Today for math the boys built minecraft sugar farms. My five year old built one first, a basic strip of three water squares with sugarcane on each side. Afterwards I asked him some questions about the sugarcane. How many sugarcane pieces could he harvest? (It would depend, he pointed out, how long he waited. He could get six if he cut it once it grew two two squares tall, or twelve if he waited until it grew to full height.) What is the ratio of water to sugarcane? What fraction of the blocks used is growing sugarcane? What if we put sugarcane at the end of the water strip as well as at the side?
What if we made a decorative square of a similar pattern? Then how much water was there compared to sugarcane? Did we have to count the sugarcane squares individually or could we notice patterns? (Like eight sugarcane in the center square, 12 for the rows of three on the outside and then four for the little squares all by themselves? 8 + 12 + 4 = ?)
We moved over to using the tile blocks so that my oldest son could make his minecraft sugarcane farm. Using the tile blocks we could move pieces around, so I replicated the minecraft pattern and then asked what would happen if we moved two of the water “edges” out further so that the shape becomes a bit more of a rectangle. By physically dragging the “water” squares over we could see that now there was more room to add more sugar-cane blocks.
My older son was working on what I was sure was going to be a magnificent sugar-cane farm complete with lilypads to use as stepping stones and a fence around it to keep out minecraft animals with the water placed kitty corner to maximize the amount of sugarcane that could be grown in the space.
I wanted to see if I could help my younger son see the logic to his older brother’s farm so before he looked at the computer screen I started to nudge him towards building a similar pattern with the tiles. We started with four seperate waterblocks each surrounded by the four sugarcane that they could support. We talked about the empty space in between and then started moving the water blocks with their associated sugarcane around to fit them together better so there wouldn’t be any empty space left.
Moving tiles around like this really reinforced for me the limitations with minecraft. In minecraft you don’t move anything, you simply change the identity of the square that is there – converting something from filled to empty to filled as something else. You cannot move things thought it may feel like moving something if you destroy something in one location so that you can use that same resource elsewhere. It’s not as much moving as having a quota of how many blocks you can identify with any particular identity. (So if you are putting out an obsidian block and you put it in the wrong place you can’t nudge it over to the right place you have to destroy that block so that you can create a new block in the right place. Your inventory is in some ways more a quota of available identities for blocks.)
Anyway, we slowly nudged the math tiles over so we could see how the little crosses of one water and four sugarcane could fit together, talking about the ratio of four sugarcane to one water, and how that compares with the earlier designs where with water blocks touching each other they reduced how many sugarcane they could support. We could talk about both ratios and fractions. There is 1 water block to every 4 sugar canes. Water makes up 1/5th of total blocks.