Mind Maps

While learning about statistics and the different ways to display the data, one of our assignments was to construct a mind map. I had honestly never even heard the term "mind mapping" before so I had to do some internet research to even figure out how to construct one. A mind map is basically a thought bubble with several different branches and subcategories relating to the original thought. Click on the link for some helpful mind map guidelines.

Here is the list the teacher gave us of mandatory terms we had to use in our mind map...

Mind Map Required Words: 

Bar Graph 

Pictograph 

Pie Chart / Circle Graph 

Histogram 

Stem and Leaf Plot 

Line Graph

Scatterplot 

Dot (or Line) Plot

Frequency Table 

Box and Whisker Plot 

Categorical Data

Numerical Data 

Discrete Data 

Continuous Data 

Mean 

Median 

Mode 

Range 

Mean Absolute Deviation 

Optional Words: 

Data, Outlier, Cluster, Gap 

Just looking at that list gave me anxiety because I knew that several of the words could relate to multiple different items so my mind map was going to be so clustery and I am not a clustery type of person. I like neatness and order so I was dreading having to do this assignment. 

The teacher said we could create one on paper if we liked but also gave us several different websites that have mind mapping software you can use such as popplet, mindomo, mindmeister, and bubbl.us. In the end I chose bubbl.us to use but when I tried to construct my mind map strictly on the website I found it very difficult to organize my thoughts so I ended up making a rough draft on paper first. Below is a picture of my rough draft. It may be hard for you to read it because I started to run out of room so I had to write pretty small for some of bubbles. I also had to circle each bubble in colors that matched each stem so that I could differentiate between the different categories since everything ended up so close together. All of the bubbles are colored in with pink because that was how I knew I recorded it when I was finally putting it into the final draft on bubbl.us. 

I'm not going to lie, this rough draft took me several hours to construct. I had to go back over the material, read the chapter in the text book, and look things up on the internet because I was still cloudy on exactly what type of information each data display used. I mean, I new what a bar graph was but I didn't know EXACTLY what the difference was between a bar graph and a histogram was until this assignment. 

Once I had my rough draft completed it was time to make my final draft on bubbl.us. This took me about 1 1/2 more hours to construct because not only had I never used this software before,  I also needed to clean it up a bit. This honestly gave me even more opportunity to really comprehend the information. Here is link to my completed mind map. I got full points for the assignment but my teacher did let me know that I had a line connecting variance and MAD and I shouldn't have since they are not related so just ignore that part. It honestly ended up being the best study guide for the mid-term. 

Even though this assignment took a long time to construct, I learned more about data displays in those couple of hours than I had in any math class ever so the assignment I had been dreading because it wasn't catered to my individual learning style ended up being one of the most helpful math assignments I had ever done. The lesson I learned as a future teacher was to offer activities and assignments that cater to all different learning styles because even the students that think they will get nothing out of the assignment will end up learning something new in the end. Plus, teaching students different ways to learn just opens up the door to creative thinking and reasoning in their future endeavors so don't be afraid to teach a learning style that may not be your forte because your students will ultimately benefit from it. Happy teaching! 😊

Graphing Activity

In my math class (teacher prep math class - second semester) we do LOTS of activities. These activities are designed to not only reintroduce the material to us students but to also demonstrate how to teach the material to our future students in ways that help them to understand the concepts better. Last semester when I realized that we would be doing activities nearly every class for two full semesters I wanted to just die because I hate group activities (I know, I know, teaching is one big group activity so no need to point that out to me haha.) The first few weeks were rough, I'm not going to lie. First of all, I purposely sat at a table of four that already had three out of the only four guys in the entire class sitting at it because I figured guys are usually good at math so they could help this old lady out with refreshing her math memory. So here I am, the oldest person on class (and I'm pretty sure you can include the teacher in that calculation as well) sitting at a table with guys that are younger than own my son. Luckily for me, they all were really cool and that semester was a blast! Seriously, I have never had so much fun in a class or with group activities in my life. Shout out to Uriel, Jacob, and Michael for breaking me out of my group activity phobia. You guys are awesome!

Probably one of the most popular group activities this semester was graphing M & M's. The teacher handed out an activity sheet and a Halloween size bag of M & M's to each student in class. Before opening the bags, we were asked to make conjectures as to what color we thought would occur most often, what color we thought wold occur least often,  and if we thought our bag would match the rest of the class data. After we made our conjectures we were instructed to open our bags and record the data - first by placing the M & M's on the graph provided in the activity sheet and then by coloring in the graph with crayons like this...

This type of graph is called a pictograph which is basically a picture graph. Once this was complete we were allowed to then eat the M & M's....yum! Once everyone had completed their pictographs it was time to collect all of the class data. We did this using another kind of graph called a dot plot. Dot plots are a super easy way to collect data from a group. We have 24 students in the room but if you had a really large group it probably would not be the way to go since you have to be consistent on the placement of the x's otherwise it would be kind of hard to read. Basically you make a line graph, add your data points and then call on the students one by one to give your their individual data. In the picture below, each student gave a number for how many of each color they had in their individual sample.

Be careful when calculating the totals though because it is really easy to want to just count each individual x but one x counts for the number it is representing. For example, one x above the number 5 actually counts for five and not one.

Now that we had the class data it was time to move on to a pictograph and a bar graph using the new data set.

Notice the difference in the pictograph from my individual data set and the class data set? Since the class data set was much larger, we had to have a key at the bottom showing that each circle represented 10 M & M's. We had 92 green M & M's so had we not done this our pictograph would have either been too small to read (in order to fit on one page) or would have taken up several pages which is impractical. However, because we had 92 green M & M's and not a even multiple of 10, we had to color in part of a circle to represent the extra two. This can make pictographs hard to read exact data values.

Our bar graph was horizontal but you could also make your bar graph vertical, which is what most people are used to seeing. Note that the bars on a bar graph do not touch. If the bars touched this would be a different kind of graph altogether called a histogram. Bar graphs measure categorical data like the data we have here. We have our categories (colors of M & M's) on the horizontal axis and their frequency occurring on the vertical axis. Histograms measure numerical data (numbers) and their frequency occurring. For example, let's say we were wanting to measure the weight of every student in class. In my class, we have 24 students so in theory we could end up with 24 different weights. That would be a pretty boring chart because we would have 24 bars on the horizontal axis (bottom) and each bar would only go up to 1 on the vertical axis (side). It would be better to have a weight ranges (like 100 - 125, 126-150, etc.) and then chart the frequency occurring for each range. Since both the vertical and horizontal axis are numerical in value, our bars would touch each other and therefore our graph would be called a histogram and not a bar graph.

I hope I was able to explain the activity and the differences in the types of graphs in a way you were able to understand. It really was a fun activity and you really do learn concepts better with activities such as this. I also came across this website Teachers Pay Teachers where teachers buy and sell original education materials. Here is a link to a creating pictographs and bar graphs page on the site. The site has tons of other resources that could be helpful to you in your classroom as well. Happy teaching! 😊