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?

Boosterthon Time!

It's hard to believe that the chefs at Culinary Court like ANYTHING more than they like reading, writing, math, science, and social studies......but they actually do!!!  What could they possibly enjoy more than learning with their very own Top Chefs at Culinary Court???

BOOSTERTHON!!!

Our students are working hard to gather pledges for every lap they will run next Wednesday, and the countdown is on!!!  In addition to helping your child phone family and friends this week, you can support us all by planning to come cheer on our teams of runners as they race around the Boosterthon Speedway -- not once, not twice, but UP TO 35 TIMES!!!

So mark your calendars, families.  Bring your banners and your bells.  Pack your signs and your smiles.  Plan to be energized and entertained as you watch your fourth graders burn rubber on the Highway USA Boosterthon Speedway!  

We promise, you won't want to miss it!!!

Pssst!!!  Writers, did you catch the alliteration in this blog post?  Where is it?  Just for fun, try writing your own alliterative sentence about Boosterthon!  

Recipe Secrets!

Pssst!!! 

Here's a little homework hint from the ELA kitchen:

Did you know that, when referring to the infinite resources we access with our web browsers, the word "Internet" is a proper noun?  Think of the Internet as one big place people visit to get answers, connect with people, share information, and virtually explore the world.  We already know that specific places, such as Chets Creek Elementary, St. John's Town Center, or Walt Disney World, are all proper nouns.

In contrast, the word "website" is NOT a proper noun.  Why?  Just like the word "school" or "mall", this word could be referring to many different specific places, and we don't know exactly which one.  An exact website, like Culinary Court, should be capitalized, showing that it is a special place and therefore a proper noun.

Keep this hint in mind when you're completing your study guides this week, chefs!

To read more about tricky proper nouns, check out Grammar Girl's post.  

Nonfiction Text Structures

As we continue in our journey exploring nonfiction, we dig beneath the features of the text (captions, photographs, text boxes, maps, charts, diagrams, labels, glossaries, indexes, etc.) and begin to uncover the structure of the piece. Even though all nonfiction pieces are written to inform us about a topic, some authors decide to build the text in a certain way, based on exactly what they are trying to teach us. Take for example our sample paragraphs in our foldable, about crocodiles. An author could teach us about crocodiles by: describing them, sequencing their mating process in time order, cause and effect of relationships between crocodiles and crocodile birds, problems and solutions for the hunting of crocodiles, and/or comparing and contrasting crocodiles to other classifications of crocodiles like caimans and gavials. These are known as the five different nonfiction text structures.

We made foldables to help us learn the differences between each structure!

Sometimes, an author may choose to use more than ONE text structure in their piece. In a book about Wildfires, the author may teach you about them by giving you a description of what they are in the first section. Then, they may show you the chronological order of events that happens during a wildfire. In another section, they might give you all of the effects of a wildfire. The way we decide which structure an author is using is by looking for signal words. Next, we ask ourselves, "How did the author teach me about this topic?" and "How did they build their ideas?".

These readers are highlighting signal words they find in their article. With the help of their
foldable and graphic organizers, they can determine the structure of the text.

Writers, how could this information we have learned about text structure help us when writing an informational piece?

Readers, why is it important to uncover the structure of a text? Why does it matter?

Justifying Area

Our recent emphasis in the Math Workshop has been with estimating and justifying the area of irregular shapes.

One tool that we have used to justify the area formulas for rectangles and right triangles has been the Geoboard.

Formula for Rectangles (Area = Base x Height)
Formula for Triangles (Area = 1/2 Base x Height)




Consider the irregular polygon shown on the Geoboard template below.

What is the area of this pentagon?  During Math Workshop, we have approached the task of finding solutions to problems similar to this by decomposing the figure into smaller rectangles and right triangles so that we can use the area formulas for the smaller parts and then put those smaller totals together to find a justified total area. 

The green rectangular area in this pentagon has a base of 3 units and a height of 2 units, so the area of this rectangle is 6 square units.   Area of a Rectangle  = Base x Height, so 6 = 3 x 2.

The right scalene triangle (red) shown on the grid is exactly HALF of 2 square units (the dotted lines are shown to illustrate this idea). 

Therefore, the area of the triangle is 1 square unit.
Area of a Triangle = 1/2 Base x Height

The base of the triangle is 1 unit and the height of the triangle is 2 units.
(1 x 2) ÷ 2 = 1

A right scalene triangle is exactly half of a rectangle. 

The right isosceles triangle (blue) shown on the grid is exactly HALF of 1 square unit (the dotted lines are shown to illustrate this idea). 

Therefore, the area of this triangle is 1/2 square unit.

Again, Area of a Triangle = 1/2 Base x Height

The base of this triangle is 1 unit and the height of the triangle is 1 unit.

(1 x 1) ÷ 2 = 1/2

A right isosceles triangle is exactly half of a square.

All decomposed parts are then combined to identify the total area of the figure. 

The area of the pentagon is 7 1/2 square units!!

Students, you can have fun with virtual Geoboards by clicking the link below, which will take you to the Virtual Library of Math Manipulatives. (A parent may have to install Java in order for you to utilize this site.)

Click Here: VIRTUAL GEOBOARD FUN

Also, if you would like to practice with transformations, you can click the links below for some more virtual fun! 

Virtual TRANSLATIONS (Slides)  

Virtual REFLECTIONS (Flips)

Virtual ROTATIONS (Turns)

If you utilize these online resources, leave a comment to let your teachers know so you can earn some extra Behavior Bucks!

Author's Purpose: Bringing the FAT-P to Readers' Workshop

We all know that the Super RUPR has a trusty sidekick, the FAT-P.  Culinary Court writers came to rely on these superheros when preparing to respond to a prompt.  But how can Culinary Court readers use the FAT-P to help them as they're reading?

First, let's remember what FAT-P stands for:

Format
Audience
Topic
Purpose

As writers, we've learned to always keep our audience in mind.  We should be aware of them and write to help them understand our main ideas and purpose for writing.  As readers, we can remember how we planned our writing specifically to support our main ideas and make our meaning clear to our readers.  And, if we did this as writers, wouldn't it seem logical that professional writers might do this to help us?

We know authors write for a variety of purposes. We know three main purposes are to explain (teach), entertain, and persuade.  Often the format an author chooses can help us determine the purpose, but it's not always that simple.  Being the sophisticated readers we are, we know that writing purposes often overlap.  One piece of writing might be written for more than one of these purposes.  For instance, in the poem "Dreams" by Langston Hughes, we know that Mr. Hughes is writing both to persuade and entertain.

Dreams

Hold fast to dreams
For if dreams die
Life is a broken-winged bird
That cannot fly.
Hold fast to dreams
For when dreams go
Life is a barren field
Frozen with snow.

~Langston Hughes

As we discussed in class, the main purpose of this poem is to persuade readers, but Mr. Hughes also wanted his reader to be entertained, which is why he chose the format of a poem.

Considering the format and genre of a piece of writing can be very revealing when discovering an author's purpose, but there are exceptions.  For instance, we've read many pieces of text recently about slavery and the Underground Railroad.  The Storyworks article, "From Slavery to Freedom", is jam-packed with facts and details, teaching its readers all about Harriet Tubman and her accomplishments on the Underground Railroad.  It isn't surprising that the main purpose of this article is to teach or explain, as articles are most commonly linked with informing.  However, any story that is also based on true facts, such as Henry's Freedom Box, is also written to teach.  Authors of true stories, or narrative nonfiction, considered their audience and topic when they determined their format, selecting a format that would allow them to teach while they were also entertaining.  As another example, folk tales and fables, though they are considered a genre of fiction today, were originally told to teach or explain.  Because newspapers, magazines, textbooks and the internet did not exist when these stories were first told, elders orally told tales, or stories, for the purpose of explaining parts of the natural world, such as why the tortoise has a "cracked" shell, and teaching life lessons, such as the importance of telling the truth.

Understanding the main purpose is just the first step to determining the complete author's purpose.  An author's purpose also includes the main idea of the piece.  Take, for example, this blog post.  Considering first the format, a blog post, we begin to understand that this article is written to inform.  But readers will miss the boat if that's all they know.  What are the important main ideas of this blog post?  What lessons am I, the writer, trying to teach my audience?  Combining the main idea(s) of a text with the purpose will help a reader fully comprehend what they've read.

In the coming weeks, readers will analyze a variety of nonfiction pieces to determine how the author organized their writing to support their purpose.  We will use signal words and identify important ideas within each text to determine what text structure, or organization method, each writer used.  Then, we'll use this understanding to help us create a complete author's purpose statement.

***Psssst!  Reader-writers, did you spy an idiom in this post?  Where is it?  What does it mean?***

The Need for Speed

Running the CCE Track

Today all of the Culinary Court kiddos ran their fastest as they were timed running a 58 meter dash and a trip around the CCE track. Mr. Pinchot and Mrs. Phillips recorded each students' individual running times so that we can take this DATA and determine how fast each child can run (from meters per second to miles per hour averages). Students will practice calculating speed (distance divided by time) and then correlate these times to speeds of several common animals (cheetah, etc.). We will also compare this data with information we collected in another previous lab on rolling marbles down various sized ramps. Correlating these experiences to our text (Ch. 6, Lesson 2) will be a piece of cake.

In addition, on our bus ride to MOSH, we experienced speed, acceleration, and velocity first-hand, which made for some interesting conversations both during the bus ride and after we returned to school!

Parents, be sure to ask your child about the above-listed terms while you are traveling together in your car. You can also ask your child about friction, reference points and relative motion. Your child should be able to explain what all of these terms mean. :-)

Happy Sciencing!!

Multi-Digit Multiplication Makes a Transition

Our work with multi-digit multiplication has certainly made progress over the last few months. Here is a review of the development of this learning trajectory:

Multiplication Cluster

This strategy of decomposing one of the factors has empowered students to learn how to solve problems using mental mathematics. It has reinforced the concept of multiplication in that one factor represents the size of groups while the other factor represents the number of groups.

Open Array Model 

This model has been fantastic as we have made sense of multiplication with larger factors because it has helped us not lose sight of the value of each factor and it has enabled us to decompose BOTH factors and keep track of finding all of the needed partial products.

Transition to the Traditional Algorithm

Recent efforts in math have been to use this model (which also decomposes both factors like the open array does) to understand how and why the traditional algorithm works. With this model, we practice multiplying in the same order that is used with the algorithm, but without the succinct regrouping. *Notice that the SAME four smaller problems solved here match the four smaller problems in the open array model above. These SAME four smaller problems are also calculated in our heads when using the traditional algorithm (below) too!

Traditional Algorithm

Aah......our final destination. Now that we have explored the concept of multiplication so deeply, we feel our students are ready to truly understand how and why this succinct strategy works. They must be able to explain it, though, if they are to use it as a primary strategy in class.
Can you see how all of these strategies are related? :-)

Deep conceptual understanding is realized when one can solve a problem in multiple ways and make connections between strategies and models in how they are related and why they work. Mathematical conversations have never been more fun!

Force and Motion

Gravity is a force that pulls objects toward the center of the larger mass (which is always Earth since we are always on this planet). All matter (anything that has mass and takes up space) has gravity though- a pencil, a piece of bread, a paper clip...... we just don't feel the effects of gravity on these smaller objects (and our own gravitational pull) because the Earth's pull is SO much stronger than everything else.

A force is a push or a pull. A force can give energy to an object causing the object to start moving, stop moving, or change its motion. Forces occur in pairs and can be either balanced or unbalanced.  
Some examples of forces are gravity, friction, air resistance, and magnetism

Balanced forces do not cause a change in motion. They are equal in size and opposite in direction
In our lab on changing a marble's speed, we learned that gravity is one of the forces acting on the marble, which is why it rolled down our ruler ramps when we released it for each of our trials. We also learned that friction was another force acting on the marble, which helped the marble slow down and eventually come to a complete stop after it rolled down the ramp and across the floor. Once the marble came to a complete stop, the forces on the marble were balanced (and there was no longer a change in the marble's motion).
Forces were UNBALANCED while the marble was rolling down the ramp and across the floor. Any time there is movement with an object, forces are not balanced.

In this Tug of War example, forces are NOT balanced. The group on the left is pulling with more force than the group on the right (the group is moving in the direction of the greater force).

In this Tug of War example, if both groups of people are pulling in opposite directions with the same amount of force, the rope will NOT move and forces will be balanced.

If two forces are working in opposite directions (against each other as in the Tug of War example), we subtract them. If we could measure the force that the left group is using to pull the rope in their direction and that the right group is using to pull the ropes in the opposite direction, we could subtract those forces to find the NET FORCE.

In contrast, if two force are working together in the same direction, we add them together. Person 1 + person 2 + person 3 (all on the left) are working together to pull back to the left. If we add their individual pulling forces together, we would get their combined total force.

Click here to review balanced and unbalanced forces: Quiz Yourself 

For Behavior Bucks, leave a comment offering two new examples- one for BALANCED forces and one for UNBALANCED forces.