Number Conservation / Conservation of Mass

L and E (40 months) are really good at counting, but I also want them to have number sense and know they can solve mathematical problems using logical reasoning and intuition as well as standard processes (counting).  We've been doing a lot of "magic tricks" with math lately to work on the concept of number conservation.  According to psychologist Jean Piaget, this ability doesn't develop in kids until 7-12 years, but I think my kids are already catching on to it, or at least asking questions and thinking about the problem.  Here are some of the exercises we've been doing...

We use small snacks a lot because eating them adds to the fun.  One thing we do is have the girls count out 5 goldfish crackers, then I ask them to separate them into different piles or put them in different shapes, spread them out, etc.. and then tell them that they are amazing magicians and can tell me how many there are without counting them.  At first the girls looked at me blankly.  Then I asked them if we added more goldfish?  (No.) Did we eat any goldfish? (No.).  So we still have... five!  Once the girls caught on, they were pretty excited that they knew how many there were without counting.  (Of course I made it into a big dramatic production for extra fun).

Along those same lines, we also line up various snacks so it is obvious that there are the same number of objects of each type of snack (put them in pairs).  Then before the kids have time to count the goldfish, I put them into my fist and then see if they use the count of the different type of snack to tell me how many goldfish are in my hands.  Sometimes we extend it when I have one of them slip an additional cracker into my closed fist or remove one and then ask the girls how many there are.

Another favorite is putting the goldfish crackers in 'chairs' and then removing either chairs or goldfish.  Then I ask if there are more goldfish or crackers and how they can tell.  In the picture above, we worked with crackers placed in a circle because it's harder for the kids to solve problems by counting because they always forget where in the circle they started counting.

We're also working on conservation problems using non-discrete values.  in the photo above, all three cups are actually holding the same volume of water.

 

Most of the fun in this exercise involves pouring water into the cups and from one cup to another.  I'm not sure if my girls really understand that different size cups of water can really hold the same amount of water when the water levels differ, but it's great for them to explore this concept, ask questions, and make predictions.

All these activities are so simple and require no preparation or special supplies, and the kids have a great time doing 'magic tricks' with math concepts.