

Ø  In this inverse parent function, it shows the opposite of proportional. If x doubles, y is cut in half.

*Also, some functions can be more than one of these relationships at the same time.