The King's Chessboard (estimation/measurement)

I began class today by reading a story called The King's Chessboard by David Birch.  I found this activity years ago in the book, Math and Literature (Grades 4-6) by Rusty Bresser.  

The story tells of a king who insists on rewarding a wise man and in the process is taught a lesson on both humility and mathematics.  Basically, the king agrees to give the wise man one grain of rice, doubled daily, for 64 days.  As soon as I read the reward, my kids knew the king was in trouble!  All of them recognized this reward as being the same as the "Million Dollar Dilemma" we solved on Monday.  They were interested to see how the story played out knowing that doubling numbers increases them very quickly.  

Before moving into the math problem for the day, I had the kids transfer the data from "Million Dollar Dilemma" onto a chart, explaining that we were going to need to know how many grains of rice were delivered each day.  Once we had the chart complete (which took very little time as we had done the math Monday),  I posed the question:

On which day would enough grains of rice be 

sent to feed our 5th grade?

I asked the classes how we would solve this problem.  What do we need to know?  They all agreed that the first thing we need to know is the number of 5th graders (56).  Then we needed to know how much rice a 5th grader could eat (1/2 cup).  Next, how many grains of rice are in a 1/2 cup?  

At this point, it was time to estimate.  I gave each group 1/2 cup of rice and a teaspoon.  I asked how we could use these items to determine the number of grains of rice in 1/2 cup.  First they wanted to find out the number of teaspoons in 1/2 cup (the average was slightly different for each class).  Then they wanted to know how many grains were in a teaspoon (again, the averages were slightly different for each class).

Once we had this knowledge we could determine the approximate number of grains in 1/2 cup by using multiplication.  Then we were able to use this product to determine the number of grains of rice needed for 56 fifth graders, again by multiplying.  Using this final product, we were able to determine which day enough grains were sent (Day 20).

However, I posed another question.... Is 1/2 cup of uncooked rice the same as 1/2 cup of cooked rice.  Someone in each class invariably knew that rice expands.  So, knowing that rice expands to 3x its size when cooked, the kids decided that we needed to take our product and divide by 3.  This provided us with the answer to our original question.

Here are examples of each class's work:

Johnson:

Dittrich

Whitehead

HOMEWORK:  Countdown 7.3

MSTAR and Khan Academy

Today, we completed the third installment of the MSTAR universal screener.  A brief description of the screener is below:

Middle School Students in Texas Algebra Ready

MSTAR Overview 

Universal Screener

The ESTAR/MSTAR Universal Screener is a formative assessment system administered to students to support instructional decisions.

• The content of the MSTAR Universal Screener is based on algebra-readiness knowledge and skills as identified in the Texas Response to the Curriculum Focal Points.
• Results can help teachers identify students who might not be ready for algebra and are in need of additional instructional support.
• Teachers will be able to monitor students' risk status by administering comparable forms of the MSTAR Universal Screener in fall, winter, and early spring.

After completing the MSTAR, students worked on Khan Academy one final time before invitations for the Khan Academy Banquet will be sent out.  To receive an invitation, students must have achieved 60 mastered objectives in the 3-5 instructional area.

Would You Rather: Million Dollar Dilemma

Today, I posed a "Would You Rather" question.  I found this activity, originally called "The Million Dollar Dilemma," in the January 1993 edition of the AIMS Education Foundation.

Basically, the kids are asked whether they would prefer to take $1,000,000 at the end of 31 days, or take a penny doubled daily.  Of course, most of my classes chose the million, but I never make it that easy.... we have to prove our answers!  So, we filled out a table that showed us doubling a penny daily for 31 days AND finding out the total amount of money we could make cumulatively!

My kids are always surprised by the final results!  Up to day 27 they are convinced that taking the million is the way to go, but once we surpass the million they are taken aback by the both the day's pay and the final total pay.

While working on this activity, I asked the kids to find patterns.  These are some of them:

• the day's pay always ends in 2, 4, 8, 6 and repeats that pattern then entire time (excluding the first penny)
• the total pay always ends in 1, 3, 7, 5 and repeats that pattern the entire time
• the day's pay is always $.01 greater than the previous total pay
• you can find the next total pay by multiplying the previous total pay by 2 and adding $.01.

To finish the activity, I asked the kids to explain which option they would choose now.  I did specify that I expected more of an explanation other than "it was more."

To see a mathematical explanation for this activity, go to:

Ask Dr. Math.  

HOMEWORK:  Countdown 7.2

Tessellations (Day 4)

Final day with tessellations!  When students finished their project, they were asked to post a picture of their tessellation to their blog and write about the project.  To do this involves a few steps!

1. Take a picture with IPod.
2. Send to email.
3. Get a netbook and open their email. 
4. Save the picture to their documents.
5. Open a new post in kidblog
6. Retrieve the picture from their document and save into the blog.

To see the tessellations that were posted, please visit:

• http://kidblog.org/JohnsonMath/
• http://kidblog.org/DittrichMath/
• http://kidblog.org/WhiteheadMath/

I have posted pictures of Mrs. Whitehead's class working on tessellations and blogs:

Tessellations (Day 3)

'8 Heads' by M. C. Escher (1922)
By permission Cordon Art - see site information.


Today's class-time was spent working to complete our tessellations.  I have included pictures of Mrs. Dittrich's class working on their tessellation creations:

HOMEWORK:  Countdown 7.1

Science STAAR

Tessellations (Day 2)

M. C. Escher is an artist famous for his tessellation art (as seen above).

While I am not expecting museum quality art, I cannot wait to see what my classes design with the templates they created yesterday!  Today, we spent our class tracing our templates and adding the interior design elements.

This is Mrs. Johnson's class at work:

HOMEWORK:  None

Tessellations (Day 1)

Tessellation Definition

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps.

I introduced our new project in math today.... tessellations.  To begin, I read the story A Cloak for the Dreamer by Aileen Friedman.

This is the story of a tailor and his sons.  They work to create cloaks for the Archduke.  In order for the cloak to be weatherproof, the shapes used in the design must "cover a plane without gaps for overlaps."  Therefore the cloaks were a form of tessellation and a great introduction into the new project.

Next, I had the classes watch a video called, "Tessellations:  How to Create Them" hosted b Jim McNeill.

In this video, Jim McNeill demonstrates how to create tessellations using transformations:

• Translation tessellations are created when the template is slid along the paper:

• Rotation tessellations are created when the template is rotated around an axis:

• Reflection tessellations are created when the template is flipped and traced:

I also found a website that goes through the process step-by-step with student instructions that might be helpful.  The activity is called:  Tessellation Sensations.

After watching the video, I gave each student a 3x3" index card and we followed the steps to create our template.  We then traced our templates and worked on creating interior elements that would allow our template to look like something familiar.

We will begin actually tessellating with our templates tomorrow.

HOMEWORK:  Countdown 6.8

Pysanky (Day 3)

Today we posted to our blogs.  I had the kids take a picture of their paper pysanky and write about it yesterday.  Today, we put the definition, the picture, and their explanation of the pysanky on their blogs.  To see our finished products, visit:

• http://kidblog.org/JohnsonMath/
• http://kidblog.org/DittrichMath/
• http://kidblog.org/WhiteheadMath/

We have the next few days off, so my next post will be on Monday, April 21!

Have a Happy Easter!

Pysanky (Day 2)

Today we worked on completing our paper pysanky.  

Once the students had completed decorating their egg, they cut out the egg and taped the symbol meaning on the back.  Then, they got out their IPods and took a picture of their egg design and emailed it to their school email.  To finish out the day, they wrote a paragraph about their egg (who it is for, why they chose the designs, etc.).

Tomorrow, we will post the picture of the pysanky and the paragraphs to our kidblogs!

HOMEWORK:  Countdown 6.7

Pysanky (Day 1)

1. 
   Pysanky
2. A pysanka (Ukrainian: писанка, plural: pysanky) is a pretty Ukrainian Easter egg, decorated with traditional Ukrainian folk designs using a wax-resist (batik) method. The word pysanka comes from the verb pysaty, "to write", as the designs are not painted on, but written with beeswax.

   Pysanka - Wikipedia, the free encyclopedia

   en.wikipedia.org/wiki/Pysanka

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Today we began working on our paper pysanky projects.  I 

gave each student a large egg to trace on white construction 

paper.  Then, I gave them a worksheet I found in The 

Mailbox Intermediate, February/March 1996 (p. 31).  This is 

a page of symbols and colors and their special meaning.  An

example:

The classes worked on creating a design that would have 

special meaning to their family or a specific family member.

If you are interested in making an actual pysanka, please 

look at my blog from Friday.  I have listed three websites that

are very helpful in making this a tradition in your home!

Rechenka's Eggs

Every year around Easter, for the past 10 years, I have introduced my students to Rechenka's Eggs by Patricia Polacco through the Reading Rainbow DVD.  I use the DVD so that the students can watch the author, Patricia Polacco, demonstrate the Ukrainian art of dying eggs called Pysanky.

After I have shown the DVD and my students are pumped about this type of egg decorating.... I have to disappoint them by telling them that we cannot do a pysanky in class... it involves working with open flame!  I explain that I am going to give them websites they can visit to get the supplies for creating a pysanky egg of their own, but we will be doing a paper version.

I take some time showing my classes the pysanky eggs that my daughters and I have done over the years.  These are from last Easter.

10 years of Pysanky

I also showed them the Ukrainian website that showcases HUGE pysanky eggs in a parade. 

I know that many of my students are very interested in trying this type of art, so I gave them three very helpful websites:

• www.allthingsukrainian.com (kits)
• www.learnpysanky.com (ideas)
• www.beverlysgoosehatchery.com (goose eggs)

We will begin our paper version on Monday!