Filling Glasses: Noticings/Wonderings
This is a list of noticings and wonderings that the Math Forum generated. We're using a numbered list but they aren't in any order of importance.
- There are three glasses and four graphs.
- I wonder which graph does not match.
- The graphs show the height of the water (in the bowl of the glass) changing over time.
- The size and shape of the glasses matches the graphs.
- The graphs and glasses have different colors.
- Glass A starts narrow but is mostly wide, a little narrower at the top.
- Glass A stays almost the same width for a while.
- Glass A has the shortest bowl, glass B has the next shortest bowl, glass C has the tallest bowl.
- Glass B starts narrow and gets wide in a V-shape. ItŐs sides make a straight line, not a curvy one.
- Glass C has lots of curves, changes in its shape.
- Glass C starts narrow, gets wider right away, then gets narrow for a long time, then wide right at the end.
- Glass C has the narrowest bowl.
- I wonder which glass holds the most water and which the least or if they all hold the same amount.
- I wonder if I can match up the glasses to graphs by how tall their bowls are and how high the water level goes on the graph.
- The graphs all go up to the right.
- Graph 1 is the shortest graph, graph 2 is the tallest graph, graph 3 is the next tallest graph.
- Graph 1 starts with height changing fast then slows down then speeds up.
- Graph 2 starts out slow, then speeds up, then slows down for a long time, then speeds up at the end.
- Graph 3 has lots of curves like graph 2 does and like glass C.
- Graphs 3 starts fast, slows down, speeds up for a long time, then slows down at the end.
- Graph 4 is simple, does not have as many different curves as the others.
- Graph 4 is shorter than graph 3.
- All of the graphs look like they are the same width, go for the same amount of time.
- I wonder if that means that the glasses all hold the same amount.
- The graphs show the rate of change.
- The slope of the graph changes when the glass shape changes.
- If you pour water at a constant rate, then wider glasses change water height slower.
- I assume the scales are the same on the graphs.
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