Math Vignettes

The Habitat

On a rectangular board about 25 by 40 cm J was going to create a habitat.  She began in her usual way placing trees in the space and calculating a pattern that would fit for her herbivores. The lay out was symmetrical and pleasing to look at. Today, however, something different happened. She had space left in the back and she decided to add carnivores to this habitat. 
Very carefully she matched the carnivores to the herbivores and then placed trees in strategic places to hide them. She then presented this version to me, explaining how this is a food chain habitat. "This is the best one I have done," she proudly exclaims as she tells me the progression of sun to plant to herbivore to carnivore set in layers on this rectangular piece of wood. A creation of beauty, perfectly balanced that would fit under negotiating space, geometry and symmetry, etc. It is all a matter of  perspective.

Negotiating Measurement

The children are still enjoying placing macaroni beads in repeating patterns to make necklaces they actually wear day after day to school and share with one another. Today, D, decided to make one. She had not had a chance to do this and was by herself at the table. Very carefully she pulled out a piece of yarn and cut what she thought was a long enough piece. She came to me to put a knot in it as she wanted to start her necklace. I held up the yarn and asked her again if she intended this to be a necklace. She assured me she did and I asked her how she could make sure it would fit. She held it up to her neck and realized it was too short. Now we had a measuring problem. D knew she wanted the next piece of yarn to be bigger than the first one. She did not use the first one to measure from. She tried instead to take the yarn and go around her neck. Two times did it and then she took it off, measuring with her finger the correct spot to cut. This string was very long. Problem two was solved by placing it on the table and this time making sure it was still longer than the first piece but still shorter, she cut the yarn to make it smaller. The problem was solved, measurement in practice, in this case a kind of negotiation of length. 

Building Towers

There are pattern blocks at one of the pattern centres and today I watched as a child began the age old practice of building towers. There is this urge to place block on block that I have seen in very young children through to my 5 year olds. At first she piled the hexagons one on top of the other with the sides touching. This structure kept falling. Then she tried piling them up with the flat side on the table. This was much steadier and while the tower did get higher, it continued to crash. She was joined by a friend at this point and both began building the same tower, which inevitably fell. The girls did not leave but kept at this. Then something changed and the first tower was built at an angle and joined by a second tower to create an arch. It was a stable arch and the girls were very proud and satisfied to create this structure. It reminded me of a picture I once saw of the Inuit stone sculptures. This was geometry in action, much like our work yesterday with the volcano as we attempted to make a cone shape and had to figure out what shape folds into a cone.

Beach Number Stories

Today, March 11 D, wanted to create some number sentences during center time.  He sat down with the magnetic manipulative board of the beach scene and used these to check his answers.  He had to work out a way to do very long number sentences.  His goal was to do "harder sentences, I want to do both to make longer sentences."  He began to work out  a way to do what he wanted.  I will never underestimate the amount of work one will do to achieve ones own goals.  He spent about 30 minutes working and writing out the following problems.  For each problem he would set up the manipulatives and check his answer.  In other words he first created the problem and then wrote it out and then rechecked it. 
By his third problem, I decided to intervene and present some information that I thought he could handle and that he needed.  "D, because you are doing two steps in each of your problems, I want to show you some punctuation that will tell anyone who reads your sentences which part to
work on first"  These are called parentheses.  When you put these marks around the first process, this tells me to do this problem first and this problem second, in order to get this answer.  He liked this idea and then
put these marks in those problems that he had done, and the ones that followed.  I had him share his work with his classmates and then told him that he was doing about grade nine work now, a sort of pre algebra.  Here is his work, he is 6 years old:

(6 + 3) + 2 = 5
(0 + 3) - 0 = 3
(1 - 0) + 1 = 2
(2 + 2) - 1 = 3
(3 + 3) - 4 = 2