There's something fresh and new and hopeful about mornings lately and, even though I'm not doing anything ground breaking, I'm really enjoying how connected everything seems to be these days, mathematically speaking.
In mid-October I mapped out a basic math plan when it was clear the girl (now 7.5) needed and wanted more and different kinds of math challenges. I decided to call the plan 'algebra' because, from what I've read, algebra combines a number of skills and concepts that we have to start learning anyhow at the primary level. And, because the girl has often balked when I introduce new math stuff, calling it algebra motivates her to give it a try; 'algebra' is a big kid skill, and she really, really wants to be big.
So, in the morning it's been fun to open my math folders and give my lovely child her choice of math activities.
Solve for x (conceptualizing equality and sameness, sums and differences) or math card games (3 digit mental sums and differences)?
Christmas themed beginner Sudoku puzzles or Factor Dominoes?
Growing patterns or Bean Soup (fractions, multiplication, division)?
"What's division, Mama?"
"You know, like when you wanted to see if you were halfway through your reader. There were 96 pages and you figured out in your head that half of 90 was 45 and then you..."
Later that morning at the science museum she built this:
"Hey Mama, look! I got the water to cover the whole area!"
"Cool! That's an example of division, too. The water is being distributed evenly across the table."
So, here I am, trying to connect our morning math time to the bigger math picture that I'm constructing in my brain. Like algebra, as I've mentioned. What is algebra??? I did some algebra when I was in high school, but failed literally and horribly (although I aced geometry). But why let that stop me? After some research I decided that the concepts of balance and sameness, solving for unknown quantities, and growing patterns were all pretty darn interesting and relevant whatever we called it and away we went.
We began by building and analyzing growing patterns from some pattern starters I found. Here's one she came up with on her own:
And, when we do the occasional worksheet (the one below is skip counting/multiplication) I look for ways to extend the activity forward, even if I'm not completely sure I'm right. The sheet below was for figuring out numbers of feathers on different numbers of hats, legs on rabbits, and petals on flowers. She got the skip counting patterns easily, so I described the data another way by saying:
"The number of hats you have is multiplied by three feathers per hat which gives you the total number of feathers," while writing h x 3 = f. The next two examples she talked herself through the whole thing and wrote it down. But maybe it would have been better to say, "The total number of feathers you have is equal to the total number of hats multiplied by 3"?? Writing all this out has me thinking of another way I could have done that, but I think sometimes its okay for me to muddle through stuff like this.
And, if skip counting is coming easily, why not challenge her to fill in the chart backwards instead? Ooooh, that was cause for consternation, but she had been saying "This is easy, this is easy, " all morning. I know for sure she needs more experience with subtraction, I know being able to invert a procedure or concept is an important skill, and I also know that if something is too challenging she'll just give up. So, here was an opportunity for deepening her experience with a skip counting chart and providing just the right amount of challenge at the same time.
Anyhow, it's nice to be entering a stage with her where we can sit down and 'do math' outright instead of trying to leave it around the house for her to discover, although I'm keeping that strategy in my kip for now! More than anything, it's been lovely doing math, in the morning, with the winter sunlight streaming in, with a child who is finally (finally!) allowing herself to be interested and excited about exploring this mysterious and wonderful subject.