Saturday, August 21, 2010

Math At The Pumpkin Patch

So, I get asked a fair bit about how we do math here. Now, I know you don’t mean the literal “how” because surely it’s obvious the things that we do for math. I guess that means more, how we fit it into our day. Maybe the best way to explain is to show you a few excerpts from our day..

I had planned to start Morgan on a new math game entitled What’s The Difference? last week, but due to being down with the tummy bug we never got to it. So today after we’ve accomplished Bible, our read aloud, and the kids reading I say, “Muggins, want to play a new math game?”

He rarely says no, and is eager to run and wait for papers to come out of the printer for us to use. It is not necessary to have papers with neat little boxes on them to play this game, but because I don’t want to frustrate him should his numbers not line up I made a game sheet. He’s back in two minutes and while he was gone I located pencils and pulled out our deck of math cards.
I’ve all ready pulled out the 0-9 cards and have them shuffled and ready to go. Morgan passes us each a math paper and I explain the game, “We’re going to do something called borrowing, and it’s exactly what it sounds like. Sometimes numbers need help from their neighbors so they simply borrow from each other.

“In the top six boxes we have to put numbers that we find on the cards when we draw them. Then we’ll do the math fact to find out what our answer is.”
“This is going to be easy, it’s a lot like Sum It Up!” 
“Yeah, only we’re subtracting this time so instead of a big number we want the smallest we can get!”
We let Jayden flip the cards over because he’s decided he’d like to be our helper. He flips over a card and is unimpressed with the number and shoves it back in and pulls out another. Morgan is insulted by this gesture. Jayden tells him to be quiet, and I sigh.
“Jayden, you can help us, but you can’t swap the numbers. You must tell us exactly what the number on the card is okay?”
He sighs, but complies. We get our six numbers written down and I tell Morgan to watch me do my math while I silently pray I won’t need to use my fingers to find out the difference. As I do my problem I explain to him that 5 is smaller then 8 so I need to borrow. He listens, but doesn’t quite comprehend, which I soon realize when he does his own problem.
When I point out he needs to borrow he says, “I don’t understand. When I add I can easily swap the two numbers and still get the same answer. Why can’t I do it with subtraction?”
To help him visualize the problem I pick up the extra cards, “Pretend these are candy bars. I’m going to give you 5. Now, I want you to give Jayden 8 of those candy bars. Can you?”
“No, because I wouldn’t have enough. Plus, he’d get more then me, and I’m not saying that to be selfish, it’s just that I’d like a candy bar too, you know if it didn't have sugar in it.”
I make a mental note to refrain from food talk while doing math, “You’re right, you can’t. So that’s why 5 needs to borrow from his neighbor.”
I then have him cross out the number to the left of 5. I explain that when we add 10 to 5 we get 15. He crosses out 5 and writes 15. So I explain that there’s absolutely nothing wrong with what he did, but next time if he’d like to save himself time he can just stick a 1 next to the 5. He finishes his math problem and is disappointed to see he ended up with a negative number which doesn’t count in our game.
We play another 4 rounds of this game, and slowly he’s able to see how to avoid the negative number issue. However, in his effort to avoid negative numbers he’s not getting much borrowing practice in and as a result is ending up with larger numbers. I suggest we put the game away and play some more tomorrow. He’s only slightly disappointed, because while he really wants to win a round he’s starting to get a little frustrated.
I suggest lunch and over lunch Morgan says, “I’m glad you were helping me figure out where to put my numbers, but when we play next time I think I’ll try it myself. I really want to be able to do it as good as I do the adding game.”
“Fair enough, but will you mind if I copy you sometimes?”
After lunch I pull out Joey-Joey which is freshly stocked with new fact families (4 & 5, addition and subtraction on top of the 1 and 2 family, doubles, & 10 family) we play 3 rounds. They don’t go as well as normal. 

Jayden was frustrated he couldn’t answer some of the new questions quickly and thus tried to hunt in the tin for the older facts. This caused accusations of cheating and slowed the entire game down while they were both lectured about being poor sports. I suggest that tomorrow we play sitting next to the hundreds chart so they can use it to help themselves along until they get quicker at the new facts. 
While the boys run off to play, I jot down notes on my Homeschool Journal & on my Game Log sheet. I realize that while I like using the bigger blocked pages for logging extra notes about our game playing, that I need to work on a better layout, because I’ll end up with way too many Game Log sheets by the end of the school term.
Today we opt to do math before reading & I pull out a number tracing paper for Jayden. This isn’t something I normally hand out as both boys are fully aware of how to write their numbers, but Jayden lodged a complaint recently.

He stated that his twos were sloppy, his fives were squashed, and that he was struggling to fix them. So I pulled out a sheet from a Crayola Number & Letter pad and hand him a marker. 
“Here Jayden, because you were frustrated with writing numbers I found this paper and thought you might want to trace the numbers for practice. It’s not about how fast you can do it, but about how great your numbers look when you’re done.”
He eagerly takes the paper and sits at the table with it while Morgan and I take off with What’s The Difference? again. We get in a few extra rounds today because I don’t have to explain how to play the game or what borrowing is. 
Morgan makes the choices on where to put his numbers occasionally asking if he’s making a wise move. I offer ideas and suggestions and say things like, “I might put it here because then you know for sure you won’t get a negative number, but if you put it over here and then draw a 3 you’ll get a really low number. You have to choose for yourself.”  Sometimes he takes the advice and other times he makes his own choice.
He does well, but then has a “moment” and attempt to work his problem from left to right instead of right to left. I don’t catch it until he tells me his answer, I remind him to always start at the side farthest away from the math symbol. He reworks his problem and is delighted to find out he beat me. We play another round before putting it away.
Today we sit next to our hundred chart, which means moving the dog’s food and water out of the way, to play Joey-Joey. This eases yesterday’s frustration and we manage 3 rounds (3 minutes each) before we put it up for the day.
Morgan and I settle in with fresh game boards for more What’s The Difference? I want to be sure the concept of borrowing is well cemented before moving on to anything else. I also don’t want to confuse him by reviewing Sum It Up! So this is our sole game this week. It’s not uncommon to focus on one game, but often times we’ll play more then one in a week. 

Today I ask Jayden if he wants to play Jr Star Traveler, he acts unsure until I say, “Oh you know, the star game where you have to try and not get your star all colored in!” He agrees as long as he can use one of my special scrapbooking markers. I’m not keen on the idea because they are permanent, but I relinquish the marker in the name of education.
I get the game set up and remind him of the rules. He starts off slowly and I have to send Morgan off on an errand to keep him from attempting to over help.  Once I’m sure Jayden is well on his way I agree to let Morgan play with him for a few minutes.
We keep things short today as we had quite a late start on our school day and the boys very eager to dig into their new supply of books from the library. So after 3 rounds Jayden hands his game over to Morgan and announces, “I beat the start twice!” 

I skip Joey-Joey today because Jayden has worked on both addition and subtraction with his game. While I’m keen for the boys to be quick on their math facts, I figure we can skip it today because both have easily covered a variety of math facts.
Today is going to be a half day of school for us as Nana is due back in town after a long vacation. The boys have been ready to head to the airport since Monday and I know their focus will be more on the planes overhead than anything else.
I announce that I found some fun math papers online, “Anyone want to try them out?” Morgan is always eager and runs upstairs to check the printer for the paper. 
The papers happen to be from & Jayden thinks it looks fun and would like to try one too. I’ve set Morgan up with a 3rd - 4th grade level paper and print Jayden out one from the 1st - 2nd grade section. Both eagerly sit down at the kitchen table and set to work.
When the boys do math papers that work on concepts we’ve all ready covered I try not to say anything at all unless they ask me. I might hover in the same room or, because we have an open plan kitchen/dining/lounge area I might wander to one of the other corners and work on something. Updating our Homeschool Journal, embroidery, answer an email, or day dream out the window while wishing the ocean was warm enough to swim in.

Morgan takes a look at his paper and is excited to set to work on the pyramid math problem. The idea is that you take the bottom line of melons and add two together and place the answer above them. You continue in this fashion until have a whole new row of numbers; eventually you will have one melon with a large number that will answer what the heaviest watermelon ever recorded was. 
This pyramid not only works on adding & carrying, which he successfully manages without problem, but it also encourages him to get a scrap of paper and transfer a horizontal problem into a vertical problem. I’m glad, because he recently said he was struggling with that and we’d set up a few fun problems on the white board to help him climb the hurdle. It takes him a few minutes, but he reaches the answer and when I check his work he’s made one minor mistake when taking his answer from the scrap paper to the actual math paper. It’s quickly fixed and all is well.
He debates between adding fractions with like denominators and doing some square foot work. He has to determine the size of each friend’s garden by reading a graph and adding up the answers. He’s able to do this on his own and then debates tacking the fractions. While he’s eager to do them he’s also staring out the window at the rain, “Do you think Nana’s plane will be late?”
“Yes, she all ready called, but not by much. If you’d rather save those fractions for tomorrow you can.”
There’s also a code that needs to be broken and to do so he’ll need to answer some triple digit addition and subtraction problems which will help us see if he can tell when to borrow and when to carry without confusing himself. I’m eager to see if he can do this without help, but I also know he’s reached his limit and that his concentration level is gone. 
He puts away his math paper and decides to go wrap the homemade present and card he has made and can’t wait to deliver.

Jayden, in the mean time, has tackled all the problems on his paper with very little help. I was delighted to see addition and subtraction facts with counters, but he had to decide, based on the clue words, if he was adding or subtracting. He’s spend a good portion of time working on word problems the past month and I’m happy to see it has paid off for him.
Last month I wrote out two word problems a day for him basing it on people in our home, games we’ve played, and even favorite characters. I was, however, chastised for one problem when I indicated that 6 penguins were strolling through the zoo and Dr. Blowhole snatched 3 of them. He changed my problem to say, ‘5 penguins were strolling through the zoo and Dr. Blowhole grabbed 2 of them.’ Apparently he couldn’t move beyond the show he’d watched and was greatly insulted by my attempt at entertaining him with math.
After tackling the addition and subtraction problems he moves on to a graph problem as well. Half his data is missing and his job is to fill it in. Again, this requires adding and subtracting and he manages all but one problem correctly. I help him fix the mistake and he answers the questions based on the graph that is now filled out.
There’s also some clock work to do, and he does great with all of the analog problems, and mixes up the digital clock. I find this slightly amusing; I explain where’s he gone wrong and he corrects his work without help. 
The last set of problems are some greater and less then problems. Before he starts he asks, “The mouth eats the bigger number, right?” I nod and he races through the work. He’s drawn some mean looking flowers gobbling up the big numbers and is proud of his work. I help him punch holes in the paper and we file it away in our math notebook.
I’m quite pleased that both of them are capable of doing a grade level paper without help and completely understand the concepts. While we’ve played no games today and didn’t do a vast amount of written work I don’t mind. We often try to do some written math at least once a week. This allows us to see that the boys are truly comprehending what they’ve learned, but I don’t stress about handing them a math paper each and every day.
Today, for school, we only tackle finishing off our read aloud. We’re so close to the end we refuse to put it down before finishing it off.  Then, while eating lunch we opt to watch Liberty Kids, which is an historic cartoon taking place during the Revolutionary War. The boys are so excited about a playdate at a friend’s house this afternoon I decide that watching a cartoon we can pass off for American History is a better choice then trying to convince them to stop watching the clock (who taught them to tell time anyway?) and pay attention to whatever game we would have played or finishing off that paper from yesterday.
This could be a typical ordinary week for us. It’s true that sometimes over meals we drag games into play. For instance a week or two ago I pulled out the game Digit Place again. It’s a simplistic game, and it’s fun to play to help with number neighbors and many other math skills. Instead of using paper I drew the board on our whiteboard. After playing a few rounds over lunch we left the game board. Mr S came home and spotted it and set up a few rounds over tea. 

The boys have also been known to request some of math games “just for fun” because they enjoy them so much. I’m also good for making up word problems over breakfast, just for fun. I’ll say incredibly nerdy things like, “So last night after you went to bed the farmer next door was making such a fuss I ran outside to see what was up! Turns out, he wanted to buy his sheep little gum boots but he had no idea how many boots to buy for 6 sheep. I promised I’d help him, but that I had to get my sleep first. So, do you guys know how many boots I should tell the farmer he needs?” 
Sometimes, Jayden will look at me and say, “Mom are you being serious? Like did the farmer really ask you that?” Sometimes I don’t give a straight answer, at least not until after we’ve worked out the problem.

I like the idea of bringing the problems into real situations. Which, funnily enough I’ll hear the boys doing while they are playing. I’m actually looking at purchasing a few of these so we can start making our own math story book. The idea is that we each write and illustrate a story. You’d use the picture to find the answer to the math problem. I’m pretty sure my two coloring and drawing maniacs will enjoy leaving me stories as much as I will enjoy leaving them some.


Anonymous said...

I really enjoy your blog and have used many of your math ideas with my 3rd grade daughter. I usually print the math papers on card stock and laminate with clear contact paper to make them reusable. We use a dry erase marker and just erase it after we are finished so we save on paper and ink. Thanks for all your wonderful posts!!!!

Phyllis said...

This was very interesting to read. It was nice to see how math is naturally integrated into your days.

cordova607 said...

Thanks for all of the great ideas and websites! You have a really great blog here!