Friday, May 11, 2012

We're back! Update on Math Learning and Activities!

We're back! Well, sort of. Just before our big move the motherboard on my computer died! I have luckily taken many photos with my phone that I can use here and am utilizing our new library as much as possible until our computer is back. We're quite please with our new home (and state!) and Tyler has adjusted very well. He has made many huge speech and developmental leaps since just after our move and has recently started on the exciting journey of sounding out words and learning to read! I can't believe it! He is still quite focused on math though and this post will cover that. I will get to other activities and our adventures in literacy in a future post!

I feel like I do need to say again that Tyler's progress with math is not at all typical and that toddlers (he's 32 mos now) aren't expected to learn as muchs he has decided to take on. I also have to say that I can take little credit for what he's done and learned. There's surely something to say about providing materials and an environment that allowing the child to teach himself (per Maria Montessori!), but I also feel like I did a poor job with even that during the month before and after our move. It has cemented the idea in my mind that if a child wants to learn something, they'll find a way. I still enjoy and will of course continue to chase after his interests with activities to expand his learning, it's nothing but helpful for him and fun for me, but if you're not staying up late every night trying to develop activities or buying lots of expensive toys and materials, it's really, really okay!

Starting where we left off, back in our old home, we did an activity which combined one to one correspondence with pretend animal picnic! We started out with four chosen animals and a stack of four plates, bowls, spoons and cups. His job was to give one of each to his animals. I also had four fake fruits, four vegetables, four breads and four meats for him to distribute evenly between his animals. After passing each food category he helped the animals eat their food. This was a lot of fun!

This photo shows a cutting activity that combined Tyler's love for numbers with small motor work. I cut strips of paper and wrote numbers 1-5 on them, drawing a line between each  number for him to cut on. He still needs some help with scissors, but this activity was highly motivating for him!

As I talked about in a post regarding time back in January, I started a daily calendar work with Tyler this year. A bit of a "problem" arose back in March though when Tyler wanted to cross off all of the days before they were up. He wasn't trying to be destructive of course, he was simply interested in sequencing and learning how to use the calendar. In response, I dug out a several old calendars that I had lying around (it's good to be a bit of a pack rat sometimes!) so that he could mark them as he pleased. This ended up being a favorite activity for weeks. He enjoyed naming the days and crossing each off in order over and over.

When visiting our local library, we often played a modified version of dominoes, simply taking turns matching the quantity of numbers to each other in a line. This gave him more practice visualizing how much a number really is and what it means.

I finally made Tyler the sandpaper numbers! I used green card stock, cut numbers from sandpaper using templates found online, and backed it all onto cardboard. He enjoyed tracing the numbers and was soon putting them together to make bigger numbers. The latter was the most exciting part for him! Creating big numbers and learning to read them became a large interest for quite a while. I can't say that I taught him much of this, but when asked questions or showing interest, I did help him with what he wished to know.

This was an activity that I'm not especially proud of as it isn't very Montessori at all, but it was something I dreamed up and just had to make. Using his sandpaper numbers, Tyler would choose two numbers to place in squares on this board (one always being a number one, per my instructions to keep it simple), then placed the correct number of gems in the square below each. He would then count the gems to figure out how many he had all together (even if he knew the answer). He would then find that sandpaper number and place the total gems in the box below. I introduced him to the "plus" and "is equal to" verbage here as well.

Tyler started to use his abacus to count by tens to one hundred, something he can now do to at least 200 without any visuals. Skip counting by different quantities became a big interest and he continues to want to learn more ways to do it even now. I enjoy seeing him use the abacus as a visual tool.

Tyler became interested in he way numbers are arranged on a clock face and used this book to learn about that. He then began flipping the book upside down to challenge himself in reading the numbers this way. I find it amazing that I do so little to help him learn sometimes...he just goes after it himself.

In one of my last posts I mentioned that we had began playing hopscotch outside. This quickly turned into Tyler adding ones before or after the number to make them bigger then reading the new number. As you'll see, chalk and large spaces has been quite instrumental in Tyler's learning!

Then one day, after asking me to write a number nine for him a few times on his Magna Doodle, Tyler went outside and started writing numbers one, zero and nine all over our driveway.

Until we moved, filling the driveway with numbers was a daily practice for him. He couldn't wait to get outside to write in such a large space. We had the most colorful driveway on the block for sure!

We also tried Crayola Sidewalk Crayons which were wonderfully bright, but they're also great at staining clothes, so they were only used along with water play days (i.e. no clothes other than old shorts).

Tyler's numbers soon advanced to writing some 2's, 3's, 6's, 7's and 8's and putting them together to make two-digit numbers, then announcing them. This was all on his own. My husband and I would just stand back and look at each other with our jaws on the ground. He's still working on making 4's and 5's and struggles with 2 and 3 most times.

Ty also enjoyed having us make large numbers and jumping from the hundreds to the thousands etc as we called them out. It's this sort of thing that makes you have to look-up and learn that after a trillion comes quadrillion!

Tyler expressed an interest in learning how to read a digital clock, so I taught him how to read time. He still gets a big kick out of me asking him what time it is and running to a clock to tell me. In our new home he has his own small digital clock on top of one of his shelves. He will often ask me to change the time over and over again so he can read whatever it is and quiz himself! I have my eye on a Melissa and Doug face clock which I hope to purchase for him soon.

Since Tyler understands quantity quite well and which number is bigger or smaller than another, I decided to introduce the game of War to him. It isn't his favorite game, I think he finds it a bit boring, but he's done well the few times we've played.

I also created a numbers "BINGO" game for us to play using card stock and poker chips. He still enjoys this one from time to time!

I often hunt for toys and materials at thrift and consignment stores and this find, Chutes and Ladders, was perfect! We have never gotten past the sixties on the board, but Tyler enjoys playing here and there. The board is quite visually distracting with all of the ladders and slides. It makes me want to develop my own, cleaner game.

Going back to our driveway, Tyler and I collected pine cones on a neighborhood walk one day then returned home to use them as counters! I wish I could remember where I saw this idea, I know for sure that it's borrowed, so be sure to comment and take credit if it's yo

Just before we moved, Tyler's number recognition and creating large numbers skill really took off. He was able to recognize numbers past 100 on his MP3 player screen and was so proud of his abilities. That's truly what excites me the most about all of this...the pride and self esteem that he has gained through learning, and knowing how much of it he's done on his own. Flashcards and forcing a child to learn can't and won't do that! It's Montessori at its best!

This numbers puzzle was also consignment sale find. He isn't into cardboard puzzles as his fine motor skills are a big behind, but this one was very motivating and an instant hit! His ability to put the pieces together has improved now with practice. He can't resist sequencing!

Another board game that we've enjoyed and that has been helpful for understanding quantity as well as subtraction and addition has been Hi Ho Cherry-O. He shocked me the first time we played by taking four cherries (from ten) off his tree and saying "six!". This is a fun game that of course also practices valuable turn taking, especially when playing with more than two people.

Though he beat me at UNO the first time we played ("reverse" and "skip" cards removed to make it easier to grasp), he doesn't often chose to play it. This is his "I won" face here though! Great game for number and color recognition.

These magnetic numbers I pulled out just before we moved became a huge favorite with Tyler and still are, though he now mostly uses larger magnetic numbers that we purchased from Mellisa and Doug so that he has a good amount of each number. He enjoyed creating three digit numbers, then sequencing, and is still working on higher level sequencing. This is typically what he does first thing in the morning, often before I even get downstairs.

The dollar store calculator has been a favorite item for Tyler in the last few weeks. He enjoys adding and subtracting small numbers with it after I showed him how to use it. It isn't the most Montessori thing in the world, but this is what he enjoys and he's certainly learning something from it. Another thing that I've learned is that though I don't always know what he's trying to learn (sometimes it just looks like wasted time to me), something always comes of it. I have to trust that he knows what he's doing!

When packing, I found an old, soft tape measure that Tyler adores. He enjoys pulling it out to see how the numbers get higher and higher, and we also measure with it. We measure objects as well as body parts on himself, me and my husband to see the differences. y also helped me measure walls when I hung pictures. Here he decided to get his calculator out to punch our measurements of each objects and add them.

Using his sandpaper numbers as motivation, I showed Tyler how to use a spring-loaded clothes pin. His work was to clip one clothes pin to the number one and two to the number two, etc. This proved to be tricky for him and the cheap clothes pins I purchased kept sliding off of the pin, but we'll try again in the future with better pins.

Tyler showed interest in fractions after I talked about splitting sandwiches and other food items in half. We then began to cut items into halves and fourths together in the kitchen. This led to us drawing fractions on his new chalkboard (a must now that we're in a town home without a private driveway!). He enjoys creating these at times and is proud to be able to use the words "half" and "fourths" in every day life. I would really love for him to have some sort of tactile fractions for him to use in the near future.

After talking about "eating letters and numbers" (not sure where that came from), we decided to use a recipe for number and letter cookie dough by Cookie Monster that we found in one of my old Sesame Street Treasury books. Though the dough ended up being more delicate than pie crust and tricky to shape into anything for even me and my husband, Tyler did manage to make a seven all by himself! Eating number and letter cookies for the next week was very exciting for him!

Tyler enjoys large numbers such as thousands, millions, billions and trillions and being able to recognize them. I actually wrote all of them down in number form and hung them on the wall next to his chalk board so that he could create them himself and also so I wasn't writing them out so many times a day. He then asked me what 100 zeroes would be. I had no idea and had to look it up! Turns out that number is a "googol" and Tyler wanted to see it...and then requested that I add one googol to another googol. He really enjoys equations! Though I would rather he work with on quantity learning, he prides himself in knowing that answer to questions to so many addition equations. He will often tell me something like"100 plus 100 equals 200!" or "5 plus 5 equals 5!" with a smile that you can't resist.

One mornng, at a loss for what to teach him next without more Montessori-like Materials and not much time or energy to create something, I thought Tyler may be interested in learning to tally numbers. He thought it was a fun concept!

Though Tyler has been all about helping make his own food (and mine too!) we don't tend to use a lot of recipes. Cooking with a recipe is so helpful for learning math concepts and the fractions he has interest in, so we've tried to make more special meals or treats using lots of measured ingredients.

I haven't found the resources and patience for creating my own Montessori beads just yet, but I know that if he's willing, Ty should be using more tactile materials for his math learning. Until I make or buy the the bead chains, I have used popsicle sticks to create tens, fives and ones for him to create visual numbers with. If I decide to use these long term I will paint the the different quantities different colors, though they work for now. To the right he made 120, and at the left was working towards another number using a five and singles.

Again, this chalkboard has been amazing. I write the date for him each day in one corner and he loves to read it for for us (or change the number to trick us!), and here he wrote a favorite equation at the time "1 + 0 = 1". If you're interested in this chalkboard, I found it here here on Amazon for only $20! I hung it to our wall with removable picture frame mounting squares.

Can anyone figure out how this equation makes sense?! I think he's on to inventing a new kind of math. I enjoy finding these!

I'm working, as stated a bit above, on really making math more tactile and visual for Tyler, as is the Montessori way that I believe in. If you can't tell, it bothers me that I've been naturally too busy to work on this. While he can do things like count backwards from 50 or from one hundred by tens, to one hundred by fives or count by hundreds past a thousand and it's really, really neat, I want him to have a better sense of what he's saying. I recently toured a local Montessori school and was drooling over the mathematics section!

Our next post will update you on other Montessori activities we've been up to and look for a post on our adventures in reading soon as well.!Hopefully this post hasn't been to full of errors as I rush at the library. Regardless, it's great to be back!


  1. Glad to see you posting again! Outstanding Math activities! Go Tyler Go!! Thank you for sharing.

  2. I love to see that your move went well (other than the computer issue) and that you're back online, Jen! Wow - what exciting happenings with Tyler! It's awesome to see child-led learning in action! The pine cone numbers and counters started with What DID We Do All Day? I featured the activity as an activity of the week once. You probably saw it in my DIY Cards and Counters post: Thanks so much for linking up with Montessori Monday. You're doing such great work with Tyler ... I'll look forward to seeing what happens next! :)

  3. So glad to have you back blogging- I missed you!!

    Looks like Tyler has gone ahead in leaps and bounds with his maths progress- Noah is also really interested in numbers and pointing them out but hasn`t shown much interest in learning to write them or tracing them with his finger when I show him on some cards. He loves pointing out numbers out and about though so I might try a digital clock with him! He loves my watch!

    So many great activities here!

  4. Wow, what a lot of ideas!!
    I think your son and mine have a lot of common!

    Thanks for sharing !!