Here are examples of curriculum blocks, lessons, and student work from various classes City Garden School.

A week in the Local Geography Block in Third and Fourth Grade

The third and fourth grade class began the year studying local geography.  At City Garden, we start the study of geography right where we are, in our classroom and at our school, places that the children know very well.

To begin our study, we took a walk around our building and made some detailed observations.  I prompted the children with some questions like, “What is our church made of?” “Does it look like it was all built at the same time?” “What is the building used for?” “Why do you think they decided to build a church here?” These questions help the children learn observation skills. They noticed lots of details about the building and made many guesses about why things were done the way they were!

Then we came back and drew a beautiful picture of the front of the church. As we drew, we talked about the different building materials and uses of the space.

The next day, we completed a piece of writing that we created together as a class about our building and our observations.  We wrote 5 sentences!  We write together in third grade and at the beginning of fourth grade for many reasons. This writing process allows me to work on and talk about spelling and grammar with the whole class.  It also illustrates the writing process and how we can make creative, refined sentences!

Another important aspect of our local geography study is to introduce the “eagle eye perspective” … the perspective that maps are drawn from and one that children are not able to really grasp until third or fourth grade. To further their understanding, they all stood up and made a “map” of their desk from the eagle eye view.

As the block goes on, we continue to move outward and upward. The children worked on a beeswax model of our classroom.  Then we drew a map of our model and made a composition about our experience.  Many of the children mentioned how difficult it was to draw from above instead of from straight ahead!

It was a wonderful week of observing, exploring, and creating!

Math Block in the Lower Grades

In first grade, I want them to be very familiar and comfortable in counting and working with higher numbers. I want them to recognize these numbers and be able to write them. I want them to be able to do addition and subtraction up to sums of 24 on their own, which means they need to be able to hold a number within and count up from that number. I want them to be familiar with multiplication and division and to be able to complete some of these problems with help. I want their rhythmic math work to be refined, so that hand clapping and counting by 2’s, 5’s, 10’s and even 3’s are coming along. And lastly, I want them to begin to memorize their math facts under 10.

In second grade we are bringing many things together. We will be solidifying our understanding of place value, we will be working heavily in the times tables, writing all of them up to our 12’s and seeing the geometric shape they create on a circle of 0 to 9. We will be reviewing rounding numbers to different place values and we will be adding and subtracting higher numbers horizontally and working with different strategies we use in order to so do, trying to create fluidity, ease, and flexibility with these numbers.

In week one, first graders began on the ground with our mining gnomes, putting 10 gems into a bag and counting by 10’s. For example, each of them “mined” 16 gems, then we put all of our gems together, counting by 10’s up to 50 and then adding our 6 extra gems together with everyone else’s. As soon as we get to 10, we put them into another bag and add them to our 10’s. We did multiple problems like this and then had to do some on our own for book work. If you have 3 bags of 10 and 7 extra, how many gems do you have? We wrote our 10’s up to 100 and then wrote a few of these problems. The next day we did the same thing but counted by 5’s forward and backwards and we wrote our 5’s up to 80.  Following this, the next day we had a new story of a shepherd and his sheep and we counted by 2’s over and over again to try to get these memorized. We wrote our 2’s in our books this day. On Thursday we remembered Happy Addy and May and we did some addition work with sums above 10. Now we can’t use our fingers in the same way, so we learned how to hold one number in our hearts and count up from there. We did some problems on our own in our main lesson books.

In week one in second grade, we went straight to the times tables, practicing them by counting aloud and hand clapping, and then by getting on the ground in a circle and throwing a ball of yarn to the numbers as we count them. We worked on our 10’s, 9’s, 4’s & 6’s this week, drawing a beautiful drawing and then writing the times and division tables – so that we start to learn that they have a clear relationship to one another. I usually write half of them, and the students have to copy this and write the rest up to 12.

In this photo you can see that if you count by 6’s, a pattern emerges – 6, 2, 8, 4, 0. If you place this pattern on a circle of 0 to 9, the pattern creates a pentagram. Inside the pentagram, there is a pentagon. We look at all of these things! It is so exciting to see what beautiful geometric shape will arise from each times table. There are many guesses each day as to what shape it will make and then surprise when it might be the same shape of another times table. For example, the opposite pattern emerges with the 4 times table – 4, 8, 2, 6, 0, and so the same shape appears!

In week two, we all worked on addition and subtraction together through the stories of Mrs. Bluebird and Mrs. Fox. These are simple spring stories I created in order to have something we are adding and subtracting, so that the work is more meaningful. First graders worked on adding such problems as 8 + 9, 7 + ____ = 15, ____ + 5 = 14, 16 – 8, 16 – _____ = 7. I used the same story to add higher numbers in second grade such as 25 + 3, 42 + ___ = 49, 85 – 4, 97 – ____ = 92, 23 + 10, 38 + 40, 52 + ___ = 92, 23 + 13, 25 + 16, 21 + ___ = 35 and their subtraction counterparts of the same. In second grade we talked a lot about the different strategies we used to find these answers – knowing that most strategies are not “better” than others. Though we did talk about how counting up on our fingers from numbers such as 52 to 66 we can do, it will not be plausible once we get to math such as 52 + 45, so we need to find other ways! We are adding the tens together and then the ones. We are changing numbers slightly, adding them together, and then changing the answer slightly to coincide with the change we made before we added. It’s always so fun to see all the ways the children can manipulate the numbers! It’s some great math.

In this week we also learned about greater than and less than through the story of an alligator wanting to eat cookies. His mouth opens to the greater number! They loved this and it was also a great way to review and recognize our higher numbers. Then on Thursday we finished up some of our math practice worksheets we’d been doing all week and we played BINGO with our times tables. It was great review for everyone on how to get the answers to our times tables. First graders did their 2’s and 5’s and second graders did their 3’s and 4’s.

Week three of this block brought the first graders to more addition and subtraction, but using a number line. This is another great way to show how numbers can be written. Eyes widened when I told everyone in the room that our number line could keep going and going and going and going – all the way around the room over and over again! We used Peter Rabbit to hop around our number line both forward and backwards.

Second graders did more times tables – we practiced our 6’s again – because we’d all forgotten we’d done them already! It was as if we were seeing it for the first time! Then we did our 7’s and 8’s.

Here is what your children have been seeing each day on the board, and stories continued in first grade for Peter Rabbit, Mrs. Bluebird and Mrs. Fox.

At the end of this week we painted some geometric shapes and then reviewed by doing Dictations, where I say something aloud and they have to write it down. It can be as simple as me saying a number and they have to write it or I say a math problem and they have to find the answer. I am seeing what they can hold in their minds and then write down and I’m also seeing what they know and can do. For some reason, they all love dictations! It’s a favorite! First graders wrote higher numbers, did simple addition and subtraction, and simple multiplication. Second graders wrote higher numbers that involved place value, did some rounding to the nearest tens place or hundreds place, and did some times table work and higher addition.

Fractions in Third and Fourth Grade

In February the third and fourth graders dove into three weeks of whirlwind fractions in our final Math block of the year. I made a huge push to fit in some major fraction concepts into the short time period knowing that our Math Practice periods each morning for the rest of the semester will provide ample time to further hone their skills.

We began with a day of fraction review, to ease back into the swing of things. I pointed out to the students that their instinct has been to complain about math, but they might be surprised by how much they’ve already learned this year! To keep morale up during math blocks, I use gentle reminders of how capable they are to take on difficult concepts, and that I only give them what I know they can handle. As they tackle a challenging task, stick it out through the frustration, and finally gain mastery, these students are gaining the capacity to work hard. Repeated, consistent practice at working hard will benefit them for the rest of their lives.

 

In our review, we quickly worked from the basic picture and notation work in fraction identification, to more complex word problems that are designed to help them transition to addition and subtraction of fractional numbers. This culminated in designing their own ‘dream gardens,’ with labeling the fractions for each crop or flower on a garden map. Though their gardens quickly became more like exotic zoos, it kept them excited. All of our activities remain focused on gaining comfort in visualizing the whole, being broken into smaller and smaller parts.

 

Next, I introduced Equivalent Fractions. I explained that fractions like to behave similarly to the trickster, Loki, from our Norse Myths. They wear disguises to try to confuse us, but with the right tricks, we can reveal what they really are underneath! We learned how to work from a fraction in its simplest form up through its many other names. For example, 1/2 can be 2/4,3/6,4/8, etc. By learning how to write fractions in many ways, the students found it easy to work backwards and simplify fractions the next day.

Armed with this understanding, they were ready to begin adding and subtracting fractions with matching denominators. They were thrilled by the simplicity of the adding and subtracting, noticing that “it’s really just like first and second grade math!” The only added step, is remembering to simplify their final answers down to the simplest form. At this point, all students were able to do this confidently, probably 85% of the time. We continued to practice this skill in all of our examples.

 

We supplemented addition and subtraction with making jumps up and down a number line. This helps me gauge their ‘big picture’ understanding and number sense when it comes to fractional numbers. It is important for the students to grasp how endless fractions are hidden in between whole numbers, and that we can count by them as easily as counting by 2’s and 4’s.

On Friday, before a Valentine Party, my class spent time checking their work from previous days and getting individualized help from me on simplifying fractions. When finished, we dove into some complicated form drawings. Emma practiced a metamorphosis form, that was quite a challenge, and the 4th graders began an intricate Celtic knot. Similar to our math work, I asked them to try something that they found impossible at first. Then, with practice and guidance, their forms became consistent, balanced and lovely. I saw a class that could work hard, and quietly for a long stretch of time, while also supporting and complimenting each other. It provided a fitting and heartwarming mood for Valentine’s Day.

A three-day weekend followed the Valentine party, and we started our week back up with a thrilling celebration on Tuesday in German class for Karneval or Fasching. Needless to say, it was a little hard to come back to math after all of that excitement! To their credit, however, the third and fourth graders managed to take on some challenging fraction work and fit a lot into our short week.

We began by learning “Butterfly Fractions” on Tuesday morning. This was a fun method of setting up their fraction addition and subtraction problems to help lead them through a new complicated process. Now that we are beginning to add and subtract fractions with unlike denominators, they need to keep their work neat and clear to understand each step of the problem. The butterfly structure led them through cross multiplication and solving for the least common denominators. It was delightful to see how the drawing element kept them engaged and led to beautiful main lesson book pages from students who normally struggle with neatness.

 

We continued practicing this on Wednesday with time for all to complete their problems and work through questions with me. As I work with individual students, I am constantly assessing their mood and looking for signs as to what might be affecting their learning. Often, it has to do with their confidence level, and ability to stay calm when faced with uncertainty about a new skill. Especially in the fourth grade, children feel strong waves of emotions in rapid succession. I am sure all of you are seeing this at home. I strive in the classroom to keep us all in the feeling world of stories, imagination and vivacious curiosity, and out of the depths of personal, and fleeting emotion. This can be a challenge as they feel their self-confidence threatened during moments of math struggles, and are tempted to quickly compare themselves to others. Luckily, they love to laugh as much as whine, and our whole day can be saved by a good joke.

Keeping this delicate balance in mind, the stories throughout this block came from daily reading of “The Lion, the Witch, and the Wardrobe.” Though a few students have already read this one, I found it still served our need for release and some thrilling magic after difficult math work. I appreciated the patience of the children who had read it already, as they did a pretty good job in keeping it a surprise for the rest of us!

To infuse the new content with some fun, I decided to introduce how to fix ‘Improper Fractions’ on Thursday as monsters that must be slain! Each student got to illustrate their own monsters in their Main Lesson Book, some scary, many very cute. When I introduce imaginative names for fraction concepts, they are paired with the proper vocabulary as well. I want to ensure that they know the terms without being too bogged down by them, and ultimately have a strong ‘number sense’ for what it all means in terms of fractional and whole numbers.

 

Friday morning was a day of reviewing the week’s new concepts. They got to choose review problems from color coded columns to challenge themselves to try a bit of each category, while getting to do more in the areas they like best. This provided me with useful insight into who is most comfortable with what topics. We ended the week with a beautiful painting of “The Prairie Waiting For Rain.” I told them to imagine a grey-blue sky, over a golden prairie, as the first storm of spring rolls in. We referred to our compass on our classroom walls and discussed which way we might be facing, and from which cardinal direction a storm would move in.

 

In the third week we wrapped up our final math block. The two new fraction skills for this week were multiplying and dividing fractions. After the difficult adding and subtracting from last week, these skills proved much simpler to understand. I revealed that division is simply multiplication with just one easy adjustment, and the students picked it up quickly.

  

The children are strengthening their understanding of the many ways fractions can be written and manipulated, which will provide a strong foundation for all of their fraction work in the future. We will use the remainder of the year to continue to practice and build confidence in all kinds of fraction problems. It provides a chance to mix the newer skills with the old, and allow for plenty of review. This practice will occur both in the morning 15 minutes of math warm-up, as well as during our extra time after lunch. I will incorporate a variety of math games and activities to help us review all we’ve learned this year.

Nature Studies 1st and 2nd grade

Our class spent the last 3 weeks in a Nature Studies block. In first and second grade, Nature Studies serve as science instruction integrated with language arts. A 6 to 8 year old child wonders about the world and asks many questions. Rather than answer their questions with analytic responses, we tell stories that capture the scientific concept while still leaving room for mystery and magic. The stories keep their imaginations alive so that the child can still wonder about the concept and explore it. This is the opposite of responding to a child’s question with a factual answer that often inhibits further curiosity. In telling a story, we meet the child in their developmental place. It is not until 12 or 13 that a child can understand abstract concepts and think critically, and these are mental constructs needed for analytic thought.

By telling a Native American story about The Great Bear in the Northern Sky, where the children hear about four brothers who hunt a great Medicine Bear only to find that they chased the bear right into the starry sky, the children hear about Ursa Major and how it revolves around the North Star in a way they can comprehend. Then they are excited to look up into the night sky and see the Bear from the story they have heard.  In middle school, they will take an astronomy class and learn how constellations in the northern sky circle around the north star and that this is related to our planet’s rotation in space.

Our hope is that the story they heard as a young child helps to foster a sense of wonder in the scientific explanation they receive when they are older. The Native American legend also gives a connection between science and humanities, which helps integrate the scientific concept into its place in history. When he/she is older, the child will remember how people interpreted the stars before modern scientific methods emerged, thereby integrating the new information more fully. We may begin slowly in Waldorf education by waiting to teach reading and writing until 1st grade and by holding off on analytic science instruction until 4th grade, but the rich and deep experience the children receive at appropriate times according to their developmental capacities broadens their outlook and their abilities.

So, I told many Native American legends in this block. We began by talking about the Ais, a Native American tribe from Ft.Pierce, FL – which is where I grew up. I personally learned much about these people this past summer and wanted to share with my class about the area I grew up.  We learned about their homes, communities, tools, foods, and activities along the coast of Florida. I used this opening to introduce three more letters to the first graders and to continue with long and short vowel sounds for the second grade. The next story was an Iroquois legend about the Four Winds. Again, I introduced the last of our letters to the first grade and worked on short and long vowel sounds with second grade. We drew pictures and talked about these stories as a class. We learned how the Ais people made everything from items in nature and how useful it all was. We learned about the seasons in the story of the Four Winds and the type of weather characteristic of each. I told another Iroquois legend called “The Corn Maiden” which explained how they were given corn to grow and eat and then a Penobscot Tribe story that told how they found a second planting season in late summer. Then I told a Salteaux story about maple syrup! With these stories, the first graders began to write sentences into their main lesson books. After all of our letter work, they were ready and they were excited! Second graders helped compose all of our sentences and wrote two sentences into their books following the pictures we drew for each story.  

We finished our block with two stories about the sky. One mentioned above and the other about the origin of the Milky Way. We tried to use birthday candle wax as a resist on our painting paper and then paint a deep purple night sky to show the span of stars – which was cornmeal falling from a Spirit Dog’s mouth as he ran panting across the sky!