Summative Task for Quadratics – #MCF3M

My Grade 11 e-Learning math class is completing a unit on quadratic equations. I have a few things happening for their summative assessment, but the part I find most interesting is the following “experiment”. It’s heavily based on the Leaky Tower task from TIPS4RM at EduGAINS.ca. I’m going to test it out tonight with my kids before I finalize the evaluation criteria and post the task. If you have feedback, I’d love to hear it. I’ll be adding photos to help explain the setup.

Leaking Bottle – Summative Task – Part 1

You’ll be completing a short experiment and writing a report to go with it. You can get help from a classmate, family member, etc. while running the experiment, but just as an extra set of hands. No one should be helping you with the math part.

Preparation

Gather the supplies you’ll need:

  • a clear, disposable, empty, plastic bottle
  • a ruler
  • a watch, phone, or other time-keeping device OR a video-recording device.

—photo here—

Carefully poke a hole in the bottle about 3cm from the bottom. Seriously, be careful here. You might try using something sharp, like a pin or a nail, to start the hole, then widen it with a pencil. You want the final hole to have a diameter of 3-7mm. Don’t worry about being super-precise.

—photo here—

Hold a ruler next to your bottle, or tape a ruler to your bottle if you need both of your hands free. You want to be able to measure the water level, so put the “zero” end of the ruler at the bottom.

—photo here—

Cover the hole and fill the bottle with water. If your bottle has a tapered top (like the one pictured here), only fill it up in the cylindrical section (i.e. before it starts to narrow). You can cover the hole with your finger, or you might try a piece of tape (if you use tape, fold the end on itself so it’s easier to remove).

—photo here—

Data Collection

If you’re recording video (easier, I think), start recording. If you’re just using a watch or other timing device, wait for a “good” time, like a whole minute, for a starting point.

Uncover the hole, letting the water in the bottle flow out into a sink or another container. Don’t make a mess; nobody wants a mess.

—photo here—

If you’re using a watch, use the ruler to record the water level every 5 or 10 seconds or so. Pick an easy time to keep track of. Record measurements until the flow of water stops.

If you’re recording a video, let the water finish flowing out, then stop the video. Play the video back, noting the height of the water every 5 or 10 seconds or so.

Analysis

You now have a table of values: time (independent variable) and height measurements (dependent variable). If you didn’t get good data (you lost track of time, the video didn’t work, etc.), perform the experiment again. It doesn’t take long.

  1. Using Desmos, create a scatter plot for your measurements.
  2. Find an equation to fit the data as best you can.
  3. Identify the key points on the graph.
  4. How should the equation you found be restricted? i.e. what should the domain and range be?
  5. Write the equation you found in Standard Form and Vertex Form.

Leaking Bottle – Summative Task – Part 2

One small change

Repeat the above experiment, but this time put another hole about 7-10cm above the first one. Uncover them at the same time, so water will flow out of both holes.

—photo here—

Your analysis will be a little more complex, because you won’t have a single, nice equation that can accurately model the data.

  1. Using Desmos, create a scatter plot for your measurements.
  2. Find an equation (or equations!) to fit the data as best you can.
  3. Identify the key points on the graph.
  4. How should the equation(s) you found be restricted? i.e. what should the domain(s) and range(s) be?
  5. Write the equation(s) you found in Standard Form and Vertex Form.
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