for Diza, 9.27

1. Find

3333 x 55=
33 x 5555=
333 x 555=

2. A: C is lying;
     B: C is lying;
     C: I do not!
In fact, exactly one of them is lying. Who?

3. Solve
a:
3x + 2y=1;
2x + 3y=4.

b:
 x - 3y=7;
2x - 8y=12.

4. Pete makes 3 pancakes every minute. At noon, when there was 12 pancakes on the plate, the Pancake Eating Monster appeared, and started to eat pancakes, 9 a minute. When he will find the plate empty and starts biting Pete?

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?

  

Math 1.0 September 11 2016

Using plots to understand Velocity = distance / time

We are going to watch "How a top dragster works" by Car and Driver Magazine on YouTube:

It shows the distance at 0.5s intervals (also shows speed but we will focus on distance)

• watch video and record time and distance
• create a table with columns name time and distance

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
4.0	1000

• create a plot
• x axis = time in seconds from 0 to 4
• y axis = distance in feet from 0 to 1000
• ask: when was car going fastest? when was it going slower

Which way to the city of Lies?

Citizens of the City of Lies always lie. 
Citizens of the City of Truth always tell the truth. 
A citizen of one of those cities (you don't know which) is at the intersection. What question could you ask to them to find the way to the City of Truth?

You are at an unmarked intersection ... one way is the City of Lies and another way is the City of Truth. 

City of Lies or Truth Puzzle - Solution from mathisfun.com

Math 1.0 August 28: Two Dice Combinations and some Puzzles

Two dice combinations

Last week we had one dice, we figured out the possible outcomes, and then kids rolled dice, counted number of rolls for each case 1-6, and plotted them as histograms. 

This week we started by identifying possible outcomes of two die:

And then we counted the number of possible ways we could get each value between 1 and 12:

Left: possible outcomes of rolling two die
Middle: # of ways to get each outcome
Right: observed totals for class

So this week we saw that with two dice (unlike with one) we were more likely to roll numbers in the middle (7 is six times as likely as 2). The goal was not to begin computing probabilities though for those paying attention the probabiliity of rolling 7 (abbreviated p(7)) =1/6 and p(2) = 1/36.

  

While the students were busy rolling dice, Dr. Barishnikov found a website that simulated lots of dice. We looked at 1000 rolls of a single dice, and found the same as last week that there was an even probability of each outcome. Then we increased it to 2 dice. Below is what happens when we roll twenty dice (note: students thought rolling as many dice as many times as possible was very awesome).  

 Puzzles

Dr. Patel posed a puzzle: Who stole the diamond?

September 4, 2016 - Math Circle 2.0

Warm up

We reintroduced the number line and used it for addition and subtraction.

Coordinates

The robot cat and dog were visiting a new town and wanted to meet up.  Anya and Beans controlled the robot dog.  Willa and Ellie controlled the robot cat.  The students led the cat and dog to meet in the same square to have a party.

Die mapping

The students were give a single die and they then mapped it in two dimensions on a sheet of paper.  They then cut and folded the paper to reproduce the die.  They did a great job getting the sides of the die correct.

August 28, 2016 - Math Circle 2.0

Warm up

Beans has 6 cookies.  Ellie has 4 cookies.  How many more cookies does Beans have?

Coordinates

The robot dog was on the move in Urbana and she could move in all four directions.  The students successfully navigated the dog to the cat house party.  Next week.... The dog and cat will need to meet up by being programmed independently.

Patterns

We reviewed patterns from last week and then introduced a new pattern... A pattern that doubles.  Next week...  We will introduce a pattern that has two components - both shape and size.