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Final Fractions Block- 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.

Fraction Review

Fraction Review

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.

Garden Fractions

Garden Fractions

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.

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Equivalent Fractions/Fractions in “Disguise”

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.

Adding and Subtracting Fractions with Like Denominators

Adding and Subtracting Fractions with Like Denominators

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.

Adding Fractions with Unlike Denominators

Adding Fractions with Unlike Denominators

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.

Improper Fractions

Improper Fractions

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.

Wet-on-wet Watercolor

Wet-on-wet Watercolor

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.

Multiplying Fractions

Multiplying Fractions

Dividing Fractions

Dividing Fractions

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.

Norse Mythology in January- Third and Fourth Grade

In January our classroom was full of back-to-school energy after winter vacation! It was fun to see the girls return with stories of their adventures over break, and enthusiasm for sharing. We began with some journaling. I had them write for 20 minutes about anything they wished to share about their winter vacation. Then I read excerpts from my own journal I wrote in fourth grade. We discussed how helpful it is to get your thoughts on paper, especially when facing big life changes and transitions.

Next, we worked on a couple form drawings to get us back into our class rhythm. The fourth graders started with a Celtic knot and then progressed to creating small Norse characters with knotted bodies for their Table of Contents pages. Emma practiced a mirror form to border her Table of Contents.

Norse Knot Creature

Norse Knot Creature

Norse Knot Creature

Norse Knot Creature

We returned to Norse stories with the tales of Balder-the God of Light, Heimdall- the Watchman, and learned how Njord, Frey and Freya came to live with the other gods in Asgard. Freya is the first goddess to be introduced in greater detail, and she rides in a carriage pulled by grey cats. Needless to say, the girls love her.

Balder, God of Light

Balder, God of Light

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Freya was the basis of our main lesson bookwork at the beginning of Week Two. We completed a drawing and recalled the story before they began their independent writing. I was very pleased with the students’ focus and motivation to improve their writing this week. The fourth graders each wrote 7-10 sentences on their own about Freya, which required some tricky summarizing of multiple days of stories. In addition to their ability to sit down and write on the rough draft day, they each returned the next day with fresh eyes and willingness to identify any weak sentences and areas for revision. We discussed how self-editing will be a useful skill for the rest of their school career, and that even the most accomplished writers find it difficult.

Freya and her daughter, Noss

Freya and her daughter, Noss

 

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To add another necessary skill to their toolbox, we introduced dictionaries this week. The school used some of the materials budget to purchase 5 student dictionaries for my class, and the girls love them! It is yet another example of how their enthusiasm for knowledge and learning catches me off guard and brightens my day. I asked them to first alphabetize their spelling words, then look up the definition to each. Though they did not all finish their lists, they quickly learned strategies to speed up their searches. We will continue to practice using the dictionaries in various ways throughout the semester. Now that the students know how to use them, they are hungry for new words!

On Thursday we painted an image of the rainbow bridge, with Heimdall in the center keeping watch. This required a good sense of spacing to fit in all of the colors of the rainbow across the page, as well as control over the brush while lifting off color to form Heimdall’s body.

Heimdall watching over the Rainbow Bridge

Heimdall watching over the Rainbow Bridge

This week, in addition to writing about Freya, the students drew and composed sentences about Bragi, the God of the Bards. Since the story explained how the beauty of verse was introduced into our world, it began our class exploration of poetry. We started simply, with each student describing herself with words that use the letters in her name. They completed this in their journals on Friday, and we will continue to add to them.

Bragi, God of the Bards

Bragi, God of the Bards

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Our final activity for the second week was a dramatic reenactment of the Valkyries and the Valhalla. This was my special treat to the girls for working hard all week, and they really got into the story! We used props to help us embody the warrior women who pick up fallen heroes from battle, and bring them to feast and fight for eternity as Odin’s heroes in Asgard. It was hilarious, and I’m sure they’d be eager to provide your families with a replay!

In our final week of Language Arts, we tackled the stories of Frigga and her Goddesses, Freya’s Necklace and Idunn’s Magical Apples. With a short week, we limited our writing work to summarizing last week’s reenactment of the Valkyries and the Valhalla. I began with a lesson on paragraph construction. We discussed the key components of well-structured writing, and that a clear structure helps the reader follow your train of thought. I gave plenty of silly and confusing examples of jumbled writing, then we wrote a 5-sentence paragraph together about the Valkyries. With an example before them, the 4th graders were challenged to limit themselves to writing only 5, well-composed sentences about the Valhalla and the life of warriors in Asgard. Emma went straight to copying our group paragraph into beautiful cursive in her main lesson book.

Our drawing of the Valkyries took us multiple days to complete, as it included many women on horseback and a battle scene. It was a challenge, and had us all marveling at the complexity of drawing a horse’s legs!

The Valkyries and Odin flying over a battlefield

The Valkyries and Odin flying over a battlefield

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We fit painting in on Thursday, and reveled in the vibrant colors of pink and purple. The students were directed to place strong Prussian blue and Carmine red on their paper, and then had the freedom to explore the wide range of shades in between purple and pink. We threw out many names for the hues as they were unveiled, and I challenged them to try and achieve a smooth, gradual transition between the colors. Though this was a color experience without a clear form, it was challenging and required good control over the amount of pigment and water used. The girls were pleased with the results, and it was a nice release after our precise and focused work on the drawing. The wide, steady, sweeps of a brush during wet-on-wet watercolor is wonderfully soothing, and smoothes out the self-criticism that creeps in as we take on more challenging art projects.

We are continuing with daily math practice each morning.  Over the three weeks we reawakened our memories of fractions from before break, and practiced putting a range of mixed numbers into increasing or decreasing order. We also kept fractions alive in word problems and math games to help prepare us for our next block.

We continue to rotate between silent reading and our group reading of “Abel’s Island” in the last half hour of each day. I take ten spelling words from the reading each week, for our Thursday quizzes.

In Circle we learned a poem about winter, and sang songs that incorporate more movement and marching. This really woke us up in the morning, even on the sleepiest days! In our King Winter song, we progressed from first marching all together, to maintaining various rhythms of claps and instruments simultaneously. This is a great challenge for students to maintain contrasting rhythms while continuing to sing together as a group. Additionally, I incorporated some coordination games that worked on our dexterity and required crossing our midline, adding to the element of challenge and fun.

Our Winter Song used in rhythmic work:

King Winter is now in the land.

He reigns with cold and freezing hand.

He makes Jack Frost touch nose and toe, and brings us bright and shiny snow.

Fractions block 3rd and 4th grade- December

After returning from Thanksgiving break, the third and fourth grade class began our second math block of the year. With a solid preparation in arithmetic skills from earlier in the fall, we were ready to introduce the idea of fracturing whole numbers into smaller pieces. We wait to work on this concept until students are developmentally able to understand how a whole object can be made up of infinitely smaller parts. To keep fractions from becoming too abstract, too quickly, we spent the majority of this first block using our hands to divide real objects into smaller and smaller pieces.

I began with a dramatic demonstration of fracturing, by channeling my inner ‘Thor’ and smashing some ice cubes with a hammer. Each student took their turn, and as we cleaned up the bits, we took note of the wide range of sizes of the pieces. Though it was a dramatic and entertaining method of breaking something, we all agreed that when you are put in charge of splitting objects in real life, you often want them to be evenly divided. After the ice, we progressed to splitting an orange, and discussing many hypothetical pizzas, pies, and cakes until our mouths watered. In addition to many food examples, one of our class parents lent us some of her home school fraction tools. These provided us with great new options for hands-on building and rearranging of fractions. The combination of food and tools allowed us to introduce many different ways of dividing shapes, and practice identifying halves, thirds, fourths, eighths, etc.

To further aid in this process, we began a new main lesson book for Fractions. Each student received 10 paper circles at the beginning of the block. Since I lead most of our watercolor painting, I decided to provide the students this chance to choose their own color combinations for each paper circle. They loved it and were pleased with the outcome. Once the circles were beautifully painted, we began with a page dedicated to “One Whole” with a simple full circle. From there, we progressed incrementally up to sixteenths with the appropriate slices cut from the paper circles. It is amazing to watch how much better the students are able to conceptually understand dividing a circle, when they do it with their own hands. Through drawing the lines, splitting the wedges in half, and cutting on their own, it began to sink in. Labeling the slices with the proper notation allowed the students to learn the written form through their recognition of the corresponding illustration. The different sized wedges also provided a basic visual understanding of equivalent fractions before I ever formally introduced it in class.

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Whole

 

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Halves and Fourths

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Sixths

To encourage a flexible understanding of notation, I progressed from asking math questions orally to writing them on the board as well. I wanted to cement the connection between the visual shape of a fraction, its written name in notation, and its oral name. As we worked on this, we transitioned into identifying other real-life scenarios that incorporate fractions. Our list was a great review of their measurement blocks from last year including time, length, weight, liquid volume, distances, money, etc. This allowed us to move from merely dividing shapes to considering fractions of groups of things, as well as other numbers. For example: How many years are in ½ of a decade? Or how many minutes are in ¼ of an hour? Or simply what is ¼ of 20?

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Rectangle Fractions

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Time Fractions

Seeing these problems written out helps us transition from thinking through the concrete act of cutting something into pieces, to carrying out the mathematical operations of multiplication, division, addition and subtraction on fractional numbers. We have just begun simple multiplication of fractions such as ½ x 2= 1 and ¼ x 24= 6. The students are noticing how helpful knowing their multiplication tables is for working with fractions! We will continue in the next block to manipulate increasingly complex fractional numbers, as well as to work towards a real understanding of what you are doing to a number when you multiply versus divide it by a fraction.

For reading work during this block, students read any time they finished their work or were waiting for me. They have independent silent reading during our extra time at the end of the day, at least once a week. Tuesdays, we have reading group all together. I have been very pleased to watch as group reading helps the class work on patience and cooperation with each other.  Our current book is “Abel’s Island” by William Steig. It is not a long book, but it is demonstrating an impressive range of vocabulary and keeping all of us on our toes! We revisit many of these words on our weekly spelling lists and quizzes.

For our class stories at the end of each main lesson, I continued reading “The Magician’s Nephew” by C.S. Lewis. We were all captivated, and it was a great change of pace from our math work. We managed to finish the book for a satisfying end to the block, just in time for winter break!

Human and Animal block 3rd and 4th grade- November

In the fourth grade curriculum, “Nature Studies” from the earlier grades, transitions into the “Natural Sciences”. With our first Human and Animal block, our class explored what it means to be human and looked at our relationships with the living beings and environments that surround us. Our study really began and ended with the human form. We started by discussing the shape and functions of the three main sections of our bodies: head, trunk, and limbs. Once we discovered that function follows form, we began to move outward and compare these aspects of our bodies to those of various animals. Through this comparison, we found that we share much with many different animals, and that these similarities provide us with a wide diversity of physical abilities.

The Three Parts of the Human Being

The Three Parts of the Human Being

The Human Body as the Sun, Moon and Stars

The Human Body as the Sun, Moon and Stars

While maintaining this sense of connection to animals, we also discussed what sets humans apart from other animals. Our unique ability to walk upright gives us the use of our hands to do many incredible things. The students were asked to reflect on what we use our hands for, and the power that this gives us. As third and fourth graders, the students are becoming very curious about their role in the world. We discussed the responsibility we all have to use our hands to do good work, and how exciting the possibilities are. With the creative power of their minds and the dexterity and skill of their hands, they can do anything! This wondrous realization will continue to help assuage the hints of jealousy they feel as we discuss some of the impressive abilities of other animals.

A Reflection on the Senses

The Five Senses

During these discussions of other species, and the artistic process that followed as we drew each unique animal form into our main lesson book, the value of incorporating the arts really struck me. We all carry around images of animals in our heads, as well as impressions of who they are and how they behave. For the fourth graders, many of whom have had the Waldorf experience since kindergarten, these images were developed out of fairytales and fables. Those rich stories fed their imaginations and helped them form an initial emotional connection to animal characters. Paired with outdoor play, nature studies on school hikes, and general outdoor exploration, they began to form their own understandings of animals while maintaining awe towards the power of nature’s mystery and wonder. As a teacher, I wanted to maintain this deep, imaginative relationship each child has to the animal kingdom while moving towards a more analytical understanding of biology. Fortunately, this question is answered by the rich artistic component of our curriculum.

Wet on Dry Watercolor- Eagle

Wet on Dry Watercolor- Eagle

Just as in a science lesson, drawing an animal form must be anchored in close observation of your object of study. What I found while leading my class from a vivid mental picture of an animal in its natural habitat to a real-life drawing on paper, is that the drawing process pulled out more nuanced questions and details about the animal’s nature than I ever could have included in a lecture. Best of all, they were generated by the students’ own imaginations! As one carefully shapes a muscular leg of a lion with crayon, one cannot help but wonder at its power and strength. The shape immediately pulls your imagination out of the classroom and into the savannah. Similarly, you cannot draw a dreamy cow’s beautiful eye without pondering what that cow must think about as it chews its cud all day. To draw an animal or human form accurately is to study their whole being with your whole being: hands, head, and heart.

The Cow

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The Lion

The Lion

In three short weeks, we dove into animal behavior and physiology on a deeper level than I could have imagined. Along with drawing, we used song and verse to develop our understanding of the behavior of contrasting animals even further. When used together, music, drawing and poetry serve to breathe warmth into the sciences and ensure the students carry an imaginative, artistic, and emotional understanding of animals with them as they continue biology in later grades.

Gifts from Animals

Gifts from Animals

Norse Mythology- Fourth Grade

The fourth grade language arts curriculum is based on the stories of Norse Mythology. These tales from Scandinavia are full of epic battles, trickery, jealousy, greed, and magic. The excitement and conflict woven throughout these stories speak directly to the transitioning worldview of the nine and ten-year-old child. These Nordic gods are not idyllic and infallible- they are flawed and petty, as well as mortal.  Though they live long lives, they can eventually die, and this adds an element of reality and consequence to their adventures.

The fourth grade student is endlessly curious about the world around them. They are now beginning to be aware of how large the world really is, and they want to know how it fits together. This is the reasoning for including geography and zoology in this grade. The Norse story of Creation, however, also addresses similar questions as these blocks: What makes us human? How do we fit into the world? What role do we play in taking care of the land and animals around us?

An additional part of figuring out who they are and how the world works is the realization that there is room for ‘grey area’ in most things. The Norse myths demonstrate a wide range of moral ambiguity as Odin, the All-Father, attempts to settle disputes between the gods. Unlike the straightforward sense of justice served in the fairy tales from first and second grade, the students are beginning to toy with ‘rooting for the bad guy.’ They love the mischievous character of Loki, and find themselves empathizing with him in his trials.

Language arts blocks provide us with time to process these big questions while diving into story and exploring this rich mythical world. I established a steady rhythm of hearing a new story at the end of one day, and returning to it the next day to complete our application and bookwork portion. We first revisit the story to recall what took place, then work on a drawing in our main lesson books, and finally complete a writing component. The writing is taken from the story, and provides the opportunity to work on a variety of writing and grammar skills. We began the block by creating these written summaries of the story as a class, with me writing the sentences on the board after we reached a consensus on what to include.

After only a few days of this method, we switched to independent composition. To maintain clarity and ensure the students include the most necessary components of the story, I provided a suggested outline on the board. This often got them past the wall of not knowing how to start, and inspired wonderful writing! We increased our independent writing from just a few sentences to between six and nine by the end of the block. We are trying to develop the full writing process from ideas, rough drafts, and editing, to the final version. At this point, the students are able to self-edit for a couple of key elements in their writing, including capitalization and some punctuation. Next, they bring their writing to me for final spelling and sentence structure edits. They are then ready to complete a beautiful version in their main lesson books to accompany their drawing.

When paired with new grammar concepts and spelling work on the side, I saw amazing improvement in both their writing skills as well as their confidence. This enthusiasm comes from watching their rich mental images of the Norse myths translate into both beautiful drawings and words on the page. When I challenge them to do the stories justice, they are proud of their work and it allows the image and feeling of each character to live inside them.

In this first Norse mythology block we heard the Creation story, learned how the worlds fit together on Yggdrasil, the World Tree, and met Odin, Thor and Loki. We will pick back up in January with many more! Until then, we will continue with weekly spelling words, reading group, independent reading, as well as writing composition as it applies to the blocks to come.

Here is some of our work!

The first beings emerging from the fire and fog

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The sun and moon being pulled across the sky.

The sun and moon being pulled across the sky

Yggdrasil, the World Tree supporting the 9 Norse Worlds

Yggdrasil, the World Tree supporting the 9 Norse Worlds

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Odin, the All-Father

Odin, the All-Father

 

Loki and his Monstrous Brood

Loki and his Monstrous Brood