Overland Trail Case
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In the Overland Trail unit our class traveled back in time to the 1850s and used math to figure out the different things we needed for the trip and distances still to come. We did all sorts of things like using tables of information and lines of best fit to make useful predictions and estimates. We learned how to create graphs representing equations and wrote equations describing graphs. We figured out how to solve and graph problems involving distance, rate and time. I can use variables to develop algebraic expressions from words and use words to describe algebraic expressions. I am now able to algebraically manipulate a linear equation from standard form to slope-intercept form. Finally we learned how to graph and determine an equation given two points on the line. These six standards are just the main ones out of everything we did in this unit.
In the first standard we learned about using tables of information and lines of best fit to make predictions and estimates. To begin, we learned how to make the scale and plot the points. Then we learned a line of best fit was put in to the data to best suit it. We used the slope to figure out how fast a wagon train was going or how many miles it had gone. It was mostly for distance or time problems. I could use these in the future when I am traveling in a car and need to know when to stop for gas. For example, in homework 25 we used graphs to show how fast Jillian and Steve were going and to tell who would get to the river first. Graphs are one of my favorite aspects in math because I understand them so well.
The second standard for this unit was being able to create graphs representing equations and write equations describing graphs. We started out by finding the variable which was the changing part of the equation. Then we found the constants and put the two together. When we wrote equations for the graphs we would find the change in x and divide it by the change in y. That would give us the slope of the line, then we had to find the y intercept. We did this by picking one of the points and substituting it in for our equation. Y=Mx+B where m is the slope, x is the variable, and b is the y intercept. If two points were 2,4 and 4,6 the change in y is 2 and the change in x is 2 so you divide 2 by 2 and that equals 1 so the slope is 1. 4=12+2.The difference between the slope and Y is 2 so the y intercept is 2. For example in homework 17 we made a graph and an equation for each of the lines. Each of the lines represent how much money the college students have after a certain length of time. I liked this unit very much because it came easily to me.
The third standard involves solving and graphing problems that involve distance, rate and time. In DRT problems (distance, rate and time) you are given two out of the three, distance and rate of travel, rate and time, or the time and distance, then you need to find whichever one is not given. An example of this is on page 278, Catching Up by Saturday Night. First you figure out a possible pair of rates, one for the main part of the wagon train and one for your group so you will catch up with the main group by Saturday night. You have 3 days of travel to catch up. If the wagon traveled 15 miles per day and my family traveled 20 miles per day we would catch up in time. In question two we used those rates to figure out how far down the trail we will catch up to the main group. Then we found more pairs of rates that satisfy question 1. I found DRT problems relatively hard for me and I just barely got through them.
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