Simulic
English

Quantities changing together – sketching graphs for filling vases and a bike ride

MathematicsFunctions & GraphsAges 15–16

Loading…

Use with my class ✨ Customize with AI Report a problem

Fill a cylinder, a cone, a round flask, a bowl or a vase you design at a constant rate, or follow a bike ride; drag points to sketch the height–time or distance–time graph, then compare it with the true graph. A tandem animation runs the vase (or the bike) alongside the graph and colours the intervals where it is increasing, decreasing, concave up or concave down; a variation table and the greatest and least values are read straight from the graph, without calculus.

Lesson: Functions and graphs: qualitative graphs, intervals of increase and decrease, variation tables

What it shows

When water flows into a vase at a constant rate, the volume grows steadily, but how fast the level rises depends on the width of the vase at the water surface: wide sections fill slowly and narrow ones quickly. The height–time graph therefore always rises, yet it bends down where the vase widens, bends up where it narrows and is straight where the sides are vertical. The bike ride adds intervals where the distance from home increases, stays constant and decreases, so the graph has a greatest value. Students predict first, then compare with the true graph.

How to use

Choose a Vase, drag the orange points to sketch your predicted graph, then press Play or drag Time to watch the vase and the graph move together. Press Show true graph to compare and read the score. Use Highlight to colour increasing and decreasing or concave up and down parts. On the Bike ride screen, sketch the distance from home and read the variation table and the extreme values.

Parameters you can change

  • Screen Filling a vase, Bike ride
  • Vase shape Cylinder, Cone (wide at the top), Round flask, Bowl, Design your own
  • Flow rate 20–200 mL/s
  • Ride To the park and back home, Over a hill to a friend's house
  • Colour the true graph by Automatic for the screen, Increasing / decreasing, Concave up / down, No colouring
  • Show the true graph from the start
  • Animation speed 0.5–4

Questions to explore

  1. Why does the height–time graph of a cone that widens upwards bend downwards?
  2. What vase shape would give a straight, then curving-upwards height–time graph?
  3. On the ride, when is the distance from home greatest, and how does the variation table show it?

Related simulations