# Engaging students: Venn diagrams

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Amber Northcott. Her topic, from Probability: Venn diagrams.

How could you as a teacher create an activity or project that involves your topic?

There are a few activities you can do with Venn diagrams. One idea is for the first day of class you can put up a big poster with a Venn diagram on it or you can draw one on the board. One circle can be ‘loves math’, while the other is ‘do not like math’. Then of course the center where the two circles intertwine will be the students who love math, but yet don’t like it. When your students come into the room you can have them put their name where it seems fit. This way you can get to better know your students on the topic of math. Another idea is that when you get to a topic, for instance arithmetic and geometric sequences, you can create a giant poster Venn diagram or draw it on the board. Then you can have your students write one thing that either arithmetic has or geometric has or both of them have. Once each student has put up just one thing on the Venn diagram, you can start a class discussion on the Venn diagram. While the discussion goes on you may fix a couple things here and there or even add to it. At the end each student will have their own Venn diagram to fil out, so they can have it in their notes.

How can this topic be used in your students’ future courses in mathematics or science?

Venn diagrams are an easier way to compare and contrast two topics. It can help differentiate between the two topics. For example, how are geometric and arithmetic sequences different? Do they have anything in common? What do they have in common? This helps students identify the topics more thoroughly and helps them get a better understanding about each topic.

How has this topic appeared in the news.

Not too long ago Hillary Clinton posted a Venn diagram about gun control on twitter. In response she was getting mocked and criticized. A short article on thehill.com goes into the mockery by showing pictures of people’s tweets to Hillary Clinton. Some had two circles separate from each other with one stating people who know how to make Venn diagrams and the other one stating Hillary’s graphic design staff. The other article from the Washington Post actually goes through her Venn diagram and fixes errors. These errors include the data in the Venn diagram.

Letting students see this, would definitely cause a discussion. I think we can turn the discussion into whether or not we think the Venn diagram was wrong. By having this discussion, we can learn more about what the students know about Venn diagrams and shed more light on how we can use the Venn diagrams in many different ways for many different topics.

References

https://www.washingtonpost.com/news/the-fix/wp/2016/05/20/we-fixed-hillary-clintons-terrible-venn-diagram-on-gun-control/

http://thehill.com/blogs/ballot-box/presidential-races/280706-clinton-mocked-for-misuse-of-venn-diagram

# Engaging students: Factoring polynomials

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Irene Ogeto. Her topic, from probability: Venn diagrams.

A2. How could you as a teacher create an activity or project that involves your topic?

As a warm up activity to a lesson on Venn diagrams, I could set up a model Venn diagram made out of tape on the classroom floor or in the hallway outside of the class. The topic for the activity would be comparing the number of students who prefer to play indoor sports versus the number of students who prefer to play outdoor sports. I would ask the students who prefer to play outdoor sports such as soccer, baseball, football or field hockey to stand in the circle that represents outdoor sports. Then I would ask the students who prefer to play indoor sports such as bowling or table tennis to stand in the other circle. Next, I would ask the students who prefer to play both indoor and outdoor sports such as basketball, volleyball or badminton to stand where the circles intersect. Lastly, I would ask the students who don’t prefer to play any sports to stand outside the two circles.

With this activity we can explore these questions:

• How many students prefer to play indoor sports?
• What is the percentage of students in our class prefer to play indoor sports?
• How many students prefer to play both indoor and outdoor sports?
• What percentage of students in our class prefer play both indoor and outdoor sports?
• What percentage of the students in our class prefer to play sports?

C1. How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

Venn diagrams have appeared in children’s TV shows such as Cyberspace. In this episode of Cyberspace which is was aired on PBS in Season 1, the Cyberspace squad uses a Venn diagram to rescue the Lucky Charms. The squad uses the terms “or” and “and” with respect to sets to find the Lucky Charms. Motherboard tells them that the Lucky Charms is both blue and tall. One circle represents the blue bunnies and the other circle represents the bunnies of another color. The area where the two circles intersect represents the area where the tall and blue bunnies are. The squad works together to find the Lucky Charms using applications of Venn diagrams. Venn diagrams can be used to explore possibilities and combinations of things. This video can serve as an introduction to a lesson on Venn diagrams. It enables students to see how math is part of culture, as it is found in television shows.

Episode 112: “Of All the Luck” http://www.pbs.org/parents/cyberchase/episodes/season-1/

D1. What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

John Venn (1834-1923) the famous mathematician, devised a way to picture sets by creating what is now known as Venn diagrams in 1881. John Venn was born in Hull, New England, United Kingdom. He was a lecturer, president of a college, and a priest for some of the years in his life. Venn wanted to show how different groups of things could be represented visually. John Venn called Venn diagrams Eulerian circles because they were similar to the Euler circles created by Leonhard Euler. While they share similarities, Euler circles and Venn diagrams are different. Venn diagrams are more sophisticated and are used to represent all possible combinations of classes. Euler circles differ in the sense that the circles do not always have to intersect and do not always represent all possible combinations. Some people still refer to Venn diagrams as Eulerian circles to this day and often some people use the two terms interchangeably. Despite the differences, both diagrams are used in math every day.

References:

http://www.venndiagram.net/the-history-behind-the-venn-diagram.html

http://www.mathresources.com/products/mathresource/maa/venn_diagram.html

http://www.pbs.org/parents/cyberchase/episodes/season-1/

# Engaging students: Venn diagrams

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Michelle McKay. Her topic, from Probability: Venn diagrams.

A. What interesting word problems using this topic can your students do now?

In my opinion, you can create a word problem with Venn diagrams on just about anything. To make a word problem more interesting, you can relate the problem to an upcoming event or holiday, make a cultural reference, or even discuss students’ hobbies (i.e. video games, books, etc.).

On Valentine’s Day, a survey of what gifts a women received from their significant other yielded surprising results.

76% of the women surveyed received a card.

21% received chocolate and a card.

5% received a card and flowers.

33% received chocolate, a card, and flowers.

If a woman from the survey was selected at random, what would the probability of her having not received a Valentine’s Day gift be? What is the probability that she received any combination of two gifts? What is the probability that she received a card and flowers, but not chocolate?

B.     How can this topic be used in your students’ future courses in mathematics or science?

Venn diagrams are an excellent way to organize information. They can organize and be a visual representation of gathered statistics (like in the above section). They can also organize general ideas and concepts, distinguishing them as unique or shared amongst other ideas/concepts. A student can use Venn diagrams in either of these manners for both math and science classes of any difficulty.

B. How does this topic extend what your students should have learned in previous courses?

When using Venn diagrams to represent statistics, it reinforces the idea that parts cannot be larger than the whole. We know when using Venn diagrams for statistical data that the decimals must add up to 1 to represent 100%. Students should realize that adding the decimals and getting a number that is larger than or smaller than 1 means they miscalculated or there is “missing” data. By “missing” data, I mean to say that they did not enter in all the given information correctly.