Sunday, February 9, 2014

Penny Jars and Cube Towers

Our Math Workshop emphasis in recent weeks has been centered around analyzing relationships between two quantities in situations of constant change. These situations have started out very concretely, through using actual pennies and linking cubes, and then representing these situations more abstractly with arithmetic expressions.
In the above "penny jar" situation, there is a starting number of 5 pennies in the "jar". Then, 6 pennies are added each "round". The total number of pennies shown is (5 x 6) + 5, or 35 pennies. Students have been challenged to extend patterns such as this one, in order to determine the total number of pennies for any round. If asked to identify the number of pennies in the 20th round, for example, students would determine that there are 20 groups of 6 pennies (20 x 6), and then 5 more (+5) when including the "starting" pennies in the jar: 20 x 6 + 5 = 125. There would be 125 pennies in the jar after 20 rounds of adding 6 pennies each round. The most general arithmetic expression to represent "any" round might be n x 6 + 5, or 6n + 5.

These Investigations (from our Scott Foresman curriculum tool) have provided tables, such as the example shown above, in helping students make sense of (and represent) these situations algebraically.

In the above "double tower" situation, there are two skylights. As new "floors" are added to the double tower, the number of skylights never changes. Students have learned to represent this as "+2". Each time a floor is added, however, the double tower gains 6 new windows. The example above has 2 floors. This would be represented as 6 + 6 + 2, or 2 x 6 + 2. There are a total of 14 windows on this tower. Again, students have learned through active exploration (by actually constructing various towers with linking cube manipulatives as they fill in provided charts) how to represent this situation with a general arithmetic expression: n x 6 + 2 (6n + 2). How many windows would be on the 100th floor of this tower? To solve, students would simply calculate 100 x 6 + 2. A 100 floor double tower would have 602 windows.


Upcoming investigations will include building, analyzing, and representing Corner Towers & Square Towers. Students will be challenged to represent these situations of constant change by creating an arithmetic expression using a variable so that the number of windows on ANY given floor can quickly be determined.






Happy Mathematizing,




Saturday, January 25, 2014

Navigating Historical Fiction: Focusing on Setting First

Readers at Wild Adventures are quickly falling in love with a new genre -- historical fiction!

Often, when students come to fourth grade, they still think books are one of two "genres": fiction or nonfiction.  This year, readers are learning that calling a book "fiction" or "nonfiction" is like saying a dog is an animal or an oak tree is a plant.  There is so much more that we could say!  We can consider "fiction" and "nonfiction" the "kingdoms" of the literary world, and now that we're older, we are getting to know the "species" within each.

Recently, we learned that we read historical fiction much the same way as we would read any other type of narrative text (mystery, realistic fiction, narrative nonfiction, etc.).  We focus deeply on the characters.  However, as we read stories that take place in times (and sometimes places) far away from the world we live in, we also need to pay careful attention to the setting.  Where in the world is this taking place?  When in history is this story set?  Once we've established the where and when in a global sense, we move towards understanding the traits of the setting, just as we would understand the traits of a character.

In our newest read aloud, Esperanza Rising by Pam Muñoz Ryan, the year (1930) and geographic location (Aguascalientes, Mexico) are clearly announced to the reader.  As we read on, we learned Esperanza's family owns and lives on a vineyard and ranch, El Rancho de las Rosas.  But in order to truly understand Esperanza's story, we have to understand what kind of place and time this really was for the people living within it.

"Everyone who lived and worked on El Rancho de las Rosas was gathered at the edge of the field:  Esperanza's family, the house servants in their long white aprons, the vaqueros already sitting on their horses ready to ride out to the cattle, and fifty or sixty campesinos, straw hats in their hands, holding their own knives ready."

This passage revealed to many readers in our room that Esperanza's home was a wealthy home.  It was the kind of place that probably left Esperanza wanting nothing she didn't already have.

Later, as we read descriptions of the fiesta that occurred each year after the harvest, and Esperanza's thoughts about her future Quinceañeras, many readers said they could tell it was a traditional home, consistent and predictable from year to year.  We know that carrying these understandings with us as we walk with the characters through their story is important because it helps us have empathy and a deeper understanding of the characters behaviors, actions, choices, and traits.

Readers, revisit this passage from the first chapter.  Think carefully about the details Pam Muñoz Ryan included.  What words would you use to describe the setting of our story after you've reread this passage closely?

"He swept his hand toward the grapevines, signaling Esperanza.  When she walked toward the arbors and glanced back at her parents, they both smiled and nodded, encouraging her forward.  When she reached the vines, she separated the leaves and carefully grasped a thick stem.  She put the knife to it, and with a quick swipe, the heavy cluster of grapes dropped into her waiting hand.  Esperanza walked back to Papa and handed him the fruit.  Papa kissed it and held it up for all to see.  
'¡La cosecha!' said Papa.  "Harvest!"
'¡Ole! ¡Ole!'  A cheer echoed around them.
The campesinos, the field-workers, spread out over the land and began the task of reaping the fields.  Esperanza stood between Mama and Papa, with her arms linked to theirs, and admired the activity of the workers.
 'Papi, this is my favorite time of year,' she said, watching the brightly colored shirts of the workers slowly moving among the arbors.  Wagons rattled back and forth from the fields to the big barns where the grapes would be stored until they went to the winery."

I can't wait to see your thinking in the comments below!
 

Sunday, January 12, 2014

Multicultural Luncheon

Multicultural Luncheon on PhotoPeach


Plantain chips from Cuba, Empanadas from Mexico & Colombia, Tea & Cookies from England, Scones from Scotland, Petit Fours from France, Swedish Meatballs from Sweden, Eggrolls from Vietnam, Pasta from Italy, Baklava from Greece, Latkaes & Gelt from Israel, Rolled Cabbage from Romania, Enchiladas from Mexico, Apple Dessert from Germany, Brats & Sauerkraut from Germany, Dessert from India, Matzah Ball from Central Europe, Pastry Meringues from France.....We had a delightful time with our family members who were able to attend. What a great opportunity for fellowship and fun! Many students even tried "new" things that they had never tasted before. Thank you to everyone who was able to contribute toward our luncheon's success.

St. Augustine

St. Augustine 2014 on PhotoPeach


Our trip to St. Augustine was a memorable one. The weather was perfect and our tours were very informative. Here are a few FUN FACTS that we learned while there:

1) The Castillo cannons could shoot a cannon ball a distance of about 3 1/2 miles.

2) The Catholic Cross where Pedro Menendez first arrived in St. Augustine is 208 feet tall. If it were any taller, it would need a red light to be visible to airplanes!

 3) The oldest resident of St. Augustine is "Old Senator"- very large oak tree.

4) The Lightner Museum used to be one of Henry Flagler's hotels- there used to be a large indoor pool in there that measured 150 feet by 60 feet. (What was the area of this pool?)

 5) St. Augustine marks the beginning of the Trail of Tears (which we will learn more about later this year).



Students, what other FUN FACTS can you remember? Leave a comment to tell us something interesting that you learned and you will earn $5 behavior bucks!

Saturday, January 4, 2014

Decisive Decimals


Upon returning from our holiday break our main mathematics focus will be to take our understanding of decimals to new levels by exploring them precisely on models such as grids and number lines. We will also review strategies for comparing and ordering decimals, which we explored back in December.
Here are three helpful strategies we have already learned:

Convert decimals to fractions with like denominators.

Convert decimals to their percent equivalents.


Visualize the values to compare decimals. 

Happy Mathematizing,

Thursday, December 5, 2013

Fun with Fractions

In Math Workshop, we have been been studying area models of fractions. Through homework, we have also been reviewing fraction concept using linear models (number lines) and set models (groups of objects). All of these models are important in helping to develop conceptual understanding of fractions.
The links below are helpful in reviewing some of the "big ideas" we have been studying in class. Use them to review and clarify your understanding of fractions. :-)

What are fractions?
Fractions

How can you make and identify equivalent fractions?
Equivalent Fractions

How do you find the "Greatest Common Factor" to put a fraction in lowest terms?
Greatest Common Factor

:-) Enjoy.
Students, leave a comment to share your thoughts on these Study Jams links.

Tuesday, November 26, 2013

Reading True Stories

Just when you thought you had nonfiction reading all figured out, in walks the black sheep of the nonfiction family -- NARRATIVE nonfiction!

Savvy readers know that narrative nonfiction is just a nonfiction text (a text designed to teach its reader) in disguise as an entertaining story.  But those same savvy readers know that a story is a story is a story, no matter whether it's true or false.  And how do we think about the stories we read?  We think about the characters!  This means we temporarily set aside all that we've learned about reading nonfiction -- boxing in main ideas of sections, listing (with bullets) the details that support those ideas, turning headings into questions, and using text features to deepen our learning -- and return to our sticky note type thoughts.

Readers should ask themselves: 

  • What kind of person is this character?  What are their traits?
  • What does this character want or need?
  • What are their obstacles, dangers or struggles?

After we finish the text, we can use the "Somebody-Wanted-But-So-Then" one-sentence summary frame to help us focus on what this true story taught.

When we read Bamboo Valley: A Story of Chinese Bamboo Forest, we realized quickly that we needed to expand our definition of a main character to include animals, or perhaps even plants.  In this story, readers found the main character, a young panda, used his persistent, peaceful nature to overcome many obstacles to surviving alone in the forests of China.  They summarized this book like this:

The panda wanted to find a new home with water, live bamboo, and shelter, but everywhere he looked there was already another animal living there or no foodso he kept looking and walking for many miles, then he finally found a new valley with live bamboo & water.

But just thinking about what you read isn't always enough.  Just as we would ask ourselves, "Why is this important?" after we finish an informational text, we must think deeply to find the unifying ideas within a narrative nonfiction.  One strategy for digging deeper into a true story is to think about the character's choices, challenges and lessons.


Today, our readers recognized that, on a December 1st, very long ago, Mrs. Parks made a pivotal choice, or a choice that changed the course of her story, when she said "no" to not only the bus driver, but also the police officer, when she was asked to give up her seat.  Readers quickly saw that the immediate consequence of her arrest was only one of many effects of this choice.  (We learned that the word "consequence" doesn't always mean "punishment"!)  As a result of her personal choice, the women of her community organized a bus boycott, Dr. Martin Luther King, Jr. brought national attention to her situation, and people all over the nation sent their support to those boycotting the buses.  Ultimately, her simple choice to say "no" led to change on a national level.  To us, this meant we could make a small choice -- whether it's picking up trash on the beach or playground, or inviting someone to join us at the lunch table or on the recess field -- and know that our small choice could somehow lead to a big change, bigger than we might ever imagined possible!

Readers, we thought about so much more today.  What were some of your "take away" thoughts after reading Rosa, by Nikki Giovanni?  What do you recall about her challenges?  What helped her through these challenges?  How could we carry a little piece of this story and what it's taught us into our lives today?  Take a moment to share with the world and our Chets Creek community what lessons we could take from this remarkable story.