We had an amazing first day of our winter term; I thought it might be a trifle difficult to ease back into rhythm but I am so glad I was wrong.
We began the day with the familiar pattern of waking, eating breakfast, doing morning chores, and accomplishing morning hygiene (if the boys brush their teeth and their hair it is an accomplishment). Papa is the foundation of our morning rhythm; he must wake and go to work and so we wake with him and begin our day at home.
We gathered in the family/learning room and recited several multiplication tables; I will add the bean bags in and we can switch off who answers and who calls out the mental math problem.
Using the Live Ed grade 4 book as a guide I decided we would learn a song for part of our morning gathering. I selected the chorus of California Here I Come as I am certain I learned it in 4th grade and I figured it will pertain to our later study of state history. We went through the song several times and the boys were joining in by the third run through. The boys then copied the first two lines into their social studies main lesson books (I had written them in chalk on a small slate) and then decorated the page.
(Eventually we'll get back to journalling; this was a nice way to ease into writing again.)
We reviewed some of the things we had learned in our previous blocks; the basic parts of speech, the various geographical areas in Southern California, and a few others.
Our math main lesson this month is long division, but the block begins with long multiplication, or multi-digit multiplication. We reviewed carrying numbers in multiplication and then delved into the main lesson material. The boys really seemed to get what we were doing. I must say that using arithmetic books from Paper Scissors Stone was a big help; the grids are perfect and I find myself wondering why we never used grid paper for these types of problems when I was in school.
I often think of early mathematics as bringing language and order to concepts the children have already internalized. Teaching long multiplication (or multi-digit multiplication) is simply teaching a child how to write out a longer multiplication problem and how to solve it in a systematic way; Papa says it is the first algorithm a child learns. A simple example would be 12 X 12; my boys know that one way to solve this problem is to multiply 12 X 10 and add that product to 12 X 2. (Another way would be to memorize the multiplication tables, and we're still working on that.) Doing it that way is common in mental math, but unwieldy in written math, and so we introduce standardized ways to write and solve problems.
I think it is important to understand the why of written math to help avoid the idea that math is something that few people use in their everyday lives. Written math helps us figure problems efficiently and correctly, yes, but we do have calculators and once we are past schooling we usually use them for the more difficult multiplication and division problems. No, written math is also about communicating; math is a universal language and is also the language of science. We need to know the fundamentals of written math to progress to more difficult equations and complex ideas.