When it comes to math, multiplication is the meat-and-potatoes of 3rd grade. By the end of the school year, the children will know fluently their basic multiplication facts! Those they don't have memorized, they will be able to attack with several mental math strategies they've acquired throughout the year. This week, we have begun to lay the foundational work for understanding what exactly it means to multiply.
The visual model most commonly used to conceptualize multiplication is the array. An array is a group of objects arranged in equal rows.
The children are taught to think of the multiplication symbol as saying "rows of" or "groups of." For example, 3 x 2 means three rows of two or three groups of two. If a student were trying to figure out 6 x 5, she could use counters to create 6 rows of 5, as in the array pictured above, then count the total. The more hands-on experience the students have with arrays, the better they are able to conceptualize multiplication as the addition of groups. Being able to visualize groups will eventually help them mentally solve multiplication.
Today we played a game to practice creating arrays. Partners took turns rolling a die twice. The first roll told them how many rows they needed. The second told how many counters should be in each row. Then they added to find the total. After 5 turns, they added all of 5 of their totals. Whoever had the highest score won!
Our first conceptual humanities unit is called "Building a Community." During this unit, social studies and language arts standards combine to form a study of civics and government. We began by learning about "rights," the protection of which is the foundation of any civilized community. You can read more about our discussion of rights here.
Last week our unit lead us to think about how rights are in play in the classroom. In partner groups, the students brainstormed what rights we have in the classroom. Then, partner groups combined to form small groups who refined their lists to make them even better. As a class, we shared and consolidated our lists of rights and brainstormed what rules we could put in place to protect them. The students pointed out that some rights are protected by me and some are protected by them. Conversations like these bring out such interesting comments and connections from the students each year. This year it was very important to the class that they be acknowledged for their hard work!
Finally, we used our list of rights and rules to create our class constitution. By creating and signing our own constitution, the students gained a sense of power and ownership over the culture of the classroom along with an intrinsic understanding of the nature of rights and laws.
Our first conceptual humanities unit has begun, and we are building understanding from the ground up. As noted in your curriculum map, the unit is called Building a Community. During this unit, the students will develop an understanding of what it takes for a community to function. We begin by learning about our rights and the laws that protect them, then move on to the levels of power in the government and how elections work. We look at all of this through the lens of "cooperation." After all, society cannot function without cooperation between the government and its citizens.
To get the students in the right frame of mind, we began the unit with a creative writing activity. "Imagine a world with no grown ups, no leaders, and no rules. What would it be like?" Their writing was very thoughtful and entertaining, and contained mixed opinions of what that world would be like. Some were nightmarish, some were a kid's dream come true! Putting themselves in this imaginary situation paved the way for an important conceptual discussion about whether we really need leaders and rules.
Over the next few days we did some processing activities and reading to develop an understanding of the concept of "rights." We came up with our own definition of rights - something you can do that no one can take away from you.
We later had a meaningful entry point into the relationship between rights and laws. It all started with our classroom recycling bin. In the first few days of school, I began to notice food items and tissues in the bin. I sat the class down and reviewed what sorts of items do and don't belong in the recycling, and called their attention to the bold sign above the bin that says, "Recycling." Unfortunately, the problem persisted. My next move was to enlist the help of some middle school girls. Our school's recycling program is run by the middle schoolers, so they came and taught a hands-on lesson to the class where the students sorted items into "recyclable" and "non-recyclable" categories. Spoiler alert: the problem persisted.
Perusing through NewsELA.com, one of my favorite resources for current event articles written for kids, I happened upon an article about the waste crisis in Malaysia. Perhaps you've heard that Malaysia is closing hundreds of its recycling plants and returning waste to countries who recycled incorrectly. When bags of recycling are tainted by old fruit and other trash, the entire bag cannot be recycled. The effect becomes exponential when we're talking about 55,000 tons of contaminated waste! That's how much was sent to Malaysia's recycling plants, and that's how much they are stuck with, since it cannot actually be recycled. Because of this, the Malaysian government has created new regulations and is no longer accepting other countries' waste.
Reading this article, the students were able to see beyond the scope of our classroom to the potential global effects of irresponsible waste management. After reading and discussing the article, I posed a writing prompt to the class:
Do we need rules and laws? Why or why not? Use an example from the text to support your answer. Every student was able to make the connection between Malaysian citizens' rights to have a clean environment and the necessary laws about waste management. Not only did this activity help them to understand the consequences of their actions, but it also gave them a reality check: A world without rules would be chaotic and full of negative consequences.
I'm going to level with you -- the students are still putting trash in the recycling (insert face-palm emoji here). But at least they are beginning to understand on an intellectual level the relationships between actions, rights, and laws.
Next week, we will develop a list of what our rights are in the classroom. We will then decide what rules we can put in place to protect those rights. Their ideas will be put together to form our class constitution! Blog post to come!
What is it made of?
Hundreds, tens, and ones, of course!
4 hundreds, 6 tens, and 3 ones, of course!
True. But is that the only answer?
This is the question that we pondered this week in math. Students worked in groups to show 463 using a different amount of hundreds, tens, and ones.
In the picture below, you will see the different group's solutions. How can we be precise? I asked. Precision was our "habit of the week" last week (blog post coming soon), so we thought about ways we could double-check that our new representation still added up to 463. We decided that the surest way would be to use the paper/pencil addition method to add up the hundreds, tens, and ones. This allowed us to practice a new mental math strategy: add a 0 to the amount of tens you have to figure out what number they represent! For example, 17 tens equals 170! You can see in the left column that we tried using 15 for the value of the tens, and we didn't get the correct answer. We needed to put 150!
Decomposing numbers in this way builds flexibility in the students' minds, which is important when trying to understand how numbers work, exploring relationships between them, and refining our mental math strategies.
As we know, it takes practice to build flexibility. We practiced our mental flexibility by playing a mathy version of the classic card game War. In this version, each card has a description of a number on it.
Each player flipped over their top card, then used our addition strategy to figure out what number it represented.
Just like in the classic game, whoever had the higher number won that round.
You've seen homework this week with similar number riddles. If your child found them difficult to solve, don't be afraid to make up some of your own and practice adding them up! Just choose a certain amount of hundreds, tens, and ones, and make sure that at least one of those numbers is greater than 9.
It's the beginning of the school year, and the 3rd grade walls and bulletin boards are bare. They are ready for a new class to come make their mark -- to make their classroom their own. Having a sense of ownership over one's environment can help students to feel safe and secure when they are at school. And as you probably know, a child who feels safe and calm is ready to learn!
We spent the first couple of days of school creating our class birthday chart, daily schedule display, and environmental print labels. These activities allowed the students to have fun and be creative, while simultaneously allowing us to practice our classroom procedures. For example, in order to decorate a label we need to first learn where the art supplies are and what the rules are for how to use them. In order to sit and work, we need to first learn where we are allowed to sit and what the rules are for that type of seating. If a student finishes her work early, she learns what her "I'm Finished" choices are. Transitioning from one activity to another, we learn procedures for following a signal and cleaning up. In this way, the students were creating their environment and familiarizing themselves with their environment at the same time.
(In the slideshow below you'll see that one student is working on our collaborative puzzle, one of our "I'm Finished" choices).
In addition to helping decorate the room, the students also got the chance to explore the different areas of the room and discover their purpose through a scavenger hunt! Working in pre-assigned pairs, the students had to locate 6 specific areas of the room and complete a task at that area. Each task was designed to help them understand more about how to use that area. For example, one task was to locate the construction paper, cut out a design, and put the scraps in the scrap paper bin. In doing this task, the students learned where the paper and scissors are kept, as well as what to do with their leftover scraps! Watch the video below to see them in action!
You can read more about the 3rd grade classroom environment in this week's Shabbat Shalom. Have a great week!
Our last conceptual unit of the year is called "The Changing Faces of a Story." During this unit, we read lots of different stories and discuss the element of change. This could be a change of heart that a character experiences, a change in setting, or even a cultural change as a story is told across the world! One of my favorite lessons in this unit is in the very beginning, as the students begin to articulate what they already know about change. In the video below, groups of students work to make a list of things that never change. How many can you think of?
Some items were not able to be agreed upon, such as "water." At first you might think, "Of course water changes! It changes from liquid to solid!" But isn't it still water? Just frozen water? This was a very rich discussion in our class, and we had students on both side of the debate. Discussions like these help us to practice a very important way of thinking: that the purpose of discussion is not to be right, or to prove someone wrong, but instead to sharpen our own way of thinking! A tough concept for 3rd graders, but an important one no doubt!
Third grade is the year of the essay. This is the year that students build upon their prior knowledge of what makes a complete sentence and what makes a good paragraph, and put it all together to create works of writing that contain multiple paragraphs around the same topic, complete with an introduction and a conclusion. Throughout the year we have practiced several elements of essay writing, like creating a "lead" that will hook your reader, and leaving the reader with a call to action or a look to the future in the conclusion.
Our most recent essay writing venture included a new element: the authentic audience. Writing for a real purpose tends to bring out the voice and passion of the student, as well as helps the student to understand the importance of good writing. Who is our authentic audience? Teachers!
The students have been working hard to create a persuasive essay that will convince hesitant elementary teachers to try teaching a specific economics project. The 3rd graders were shocked to hear that most students don't learn economics until high school! Why is that? Many teachers are afraid! They are afraid the concepts are too difficult, that they don't have time to teach it, or that young students won't find it interesting. I told the class that even though I go to conferences and talk to teachers about how fun it is to teach economics, they would most likely be convinced if they hear from the students themselves!
After exploring the concept of persuasion through advertisements and a fun simulation (from which I sent pictures via email), we brainstormed what fun lessons and projects helped the students learn economics this year. Ideas included the mini-economy, our class business, The Lemonade War, Arthur's Pet Business, and play-dough economics activities. I asked the students to consider their journey of learning, and which of the activities would stick with them the most once they leave 3rd grade. Each student chose a topic and began to write, hoping to persuade elementary teachers to try it.
Here is a video of students finishing up their final drafts (a couple of them were already finished, so they are working on other things). I highly recommend stopping by the 3rd grade hallway to read their final products!
Enjoy the photos below from our March market. For the first time ever, we incorporated our school community! The 2nd graders, as well as a few teachers, stopped by to check out the shops. They were each given 10fbm's to spend. Knowing the market of consumers would be more diverse this time around, a few of the businesses made adjustments. Hover over the pictures to read all about it!
Our February market was one of the best mornings of this school year to date! I sat in awe observing the 3rd graders as they showed interest in one another's accomplishments, negotiated prices, made informed decisions with their money, and moved through this open-ended activity with such harmony. You could feel it in the room, this energy of excitement, busyness, learning, and doing.
The businesses themselves were the same as the previous market, so I won't add captions to the photos (see previous post for descriptions). However, there was one new business -- Yakira's spin art! As you can see in the photo, this addition was quite a hit!
The great thing about having repeat businesses at the market is the opportunity for improvement. Iterative learning is all about doing an activity or project more than once, so that students can reflect, make a change, and observe the results. Lila and Leon added a service to their business -- body painting! Dovid-Meir and Rena added more good outcomes to their game. Even Yakira, whose business was new, decided to raise her prices midway through the market in response to her product's popularity! I also made an adjustment to my ticket-selling business by adding experiences that were recommended by my consumers (the students). They said they wanted to be able to purchase time on our class computer as well as time on the brand new HUGE computer in the computer lab. I added those tickets and made sure to explain to the class that smart business-owners listen to what the consumers are asking for.
Iterative learning doesn't just happen. Students need some support and prompting to help them make the most of the process. One important step in this process is reflection. After each market, the students sit down to reflect about their experience and to develop ideas for the next market while it's still fresh in their minds.
I'm always so delighted at how collaborative the mini-economy and markets become. This student recommended that I sell classes that the students can pay for. This idea completely blew my mind! In 4 years of teaching economics this thought had never occurred to me! When given the opportunity, children have the capacity to teach us so much.
I'll leave you with what the students said they enjoy about the market experience:
Our next market will take place Friday, March 29th. Keep your eye on the blog!
Did you know every month our class holds a classroom market? It's true! And what's more, it is the students who run the show!
Market day is where our growing knowledge of economics comes to life! The students have prepared for this day by creating our class currency, earning their weekly salaries, creating business proposals to sell goods or services, and advertising for their businesses using posters, invitations, and word-of-mouth. Market day usually takes place at the end of every month; however February's market will be tomorrow due to some scheduling conflicts. More details about the creation of our mini-economy can be found here.
Let's take a look at the fun!
Here are some pictures of the students at their various booths during January's market. Hover over each picture to read a description of that business.
I ran a business at the market as well, selling tickets for special class privileges, such as time on the iPad or bringing a toy to recess.
Now take a look at the market in action!
Little people, big minds.