Developing Mathematical Thinking

Most days, after lunch, I offer a variety of math manipulatives for the children to learn  play with.   They don't realize that they are sorting, patterning, organizing data, or learning, they are too busy enjoying the materials.  I change what's available each day, and make sure there are both open ended activities and more structured choices available.  The kiddos use what interests them, or join in with what their friends are doing.  I do a lot of watching and listening, and ask "what if..." and "could you..."  

On the table in the foreground you can see children using felt rectangles to define their space as they work with plastic beads shaped like vehicles, and a toy with foam shapes to sort.

 

 I have a dozen or so baggies with buttons in them for our Venn diagram sorting.  As you can see, this one has red/black/both, others have options like star/blue/both, or  yellow/flowers/both.  I started with my button box, and made sets with what I had on hand. 

 Look how this child is using the cuisenaire blocks to build a 3D structure.  I love how she is using a blue and an orange block in this picture, but in the following one she has changed to 2 blue ones (of equal length) to support a crosspiece.

 Here's a close up of the vehicle beads.  We've only had these a couple of weeks, and most of the children are still sorting by vehicle type.  One day last week I joined in the play and sorted by translucent/opaque and sub sorted by color.  A couple of kiddos joined in.  I'll watch and see if that idea reemerges.

 Here the kiddos are playing a game of Grab and Graph Pattern Blocks, a freebie I found via Pinterest, at http://petersons-pad.blogspot.jp/search/label/graphs.  They grabbed a handful of blocks, sorted, counted, then graphed.  Awesome activity!

 Here the children are using mini erasers to sort.  We're using the felt rectangles to define our work spaces.  You can see how this child started out by stacking the yellow and green rectangles, then carefully sorted triangles and butterflies, before running out of steam on the various other shapes and colors.  Look how proud she is of her work!  She'll keep choosing math games to play, because she's having fun while she learns.

 This fun game is called Mosaic Mysteries, and came from Discovery Toys many years ago.  It is made up of hundreds of variously colored trapezoids, and just fitting them into the hexagon board is a puzzle, as the children have to orient each trapezoid differently so they all fit together.  Here you can see this kiddo worked really hard to recreate a pattern with the blocks.

 Here are some more pattern blocks.  In this case, the boys have worked together to fill a space completely.  Several of the shapes fit together in a lot of ways, but the squares and narrow diamonds have different angles than the other shapes, and provide a real challenge.

 This is a money counting game I came up with.  We enjoy the Jack Hartman song "Show Me the Money" on youtube.com, so I took the words, added images of coins, and made a game board.  The children roll the dice and take that many pennies.  As they are able, they regroup the pennies into nickels, dimes and finally a quarter to end the game.  When I very first started teaching,  I used fake coins, but I quickly realized the value of using real money.  In 18 years of using real money, I've only ever had one child take any home with them!  In that same time, hundreds of children have seen and felt and handled real money, and know what it really looks like, and the weight of it in their hands.  It is shinier and much more interesting to the kiddos than the fake stuff, which they all know is just a toy.  I've saved money by not purchasing fake coins, and I can spend these if I ever need to.  Real is definitely better!

 Puzzles!  We do lots of jigsaw puzzles.  Again, I change out what is available all the time, and have puzzles out to meet the needs of all my learners.  Many of the kiddos start out with just fitting pegged puzzles together, simply matching the shape of the puzzles and holes.

 We work up to the 100 and 150 piece puzzles.  Almost done!

There are so many ways to incorporate mathematical learning into our every day activities!

Seed play

Today I thought I'd share some of our fun seed play ideas.  I have to give credit to Tom Sensori, of http://tomsensori.blogspot.com/ for really inspiring me with his contraptions for play, and to many many pinteresting people who have shared their ideas too.  My kiddos have not grown tired of seed play, at least partly because I change it up every week or so.  Here are some of our recent ideas:

Plastic critters to hide and seek in bird seed...

 

 Pirate treasure!  Compasses, plastic coins, jewel gems, some cardboard treasure chests, old mismatched earrings, shiny bits and bobs... whatever you have on hand.  And of course, telescopes (cardboard tubes)!

 On this particular day we couldn't get outside, so I put a car slide toy in a huge, flat cardboard box, added pinto beans (I found a 10lb bag at Costco) and some kiddos, and viola!  Fun in a box.  This was really noisy too, so I was relieved to be able to put it away once the kiddos went home!

Water play toys and tubing with bird seed.  The seeds clogged up the toys, so we had lots of fun wriggling fingers and sticks down in the seed to unclog them.  The tubing is from an old game that I bought at a garage sale, just so I could have the tubing.  As the seeds move through it, they make a lovely, soft sound.

 This was a huge pile of nuts in the shell, plus popsicle sticks, corks, clothes pins... all natural woody materials.  The different shapes went down the tubes in different ways, but the pecans were everyone's favorite.

 This contraption was made with a shallow box that photo frames came in, and another, slightly larger box.  I created a drawer with the shallow box, and the kiddos put pinto beans down through the holes in the top, and enjoyed putting their hands down into the box to retrieve them, as well as sliding the drawer out of the way.

As you can see, none of these toys cost much money - you can see the cut off 2 liter soda bottle cup, an empty candy tin, and an old toy being used as scoops, boxes being reused before they're recycled, the nuts were none-the-worse for wear for being rolled... these creations are inexpensive, and just require some old boxes, duct tape, and imagination to build.  The seeds can be stored and reused, and aren't too hard to clean up.  The only thing that really gets used up is the bird seed, as it is hard to get it all up!  Not to worry, as soon as the kiddos leave, the seeds we didn't pick up become squirrel and bird food.

So what do the kiddos learn from our seed play?  Co-operation, fine motor control, the various ways things can move, gravity, language skills as they talk about what they are doing, imagination... all terrific skills for preschool and kindergarten kiddos to develop.  Won't you join the fun?