Week 3

In our third week of Math 251 we continued, and elaborated, on the topic of Venn Diagrams. Instead of using simply the intersect, union and compliment sentences, we applied these diagrams to real life situations.
These are a great tool when discussing percentages in a survey of people. For our example we used winter sports, the survey included the following categories:
a. people who snowboarded
b. people who skied
c. people who snowshoed
d. people who snowboarded and skied
e. people who skied and snowshoed
f. people who snowshoed and snowboarded
g. and people who did all three.

They would fit within the Venn diagram like so:

Figuring out how to fit all of the numbers into each category taking into account that theoretically someone who falls under the "likes snowboarding" category could also "like skiing" and could potentially "like all three" is a great mathematical challenge that we were able to address. 

Primarily the concept of starting at the center amount and using that to work your way to the outside numbers.

For a more detailed walk through of a Venn diagram word problem I've provided a video:

http://www.youtube.com/watch?v=MassxXy8iko

Week 2

This week in Math 231, we introduced the concept of Venn Diagrams. Something seemingly outdated and for children, in fact takes a whole new light in this class. The concepts of unions and intersections of groupings create a much more complex concept than once believed.

The concept of a Venn Diagram originates with two groups and their populations and intersection of populations.


For example; people who like country music and people who like pop music are in two separate circles, and those who like both both would fit in the center segment.


The next concept of the Venn Diagram was isolating certain populations of this diagram. For example, to show exclusively the population that like pop AND country music. Written as A intersect B.


Another idea, was exhibiting the entire population, this is called a union and is written A U B


An idea in which you isolate everything but a certain aspect has a line over the subject. So A with a line over it is everything but A


So to combine these events one could draw everything BUT the INTERSECT of A and B and would look like this.


There are many things you can do with a Venn Diagram and I think its a great visual way for kids to learn.

Week 1

Subtraction can be a struggle for all people, from elementary aged students to the teachers that are attempting to instruct them. An effective way for many people to learn is visual aid, we worked with one such device in class this week called a number line. With this tool, we discovered a creative and helpful way to visualize the act of adding and subtracting, and proved that there are many different ways to come to the same answer.

One example we used was 65-48, my initial number line looked like the following:

17__(-3)__20___(-5)___25________________(-40)___________________65
<-------------------------------<-----------------------------<---------------------------------<

The arrow indicated the direction we are working, because though you would start with 65 when subtracting 48, the visual line still must read from left to right. So in this example the numbers -40, -5, and -3 all add up to -48 which is the number we're subtracting. Being able to break up the number into clearly visual parts is extremely helpful for new math learners and a great tool for teachers.

A clearer example of this method is shown here:



With a new tool under my elementary education belt, until text time!

photo cred: http://learnzillion.com/lessons/1583-solve-subtraction-problems-using-a-number-line