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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.

  1. There are three glasses and four graphs.
  2. I wonder which graph does not match.
  3. The graphs show the height of the water (in the bowl of the glass) changing over time.
  4. The size and shape of the glasses matches the graphs.
  5. The graphs and glasses have different colors.
  6. Glass A starts narrow but is mostly wide, a little narrower at the top.
  7. Glass A stays almost the same width for a while.
  8. Glass A has the shortest bowl, glass B has the next shortest bowl, glass C has the tallest bowl.
  9. Glass B starts narrow and gets wide in a V-shape. ItŐs sides make a straight line, not a curvy one.
  10. Glass C has lots of curves, changes in its shape.
  11. Glass C starts narrow, gets wider right away, then gets narrow for a long time, then wide right at the end.
  12. Glass C has the narrowest bowl.
  13. I wonder which glass holds the most water and which the least or if they all hold the same amount.
  14. 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.
  15. The graphs all go up to the right.
  16. Graph 1 is the shortest graph, graph 2 is the tallest graph, graph 3 is the next tallest graph.
  17. Graph 1 starts with height changing fast then slows down then speeds up.
  18. Graph 2 starts out slow, then speeds up, then slows down for a long time, then speeds up at the end.
  19. Graph 3 has lots of curves like graph 2 does and like glass C.
  20. Graphs 3 starts fast, slows down, speeds up for a long time, then slows down at the end.
  21. Graph 4 is simple, does not have as many different curves as the others.
  22. Graph 4 is shorter than graph 3.
  23. All of the graphs look like they are the same width, go for the same amount of time.
  24. I wonder if that means that the glasses all hold the same amount.
  25. The graphs show the rate of change.
  26. The slope of the graph changes when the glass shape changes.
  27. If you pour water at a constant rate, then wider glasses change water height slower.
  28. I assume the scales are the same on the graphs.


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