Data Displays

April 26th, 2019

When you hear the words data displays what exactly do you think of?  Did you know that displaying data could actually be fun and your students could learn while doing something fun and productive?
I am a very visual learner and by creating graphs, I can display data and learn from it all at the same time.  I am able to use my creativity which makes it fun for me because I am creating a masterpiece to showcase my work, well at least I like to think so!

This day in class we made data displays to show how you could display Categorical and Numeric Data in a nice visual way and have fun doing it. We learned about Continuous data and Discreet data and what graphs are good for using certain data sets.  The data displays we made in class had us listing the advantages and disadvantages to each graph so there is a lot of information in these 2 foldables that we can use in the future.  This is my second time making these so I knew what to expect and tried to do better than I had previously.  

Categorical Data Display

Numerical Data Display

Each fold out shows us an example of the graph and the Advantages and Disadvantages that come along with using each graph to display said data. Gives you the pro's and con's to think about for when you have that need to display data.  We use and see things like this is every day life and we can easily use this as a teaching tool with future students.

Important parts of a graph that are essential to having a good graph: #1 A title that describes the experiment.  #2 Lables - each axis should be labeled with the quantity being measure and the units of measurement. Horizontal x-axis the independant variable and Vertical y-axis the dependant variable, both must be labeled. #3 Scale of graph. #4 Symbols - if using symbols you must include their representation.  #5 Legend.

Types of Graphs

Pictographs - A pictograph is a way of showing data using pictures(symbols).  Each picture stands for a certain number of things, like above each basketball stands for 10 games played.  So Terri played 20 games because she has 2 basketballs, Sue played 10 games because she only has 1 basketball and Maddie only played 10 games as well.

Bar Graphs - Graph using rectangular bars to show how large each value is, bars can be vertical or horizontal.  The bar graph above shows how many kids have dogs, fish, cats, lizards, and spiders for pets.

Circle Graphs - Also known as pie charts shows whole and parts of the whole, values are represented and labeled.  The pie chart aboves shows favorite colors in class, 50% of class likes blue, 25% like pink, 12.5% like salmon and 12.5% like purple.

Stem & Leaf - This is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).  The stem and leaf above shows the 19 test score of students in class.

Histogram - They are similar to a bar chart, but a histogram groups numbers into ranges.  The height of each bar shows how many fall into each range.  Because they are in ranges the bars are connected, the only time there would be a gap is if no one or thing was in that range.

Dot Plot - A dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles like the one above, each dot represents a certain thing in this case the if it is blue it represents a boy and if it is pink it is a girl. The dot plot is graphing bed times in 2nd grade.

Some others we used in class but not pictured above.

Line Graphs - Used to show how data changes over time, continuous data.

Scatter Plots - Used to show relationship between 2 data sets.

Box Plots - Used to show Median, Quartiles and extremes of a data set.

There are other types of graphs but these are the ones we used primarily in class.  The National Center for Education Statistics, NCES has a very cool tool you can experiment with and make different graphs online.  I found the site to be very educational.

Displaying and Interpreting Data

This video does not show all graphs but it is catching and cute! Enjoy, Terri

Attributes

April 24th, 2019

As we start to take a look into Geometry we discuss Attributes of shapes and this is so important when talking about geometry.  The link above goes to a great attribute core lesson Standards 3.G.A.1 that I really enjoyed watching, I think it used great simple graphics and was easy to follow along and understand.  So what are Attributes?  An Attribute is a feature or characteristic used to describe an object.  In our case we are describing shapes, different sizes, different colors, different attributes that make them similar or individual, alike or not alike.

We did an activity in class with shapes and we had to figure out their different attributes and had to fill in a chart.

Attribute chart

We then got to play with shapes and we made one difference trains with out shapes, meaning we made a train of shapes and each shape next to each other had to have only one difference in an attribute between them.

We had 5 shapes, 3 different colors and each shape had 2 sizes a large shape and a small shape for each shape in each color.  We made difference trains and also made Venn Diagrams and played the What am I game?  We had 30 shapes, as the professor named off the attributes we took away the opposite of what was said it was or took away what she said it was not.  

Can you guess me shape?

* I am not red---------> so we took all reds away

* I am not a circle--------> took all circles away

* I am not large--------->took all large shapes away

* I am blue----------->took all colors but the blue away, so all the shapes in front of us are blue.

* I do not have obtuse angles------> took everything away with more than 90 degrees.

* I do not have right angles-----> took everything away with right angles

What am I?   I'm not telling! Figure it out for yourself ;)

Measures of Central Tendency The Median and IQR

April 22nd, 2019

In my last post with Measures of Central Tendency I mentioned Inter Quartile Range and I wanted to show you just how we use those numbers and what they mean.
We use our Measures of Central Tendency to find the IQR Inter Quartile Range which is a measure of statistical dispersion, being equal to the difference between the 75th and 25th percentiles, or between the upper and lower quartiles.  We use a Box and Whisker Plot as an explanatory data analyses, its basically a type of graph that shows spread/distribution of data.  Using our data from Grab a Handful Activity we are going to continue to analyse data by making a Box and Whisker Plot.

The first thing we are going to do is order the data from least to greatest and make a number line with that range from the least to greatest numbers.

Now we need to find the Median (middle number) (also know as Q2).  We know from our Measures of Central Tendency the Median is 10 so we are going to draw a line to represent the Median.

Median is showed in pink. Also is Q2

Add Ordered Data #'s 235 and divide by 22 to get Mean

                                 

Next we are going to make draw 2 lines that represent the Minimum = MIN and Maximum = MAX

Min and Max lines then we will complete the box.

Now we need to find the Lower Quartile and we do this by looking at the data on the lower half below the median which is 7 7 7 8 8 9 9 10 10 10 10.  We take these 11 numbers and do the same to them as we do when finding the median of the whole data set to find the middle number and that would be a 9.  The #9 is Q1 the 1st Quartile.  We do the same to find the Upper Quartile but use the numbers 10 11 11 11 12 12 13 15 15 15 15, the middle number is a 12.  The #12 is Q3 the 3rd Quartile.

Q1 and Q3 are shown in Blue and box is completed

The Box and Whisker Plot shows the 5-number summary: Minimum, maximum, median, lower and upper quartiles.  The next picture shows how it is divided into Quartiles and will show that in Orange with percents written.

Most of the class picked between 7 and 10 within the 1st 50% of data set

Range: 8

Min: 7

Max: 15

Median: 10

Q1: 9

Q3: 12

Grab a Handful with Measures of Central Tendency

April 22nd, 2019

Take #2 I did not have forethought during this activity to take pictures this time around which really bothers me but they are included in my previous Grab a Handful post earlier in my blog. One thing I would like to point out as our class grabbed handfuls of Unifix blocks no one felt the need to grab huge amounts so we didn't have a huge gap in outliers.  Now, you ask what is an outlier?  I'll get to vocabulary in just a second so this all makes sense.  Measures of Central Tendency is a summary statistic that represents the center point or typical value of a dataset.  The measures indicate where most values in a distribution fall and are also referred to as the central location of distribution.
A dataset is a collection of data and today we collected data by grabbing a handful of Unifix blocks. We then counted each individual person's blocks in class and compiled our data to come up with our Measures of Central Tendency.

A Math Manipulate Unifix Blocks at Lakeshore

We had a total of 22 students participate in the activity and each student grabbed a handful, the total number of cubes grabbed were 235.  Now we need to find our Measures of Central Tendency which are Mean, Median and Mode but first let me define them so our understanding is clear and we can then find our measures.

Mean also called the average, the mean would be the average of all blocks grabbed. 

Median is the middle value(s) of data set when ordered least to greatest. 1/2 the data is above the median and 1/2 the data is below the median.

Mode is the most frequent occurring data point in the set of grabbed blocks.

Grab a Handful Ordered Data

7 7 7 8 8 9 9 10 10 10 10 10 11 11 11 12 12 13 15 15 15 15

We can see most people grabbed 10 blocks over any other amounts of blocks grabbed and therefore since 10 is the most occurred it will be the Mode of this data set.

The Median is the middle value when ordered least to greatest and because we have 22 participants(you cross off numbers at each end of data set  til you get to the ones in the middle) we had two values, when this happens we add the two together 10 + 10 and we get 20, we then divide by 2 (because there were 2 #'s) and we get 10.  The Median of this data set is 10.

Now to figure out the Mean which is the average of all Unifix Blocks grabbed we are going to add all blocks grabbed 7+7+7+8+8+9+9+10+10+10+10+10+11+11+11+12+12+13+15+15+15+15 = 235,  we then take 235 and divide it by the number of participants which is 22.  235/22 = 10.7 (rounded)

The Mean of this data set is 10.7.

Mean = 10

Median = 10

Mode = 10.7

Range = 8

To find the Range of data set you take the Max # of grabbed blocks and Min # of grabbed blocks and you subtract them.  Our max was 15 - 7 our min and that gives us a Range of 8.  (15 - 7 = 8)

Now to answer your question what is an Outlier?  An outlier would have been a number like say if someone grabbed 24 blocks, it is a number that lies distant from our max #15.  Had someone picked 24 that would be our max # but would be an outlier for it sat a distant from most of our data set.  Outliers tend to throw off the numbers of the mean.  An outlier is a point which falls more than 1.5 times the Inter Quartile Range above the third quartile or below the 1st quartile.  Now there's some words you've never heard before and that will be vocabulary for another day because that is a whole other story and lesson.

Here is a movie on Math Antics describing everything I just went over

I love Math Antics, if you have never seen it I suggest you check it out because it has some great resources for teachers!  I love ROB, he does a fantastic job explaining simply!

The following charts I found by looking around A Maths Dictionary for Kids site  this is an AMAZING site. You are allowed to print out all pdf's to use for educational purposes and they have a little of everything.  The pdf's are nicely illustrated and explained in a way everyone should understand. I think this is a huge resource and I'm happy to have found it, even for my own use.

These get me so excited! Have a great day, Terri

Math Manipulatives

April 20th, 2019

Manipulatives are physical objects and in general, goods gifts to teachers.  They are amazing teaching tools that get students engaged using their hands and their minds to play, manipulate and find solutions.  Curriculum standards call for use of mathematical manipulates and are essential in teaching mathematics.  Here are different ways we may use manipulates in a class room according to Arizona Mathematics Standards:

■ sorting—a pre-mathematical skill that aids in comprehension of patterns and functions 

■ ordering—a pre-mathematical skill that enhances number sense and other math-related abilities 

■ distinguishing patterns—the foundation for making mathematical generalizations 

■ recognizing geometric shapes and understanding relationships among them 

■ making measurements, using both nonstandard and standard units with application to both two and three-dimensional objects 

■ understanding the base-ten system of numbers 

■ comprehending mathematical operations— addition, subtraction, multiplication, division 

■ recognizing relationships among mathematical operations 

■ exploring and describing spatial relationships 

■ identifying and describing different types of symmetry 

■ developing and utilizing spatial memory 

■ learning about and experimenting with transformations 

■ engaging in problem-solving 

■ representing mathematical ideas in a variety of ways 

■ connecting different concepts in mathematics 

■ communicating mathematical ideas effectively

Various Mathematical Manipulates

Manipulatives are important tools in helping students to think and experiment by giving them a more concrete way to compare and reason the concepts, guiding their thought process along so the can come up with tangible results.  Some of the favorites used in classes are Base Ten blocks, Pattern blocks, Unifix cubes, Teddy Bear Counters (now they have bugs and other kinds), Judy Clock, Calendars(used daily), Rulers, Attribute blocks, Ang Legs, Cuisenaire Rods, Spinners and the list goes on.  I found this website Hand 2 Mind, it has a great manipulative glossary and you can also makes purchases of manipulates, but I found their descriptions to be educational explaining what they can do or be used for.

I started to do some research in Manipulates and saw a lot of research that had been done by NCTM, National Council of Teachers of Mathematics, which is also an online publication and has tons of resources(membership).  I read several reports on the use of manipulates and their name came coming up so I wanted to include it here because they seem to be some leading research showing the use of manipulates increase the persons thought process, taking concrete ideas into abstract building that conceptual understanding.

Our class has used many manipulatives and I will continue onto my next posts the ideas we used them for and dive further into another concept.

Metric Measures in 4th Grade

April 17th, 2019

My 1st day of Service Learning.  The last two weeks they have been doing AZ Merit and today is their first day back to regular curriculum.  I am doing my Service Learning in Mrs. Bare's 4th grade class.  Her class walks in after specials and she is up writing on the white board and she turns around and says, "Warm Ups on the board!" I got the biggest smile and honestly learned to have a new appreciation for "Warm Ups"! I honestly never cared for Warm Ups or Exit Tickets because they make me have to rush and for some reason my brain tends to freeze when under pressure.  Time constraints cause major pressure for me but these kiddos in class handled it like champs, they scrambled about for a minute, sat down at their desks and had white boards and markers out in seconds ready to roll.

Warm Ups on Board in Service Learning Class

"What does the word Product mean?"  One students answers, "the sum of 2 numbers."  Teacher asks, "What do we do with the 372 and the 6?"  Another student says, "we add them."  "Are you sure?" Mrs. Bare asks.  Another students says, "We multiply them!" YES! She gives them all a few minutes and says,"White boards up!"  Now while most students did get it correct their were still a few that did not but these were students I observed not really paying attention and in their own world sort of to speak.  They then did the fractions problem and we started the daily lesson which was awesome!

The daily lesson was on measuring length and Mrs. Bare introduced Metric Measures to the class.  She started out by everyone making a help sheet so they will be able to do conversions on their own by referring to the sheet to help them.  I made my own at home to share with you.

Metric Conversions Chart Mrs. Bare did with 4th Graders (This one I made)

The students then made conversions that were written on the board.  

Examples:  4m = _____cm  You take the 4m and multiply them 100 and you get 400cm.

4m = _____dm  You take 4m and multiply by 10 and you get 40dm.

380m = _____hm  You divide 300m by 100 and you get 3hm.

_____mm = 12m  You multiply 1,000mm by 12m and you get 12,000mm.  The students first found the differences and figured out what was needing to be done to solve the problems.

Interesting Facts about M&M's

April 12th, 2019

M&M's Wikipedia

So it just so happens that there is a formula to what color of M&M's we all get in one bag of candy.  Our Professor actually sent an email to the the Mars company and got a response back telling her the exact percentages of color M&M's that go into each bag:

Blue 25%

Orange 25%

Green 12.5%

Yellow 12.5%

Red 12.5%

Brown 12.5%

Now compare that to our class totals let's see how close we came:

Blue 60/309 = 19%

Orange 55/309 = 18%

Green 62/309 = 20%

Yellow 33/309 = 11%

Red 48/309 = 16%

Brown 51/309 = 16%

So our total in class was off percentage wise just a few here and there but it allows you to see the comparison between the Companies proposed mix in bags to our actual mix.  I never knew Mars had an actual set formula so this was an interesting fact to me and wanted to share it. I know I often wondered how the mix of colors came about.  How about you?

Thanks for reading, 

Terri

Graphs - M & M's Yum!

April 10th, 2019

So your sitting in class and your teacher hands you a bag of M&M's, tells you NOT to eat them and it's lunch time!
Today we used graphs to display data and to explore the relationships among the data and today it happened to be All about the M&M's!  We would be collecting individual data about our bag of M&M's then combining our individual data's with the class as a whole to see if we could find the relationship between what colors of M&M's happen more often?  Is there a set color or amount to the M&M's in our candy bags?

So my individual bag had 4 brown, 2 blue, 3 yellow, 0 red, 2 green, 2 orange.
Our Class data of 20 people in class was 33 yellow, 51 brown, 60 blue, 62 green, 55 orange and 48 red, a total of 309 M&M's.

Statistical data is often displayed graphically, we did just that today and by presenting the data as a set of numbers it made it easier to study the relationships in the data.
Here are a couple of pictures I took during our activity in class.  We took our grouped data and put it into a pictograph.  We had the color of M&M's and each M&M on the graph represented 10 M&M's,  We also made a bar graph and each bar represented the number of M&M's we got in each color.  We had 16% Brown, 18% Orange, 19% blue, 20% green, 16% red, and 11% yellow.

Grouped Data

Pictograph and Bar Graph with Grouped Data

Dot plots of Grouped Data 

After completing all the grouped data we constructed a strip of paper, divided it into parts that represented the colors and amounts of m&m's per color and their percentages, we then connected the 2 ends of the strip of paper making a circle.  We were then able to lay out circle out on a piece of paper and mark out the "parts" of the whole circle, the parts being each color.  We drew a big circle on the paper and colored in the parts of the whole til we made a pie chart or you could call it a circle graph.  I loved the idea of making the circle, it allowed us to see the relation of data to the graph and also the parts to the whole as we constructed it.  Here is our Example:

Circle Graph / Pie Chart

After coloring our Pictographs we were allowed to eat our M&M's because they were now be represented by colored dots on our paper rather than the actual M&M.  This was a fun activity!  This is something you could easily do with several different grade levels, the hardest part is getting them not to eat the candy!
Do Not Feed the Animals!
Terri

This video is an example of what we did we our M&M's.  The graph construction is not the same but would be a variation.  I like the way we did it making the tape diagram/fraction strips, either way would work but gives more ideas to what we have available to us to use.

By: Mcdoyal

April Showers Brings May Flowers

April 1st, 2019
Here I am back in MATH 257 and it has been awesome!  I have a bit more understanding of things and I'm observing a new teacher for 4th grade and that has been awesome as well.
Professor Klassen is also trying out some curriculum from another University and there have been different variations in her teaching style and in the work were doing.  Looking forward to class this semester.  I will be adding to my blog for my blog assignment because the things I have previously done here are part of my journey.  So sit back and wait for it!