Finding Equivalents

Recent investigations in math have focused on student justification of equivalent multiplication and division expressions. Students have been writing story problems and creating visual representations to prove these equivalencies. The process has been challenging but fun! 

Sammy's Story Problem

Justifying that 6 x 9 = 18 x 3 

"There are 6 houses with 9 cats in each house. 3 houses get burnt down so the 9 cats from the burnt down houses move in the other 3. So there are 18 cats in the other 3 houses." 

Chase's Story Problem 

Justifying that 2 x 9 = 6 x 3

"There were 2 fishermen that each caught 9 fish. When they ate dinner, there were 6 people so they each had 3 fish."

Macy's Story Problem

Justifying that 2 x 9 = 6 x 3

"There are 2 monkeys and each have 9 bananas. 4 more monkeys come, and then they have to split them with 6 monkeys. So they decide each monkey will get 3 bananas." 

For Behavior Bucks, brainstorm a story about ants invading a picnic   and sharing sandwiches for this equation: 2 x 6 = 4 x 3

Happy Brainstorming!

Plant and Animal Unit Highlights

In recent weeks we have learned all about inherited and environmental characteristics of organisms.  We have also researched instincts and learned behaviors of organisms, and we have studied life cycles of plants and various groups of animals (mammals, reptiles, insects, etc).  Students can reference the links below as a fun way to review these various science topics.

Current Topics:

Animal Adaptations

Plant Life Cycles: Plants with Seeds

Plant Life Cycles: Angiosperms

Plant Life Cycles: Plants with Cones 

Plant Life Cycles: Plants with Spores 

Animal Life Cycles  

Upcoming Topics:

Food Chains

Food Webs

An Author Celebration: Spotlight on Jordan

Through the course of the year, the ELA teachers push our readers and writers to live the life of a reader... live the life of a writer. Our classroom has a quote on our wall that reads, "You must read like a writer to write like a writer!". In Mrs. Koster's class, no one embodies this more than Jordan! Jordan is constantly pushing herself to read new books and interesting genres. Because of her reading habits, she has shown tremendous growth this year as a writer. She has shown so much growth that when the "Work Over Time" bulletin board came up Wednesday morning, her class stood outside in AWE... reading each piece and celebrating with her, even congratulating her on her work! Isn't this what we dream of as fourth grade writers? Our hope is that readers will see our piece and be amazed! We want them to feel what our characters are feeling. We want them to laugh and cry with us in our narratives.

Jordan... we are SO proud of the author you have become this year. This board is dedicated to your growth! Mrs. Koster wants you to know that it is only a tiny picture of the growth that has occurred on the inside this year!

Thank you for working hard at perfecting your craft. You are an inspiration! Never stop writing!

Mrs. Koster & Mr. Pinchot's Classes Visit Florida's Frontier!

Today, our classes took a trip to Florida's very own frontier! Did you know that Florida HAD a frontier? Sometimes, we think of a "frontier" as being only related to the wild west, but that isn't true. Did you know that a frontier is actually an underdeveloped area open for a field of discovery? We got the chance to step back in time, onto the grounds of one of Florida's eleven national parks today... Kingsley Plantation!

Zepheniah Kingsley was the owner of this plantation. The difference between a farm and a plantation is that a plantation has twenty or more slave workers. Each of the Kingsley's slaves was a part of the task system in which they worked the fields of sea island cotton each day. Their task was to pick 70-90 lbs. of sea island cotton! We learned that an adult was considered to be 10 years of age or older... that means YOU friends would be picking 70 lbs. of cotton a day! Then, the seeds had to be picked out by hand. Sea island cotton was a luxury item because it was extremely soft, with long fibers. The Florida climate is the perfect recipe for growing sea island cotton with its swampy, sandy terrain and humid air. However, we also learned that picking sea island cotton is quite different than your usual cotton, because sea island cotton grows in trees and vines up to 7 feet tall! After our tour and scavenger hunt had ended, we enjoyed a nice lunch under the palms on the banks of the river... just another day in the sweet life of a CCE fourth grader! 

Enjoy the pictures of our trip back in time...

Koster and Pinchot Historians... What did you like best about our trip today? What new facts did you add to your historian brain? What vocabulary word did you hear today that we have been studying in ELA this week? Give Mrs. Phillips and Mrs. Nash's classes something to look forward to!

Deepening Our Understanding of Mathematical Properties and Relationships

In our final weeks of school, our focus has turned back to nurturing and developing essential understandings in mathematics. Our students should be very confident with the following categories of numbers:

Odd Numbers:
* have a 1, 3, 5, 7, or 9 in the ones place, have only odd factors (odd x odd = odd)

Even Numbers:
* have a 2, 4, 6, 8, or 0 in the ones place, always have a factor of 2 (odd x even = even, even x odd = even, and even x even = even)

Prime Numbers:
* only have 2 factors (one and itself), 2 is the only even prime number

Composite Numbers:
* have more than two factors, can be even or odd

Square Numbers:
* make a square array and have an odd number of factors (can be made by multiplying a number by itself
ex: 1 x 1 = 1, 2 x 2 =4, 3 x 3 = 9 therefore, 1, 4, and 9 are square numbers)

Our current Scott Foresman Investigation in Math (Number Puzzles and Factoring) challenges students to identify numbers that contain one or more of the above-listed categories.These have been presented to the students as "puzzles"...
For example, Think of a number that is even and square.......4 works (produces a 2x2 array, 4 is even).....16 also works (produces a 4x4 array, 16 is even).

In working through number puzzles, students must also distinguish between factors and multiples. 
Factors of 8 are 1, 2, 4, and 8
Multiples of 8 are 8, 16, 24, 32.....(and so on)


Our puzzles have extended to considering FOUR CLUES at a time! We love BRAIN GYM. :-)
*Example: Think of a number that is even, a multiple of 3, less than 100, and a square number (the number 36 would work in this puzzle).


As these ideas have been reviewed and developed, we have used them to build our understanding of prime factorization. The kids REALLY are enjoying this! What an engaging and powerful way to integrate our understanding of factors, prime and composite numbers.

Our 5th grade teachers are SO excited that these "rising 5th graders" will be coming to them with a solid foundation build upon understanding of fundamental properties and relationships of numbers.

Our students are so excited and empowered too- they are even using their understanding of number to find all of the factors for large numbers such as 180 (which has EIGHTEEN factors, by the way)!!

Math Rocks!

Penny Jars and Cube Towers in Math

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.

Consider the two towers shown below: The Square Tower and Corner Tower.

How many windows (including skylights) would each of these towers have if they were 100 floors tall? Leave a comment with your answers. Be sure to share your thinking on how you arrive at your totals!!

Happy mathematizing!

The Narrative Side of Nonfiction

Readers have done lots of digging into nonfiction this year! Recently, we started to uncover another side of nonfiction, a genre called Narrative Nonfiction. These are true stories where we learn factual information, but they are told in the format of a narrative (story). We usually don't see many text features in them like we do in our "all about" books.

We can summarize a narrative nonfiction text in one sentence,
just like a narrative, by using the
"Somebody, Wanted, But, So" sentence frame.

We have also learned that narrative nonfiction, or biography, books can be divided into two piles: achievement texts and disaster texts. An achievement text will tell us how a character overcomes conundrums and obstacles to achieve something. In the beginning, we are usually introduced to traits of the character, sometimes shown through ministories about their childhood. The character usually goes on to use these trails to overcome difficulties. Disaster texts tell us about a situation that gets worse and worse for the character(s) and does not end well. We looked at the book, Pompeii: Buried Alive, and noticed some structures of a disaster text. It usually begins with an "all is well" mood, where the character is in a perfect environment. It gives us a sense that something is going to happen to ruin the perfection that is being described to us. The beginning of this book is all about the city of Pompeii and how daily life was moving on as normal. We could feel that something big was about to happen to make it a disaster text, and not an achievement! We used our reading sense!

Narrative nonfiction texts have underlying ideas. We
can uncover those ideas by investigating a character and
their choices, challenges, and lessons!

We have read MANY mentor texts to help us expand our reading minds into this genre! There are lots of biographies to explore, also! Some of us have realized that this is our favorite genre. It has definitely deepened our love of nonfiction!

The choices are endless when it comes to finding narrative
nonfiction in our classroom!

Readers, which books have you come to love in this unit? Has it opened your eyes to anything new? What are some cool things you have learned from reading these books?