math



I’ve been MIA for a while, particularly from this blog. In fact, I was thinking I might be finished with blogging. It’s something you have to do because you enjoy it, at least that’s why I do it. It’s not about fame and fortune but about sharing what we’re up to in our homeschool and sometimes, our family life and I don’t care about becoming famous. What I do care about is recording a few things for my kids to look back on and hopefully sharing some useful tidbit here and there for those of you who are also parenting and/or swimming along in the homeschooling currents with us. Maybe I’m not quite done after all.

This year Martina (and yes, I called her Minerva for a while thanks to a few creepers but I just can’t do it anymore) will be in 4th grade. We are moving away from a Waldorf focus, though not completely. What’s working for us right now is doing a lot of reading aloud in the mornings, music after lunch, then math and science, then hand work while we listen to audiobooks. Our days are fuller than they were and that’s part of advancing through the grades. I try not to answer the telephone until we are finished and often ignore my needy husband when he shows up in the midst of read-aloud time. We really do need to stay on-task this year.

In short, I’m feeling the pressure! Martina does well on the annual standardized tests required by state law each year and I want her to have that back-pat each summer. Regardless of my lack of enthusiasm for hoop-jumping, it is what it is: validation.

What are we reading aloud? So far our topics to cover are these: Vikings; the Middle Ages; English; Math; Science; Handwork; History; Nature Study; Foreign Language; Poetry; Local Geography; Zoology; Norse Mythology. Sounds like a lot, eh? But I’m not finished! We have a co-op where I teach and the Martian attends classes. I will be teaching Beowulf for Middle Grades and Norse Mythology for little people. My child will be in: Beowulf!; Girl Scouts; Celtic Choir and; Creative Gaming. Then there are the extra-curriculars! Piano; Ukelele; Recorder; dance; horseback riding; 4H.

Whew! It sounds like an awful lot and I think parents with school kids have a gigantic load what with school, homework and then soccer and PTA? Why do I think that? Oh yeah, I did it for a long time…yes, Kindy through a UNC degree for my eldest. I can’t see that either way is easier, except in specific ways that are so different they don’t even merit addressing. Parenting and schooling a child are work and no matter how you it, it’s hard and rewarding and wonderful.

Links for specific tomes are in the sidebar, listed by Grade Level and Subject.

This week we’re back on our math block rotation with measurement. Using a variety of resources, most of which are listed in the side bar but also including the awesome math information at Our Little Nature Nest, we have learned about the cubit, digit, hand and span.

On Monday we measured out the ark using a piece of hemp cord onto which we had tied knots measuring one cubit each into a ten cubit length. Because I’m lazy, I then tied sticks to either end so we didn’t have to crawl around to accomplish our measuring. Minerva was amazed at how long the ark was.

I'm at the start point with the camera, she is almost invisible!

The width and height were a little less exciting. In fact, it reminded me of a river barge like those we’ve seen in Holland and England.

We measured two of our horses and one of our goats using a Minerva Hand. My horse, who normally stands 15 hands was a whopping 21.2 and our 13.2 hand pony? He was a horse at 15 hands. Sarah, the goat, was 8 hands high.

We are reading Farmer Boy and Minerva is writing about that, but not every day. This is our autumn ‘farming’ block. We garden heavily and recently gave up raising sheep, chickens and the occasional steer in order to move to a happier place. My daughter has grown up living a farming block, so I don’t feel overly called to go way into it in the autumn. We will do another, longer, farming block come spring planting time.

Here are a few pages from her MLBs for the week. I did not have her draw anything for the Farmer Boy MLB but we are still drawing a lot. She enjoys this very much now and will take her time and really work on her drawings one she has clear idea of what my expectations are. I draw the lines for her to write on with the mama bear side of her block crayons.

math books that we used for addition review

For week one of 3rd grade we did a basic review of addition. My main guide was from Marsha Johnson’s wonderful yahoo group but like I do with everything, I tweaked it here and there. We did addition review and then a brief overview of carrying numbers. Martina caught on to this quickly, which told me that our work learning place values was solidly done.

Lateen and 10's table

The story for the week was about an Egyptian boat, called a lateen, but instead of that we used the little story we have called The Egyptian Cinderella.

Books on Egypt

During the week we also dug into each of the books pictured above for information on Nile-going boats and we listened to SotW for it’s tale of the floods and how Upper and Lower Egypt came together. This was an enjoyable math and social studies unit together. We reviewed addition of various numbers with me calling out math problems and my dd answering while tossing the beanbag back and forth. We played with our jewels, on which I have written 1 digit numbers and the symbols for the processes. I would lay out an addition problem and she would answer it. If she struggled, I illustrated with more jewels or on the white board.

Khufu's funerary barge

Part of what made this interesting was that we got to see this boat, right next to the Great Pyramid of Giza, last summer. It made the questions about if there were 12 oars on Khufu’s barge and it passed another barge with 16 oars, how many altogether? So much more interesting and approachable. My father has spoiled us with the opportunity to travel quite a lot and as homeschoolers, the trips he takes us on are the coolest field trips ever!

Summer fun

These pics are from her MLB from the summer. We did play with math quite a lot over our sort-of break. Making math fun and interesting and relevant means that so far, my little one is engaged and loving it.

This is the week we start Latin again. We finished up in May and have taken the entire month of June off but now it’s time to finish up Primer A and to become solid on the vocab in preparation for Primer B. We will be adding this to math, our only real academic subject during summer school.

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We aren’t taking the summer off though! No way. We have memberships to Colonial Williamsburg (used more when regular school is in session); the Virginia Zoo; the Virginia Aquarium. I plan on purchasing a membership to the Norfolk Botanical Gardens as well. At least once each week we visit one of these places and talk about, maybe read about or watch videos about what we see.

Music! Lots of music. Martina has the summer off from piano lessons but she still plays every day. We are also learning recorder using Oak Meadow and Usborne’s beginning recorder books. Randall has agreed to give little sister guitar lessons and even loaned her a tiny, terrible guitar to use. She can’t see over the top of mine. Today we must buy strings for TTG. It makes me really happy to see my 23 year old son forging a bond with his 8 year old sister–he’s paying it forward.

Riding lessons. We have been doing lessons twice per week but the heat is ridiculous and so we’re cutting back to once per week, hopefully early in the morning. I’m waiting to hear from our instructor now.

It’s funny how sometimes I feel like I’m just not doing enough, teaching enough, living up to the standards I set for myself. Writing it all down helps. Do you do this?

Last week we continued our math studies with the quality of 3 and the 3 times table. Each morning I told the story of the gnomes (from Barbara Dewey’s math book) and had Martina count the stones in the gnomes baskets. Addition always had 12 in her basket but also had several more hidden in her skirts. Subtraction always was missing some and had less than 12. Division always had a few but because his are always divided (or shared) with Subtraction, he also had less than 12. Multiplication always had more than 12, often 3×12 or 36.

We also did math problems on our rainbow paper and Martina drew pictures of the gnomes and rhymes (from the book Math Lessons for Early Grades)  in her MLB.

Each morning we did a clapping game where we counted by 3s to 36. One of us would come up with a clapping pattern which had us slapping hands together on the 3 beat. Our count would be one, two, THREE! four, five, SIX! and etc. We would then count 3 is three times one, 6 is three times two, 9 is three times three and etc.

Another activity Martina did on her own was to write the skip counting pattern of the three times table on our sidewalk squares and hop them, counting by 3s, forward and back. She also did the 3 times table as she hopped.

The picture above of the white board was simply a writing exercise. She will do a similar page in her MLB this afternoon. We didn’t get to it Friday thanks to a middle-of-the-might ER trip with one of my older children.

We also made a peg board for learning the patterns of the times tables through 10. My daughter traced a plate onto the log slice, we worked together placing the nails around the circle and then I marked the spots with pencil and she hammered the nails in. By the time she was finished she was too hot to enjoy playing with it but I brought it inside and that night she proudly demonstrated to her father how the pattern for 3s looked. (I wrote the numbers with a paint pen/marker.)

This was a really good week for us and our math studies. Both of us had fun and enjoyed exploring the quality of the number 3. We talked about religion; earth, sun and moon; mother, father, child; and other ways that 3s manifest in our world. Much of our quality of numbers study came from Kristie Burns’ study guide.

Links: Please see my math links for ordering information and links to sellers.

Most of my homeschooling friends are ‘classical’ homeschoolers. They are all about academic acceleration and excellence. I want those things for my daughter, too, but more importantly I want her to hold onto her magic for as long as she can. I want her to be able to see the beauty in life through her innocent eyes. I want her spirit to be fed, just as much as her brain and I want her to approach everything in life with a soulfulness that I think is lacking in our world just now. Perhaps she can be one of the people who helps create loving change. That being said, it is easy to feel like I’m doing Martina an injustice when I look at the advanced academic work some of these kids are doing! I get all wobbly and find it difficult to hold my center. To remember that I really *am* sure that what I’m doing with my child is the best choice for us…for her and that she is, after all, academically just fine. This trading of ideas is one of the coolest and most distressing things about homeschooling and my friends and I often laugh about this very topic: how we are constantly worrying whether or not we are doing the best we can by our children. Ladies (and Gentlemen if any happen to stumble across this blog!)? We are.

Anyway, on to math. We did a Singapore math course for 2nd grade. It was okay, so far as math courses go, but it was dry and not much fun. Eventually, after a chat with Martina, I ordered the Christopherus 2nd grade math book. It is a wonderland of fun with math. Then I started exploring the internet and found resources and gnomes and beauty and fun and so guess what we’re doing this summer? Yep. Math.

Typically Waldorf maths are done in blocks and that’s what we will be doing, only the blocks will be broken up by trips to the mountains and beach, rather than other lesson blocks. Our main focus is going to be this: finding the magic in math.

Resources you might ask? Why yes, tons of them! Here is my list of links: Christopherus 2nd Grade Mathematics; Waldorf Without Walls Math for Grades 1-3; Marsha Johnson’s yahoo group, where there an excellent files section with grade level ideas for all subjects; EBeth, an incredible blog with a complete math story using math gnomes for introducing the 4 processes. The 4 processes are traditionally introduced in 1st grade but I got caught up in depression last year and didn’t do much at all other than teach my daughter to read and work in our nature journals. This year has been very different and we have managed to cover quite a lot of ground in our learning…I just want to have some fun with math! So we are going to briefly go over the 4 processes, introduced by gnomes.

We started out trying to use squirrels, as is done in the Christopherus book but neither of us really connected with them. A few days ago I was reading and started thinking about those gnomes and decided to give them a try. We love elemental beings and I knew Martina would connect with them as soon as I started reading the story. If you could have seen the look on her face when I uncovered this:

It took just two days of secret sewing to make the gnomes. They are large, 6″ to 8″ tall, maybe taller with their hats. The other things came from our rock collections and wood pile. We used the first in the EBeth collection of stories for math before the big reveal and once we had gotten over the excitement of exploring the gnomes, Martina took out her Roman numeral stones and made a path by the gnomes.


Here you can see the stones with their Arabic numeral counterparts.

We also worked on place value and all four of the processes on a sheet of paper lined with yellow for ones, red for tens and blue for hundreds. I carry these colors over for one thousands, ten thousands and hundred thousands so that Martina can see the pattern and how it works and repeats. The four smaller beads above the Roman and Arabic numerals are process markers. Like the gnomes, red is division, yellow is multiplication, green is addition and blue is subtraction. I place a mixed group of Arabic and Roman numbers on our sheet of paper, along with the process marker and Martina does the problem. Sometimes we use a number of smaller beads rather than one of the larger beads with a number on it. Here are a few examples:

I also make a point of sometimes leaving a column blank so that she understands the concept of zero. If the column is blank, it simply means there is an empty set there, as seen in the last picture here in the second number tens column, 1,103 (I think! It’s difficult to see the numbers.) What you can see is the blank column and the way she had to use the colored beads in the proper amounts in order to put her answer down on the paper.

Manipulatives often make me go to sleep. In this case, we’re having a great time with them. Something about them being pretty and homemade makes all the difference.

In summary, we are going over the first grade math stories briefly but continuing to do deeper work on the four processes. We are not yet carrying numbers but are doing place value up as high as she wants to go on a given day. We are also working on the qualities of numbers once more and in more depth. We are using Kristie Burns’ guide to Holistic or Sixth Sense Math and then moving this kindy exploration into the multiplication tables. It’s a nice re-introduction to the feeling of numbers before we get to the bouncing, jumping, clapping and singing of the tables.

Finding a math program that works for us has been a difficult journey. We both need something fun and beautiful and soulful to connect with and these math stories have all of those things, right up beside hardcore work on the processes. I’m feeling much more grounded and happy with what we’re doing in math now than I have since I bought her a Saxon kindergarden program several years ago. We have found what works for us. Finally.

Summer is looming and it’s difficult to look ahead without wondering if I’m right to keep schooling through the time of year when lightning bug jars, mulberries and swimming in the pool are some of my fondest childhood memories. With the breaks we take, both planned and because life gets messy and I drop the ball, we have to keep going. It’s less about choice than it is about responsibility.

We have been in homeschooling limbo for a month or so. My step daughter moved in and the sheer volume of extra stuff was overwhelming. Her overflow took over our school area briefly. But now the stuff is sorted, my allergies and the-cold-that-wouldn’t-end are abating and the social schedule doesn’t have anything stressful on it. We’re back to center.

Today we did our school work, (which means Latin light, math and reading, when we’re taking a break from homeschooling) then I did some planning while Martina played outside.

Beginning next week we are adding Singapore math back into our math program so that we can finish the grade level curriculum; we are also continuing with the Christopherus program which is beautiful and has helped us solidify some concepts. I have seen the holes in my daughter’s math knowledge thanks to the Christopherus math curriculum and am committed to sewing those up ASAP. We’re hitting the maths hard for the next couple of months. We will continue with Johnny Tremain and A History of US; resume our Old Testament Bible block for a 2nd go round; pick back up with phonograms and grammar in an integrated unit that I will share more on in the following weeks.

Outside classes are winding down for the summer so we’ll have more time at home and to focus on some Latin catch-up and hard-core math work.

What do you do during the summer? Do you lighten the load? Stop schoolwork completely? Keep drilling away? Please, leave a comment and let me know what works for your family.

The Two Times Table Hopscotch

One of the things we’re working on in 2nd grade math, is the two times table. We are working on learning it with rhythm to get it in our bodies and also into our brains. A couple of things we’re doing are flash cards and hopscotch.

The flash cards have the entire problem on the front. The point is to memorize the tables now, not quiz her on knowledge she hasn’t yet acquired. She just reads them off and we move through quickly.

Our hopscotch isn’t really traditional but one based on the rhythm of two. Later we’ll move on to 5′s and 10′s. As Martina hops, she says the numbers or a rhythmic chant that I start her our with, such as, “one two is two, two twos are four, three twos are six,’ or, ‘one times two is two, two times two is four,’ etc. We work up to twelve and then she comes back, counting or chanting in reverse. It’s fun for her and effortless for me…well, except the part where she made her own hopscotch using my pastel chalks instead of sidewalk chalk, LOL. Now she knows where the sidewalk chalk is located.

As part of our math studies, we are learning about measurement. The recent snow was the perfect opportunity. We took a paint stirer and Martina used a measuring tape to mark 1″ increments on it. She then ran outside and stuck into the snow. The maximum depth we saw was 7″, but the wind blew like crazy and then it snowed ice for a while and by the time I took a photo, we had lost an inch of snow!

She had fun doing this little project, I was happy to sandwich a bit of learning in between snowballs and now she has a hands-on idea of  what, exactly, an inch is.

Martina's snow gauge

the final depth

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