Plus Gnome's Magic Box

To cover the concept of place value we turned, yet again, to the gnomes. Inspired by a lesson from Eric Fairman's POD I created a little story about Plus Gnome. It went something like this:

One day King Equals asked Plus Gnome if at the end of each day he could please add up all the jewels collected by all the Gnomes. Plus Gnome was honored. However near the end of the first day he was a bit overwhelmed by the large pile that needed to be counted. As he went through the pile he kept losing his place. Finally he got the idea to put each jewel into a box as he counted it. Then he wrote the number on the ground to help him remember. This worked for a little while, however his box got so full that all of the jewels spilled onto the ground. What to do?

Using the props and characters he added a second box just to the left of the first. When ever he counted 10 jewels he would bag them up. Mark the number ten on the bag and put it into the second box. Same for when the second box got full. He'd bag up ten bags, mark the new bag 100 and then put this new bag into a third box just to the left of the second.

Before the lesson I made Plus's box from an old cardboard box. We used a slate to mark his numbers, and cut old cloth and yarn to make his bags. These lessons seemed to take a long time - what with all the bagging and cutting and tying. But it really worked for Nightowl. We reviewed this for several days and each day I'd find her tugging out the box and jewels before I was ready. She was quite eager.

All this place value led naturally to column addition when King Equals asked that Plus Gnome please keep track of all the jewels collected all week. Yikes! What's a gnome to do? Well, our gnome simply put a second box on top of the first. The second box was for jewels collected the second day. Then the columns were added together. Voila! This morphed so easily into column addition on paper. Everyday Nightowl would work with her props: sometimes her gnome would race against my gnome to see who could add the fastest. Then she would draw the lesson into her math book. During the week she would do workbooks full of problems. It always made me grin when she'd see a column addition problem and mutter to herself: "Oh, that's easy."

Math Magics

After successfully revisiting the gnomes, working scads of number problems and worksheets and number facts (whew) I opted to take Nightowl in a different direction. For this I primarily used Path of Discovery, Grade 2 by Eric Fairman.

In the section on math Fairman gives a number of very detailed introductory lessons which he has dubbed Math Magics. The basics behind these lessons - equal division of shapes and symmetry. These lessons are part geometry, part times tables, part basic math concepts, part division facts and completely artistic.

We began by discussing circle. Then we worked to subdivide it into equal parts. I demonstrated this by drawing a huge chalk circle on the floor and then asking Nightowl to place markers on the edge. The markers needed to be equal distance apart. In the end we had 12 markers. Then we used yarn to connect the markers to create triangles within the circle. Every day we created a different number of triangles working to make the triangles the same. Each day we drew the large circle, did the division and then copied the image into her math book. Each day we ha a different star design made of triangles. This was very challenging for Nightowl. She was often frustrated trying again and again to create the star pattern within the circle.



Then we moved to squares within squares with the resulting subdivision of triangles. Again we started with a large shape on the floor, subdivided by yarn. I told a short story from Fairman's work to describe the subdivisions. Then we moved to the slate and then the main lesson book. This optical illusion was very intriguing. Nightowl spent an entire lesson putting together the very detailed picture on the left.

Finally, to better grasp how many squares and triangles were actually in the picture we recreated the squares within squares exercise in felt.



How many triangles to you see? How many squares?

Math - Number families and gnomes

When I mentioned Math to Nightowl her first response was the joyful yelp of: "Gnomes!" Ah, yes we love the gnomes here. It is abundantly clear to me that the Gnomes will be an integral part of our math for some time.

So we began with a short review of the processes. For this we used our new little felted Gnomes. If you don't have actual Gnomes to work with I highly recommend them. My girl really loved the little guys and they made math very, very fun.

After our review we began the serious work of number families - using David Darcy and Dorthy Harrer's books as inspiration. For example the number family for 3 is 0,1,2,3 as these numbers make up the variety of addition and subtraction sentences for 3 (1+2=3, 3-2=1, 0+3=3 and etc.). Nightowl really grooved into this concept. We spent lots of time challenging each other to list the family for various numbers.

Harrer's second grade lesson on the "Richest Number" was surprising to me. It seemed so esoteric that I wasn't sure Nightowl would get it. But I plowed through watching to see what would happen. She loved the story and had no problem dividing the numbers into their respective parts. If you haven't seen or used this resource check it out, it's great.

All of this flowed pretty naturally into beginning the times tables. Again we used the Gnomes. I created little stories and we wrote problems out forwards and backwards (3 x 2 = 6, 6/2=3 etc.). All of our clapping out rhythms and counting by 2s, 3s, etc. really paid off here. I plan to go back to the times tables later in the year.

One other note on the Gnomes. Using story to relate these important concepts really made me a better teacher. I haven't considered the quality of these concepts in ages. They are so integral to how I think and get through the day that they seem almost ridiculously easy and basic. If I'd had to approach these concepts just as number facts I would have become completely impatient when Nightowl struggled to understand. In short I'd have been limited by my own experience. Using the stories and the manipulatives forced my thinking into the magical and the wonderous. I know I was more patient and this made all the difference. Nightowl hardly even knew she was learning - it was a natural extension of the play/work we were doing. Very cool.

After each lesson she put a drawing/representation of what she'd learned into her main lesson book - which fulfilled her almost constant need to draw. Finally, to help solidify these concepts I gave her daily assignments in a variety of math work books that I picked up at Barnes and Nobel. She did these after we'd moved onto Geometery and it was really good daily practice.

Math Time

November/December 2007 was our first month of second grade math. From my viewpoint in mid-January I have to say that it really was an incredible month. Except for a short review the concepts we covered were all new and difficult.

I noticed a huge change in Nightowl during this block. Language arts lessons had a very dreamy quality. They were relaxed in that kick back on the couch with a cup of hot tea kind of way. Even the small bit of grammar we covered was very mellow. But math - it was almost frenetic. Whenever we embarked on a main lesson Nightowl became wired. It was impossible for her to sit still. She flipped and flopped and bounced all over the place. We got through the lessons but they were so active. I could almost hear the cogs in her mind turning. We ended every lesson with some big energy release - like dance party or running outside. It was amazing to watch her process. I was constantly glad and relieved that she was not trapped in a school classroom for this work. I'm quite sure she would have been in trouble for not sitting still or labeled ADHD or something of the sort. But at home it was not a big deal. Bouncing along she retained nearly everything, made some amazing leaps, learned tons and frequently made me laugh. If any of you have experienced a similar response from your kids please let me know. Wow! For the next few posts onto the actual math!

Finished!

Here they are, all ready for our first math block.
Left to right: King Equals, Plus, Times, Divide, and Minus

Money Math

Nightowl made this little clutch purse on her weaving loom. She uses it to store her money. She now earns a weekly allowance and is saving her money to purchase a flock of chicks and chicken supplies. Occasionally, her riches seem tempting so she'll bring her purse along when we do errands. She might purchase a book, stickers, etc.

With this saving and spending has come concern about how money works. Previously, she has had little interest. Watching her it became very apparent that she had no knowledge of coins, dollars or their value. So, in true homeschooling fashion we put Nightowl in charge of her money. She must keep it, count it, and consider the value. She's working on recognizing the coins, writing amounts and making change. To this end I made up a little game. I'll pull out my pocket change, hand it to her and say: "If you can tell me how much this is worth and the names of the coins you can keep it."

We've been playing for a day or so and this morning is the first day I lost. I'm out $0.36 which Nightowl has tucked away in her Chicken Fund. Bummer for me. Guess I'll need to make the game harder!

Math in May

I've started putting up my May lessons. However, my attention is somewhat divided between my blog and the community blog I'm a part of: A Taste of Waldorf. So, I've posted our May math stuff there. Check it out: Math: Odd and Even Gnomes.

Logic

During a recent trip to a neighboring town's childrens' museum Nightowl discovered a large scale chess set. That morning's chess massacre piqued her interest and we're now playing a at home. To help with the logic I've also introduced her to kid's sudoku. I found a nifty little website (Free Kid Sudoku Puzzles) with 4x4 sudoku that helps kids get a hang of the logic. We're doing a bit every day. Pretty cool.

Math, baby!

During the last couple of weeks we've been working on math: number sequence, the four processes (+,_, *, /), patterns, quality of numbers. Nightowl is really liking this subject. She asks for math every day. We are having a lot of fun with it. I'm trying to organize some dramatic math play with friends - hopefully this will evolve.

I have Nightowl here with me and I've asked her to share some of her thoughts about what we're doing these days.

Ok. I'll type whatever you want to say about what we've been doing lately.
We do Gnomes. Math Gnomes. How about you type their names?

You tell me their names and I'll type them.
Divide. Minus. Plus. Times.

What do they do?
They collect jewels.

Really? Where?
In the cave.

Why do they do that?
For the kind, kind, kind king who gives them nice homes.

So what do you do with these Gnomes?
They go on different math adventures. Like they help the squirrels find out how many nuts they have. Plus gives the squirrels more nuts if they need more. Minus takes away the nuts. And Times tells them how many times times makes...I guess. That one is tricky.

Hmm...what about Divide?
Divide divides nuts for the squirrels to share.

How do you have these adventures?
Sometimes we pretend to be the Gnomes. Sometimes you use a number grid. And you put down the numbers of all the steps they had to take. Like when they visited the Elf Queen. The squirrels in her kingdom needed help with their nuts. She asked the King if any of his gnomes knew how to count. He said yes. He said to his four Gnomes, when I saw this letter I thought of you, my funny little gnomes. So the Gnomes went to the Queen of the Elves. She said that the squirrles needed help because they have a lot of nuts and don't know how many they need.

What do you mean about the hundred steps?
The Gnomes asked the king how to get the Elf Queen. The King said that they needed to go 100 steps in any direction and once they went 100 steps the directions to the Elf Queen would magically appear in their hands. So the Gnomes went 100 steps.

Did you help?
Yes. I put down the numbers so that they would know how many steps they had gone.

Was it hard?
A little bit hard. It took me at least two days to get all 100 numbers.

So what do you do once the Gnomes are with the squirrels?
We pretend to be the Gnomes and the Squirrels. We help them figure out their nuts - they have a lot of nuts.

Which one are you?
I was all the Gnomes. Mommy was the Squirrles. Now I'm getting tired of talking.

Ok. Do you want to say anything else?
We made clay gnomes. That was fun. I made Divide and Plus. Mommy made Times and Minus.

Awesome. Anything else?
That's all I can think of. That's all for now.

Back to School

It's been busy, this first week "back to school, back to violin, back to piano." Hmmm....let's see:

This was the first week of our Math Block. We did a lot of singing number patterns, rhythm games for number patterns, working on odd and even, counting by 2s, 3s, etc. We've been playing number games: mancala, dominoes and geometric games: tangrams, blockus. One afternoon Nightowl spied Barbara Dewey's Math for Waldorf Homeschoolers book. She was delighted by the illustration of gnomes on the cover and begged to begin learning about the gnomes. Thus we have entered the world of Math Gnomes. We're at the beginning but she is delighted with the tale of the four gnomes: Plus, Minus, Times and Divide and their adventures in the jewel mine digging up treasures. She requests more of this activity faster than I can provide it. I suspect that during the next few weeks we'll be doing even more. I'd better get ready.

One morning Nightowl and Bearcub got busy with measuring tapes. I looked up from my morning tea and noticed that they were both very intently measuring all the furniture in the living room. Ta da: impromptu math lesson. Nightowl measured many pieces of furniture then noted the measurements on paper. She next cut out each item and arranged them in order from smallest to largest. She had some confusion regarding the order of the higher numbers so we got out the Unix Cubes. These little cubes attach in columns and can be used for a variety of things. Nightowl used them to figure out the numerical order of the items she'd measured. As this progressed she figured out that it was much easier to count using columns of ten. This prompted a little lesson on counting by 10s to 100.



Nightowl was also busy building this week. She asked that I include the following images of her dollhouse world - a city of rainbow buildings and multi-cultural communal living. The entire world is presided over by two Grandmas and their children. The Grandmas have been together for many, many years and have many, many children and grandchildren.

After math, our next big project has been getting ready for the homeschool science fair. This year Nightowl has selected Shells as her topic. We discussed her project, came up with several questions that she'd like to find answers for and took a trip to the library for research materials. Nightowl has been diligently sorting through the family shell collection in search of beauties to display for her project.

Finally, our biggest project was working on Rosetta. For Christmas, Nightowl received a doll making kit and this week we began the task of creating the doll. I purchased the kit on-line from Joy's Waldorf Dolls and, as it was our first doll, I took the easier route of getting several pieces created for us (the head, the wig). Our task was to take the head and attach the skin, create the nose, stuff the hands, feet, arms, legs and body; sew it all together; embroider the face and attach the hair. This was a really fun project. Nightowl helped as much as she could. She sewed the nose, did the stuffing, attached the head covering, and placed the eyes, mouth and hair.



After our first day working on the doll Nightowl had named her Rosetta. This inspired us to work even hard to get her finished - we just couldn't leave Rosetta in pieces! It was a really magical experience. Nightowl was so excited watching the creation of this doll. When we weren't working on her she would randomly pick up the pieces and hug them. I'd hear her whispering to Rosetta, telling her what her life would be like. She prepared her other dolls for an introduction to their new sister. And then she announced that, unlike her other dolls who sleep in doll beds, Rosetta would be sleeping with her. "She's not hard like my other dolls," Nightowl explained. "So she'll be more comfortable sleeping with me." Wow. Normally Nightowl doesn't sleep with dolls or stuffed animals. While she has quite a routine for putting her various doll and animal family to bed none of them get the invitation into the big bed. An interesting development.

By the end of the week Rosetta was finished!



And, true to her word, Nightowl has slept curled up with her every night since.