What is the average toothpaste?

Finding the Averages of the Ordinary

Toothpaste is something we use everyday (or at least, I hope you do)!  But did you know that there are many different kinds of toothpastes that are available to us? We will learn how to use data collected by 177 people to find the averages (or most common) and plot this data on histograms and different charts.

Standard

CCSS.Math.content.6.SP.B.5.A: Reporting the number of observations 

CCSS.math.content.6.SP.B.4:  Display numerical data in plots on a number line, including dot plots, histogram and box plots.  

Where did we first learn about averages? 

The Greek historian, Herodotus, explained in his analysis of the of Egyptian King, that three generations are roughly 100 years!  While we now know that this is accurate, between 485-420 BC, this was not common knowledge.  We know that a generation can be about 100 years, give or taken a few years, but this is a great representation of averages.  

Herodotus explained, "They declare that three hundred and forty-one generations separate the first king of Egypt from the last mentioned (Hephaestus) - and that there was a king and high priest corresponding to each generation.  Now reckon three generations as a hundred years, three hundred generations make ten thousand years, and the remaining forty-one generations make 1,340 years more; thus one gets a total of 11,340 years...".

What can you gather from the above statement?  We look at the first king of Egypt and the last mentioned (those are the qualifier, the first and the last and everyone in between).  Then we look at the number of 340 generations separating the first king and the last.  

Math Antics

Let's watch this video on Mean, Mode and Median to get a better understanding!  

Math Antics

Introduction of Data

I polled 178 people in which is their favorite toothpaste.  Here is the collection of data

   

Favorite Toothpaste	Votes
Crest	76
Colgate	63
Rembrandt	1
Aim	2
Tom's	7
Arm & Hammer	1
Sensodyne	24
Jason	1
Schmidt's	1
Ultrabrite	1
Aquafresh	1
Total	178

Finding the Mean

Now, let's find the mean.  We already have the total number of votes, which is 178.  How did we find this?  We found this by adding all of the votes together.  Next, we must divide the total by the number of items, which is 11.  Our equation is as follows:

178 / 11 = 16.18  

This means our mean is 16.18, or the average number we have is 16.18.  

Finding the Mode

The mode is the number that appears the most often in a number set.  Can you guess what number appears the most often?  First, we must put our numbers in numerical order. 

                                         

1, 1, 1, 1, 1, 1, 2, 7, 24, 63, 76

Let's see which number appears the most in our list: 

Number:      Amount in which it appears:

1                        6

2                        1

7                        1

24                      1

63                      1

76                      1

This list demonstrates that the number 1 is our mode.  

Finding the Median

The median is the number in the middle.  This of a 4 lane highway.  What do we call the the grass or concrete in the middle of those 4 lanes?  We call it a median.  

                                             

It is the same thing for a list of numbers.  Whatever the middle number in a number set is the median.  Let's look back at our list of favorite toothpastes.  

1, 1, 1, 1, 1, 1, 2, 7, 24, 63, 76

Because we already know there are 11 numbers in this particular number set, we would find the number after the fifth number, which is sixth number.  

1, 1, 1, 1, 1, 1, 2, 7, 24, 63, 76

1 is our Median.  

It is important to remember that mean, mode and median are NOT the same thing.  Let's review our numbers.  

Mean: 16.18

Mode: 1

Median: 1

Graphing

When you look at data in the future, you will see graphs and will be able to construct the same mean, mode and median from bar graphs and histograms and even pie charts.  We will dive further into pie charts next week.  Using the same data we collected before, we come up with these graphs:

This is a bar graph.  It has all the same numbers as before, but it looks a little bit cooler!

Next we have a pie chart.  This is pretty neat looking as well, just a little more crowded due to the number of toothpastes we used.  

And lastly, we have a line graph.  I would like you to create your own, but here is an example. 

Tonight, I want you to look at the latest Detroit Tiger's Batting Average and find the mean, mode and median.  You will be able to find the team's total average (mean), the median (remember, the middle number) and the most common number is the number set.  You will be able to do this with any batting average for any baseball team from now on.  

Player Name	Batting Average
Miguel Cabrera	0.323
Nicholas Castellanos	0.319
John Hicks	0.294
Leonys Martin	0.29
Jeimer Candelario	0.277
James McCann	0.273
Victor Martinez	0.26
Grayson Greiner	0.25
JaCoby Jones	0.245
Jose Iglesias	0.22
Dixon Machado	0.203
Niko Goodrum	0.189
Victor Reyes	0.143
Mikie Mahtook	0.129

I can't wait to see what you've learned!

Sources:
Detroit Tigers 2018 Batting/Hitting Scores. (n.d.). Retrieved May 07, 2018, from http://www.espn.com/mlb/team/stats/batting/_/name/det/detroit-tigers

Egyptian King Picture. (n.d.). Retrieved May 07, 2018, from https://klimtlover.files.wordpress.com/2012/09/death-mask.jpg

Grade 6 » Statistics & Probability. (n.d.). Retrieved May 07, 2018, from http://www.corestandards.org/Math/Content/6/SP/

Math Antics - Mean, Median and Mode. (2017, March 03). Retrieved May 07, 2018, from https://youtu.be/B1HEzNTGeZ4

The Early History of Average Values and Implications for Education. (n.d.). Retrieved May 07, 2018, from http://ww2.amstat.org/publications/jse/v11n1/bakker.html

Understanding a question is half an answer - ancient Greek philosopher.. (n.d.). Retrieved May 07, 2018, from https://www.123rf.com/photo_41982954_understanding-a-question-is-half-an-answer-ancient-greek-philosopher-socrates-quote-printed-on-grung.html

Egyptian King Picture. (n.d.). Retrieved May 07, 2018, from https://klimtlover.files.wordpress.com/2012/09/death-mask.jpg

Grade 6 » Statistics & Probability. (n.d.). Retrieved May 07, 2018, from http://www.corestandards.org/Math/Content/6/SP/

Math Antics - Mean, Median and Mode. (2017, March 03). Retrieved May 07, 2018, from https://youtu.be/B1HEzNTGeZ4

The Early History of Average Values and Implications for Education. (n.d.). Retrieved May 07, 2018, from http://ww2.amstat.org/publications/jse/v11n1/bakker.html

Understanding a question is half an answer - ancient Greek philosopher.. (n.d.). Retrieved May 07, 2018, from https://www.123rf.com/photo_41982954_understanding-a-question-is-half-an-answer-ancient-greek-philosopher-socrates-quote-printed-on-grung.html

Detroit Tigers 2018 Batting/Hitting Scores. (n.d.). Retrieved May 07, 2018, from http://www.espn.com/mlb/team/stats/batting/_/name/det/detroit-tigers

Egyptian King Picture. (n.d.). Retrieved May 07, 2018, from https://klimtlover.files.wordpress.com/2012/09/death-mask.jpg

Grade 6 » Statistics & Probability. (n.d.). Retrieved May 07, 2018, from http://www.corestandards.org/Math/Content/6/SP/

Math Antics - Mean, Median and Mode. (2017, March 03). Retrieved May 07, 2018, from https://youtu.be/B1HEzNTGeZ4

The Early History of Average Values and Implications for Education. (n.d.). Retrieved May 07, 2018, from http://ww2.amstat.org/publications/jse/v11n1/bakker.html

Understanding a question is half an answer - ancient Greek philosopher.. (n.d.). Retrieved May 07, 2018, from https://www.123rf.com/photo_41982954_understanding-a-question-is-half-an-answer-ancient-greek-philosopher-socrates-quote-printed-on-grung.html

Fun with Shapes!

Shapes are a lot of fun!  

By: Jennifer Kuhar

I am so excited to share this with you today!  We are going to learn all about SHAPES! When we look around our classroom, at home and even outside, we can see all sorts of shapes around us!  Not only are there 2 dimensional shapes, but there are also 3 dimensional shapes! Can you guess which shapes are 2-D or 3-D?  A circle is a 2-D shape, while a basketball is a 3-D shape, called a sphere.  I am so excited to share this with you today!  

This video is from the Singing Walrus.  Let's watch this fun video all about shapes!  

How fun was that?  What was your favorite shape in the video?  Raise your hand if you liked the square?  The circle?  Was your favorite part the music?  Did you learn a new shape?  We will have so much fun with shapes today!  

Why do we need to know shapes?  

Shapes are so important to know because we can describe the objects we use every day.  When we look at the sun, we will know that it is a circle, and not a square, right?  

Let's get started on learning our shapes!  As we go over these flashcards, remember to raise your hand if you know the answer.

 

Fantastic job!  A circle has no sides and is round.  A square has how many sides?  That's correct, 4!  What other shapes have 4 sides?  A rectangle has 4 sides, but has two shorter sides and is longer than a square.  That's what makes it a rectangle.  The other 4 sided shape is a diamond, which is like a square, but tilted.  Everyone tilt to your right!  Great job, that is a lot like a diamond.  

The shape with five points that twinkles in the sky is which shape?  Fabulous, a star!  A heart can stand for love.  What is that pizza slice shape?  Triangle!  Which shapes looks like someone is yawning and a stretched circle?  An oval!  STOP!  What is the name of the shape that looks like a stop sign?  A hexagon!  Great job!!!

Let's Review

We have gone over our shapes and watched a video all about shapes!  We are going to work on this worksheet.  When you're finished, you may play quietly at our centers.  First things first though, we write our names at the top!  

As I dismiss you, boys and girls, we are going to get our clipboards and line up at the door...

Nature Hike

Make sure you clip your paper on your clip board that is handed to you and take your pencil.  We are going to go look outside and find 2 shapes that you find.  When you see a shape, I want you to draw it on your paper.  We will do this for 10 minutes and then come back in.  Thumbs up if you understand. Great!  Stay together while we walk around the playground.  

Macaroni Art

We have learned a lot about shapes today.  We watched the Singing Walrus video, we talked about the different shapes and then we went outside to look at the shapes all around us.  Now we are going to create your favorite shape with macaroni.  First things first, write your name on the back of the paper.    Then turn it over and color your shape.  When it's time to glue the macaroni on around the outside of your shape,  remember dot, dot, not a lot".  When you're finished, make sure you put your art on the back table.

Fun at home

When you get home, you're going to find a snack that has a shape.  For example, you can bring in an apple or some crackers.  If you need help finding a shape, please make sure you ask your parents or grandparents.  Remember, we will bring these in for tomorrow to review our shapes and how we can find shapes no matter where we are.  I can't wait to see all of your shapes!

Standards:

K.G.A.3: Identify shapes as two-dimensional (lying in a plane, flat) or three-dimensional.  

Objective:  Students will be able to identify circle, star, square, rectangle, diamond, heart, and oval.  This is to master 2D shapes with some integration of 3D shapes.  

Prior Knowledge:  Students should be able to know the names of shapes; write their name; count to ten; make an educated guess; follow directions; know how to glue, cut, color; follow established routines.  

References:

Shapes flashcard.  (2014).  Retrieved March 9, 2018 from http://www.kids-    

       pages.com/folders/flashcards/Shapes/page1.htm

Shapes Worksheet.  (2015).  Retrieved March 9, 2018 from http://cdn.turtlediary.com/worksheets/

       math/kindergarten/planar-or-2d-shapes/identify-shapes/question/identify-shapes-5.png

Shape songs for Kids by The Singing Walrus.  (5 Mar 2015).  Retrieved March 9, 2018 from 

       https://youtu.be/OEbRDtCAFdU