For learning new math concepts, I stick to the Enki Education math stories, games and discovery process. This is moving the boys along at a nice, developmentally appropriate pace, and lets us work within the 3-fold learning process of open intake, artistic digestion, and conceptual output. This year we've been working on skip-counting (the introduction of the multiplication tables, which will morph into memorization work with that), and we'll spend a bunch of time with place value over the next few months. And then we'll move to working with borrowing and carrying, and measurement during the later part of the year.
But for practice we do a little work with the 4 processes (addition, subtraction, multiplication, and division) each day. I bring this to the boys from two different angles -- word problems and equations. And I also work to reinforce the connection between the two.
I initially struggled to come up with enough ideas for word problems, so I bought a couple of work books to help inspire me. I really like the one on the right, the Daily Word Problems book, because it is set up in sets of 5 related word problems (so they follow a bit of a story line on the same topic). Nice holistic feel, but not a large quantity of problems since it's only designed to offer one problem per school day, and I prefer to touch on all 4 processes each day (to help the kids see the interconnectedness and relationship between them). The other book, the Kumon Word Problem book, has many word problems per page, but they are generally unrelated to each other. Still, I use their word problems as inspirations to make up my own, as topic ideas when I'm feeling devoid of creativity. But if I was looking for a book to actually hand the kids to use (not the way I use them at all, I read the problems to the kids to work on developing their listening math skills as well), I would definitely choose the Daily book.
Like with so many other things, once I had the books and worked with them a little, I suddenly overcame my mental block, and I found that I haven't needed to use the books anywhere near as much as I thought I would. Nice to know they are there for ideas if I need a boost, though.
Each kid has their own blank tablet to write on, and I recite a word problem to them. Initially, I let them just write down the answer, but we've been at this for a couple of years, so at this point they are writing down the full equations. I purposely choose pertinent topics to their lives, as I think it accentuates the connection of math to the real world. Here's an actual example (from yesterday) of a World Problem session -- I have the "problem" that I recited to the right, the boys' answers are to the left:
"The doctor gave one of the boys some medicine. The bottles of medicine contain 10 doses each. If the boy needs to take 2 doses of medicine per day, how many days will one bottle of medicine last?"
I then asked how many bottles of medicine we needed for each boy. I didn't make them write their answers down, I just asked them to talk about how they figured it out, because they each have their own ways of going about this, and I think it's good for them to realize there's more than one way to solve a problem. Zoo Boy knew that 5 days was half of the total 10, so he knew he needed another bottle of 5, so that made 2 bottles. J divided 10 days by 5 days to get the answer of 2 bottles. (Which is very typical of their math styles -- Zoo Boy depends a lot on logic, while J almost always goes right away to an equation. Interestingly, that pretty much describes my style of doing math vs. The Map Man's as well. Hmmm....)
"Each boy has to take 2 doses of medicine per day for 10 days. How many total doses will each boy take?"
In addition to the 4 processes problems, I always add in a logic problem or two, because despite the answer being very obvious (to me and Zoo Boy), J has a bunch of difficulties with the comprehension of this type of problem, and Zoo Boy has problems seeing that there's an equation that describes the obvious answer.
A little background about this day's logic questions: With each dose of medicine, J ate a marshmallow, and Zoo Boy at a fun-sized three musketeer's bar. So here's how the logic questions read:
"How many marshmallows did J eat?" and "How many three musketeer's bars will Zoo Boy eat by the time he's done with his medicine?"
Our story theme of course changes each day, as does the order of the type of problems, but every day I make sure we have an addition problem, a subtraction problem, a multiplication problem, a division problem, and a logic problem, as well as a problem of some sort that I know J and Zoo Boy will work out differently so they can discuss their approaches to it.
In addition to the word problems, they also receive a list of equations to solve each day. For this I really do like using pages from math workbooks -- I favor the Kumon books -- I tear out one page per day for Zoo Boy, and two pages per day for J. The reason I tear them out is because there are pages I don't want the kids seeing (the pages that "teach" certain ways of doing the work -- all I want is the equation practice, I don't use these books for teaching). With my educator's discount at the various book stores, the workbooks wind up being about the same price as printing out my own worksheets (or those I search up on the Internet), and is a huge time saver because I have them all bound and waiting for me to just grab and use.
Obviously, at the pace I'm going with those, J is working twice a fast (and twice as much) as Zoo Boy, which is just about right for their different developmental levels.