February and March Math Block in First and Second 2018

As this is our last large math block of the year, we have many goals to accomplish in these 4 weeks.

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.

I am still reading, The King of Ireland’s Son to everyone at the end of our math lesson. This gives us a breather from all the work. During Reading time, we continue to work in reading groups and to partner read. We are all coming along in our reading skills!

This coming week we’ll continue solidifying these math concepts and will move forward with more complicated work!

Cooperative Games

Read below for a few updates from our Cooperative Games teacher, Mr. Wiles.

December 2017

Greetings City Garden Families!  I hope that everyone is excited for the Holiday Season, which is always a special time for our beautiful children and becomes even more meaningful to us adults as we age and experience further soul growth.  

Cooperative Games class has been such a blessing in so many ways at City Garden.  Playing games for their own sake and for enjoyment is much more fulfilling than playing competitive games that require a winner.  The children truly enjoy the opportunity to exercise their bodies and minds after lunchtime in this capacity and I am honored to be able to guide them through the curriculum as we familiarize ourselves with one another.

The goals of this class are to develop spatial orientation, awareness of our body geography, and equitable play while allowing the children time to process what transpires at the end. These objectives are met through varying left-right, above-below and forward-backward exercises; chanting rhythms or singing songs while skipping rope; circle or line games with an end goal to achieve and a debriefing conversation.  First and second graders are introduced to more basic exercises and games as they are still coordinating their eyes, limbs and sense of balance in addition to processing rules and outcomes.  I might ask them to mirror my movements in rhythm and we will repeat these steps several times as I observe their progress without correcting mistakes.  Third, fourth and fifth graders delve into more challenging movements and games that require greater attention to detail and deeper thinking upon strategy and emotions.  And believe me, emotions can run high during cooperative games!  We conclude games with a light discussion of what worked or didn’t work and how this affects our feelings.  On Wednesdays, first through fifth grades combine for exercises and games appropriate for all ages, often utilizing the school’s beautiful parachute!  It is such a joy to see their interactions in this culmination of the week’s progress.                    

All grades have memorized our opening verse and now enjoy varying the tempo and volume.  After a quick warm up activity to gather our attention, we are ready to begin games. These games generally consist of a vivid opening story that lays the groundwork for rules, rhythm, and piques their interest.  I’ve found that the children are often as interested in these stories as the games themselves and it certainly increases their attentiveness and desire to participate more fully.  Games that we have been enjoying in particular are:

Sharks & Octopuses – One person is the shark. The other children start at the opposite side of the play area as fishes.  When the shark gives the command ‘Come little fishes swim in my ocean’, the fishes try to reach the other side without getting touched by the shark.  If they are touched by the shark, the fishes sit cross-legged where they were caught, and become octopuses.  From a seated position, an octopus can try to touch the fishes that are swimming past every time the shark gives the command.  The fishes who are touched by an octopus also turn into octopuses.  The shark tries to turn all the fishes into octopuses.      

Crows & Cranes – Class is divided into two tribes and given names that begin with the same letter: e.g. Crows and Cranes.  Each tribe has its own territory at each end of the play area.  A drummer beats the drum and the first sounds of the names, (e.g. ‘Crrrr…’) is called out.  The tribes advance towards one another with the rhythm of the drum beat until the drummer calls out the full name of a tribe, e.g. ‘Cranes!’.  The Crows quickly turn round and run back to their territory trying to avoid being caught by the pursuing Cranes.  The captives are led back and ordained as members of the victorious tribe.  The process is repeated until all of one tribe has been caught.  

Wind, Moon, & Rainbows – One child is the north wind, one child is the moon, another the morning star.  The other children are shining rainbows who are scattered across the universe.  (The rainbows make an arc with their bodies on all fours.)  The north wind frees them by crawling through their arc.  With the help of the morning star, the moon finds each rainbow and touches it gently; then the rainbow sits down.  When all the rainbows are seated, the moon catches the north wind.                               

I am unable to express with words how blessed I feel to learn from the amazing teachers and students of City Garden.  I think we can all agree how special it is for our beloveds to be able to experience the fullness of childhood in this most nurturing environment.  Oceans of gratitude to you, City Garden parents, for your ardent interest in our children’s futures!      

February 2018

Hello City Garden families!  Cooperative Games class has been moving and shaking as we have gotten in a good groove together.  I’m impressed how the children have continued to improve with their body orientation and awareness, especially their ability to take on challenging movements that are new to them.  We are trying out a few new opening verses to keep things fresh and interesting, and everyone has adapted well as I expected they would.  We really enjoy the ‘Flee Fly’ verse; many of you may be familiar with, using a hand/thigh clapping rhythm to lyrics with increasing speed.  It imparts some fun word play that the children are naturally drawn to.  I have also introduced some new warm-up exercises such as leg crossovers, heel kicks, lunges, power skips and high knees.  They initially got a hearty chuckle out of watching me demonstrate these exercises, but then quickly realized the difficulty of moving all our limbs in such a coordinated fashion.  They still laugh hysterically when I do high knees with them!  As I mentioned, they have really begun to improve their ability to discern left from right and upper from lower in these movements and it’s great to see their confidence in these abilities bolstered as a result.  

Games have begun to take on more meaning and merriment now that everyone is more familiar with guidelines and expectations, and our closing discussions continue to give us greater insight and help us learn from our missteps.  An exciting new parachute game, Hair Dryer, is providing lots of laughs as it’s a real hair-raising experience!  I am so proud of your children for their continued progress and overwhelmingly positive participation in this class.  Please let me know if any of you would like to discuss games in further detail, come observe, or better yet, take part in a day of games with us.  The more the merrier in Games Class!  We’re looking forward to warmer days when we can take our adventures outside for more fresh air and larger boundaries!    

 

Heroes and Saints in 1st and 2nd grade

Part of a curriculum inspired by Waldorf education for second grade includes stories of saints and heroes from around the world. We tell these stories because they speak directly to a second grader, who is experiencing new intellectual development. Although they may have new faculties of thinking that they did not have in first grade, their minds are still far from mature. You’ll hear second graders have strong opinions such as “I hate that” or “I love this” and the following day, these same antipathies and sympathies have switched! While in first grade they wanted with all their being to please their teacher and be good students, now they begin to experiment with behavior that is naughty. However they still desire to be good. Just like their strong opinions, their behavior can change daily! And so we bring them stories that mirror their development. Fables so they can identify with the animals’ naughty behavior, and saint or hero stories so they can identify with people who have done good in the world.

This past week, our first and second grade class began a Language Arts block on Heroes and Saints from around the world. This week we heard the stories of Hiawatha, St. Werburga and the Geese, and Saint Odelia. We used these stories to draw pictures and write summarizing sentences together and also to begin lessons in grammar. I introduced naming and doing words (nouns and verbs) by looking at the sentences we had written together and picking out these kinds of words. Then we spent some time reviewing all the stories we’d heard, especially all of the kind, generous, and brave actions our saints and heroes have shown us, and we spent some time listing all of the good things we do. We will continue this next week, looking at all of the good things we do at school, at home, and around town.

Above is a chalkboard drawing the children saw all week.

We spent some time in beeswax this week, molding Hiawatha’s canoe while we listened to his story. Canoes will come home this week.

We also spent some time using our benches as balancing beams. We learned how to support each other as our friends walked along them too.

At the end of the week we painted St. Odelia, who had been cured of blindness, and in turn showed her father how he had been blind to his own faults.

 

Enjoy and see you Monday!

 

Winter Spiral Festival

One of the first Winter Spirals I remember was at Garden Gate Preschool. It was a very cold evening. Snow was on the ground. We quietly gathered, hands on our little ones’ shoulders, their hands clutching bright red apples with candles in them, their eyes bright and expectant. The evergreen spiral with snow beneath it was a beautiful sight. Each child slowly stumbled along through the spiral to light their candle and then slowly stumbled outward, placing their candles all very near to each other. Light attracts light! However by the end, the spiral was ablaze with these sweet candles, all symbolizing the sweet souls of the children, their light in our lives.

As we gather together this Friday for our Winter Spiral, we do this as the light begins to return to our dark winter days. We will add to this light, spur it along, and mark this time of year in our children’s memories. Spirals are ancient symbols and natural phenomenons, found in cave paintings, archeological sites, snail shells, and sea shells. Labyrinths have been walked for centuries as part of rituals or simply as a way to calm the mind, reflect, and focus. I can feel how walking toward the center of a spiral brings my thoughts inward and how walking out of a spiral, I see the world around me.

As our children walk into the spiral and light their candle, we surround them on this journey. It is symbolic of our love and guidance. We are here to help them light their own inward path. After they place their candle and walk out, they see their community around them, quietly holding our own lights. They feel safe to be who they are. They know we are ready to step in if needed – in case a candle falls over or blows out.

At the end of our festival, parents will blow out their candles and the only light will be that from our children’s candles, within the spiral. We ask that you preserve this festival in your child’s mind, by leaving with your family at this time. Loud and rambunctious play at the park will erase much of the feeling that the festival created. Our children get many opportunities for this kind of play, but do they get many opportunities for quiet reflection?

Let us create a beautiful space for our children at the Winter Spiral. Let them have this beautiful moment, free from distractions or anything that trivializes the experience. Take some time on Friday reflecting with your family. What did you feel at the Winter Spiral? How does it feel to be quiet and calm? Can we find this place easily or is it difficult sometimes? How do we kindle our inner light? What things make it glow brighter? What things make it dim? Do you know what light you bring to my life?

I look forward to seeing you all on Friday. May we create a beautiful and lasting memory for our children, one that boasts gratitude and reflection.

Ms. Knapp-Weber

Math in First and Second in April

Week One

First graders reviewed Mul de Plier – our multiplication character – and we moved a step further in our understanding. In the fall, we kept our multiplying simple, in the 2’s. This week, we began to see that Mul de Plier can cross her sticks many times – 3 times, 4 times, 5 times and more! The children quickly made this connection and understood what to do with their manipulatives. We will continue to practice this. Next we reviewed our counting gnomes who mine beautiful jewels and took this a step further. The gnomes fill their bags with 10 gems and we all filled small bags with our gems in the classroom, but then we added these bags together and counted by 10’s. We also learned how the gnomes wrote these numbers. Two bags = 20. Three bags = 30 and so on. They loved learning to write numbers this way and understood quickly. We also talked about “extra gems.” Sometimes they may find 2 bags full and 3 extra, so we write that number as 23.

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Second graders jumped right into their times tables. We introduced the 4’s, 9’s, and 6’s last week. All of these were introduced on a circle numbered 0 to 9. We did this on the floor (first graders helped) with yarn. We threw the ball of yarn to the 4, 8, 12, 16 etc – and found that the shape created was a beautiful 5 pointed star or pentagram. Then we transferred this image to the chalkboard in beautiful colors and the second graders drew it in their main lesson books accompanied by the times table and division table. The 9’s formed a decagon and the 6’s formed a pentagram again. Throughout all of this work I am highlighting number patterns, trying to find little tricks that help us remember how to count by 4’s, 6’s, and 9’s. We are also solidifying our understanding of the division tables, which are really just our times tables switched around. Each day we review what we did the previous day so we are keeping everything fresh and alive.

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We did lots of math practice this week – counting by 2’s, 3’s, 4’s, 5’s, 6’s, 9’s, 10’s, and 11’s with bean bags, jumping rope, and clapping. We worked on dictations and math problems from the board for second graders that they copy and solve in their main lesson books.

The story we began in this block is the book, The King of Ireland’s Son, by Padraic Column. It is a wonderfully long and complicated fairy tale that we will read for the next 8 weeks. It will be the basis for our next language arts block. The children are raptured with the imagery, the names, the storyline. It’s a great way to end our math work each day.

Our Circle has new songs in it for the math block. I’ve amped things up a bit for the end of winter and so we’re singing Oh Susanna! and Yankee Doodle Dandee and we are dancing away! We’re also reciting a poem about the Crocodile to continue with our animal theme from the last block…

The Crocodile by Lewis Carroll
How doth the crocodile
Improve his shining tail
And pour the waters of the Nile
On every golden scale!
How cheerfully he seems to grin
How neatly spreads his claws
And welcomes little fishes in
With gently smiling jaws!

The children love this poem and have little sly smiles on their faces when they recite it.
And our new tongue twister…

A flea and a fly in a flue
Were imprisoned, oh what could they do?
Said the flea, “Let us fly!”
Said the fly, “Let us flea!”
So they flew through a flaw in the flue.

Week Two

First graders were introduced to Prince Divide. We heard a long story of his struggle to remove a star rock from the narrow passageway that led out of his city. Eventually he split the rock in two with a sword forged in the depths of the earth by gnomes – made of star iron. His sword in the middle of the two halves of the rock form the divide sign.
After hearing this story, we practiced dividing with our gems (manipulatives). Prince Divide’s sword also has the power to divide items equally whenever he taps the sword on the ground, so he settles many disputes between families and village members. If 4 people bring him 12 baskets of apples and ask for his help, he taps his sword on the ground 4 times and the baskets magically divide into 4 equal groups of 3.
We then learned how to write division sentences that showed the work we were doing with our gems. This still needs practice – as I was expecting. Multiplication and division are meant to be fully understood in 2nd grade, so I’m working on laying the foundation right now. Next the children heard a story of how Prince Divide met Mul de Plier and they realized how well they could work together. Mul can multiply items for the villagers and Prince Divide can split them up equally! We looked at how multiplication is opposite of division and so the math sentences involve all the same numbers but in different order. This is still a bit foggy for the first graders, but the concept will be solidified next year.

Second graders were introduced to all of the remaining times tables this past week – including today. We did the 6’s and 9’s, 10’s and 11’s, 7’s, and then today the 8’s and 12’s. All of these were completed with geometric drawings, done on the floor with string and then put into their books beautifully. This was a large task for the 2nd graders, but they completed their work. There was certainly a capacity built for writing – they had so much writing to complete. I was proud of them all for sticking with it.

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On Friday we had a great time having Circle together – 1st to 4th grade. We sang Yankee Doodle Dandee and pairs of children lifted up a third child and twirled them around. It was so much fun! Fairy house building was a smashing success – many thanks for bringing all of the supplies. And then after a very long recess Maeve’s class and Luna paired up with students from 1st and 2nd grade to read a book to them. All of the older students were delighted to do this – it was lovely to see. We had some time to free draw and then ended with lunch time – a great ending to the week.

Week Three

At the beginning of the week, 2nd graders finished up and then reviewed all of their multiplication tables. They put a beautiful and helpful chart into their main lesson books to help them with these times tables.
First grade reviewed all four operations and practiced them with gems and in writing. We did this through story – all four of our characters worked together to distribute Happy Addy’s cookies throughout the village. Then we reviewed how we learned to write numbers above 10, talking about our mining gnomes again.

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On Wednesday, I introduced a new story to both 1st and 2nd graders. This story will take us through the rest of our math block this week. I drew a big picture of a pathway that traverses two mountains on an extra chalkboard and introduced four children – Wes, Pete, Ruby, and Laura. These four children were chosen by the king to retrieve his magic crystal from the dragon. The crystal has magical math powers and the dragon has left math puzzles all along the path to his castle that the children must solve. Our class is helping the children solve these puzzles. Each day the dragon leaves us a message in his wooden box (a poetic message!) and then our task is set before us. I’m using this story to teach addition and subtraction strategies to both first and second graders. We are working together as one group, doing simple and then more complex problems. I’m also using the story as a pedagogical one – for the 4 children have characteristics of everyone in our classroom and they will learn some lessons themselves.

So far, this story has brought us to a forest to count the trees. They had to be counted in groups of 10 or 20 and each child would count – so our class had to solve problems such as 10=8 + ___ and 10=6 + ___ or 20=13 + ___ and
20= ____ + 8.
Then the dragon had us regroup the number 20 (first grade task) and add multiples of 10 such as 10+10, 20+10, 20+30, 30+50, etc.

The children are very engaged in the story and we are working on the math. It is very difficult for some of them and easy for others. I’m trying to get the hang of our rhythm and ease up on my expectations for the second graders. Because they only came 3 days a week last year, we are a bit behind in our goals for 2nd grade math. It cannot be rushed, so there may be elements we don’t get to this year.

Week Four

This week in our math story the four children succeeded in getting the math crystal from the dragon after accomplishing some mighty tasks. They had to shorten big piles of stones in order to walk across them, fill baskets with wildflowers, and throw huge piles of sticks onto a fire in order to progress on their journey.

Each day we tackled addition or subtraction problems – first working a task in addition and the next day working a similar task in subtraction. I’m trying to get the children fluent and at ease with numbers 1 to 20 and then use that ease with higher numbers.
First graders subtracted examples such as 9 = 10 – ___. 8 = 10 – ____
They also added up to 20 in examples such as 11+9, 12+6, 10+5
Then we did this in subtraction – always trying to go from whole to parts.
19 = 20 – 1 (they must find the 1) Or – 16 = 19 – ___

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First graders also participated and helped second graders in their math. Second graders subtracted multiples of 10 in examples such as 20 – 10 = ____ or
70 – 30 = ____.
Then they added examples such as 25 + 3 or 36 + 2 and 25 + 10 or 36 + 10. And then did the opposite 25 – 3 or 36 – 2 and 25 – 10 or 48 – 10. To keep it a challenge for students who can do this easily, I always threw in something more difficult in the story. For example – the characters in our story had to throw sticks in a fire and they were taking sticks out of big piles. We were subtracting here. We started with 77 sticks and threw in 6. Well then we had 71 and threw in 2. This involves carrying and not all of them could do this in their heads or count backwards to solve the answer. The next challenge problem was 64 – 7 – a bit more difficult. For students who needed extra help, we used gems. Large gems were multiples of 10 and small gems were ones. So for the number 23 we had two big gems and three small ones. This helped with the addition and subtraction.

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We did movement this week and lots of counting. I recognized that all of us need practice counting between 20 and 100 forwards and especially backwards. The transition numbers are more difficult. 29 to 30, 39 to 40, 49 to 50 and 50 to 49, 40 to 39, 30 to 29.
One of our movement activities helps to teach students to add or subtract problems such as 12 + 6 or 18 – 11. I placed numbers 11 through 20 on the ground and asked questions such as, “What is the difference between 19 and 12?” or “What is 12 plus 7?” or “What is 18 minus 4?” The students had to walk the numbers while counting them – so 12 plus 7 – stand on the 12 and count 13, 14, 15, 16, 17, 18, 19 aloud while walking these numbers and counting the steps on your fingers.

We finished up with a day of review – noticing how much work we did in this 4 week block. We drew a cover page into our main lesson books and then brought our completed math book home.

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