Module 8

Quick Images Video 

I found the video this week very interesting. It really highlighted the way that everybody thinks of things differently. Most of the children connected the shape with a real life object such as a boat or banana. My first thought was that it was a picture of the shape, crescent. I always remember what a crescent looks like because I think of a crescent moon. I thought it was really interesting that one of the students said that she remembered the shape because it was part of a circle. I have never thought of a crescent as part of a circle, but it really is.

Case Studies- Shapes and Geometric Definitions 

The case studies outlined students' responses to seeing familiar shapes in unfamiliar positions and proportions. In Andre's case, she presented students with an array of triangles. All of the students agreed that the oddly shaped ones looked like triangles, but could not decide whether they were "real" triangles. The kids had become so accustomed to seeing a triangle depicted as an equilateral triangle that it did not feel comfortable to classify different triangles as being the same shape.

Annenberg Polygons Module

Problem A2
How many polygons can you find in the following figure? Problem A3    How many polygons can you find in the following figure?

The kindergarten class that I am assigned to this semester recently began exploring shapes. Just last week I was working with some students during their Math centers and told them "I bet I can make a square out of 2 triangles." They seemed skeptical but watched me intently. They all immediately modeled what I had just done with the triangles. I challenged them to create other shapes using the manipulatives. When I came upon these series of questions I felt it was very simple. 4 triangles and a rectangle. When I read the solution I was shocked to see so many other combinations. I went back to look at the figure again and began to see more chapes jump out that I missed the first time.

For further discussion

I have never really noticed before, but my home is filled with rectangles. Tables, doors, windows, picture frames, the television, tiles, and even this computer is composed of rectangles. Most of the circles in my home are located in the kitchen. Plates, bowls, pots, pans, and a large wall clock. I went on a hunt through the house for triangular objects but, other than a few decorative patterns, I found none.

Module 6

Annenberg Probability Module 

Problem A3    What is a random event? Give an example of something that happens randomly and something that does not. When I read the solution to this question I began to feel the same confusion that has followed me through many years of working with statistics. The solution mentioned that some things are just random while others require skill. I understand that. The example they used as a random event is what card would show up on top of a freshly shuffled deck. Where I get confused is would that actually be random? You would always have a 1 in 42 chance of drawing a specific card. SO it isn't as if the probability of pulling any one card is randomly changing. Am I just over thinking this? Problem B2    Suppose you toss a fair coin three times, and the coin comes up as heads all three times. What is the probability that the fourth toss will be tails?

This question made me laugh a little bit. Logically, I know that in a coin toss, there will always be a 50/50 chance of heads or tails. It is easy to forget this in the heat of the moment, though. I know that my odds are still 50/50 but there is this nagging feeling in your mind that the next toss HAS to have this certain outcome.

A Whale of a Tale article

Create your own probability line chart that displays events that are impossible, certain, likely, or
unlikely to happen. You should have a minimum of 2 events for each area

Dice Toss 

• Based on the data, the class concluded that 7 was the most likely outcome. Some of the students did have some preconceptions, though. For example, some students thought that 12 would be unlikely because it is more difficult to roll a 6. I think that this would be a difficult concept to get out of their heads. Like I explained earlier with the coin toss, even though you know that there is an equal chance of either outcome, it is so easy to get caught up in the results. You could toss a coin 4 times and get 4 heads in a row, but that doesn't affect the probability that you could land on tails next even though you may feel otherwise. 
• I do not think that they were too young. They were able to clearly answer their teacher's questions and even expressed their surprise at some of the results. 
• The teacher asked the students to roll 36 times because it would allow the students to collect a large amount of data to be able to see the trends. One advantage to this is that the results would be more accurate. One disadvantage is that this would take up a lot of time in class. Also the large amount of data  might be overwhelming.