Math 1.0 Sept 18 2016: Histograms, vector addition

How big are leaves? (introducing the histogram)

First we went outside and each person (4 students and 1 teacher) collected leaves. We collected two leaves from each of two trees.

One of the students four leaves,
two from each of two trees.

First, each student measured their leaves, from the tip of the petiole (stem) to the tip of the leaf. 

We recorded the length of each leaf as a table:

Length of all leaves as a table, organized by
collector. Checks were marking off leaves that
had been added to the histogram. 

Then we created a histogram. For each bin (0-1, 1-2, etc ... 13-14), we counted the number of leaves that fell in that range. We used open blocks to indicate a leaf from Tree 1 and closed blocks to indicate a leaf from Tree 2.

Then I asked the students:

Which tree has longer leaves?

How long would you expect a leaf from tree 1 to be? how about a leaf from tree 2?

We also looked at the outlier from tree 1 to confirm the recorded value and that it came from the same tree.

One of the student's measurements and class histogram.

Dragons and Unicorns at the cafe? (vectors, vector addition)

We re-visited the cafe that serves cabbages and apples. (Following from Yuliy's Feb 22 2015 lesson).

Recall that unicorns always eat 2 apples and a cabbage head, and dragons always take 2 cabbage heads and 1 apple each. How may dragons were there? The idea is draw a vector plane, with the horizontal steps representing cabbage heads, and vertical - apples. Each dragon eats a vector of (2,1) (two cabbages, one apple), and each unicorn eats (1,2). So, to get to (3,3) - three cabbages, three apples, shown as a purple point - one needs to make one "dragon step" and one "unicorn step": 

Conceptual drawing from Feb 22 2015

Homework

1. Drag Car Race 

Last week we watched a video about drag racing that showed the distance a car had gone at 5 second intervals.

We recorded this table:

time (s)	distance (ft)
0.0	0
0.5	21
1.5	75
2.0	125
2.5	231
3.0	420
3.5	783
3.9	1000

• Plot distance vs. time, with time on an x axis
• x axis = time in seconds from 0 to 4
• y axis = distance in feet from 0 to 1000
• connect the points

Questions: 

• At what time was the car going the fastest? What was the fastest speed?
• At what time was the car going the slowest?  What was the slowest speed?
• How far will the car have gone after 4 seconds?

2. Dragons and Unicorns

• Draw a graph with # Cabbages on x axis and # Apples on y axis (each axis should go to 10)

Questions

• What does a Dragon vector look like? (Draw it)
• What does a Unicorn vector look like? (Draw it)
• If there is one dragon and one unicorn, how many apples and cabbages will be served?
• draw as addition of two vectors
• How many dragons and how many unicorns for the following orders:
• 5 cabbages, 4 apples?
• 5 cabbages, 7 apples?
• 0 cabbages, 2 apples?
• 8 cabbages, 7 apples?