' Dr Ell's Math Blog: November 2009

Monday, November 30, 2009

Pattern Trains

     The object of this game is to copy or continue a ‘train’ pattern. I like using Cuisenaire rods for this game because of their versatility and potential for gradual increase in complexity– but the basic idea works with any number of materials including pattern blocks, building blocks, Legos, buttons, bottle caps, coins, and so on.
     The pictures that follow are pretty much self-explanatory, but I do have a few general suggestions. First of all, keep it fun– don’t frustrate. Reverse roles with your little person sometimes and let him create a ‘train’ for you to continue. Obviously, don’t use coins or very small objects with very young children who might swallow them. (Note- coins can be washed and probably should be.) And finally, I have found that verbalizations are very helpful to understanding a sequence. For example, a very simple train might be a sequence of alternating red and white blocks. Saying or chanting “red-white, red-white, red-white” as you lay down the pattern helps clarify the intent. Your little person can continue the “red-white, red-white, red-white” chant as she continues the train.
     As train sequences become more complex, not only color and size can be varied, but positioning variations (vertical, horizontal) can also be used.

Red-Yellow, Red-Yellow, Red-Yellow...

White-White-Red, White-White-Red...


Purple Up-Red Down-White, Purple Up-Red Down-White, Purple Up-Red Down-White...


Green Up-White-Green Down, Green Up-White-Green Down, Green Up-White-Green Down...


Yellow-DoubleRed, Yellow-DoubleRed, Yellow-DoubleRed...

White-White-White-DownPurple-UpRed, White-White-White-DownPurple-UpRed...



Pattern Block Trains



More Pattern Block Trains


Lego Trains (More Views of the Same Trains Below)






Coin Trains: Dime-Penny-Penny, Dime-Penny-Penny..., Penny-Quarter, Penny-Quartr..., and Penny-Penny-Penny-Penny-Penny-Nickel, Penny-Penny-Penny-Penny-Penny-Nickel... or, One-Penny-Two-Pennies-Three-Pennies-Four-Pennies-Five-Pennies-Nickel, One-Penny-Two-Pennies-Three-Pennies-Four-Pennies-Five-Pennies-Nickel...

Hungry Joe

     I invented Hungry Joe years ago as a way to work with very young kids on math comparison ideas. It simultaneously introduces the math symbols to go with the concepts.
     All you need are three index cards with a hand-drawn face on each:

     These are used to play a game. Hungry Joe has a crazy appetite. He always tries to eat the larger object or quantity and his ‘mouth’ opens accordingly. When two objects or quantities are equal Hungry Joe is at a total loss and his mouth just drops open into an equal sign. So if I place a large apple and a small one on the table, the object of the game is to place the correct Hungry Joe face between the apples. A large apple on the child’s left and a small on the right requires the Joe card in which the ‘open’ end of his mouth is facing left.
     The same game can be played with counters, cuisenaire rods, toys of various sorts, glasses of water or juice, M&M’s, building blocks, real world objects– big chair vs little chair or two chairs vs five chairs– and so on. Some examples (exploring both size and number) follow:

Hungry Joe will choose the two-chair option for his meal.

Oops! Hungry Joe can't decide because both options are the same.

Hungry Joe will definitely go for the two cans.

Four forks beat three.


The big vehicle makes a better meal than the smaller.   

Those fishies are the same size!

 A big turtle beats a little one. 

     More sophisticated objects/ideas can also be introduced when appropriate, for instance a dollar bill on one side, three quarters on the other and eventually regular numerals, fractions, or decimals can be used.
     Remember this should be fun or it won’t really be helpful. Your little person may want to draw his/her own Hungry Joe faces or pose problems for you to solve. Taking turns works well.
     Eventually a revised ‘Hungry Joe’ in which only the mouth on the face remains can be used as a transition to using the ‘mouth’ images as stand-alone symbols. Here are a couple of examples:

Have fun– make up your own variations.