Written by Julie Brennan, March 2006 (Kids ages 6 / 8 / 10 / 13)
I've often been asked, what does living math mean in terms of your day? It will look different in every home of course. But I decided to write what it looked like this past week.
Our days are structured primarily by the classes, music lessons and group activities, sports, and life events that occur, and any learning we do is related to those choices we make, although I do make suggestions at times. I rely a lot on "strewing" for my younger children, this page contains an article describing this idea). This week that looked like a lot of math readers on our coffee table that my 8 y/old read methodically over the course of the days, every one, often more than once. I occasionally ask, what are you reading? She tells me the name of the book, and we've read many so many times I am familiar, no more discussion is necessary, she is absorbed.
The 8 y/old has been playing The Allowance Game like crazy this week, whomever she can rope into it, younger or older than her, mom or dad. She's really into "money games" she tells me right now. I played one time this week with her and noted how much progress she and her sister have been making in adding / subtracting amounts. My 8 y/old learned the lesson that $1.99 is "almost $2" a long time ago, now the 6 y/old is working this idea to make change. Dad played with them another time and taught them counting back method to make change.
Tonight as we do every Friday we went over the kids check registers to record allowance and take out anything they have spent it on. We added up my 6 y/old's allowance, I hadn't recorded it for a few weeks because I knew she was saving up for a Dora room for her Dora house. She owed me $3 from the last room she bought, and she recorded $4 a week for 3 weeks. She figured that after the first week, she had $1 left, then added the $4 $4, she had $9. Her 8 y/old sister offered to give her the extra $1 she needed, and recorded a "transfer" in her check register. So my 8 y/old reduced her $45 in her register to $44, then added 5 plus 5 plus 5 for the past three weeks to equal 59 in a second flat. Her accuracy in mental addition is greatly increasing week by week, and she is excited and enjoys doing this.
My 6 y/old does not read as well on her own, she'll make the effort if she has to, but she'll sit on the couch with a stack of readers in her lap and watch like a hawk for an unsuspecting parent or sibling to rope in to read to her. Tonight that took the form of me reading a fun number rhymes book that had counting, skip counting and multiplication ideas in it, and the next thing I knew, my three younger kids were singing "Ten in the Bed" to a fun Ann Geddes picture book version of that famous rhyme, we went faster and faster and it was like a game. A Place for Zero is also read today, along with Highest Coldest by Steve Jenkins and an impromptu geography hunt for all the places in the book in our beginner's atlas.
One day, my 6 y/old says, "Mommy, I don't have any more math books," (referring to workbooks). "Can you get me some?" She hasn't worked one for maybe a month, so I found one she had overlooked that had dot to dots counting by fives and she got busy working a good chunk of the rest of the book that day. She will often work an entire book over the course of a few days or weeks, and then drop it for weeks.
Thursday is a day I lead a high school literature group and then work with several kids using the Harold Jacobs Algebra text while the other moms work with my kids. We have a very large white board which was the math manipulative of choice this week (and art, and science . . .). My 6 y/old created her own algebra problems after the group left last night, very creative and even accurate problems where she made unknowns in equations with boxes. She had a way of using tally marks for equations that she created that included numbers that were too large for her personal math fact memory bank. I was astounded when I saw it, it was ingenious.
My 8 y/old bee lined for the white board after the algebra class as well and asked me if this was an algebra problem: 4xx. I said, well, yes, that would be 4x squared, and you don't know what x is. She said is 4x a problem? I showed her how to set up a table - if x is 1, what is the answer? 4 times 1 is 4. If x is 2, what is the answer? 4 times 2 is 8. She filled in a data table all the way to x=5 and then gleefully noted it was the 4 skip counting table. She has also been reading about multiplication and has asked me for pages from the Multiplication Coloring book to work this week. In her art history class, she is tracking and accumulating her count of tickets to spend them on picture frames for her paintings she makes in the class. She is also involved in martial arts, and is working on certain forms she needs to pass a 4th section test she plans on taking in May. There is a point system for passing, and she is learning the point system so she can ensure she has a successful test. This week she was assigned a more difficult level of music that involved some complicated rhythm and syncopation, rests, eighth notes, etc. She has spent a lot of time - her choice - practicing clapping and counting these rhythms, along with learning another scale progression and chords of 2nd, 3rd and 5th intervals. Tonight she told me how much of her check register money she wants to put in the bank, and we will make the trip there tomorrow morning to add into her savings account.
Several games of War with Grandma round out the younger girls math week. We play a version that requires you to play 2 cards and add the sum - the largest sum wins. Great way to painlessly "drill" math facts.
My 10 y/old's math this week has been more immersion learning on a few occasions since he has already mastered much of the daily math my younger girls are working on. We have been enjoying watching The Teaching Co. Basic Math series a couple times a week, at least until it gets too hard for him. Today it challenged him - the lesson was on multiplying fractions using canceling to reduce them before you multiply. I am embarrassed to say that I never thought about why this worked, until the teacher showed at the beginning of the lesson how 6/25 times 10/21 was equal to 6/21 times 10/25 because of the commutative property a*b = b*a. This was cool to me to realize the fundamental principle behind canceling. For him it was just a cool math trick :o). Earlier this week we watched a lesson on subtracting mixed fractions with regrouping. This is right at a level that challenges him without being over his head.
My oldest (going on 14) is taking an algebra class so he's working toward filling in the gaps in his algebra knowledge that he missed when he was "grazing" on algebra related books. He did take some time to explain some math to my 8 y/old daughter from the problems left on the white board from our class. He also gave her a rather lengthy lesson today on the physics of lightning and thunder since we have had T-storms predicted tonight and tomorrow. This included diagrams of positive and negative charges in clouds and using magnets to model how the electricity behaves. Opposites attract and cancel each other out. In the course of this we talked about how negative and positive numbers have similar behaviors - you could say a positive and negative number collide and cancel each other. Interesting correlation.
This is a sort of snapshot of this week. I know I have missed a lot of the math they practiced or learned this week as much happens when I'm not watching. All of my kids have chosen / requested the math "lessons" they have learned this week and the "drill" they experienced has also been self-selected. My participation has been providing games, books and sometimes pulling out items they may have forgotten about. For my younger kids, this is kind of like when you "rotate" toys in a play area, it makes everything fresh again, so reading math readers we hadn't seen for a long time meant a LOT of math reading this week. I provide the white board and markers, they take off from there. I'm available to answer questions, to give them a different perspective, to interact with them as they learn and play.
Written March 10, 2006
Written June 17, 2006
Sometimes it just seems like we *do* a lot more math when we're not trying in the least to "do" math . . . Today was packed with it for my 8 and 6 y/old girls and I, and not a bit was planned.
First thing this a.m. my girls took the third of their new classes in Irish ballet (yes, that sounded weird to me, but it is very fun). The whole class they were counting and balancing moves to music. They memorized their steps all to numerical mnemonics, and the pattern they were dancing was geometrical. Fun to watch!
Then we went home in time for my 8 y/old daughter to practice for her martial arts test later in the afternoon. My son is advancing to an assistant instructor position and has been "tutoring" her at home to prep her for the test. A lot of work to score and add up to the magic number of points needed to win. They were working together to ensure she got a couple bonus points to give her cushion. She was calculating as much as he was. Then at 12 she took her test, and we went home afterwards to prepare for shopping.
We just learned some quilting and my husband approved a purchase of an embroidery machine, so we made a list and went to Joanne's for their 2 day 50% off sale, woo hoo! I have been waiting for this day, let me tell you. The girls went with me while the boys went with dad to the County fair, the craft and fabric store isn't exactly their thing, but that's okay, we had fun. At the fabric store, they were constantly figuring the "actual" price of the things we were picking up based on the half off cost. All threads were half off, and required you to look on the bottom of the spool for the code to see the regular price, and then halve that. They did great, even the 6 y/old was totally into it, although she had to work with rounded figures, hey, that's all I do, round and halve it. And did we get some fun colors :o).
I needed some time to browse the notions wall (the entire wall was on sale, this is the time to pick up needles and the like), so I showed them the sign that Simplicity patterns were on sale for $1.99 (my 6 y/old practiced her newly honed reading skills all day, reading signs like this aloud with complete enjoyment and abandon :o). I showed them how to locate the pattern books, how to use the color coded index and locate the sections they wanted to browse (children's and crafts), and then how to find out whether the pattern applied to their size. More math comes looking at doll clothes patterns - do they have 18 inch or 11 inch dolls? Bring out the tape measure to estimate which ones will fit. Then I showed them how to locate the pattern number, and go to the drawer to locate the pattern. The 8 y/old had no trouble, but the 6 y/old often had trouble figuring out which way to go since the numbers were in the thousands. She did great, however, once we helped her figure out what drawer to look in. Then they calculated up how much they spent on the patterns.
After spending half a bundle there, we went grocery shopping, and lots more calculations. We *really* needed to stock our home candy store, we prefer to buy in bulk and package it up in baggies ourselves. The girls helped me add up all the packages, calculate the per-ounce cost, weigh the candy in 4 oz bundles and package them up in ziplock baggies for 50 cents each. We then loaded up the basket with the bags, counted them out, multiplied them out, and compared them to what we spent. We must have weighed a few of them a bit heavy, b/c we were a couple dollars short :o), but we did pretty good.
One more funny (strange) math thing. The girls have been learning Suzuki violin, and we noticed one thing - when we play rhythms that have even numbered bows, we always end up in the same place - you always start down bow. But if it is an odd number of bows, it alternates between starting up bow and down bow. So the girls played around with creating their own rhythms and predicting whether they would always be down bow, or alternating (along with making funny little names for them - one became "chocolate cake", another "hot dogs with mustard and ketchup" to accompany the original "peanut butter sandwich" rhythm - most seem to have food names, I wonder why :o)?
And finally, we planted two more half wine barrel containers in our garden which involved estimating how many bags of potting soil to drag over and pour in, measuring distances between plantings per the instructions on the backs of the seed packages.
Whew, what a day of math! And fun!
Julie Brennan in San Diego