Tuesday, January 29, 2008

Grade Three - Books and Lesson Plans

This is my list of materials that I'd like to use for Grade Three. I'm putting the list together as I find things and get new ideas. Hopefully, I won't lose this list - as I'd lose a scrap of paper.

An Overview of the Elementary Math Curriculum - David Darcy

Natural Speller - Kathryn Stout

Quilting for the first time - Donna Kooler, Kooler Design Studio

Natural Science
Tabletop Gardens - Rosemary McCreary

Wednesday, January 23, 2008

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."

Sunday, January 20, 2008

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?

Saturday, January 12, 2008


I like homeschool because I get to do math with my cat.
– Nightowl, age 7, 2nd Grade

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!