Real Life Graphs: Filling a Beaker
Introduction
In today's lesson, you will consider how the shape of a beaker affects the rate at which it fills up. Before we start, have a quick think and write down your answer to the following question in your book:
Does a wide beaker fill quicker or slower than a thin beaker? Why?
Quick Note: in all of the animations below, the beaker fills after , but the important thing to think about is how quickly the water depth changes depending on the shape of the beaker.
Activity 1: Match the Beaker to the Graph
This interactive app allows you to change the shape of the beaker (by dragging the blue dots) and to see a graph that represents how the depth of the water changes over time.
* Have a play with this example to see how it works. Start by pressing "Fill the Beaker!". Is the shape of the graph what you expected?
* Try changing the shape of the beaker (using the blue dots). Does the graph change in the way you expected?
Be aware: the graph can glitch depending on how you design the beaker - just be careful with this.
Once you have familiarised yourself with the app, the first activity is to match the graph and the beaker below. Use the app to create each beaker (as close as possible), and determine which graph it matches with.
Beaker 1 Type the letter of the correct graph.
Beaker 2 Type the letter of the correct graph.
Beaker 3 Type the letter of the correct graph. You can't make the exact shape for this beaker, try to match its shape approximately and use that to determine which graph it matches with.
Beaker 4 Type the letter of the correct graph.
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Activity 2: Draw the Graph (given the Beaker)
In this activity, you need to draw the graph of the water level changes for six different beakers. Again, use the app at the top of the page to help you.
* For e) and f), you cannot make the shapes exactly in the app. Use what you've learned about how the shape of the beaker affects the graph to try to draw the graph.
Copy down the beaker and draw its graph into your book (the answers will be at the end, but use the app to check).
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Activity 3: Draw the Beaker (given the graph)
In this activity, you are given the shape of the graph and you need to draw what the beaker may look like. You can't now directly use the app, but you can use it to help you. Have a think about the following:
* What does a steeper line represent in the shape of the beaker?
* What does a shallower line represent in the shape of the beaker?
* When does the gradient of the line change?
Copy down the graph into your book, and have a go at drawing the shape of the beaker (the answers will be at the end, but use the app to help you).
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Activity 4: Questionnaire
The last part of today's lesson is to complete a short questionnaire linked below. It should take less than 5 minutes to complete, and your responses will help us to see what you thought of this type of activity.
https://docs.google.com/forms/d/e/1FAIpQLSctux1DKXO8rpK2XA-1Z9dX4PzXbWhgJHV5mUVkRDzPNJACCg/viewform?usp=sf_link
Once you complete the questionnaire, you can access the answers to Activity 2 and 3. Please mark and correct your work with green pen.
Finally, please send pictures of your work to me (I'll pass on to your class teacher if it isn't me!), or email me if you have any questions about today's work.
*** If you are not a student at STACS, please complete the questionnaire anyway, indicating who you are in Q1. If you are a maths teacher, answer according to the lessons you teach, and if you are a student/adult answer according to how you remember your maths lessons at your school. ***
Thank you,
Mr Winfield
Answers to Activity 2: http://tiny.cc/ifw6lz
Answers to Activity 3: http://tiny.cc/fgw6lz