I love how Desmos Activity Builder has given students the opportunity to discover many concepts in mathematics at their own pace. A well designed activity will get them to predict, test and validate their ideas, helping misconceptions come to the surface along the way. That light bulb moment when you hear your students exclaim "Oh, I get it!" is amazing. The activities on teacher.desmos.com are all fantastic, however I thought I would share a few less conventional ways of using Activity Builder.
#1.
I was helping create a test recently and wanted to include some "student" work for my students to analyze. To accomplish this I create an activity with a graph screen and then a sketch screen. Here was f(x):
And here is "Martha's" graph of the reciprocal of f(x):
Using the sketch feature to create work for students to discuss is quick and easy. It really helped me see what relationships they understood.
#2.
If students are creating their own graphs you can collect them into one activity to allow you to discuss or show them off more efficiently.
If you add a graph screen to a new activity you can paste the URl into the first line of the graph screen and that entire graph page will be loaded.
Paste a link like this: https://www.desmos.com/calculator/sr04cmo3vk as shown below.
You can then preview the activity to see each graph in turn.
#3.
Although you can make them part of a larger activity, both Card Sorts and Marbleslides can be stand-alone activities. These are options under the Labs tab. (You may have to turn this option on - I'm not sure if this is still required.)
You could create a card sort as a warm-up or exit ticket. Assuming all students have access to technology, they can complete one in a very short amount of time and you get really quick feedback (see green/red below).
Marbleslide challenges can be used at all levels of graphing and are delightful! Sean Sweeney has posted 36 Marbleslide challenges here. I will stop on that note so that you can go try them out yourself. This is the one that I am currently working on, from Set 14:
From the #MTBoS...
Last night I decided that it would be useful for my students to have more practice with the graphs of combined functions. We have come to the end of the unit on this topic so they *should* be able to pull their skills and knowledge together and figure out what functions have been combined and how to create some interesting graphs.
Here is the link to my Desmos Activity Builder file. There are four graphs of combined functions and their job is to figure what two functions were combined and how.
My students did well with the first, second and fourth, but needed help with the third. I have since added a hint that it is a composition of two functions. I think that will help.
I asked them to pair up to do this activity and I really liked the conversations that came out of it. Here is some of the reasoning they provided for the first graph (top left):
And a few for the second (top right):
I hope others might find it useful. You now have the ability to edit within DAB so feel free to make it work better for your students. Also, if you want answers, email me :)
We started with a little 3-act fun from Andrew Stadel. Here is his blog post about Filing Cabinet with all the links to the videos. Here is my blog post from the latest time I have done it with my students.
I also showed them some of Nathan Kraft's craziness (that's crazy in a good way, of course). Toothpick insanity and Starry Night.
Then we played Polygraph: Parabola from Desmos. It was a lot of fun and everyone saw how the game encouraged the use of correct vocabulary and helped you create better questions by showing you what others had asked.
We also took a quick look at Central Park.
I probably sound like a broken record, but if you haven't tried Desmos Activities, you really need to check them out!
Time to get up and get moving! Tying Knots was next. The first part of this activity involves determining the relationship between the length of a rope and the number of knots in the rope. I really like this because, unlike most linear data collection activities, this has a negative rate of change.
We skipped the part involving putting everyone's data together to be able to find the relationship between the diameter of the rope and the rate of change (but it's on the handout) and moved on to figuring out how to get the ropes to be the same length with the same number of knots.
All but one of the groups got it to work which led to interesting discussions and to me adding what you see below for next time.
I have blogged about the Tying Knots activity here, here and here and the handouts are here and here.
We took a quick look at some Always-Sometimes-Never statements and discussed how these can be really good warm-up activities that help students think beyond just their initial reaction to the statement.
I then gave a choice of matching activities.Quadratic (credit to the teachers at Sir Wil for that one), rational, right-angle trigonometry or combinations of functions.
A couple of participants then had a quick but lively game of log war. I think I originally got these from Kate Nowak, so I'll give her due credit.
And, finally, I showed off some of my students' parabolic art - art work created entirely with quadratic equations. Here is that activity's blog post and this is one of my favourites:
We started the day by looking at the remaining visual patterns from yesterday. Participants shared their strategies and we talked about finding the simplified rule IN the pattern as explained by Hedge in her recent blog post here. There were really interesting strategies used for the last pattern - the one that I had really gotten stuck on this semester. I showed them my (Dave Lanovaz's) clever solution, which I blogged about here.
I wanted to get everyone up and moving so we did the "Don't Lose Your Marbles" activity next. I don't think I have blogged about this one, so I will try to describe it in more detail. I do this activity on day 1 of grade 10 academic. It allows me to observe students working in groups and really gives me a feel for the class without them even realizing it. They also talk about math and help each other recall some of what they learned in grade 9. Each group has to determine a relationship between the height of a ramp and the distance a marble will travel after going down the ramp. Here is the handout I give.
Although the relationship is actually quadratic, my students use a linear model which works well for the relatively small data that is collected. Also, my MPM2D students have only modelled linear data so they don't have anything else in their toolkit (you could throw this wide open in Algebra II). I tell them that there will be a competition at the end (with a prize!) where they will need to determine the height of a ramp that will allow the marble to travel a particular distance (I use masking tape to put a start line and finish line on the floor - they measure the distance).
It is really interesting to watch students collect data. Some will do repeated trials and average the results, others are not nearly as meticulous. The ironic part is that most school floors are nowhere near level so attending to precision while collecting data in this activity does not guarantee a win at the end. However, I really like this activity for the math it pulls out and for the opportunity to learn about my students.
The next activity we did involved looking at this picture:
Just as I do with my students, I asked what questions they had. The participants in my class came up with a good list which I wrote on the board. They included "How big is it?", "How old is it?", "How many creatures live in it?", "How many houses could be built from it?", and so on. Great! My students do this in groups on big whiteboards and then go around the classroom to see what questions other groups came up with and together, we choose the "best" question that we can answer. This question is usually something that requires finding the volume (how big is it? how many chairs/houses/toothpicks can you make from it?). I gave them some information to help them find an answer:
What happened next in today's class was awesome! Some chose to look at the shape as a cylinder, or more specifically, as three cylinders. Others looked at it as a cone. It is actually more of a truncated cone, or frustum. I have seen all this before. What I hadn't seen that was so cool was someone who did an exponential regression on the diameter vs. height data (or was it radius? - someone will have to help me out with that question). This is what it looked like:
Wow! A perfect fit! (I had no idea.) They then used calculus - volume of revolution (which is why I think we need radius, not diameter) to calculate the volume. How cool is that?!? Clearly, I don't teach teach volumes of revolutions of solids, but it was exciting for me to learn a new way of solving this. We did look at the "actual" answer on the website, but I think that as with my students, that was secondary to the work they had done. I have blogged about this, minus the calculus part, here and here.
We spent the last part of our class time on a Desmos activity:
All of the Desmos activities can be found at teacher.desmos.com and they are really well done. They allow students to go at their own pace and the teacher can see what each student is doing the whole way through. This lets you know who might need a little individual help as they work through the activity and when you might need to stop the whole class and work through a common error. If you have not checked out these activities yet, you need to do that!
I will be attending some CWiC sessions this afternoon and doing one of my own on Which One Doesn't Belong? I have blogged about WODB? a number of times... announcing the website and incomplete sets may be the most useful links to provide here. Oh, and the website itself is wodb.ca.
