Data Collection Activities are great for introducing functions. I wonder if you were teaching remotely, how it might work to collect and analyze data? I wonder if students were given time to assemble the supplies and collect data at home, if then you could analyze it together online?
A couple of ideas new to me
M & M's, Balloons, Cups and More is a pdf of several activities published several years ago by NCTM. This is a series of six different activities where students collect data, graph the data points, determine which family of functions it belongs to and find an equation for the data. The functions include linear, quadratic, and exponential.
By the way, I found that activity on this site, Mathematics - Algebra for All. There are a number of great activities linked there. Definitely a place to bookmark!
Walk the Plank - When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.
And from a previous post ...
Linear (and Quadratic) Function: Pass the BallAll the information needed for this activity is in this blog post. Students pass a ball to one person, timing the event. Then to two people, three people, etc. This is a very easy lab to set up.
Another activity is the message/whisper chain. Students will enjoy this lab!
The Wave Lab is also a great introductory lab suitable for linear functions!
Pass the Book is similar to the previous two!
If you teach Algebra 2 and want to review both linear and quadratic functions in a single activity ... consider this looking through a tube idea!
Quadratic Function: Stacking Starbursts and Kangaroo ConundrumBoth of these activities are simple, table top activities that result in quadratic patterns. I provide instructions in this blog post.
The Water Flow Lab looks fascinating ...
And EVERYONE loves a catapult! Check out this data collection opportunity!
Square Root Functions: Inclined Plane Data CollectionA copy of the instructions can be found here. Students roll a marble on an inclined plane - varying the distance of the roll, and measuring the time it takes to reach 0.
PhET has a pendulum virtual lab worth investigating if you don't have materials!
Exponential Functions: M 'n M Data CollectionThis is popular for obvious reasons - students love to eat the m 'n ms after the experiment is complete. We do both parts ... exponential growth and decay. The handouts with instructions can be found here and here.
Paper folding also works for exponential functions ... and requires little preparation or materials!
Mathy Cathy explains how she uses the Sierpinski Triangle to model exponential functions!
Rational Functions: Spaghetti Cantilevers
Instructions are online. Students bundle 2, 3, 4, 5, 6 pieces of spaghetti and hang a weight from the end without breaking the spaghetti. They collect the data and analyze it. The rational function is the model for the cantilever.
MORE IDEAS!Several labs are shared in this conference handout!
Also check out this Twitter thread where folks shared ideas for labs!