Desmos Activity Builder as a tool for instruction

Note:  When I started writing this post, I intended for it to be about the most recent Desmos Activity I taught, which was on square and cube root graphing.  The ideas in this post are useful for much more than just the teaching of this one topic, so I'm hoping to both tell about the activity and clarify my thinking about using Desmos Activity Builder as part of instruction.

For context, the book that I use for Algebra II starts in Chapter 2 with transformations of the absolute value function. Chapter 4 includes quadratics, Chapter 5 is cubics, and in chapter 6 it is square root and cube root functions.  By the time students get to graphing of square and cube root functions they have done a lot of graphing by hand and talked about transformations several times.  

Lesson:

1.  Warmup: On the whiteboard I put a blank table of values for y=x^2 and y=x^3.  Students talked with a partner about how to complete the table, and we wrote the values on the board. (Activating prior knowledge, partner talk, no technology, no paper)

2.  Connecting concepts:  I showed this Desmos pre-made sheet for parabolas in vertex form for a reminder of how a, h, and k transform a graph.  Students watched and shared observations with partners, then we shared out as a class.  The visual below stayed on the whiteboard for students to reference throughout the class (formative assessment, teacher uses technology, no paper)

3.  Developing the concept: I asked students, what is the inverse of squaring?  Cubing?  What is the relationship between the points on a function and its inverse?  We used our tables of values from the warmup to come up with a table of values for the square and cube root function.  I wrote the standard form of each function below its table of values.  
(anchor charts, no technology, no paper)

Steps 1-3 took about 10-15 minutes.  We saved a lot of time by not requiring students to write anything down, and also by not having them do anything on the computer.  

4.  At this point in time students logged on to this Desmos Activity, and I modeled screen 1 for them.  

One tip that helped students the most was to type in the standard form y=a*sqrt(x-h)+k (DON'T add sliders), and walk through my thought process.  I asked myself the following questions:

• Did the y-values get multiplied by a number?  If not, a is 1.
• Did the graph shift horizontally?  If not, h is zero.
• Did the graph shift vertically?  If not, k is zero.

So for screen 1 with a vertical shift of 2 we typed y=1*sqrt(x-0)+2.  Students started asking questions about whether or not they could type the function in another way.  I told them yes and emphasized that the focus was on the thinking process, which would help them complete the problems in our activity.  (modeling, think-aloud, teacher and students using the technology)

5.  Students were given a few minutes to complete screen 2, and move ahead to other screens if ready.  We came back together one more time to go over screen 2, and I again modeled my thinking by asking myself the series of questions above.  I called on students (popsicle-stick style) to answer my questions as I built the equation for our transformed function.  (more think-aloud, formative assessment, equity)

6.  Students work on the activity:  I used the teacher dashboard to monitor student progress.  The teacher dashboard allows easy collection of sooo much data.  I am able to check in to see if all students have finished a particular screen, and if not I am quickly able to identify who isn't progressing in the activity and make adjustments accordingly.  This type of info ensures active participation in a way that I can't make happen with a paper worksheet.  Another great aspect of the teacher dashboard is that it becomes obvious very quickly if students are getting stuck on certain problems or if there are common misconceptions.  Desmos is helping me to formatively assess student learning and make real time adjustments.

7.  Summary/Closure of the activity:  This one is tricky because often each class is different in terms of how far they get through an activity.  I don't know if it is just me, but it seems like students can't generally finish all of the screens that I include in my Desmos activities.  At first I thought this was a problem, but now I am taking a different view.  Having extra screens provides a natural way to differentiate.  If students are struggling on the beginning screens, I can adjust the assignment so they have a more reasonable goal.  If students are excelling, I can send them to challenge screens.  As long as I have a game plan for how I am going to bring the class back together and summarize the learning, I am fine with having too many screens.  I am also allowing myself more flexibility in choosing a closing conversation, by letting it develop after I see where the students are at in their learning.  Ideally one of the activity screens will work for a closing conversation so data can be collected.  Students were successful with this activity, so a more challenging closing activity was appropriate.  In one of the classes that I taught we looked at the screen below, both for the challenge, and for how it would help students with their homework assignment for the night.  (Pair-work on computer, class discussion)

I'm very interested in continuing to explore how to use Desmos Activity Builder in instruction.  I've seen how powerful it can be in helping to introduce and build connections between topics.  One thing that I've learned this past semester is that planning for how to integrate a Desmos Activity into instruction is key to its success.  The strategies in this blogpost are ones that I routinely incorporate when I use Desmos as a teaching tool, and they also aren't different from strategies used in my non-technology lessons (Activating prior knowledge, formative assessment, anchor charts, modeling, think-aloud, think-pair-share, calling on all students).  There was a good amount of explicit instruction and modeling at the beginning to help students build the knowledge needed and to understand the directions.  This was mostly done without the computer.  Once the expectations and knowledge were in place students were prepared to practice using the Desmos Activity.

An area for growth:  Teachers that I work with are sometimes concerned that there are no notes in place when we use a Desmos Activity to introduce material.  I agree that there should be some sort of paper that students can reference throughout the chapter when they need to recall the learning.  I want to stay away from requiring notes during the Desmos Activity because there can be processing issues for students due to too much input.  This distracts from the learning.  Maybe jotting down key ideas in a notebook or foldable at the end of class or the next day would work?  Please share in the comments if you have ideas.

Next Steps:  I want to continue to think about best practices for using Desmos in instruction.  I'd like some sort of frame-work that I can use when I work with other teachers (I'm an instructional coach at the high school level).  This would make for richer debrief conversations and help with sustaining professional learning.  I'm also interested in using student work from the Desmos activities in summary conversations with students.  

It would be great to hear from others that are using Desmos as part of instruction, so I hope that people keep blogging about their experiences.  Audrey McLaren's Real-Time Story of the Desmos Activity builder has been a great starting point for learning about what other teachers are doing.  You can read her post here.

Desmos Activities

Desmos Activities

The Desmos activities on this page are ones that I created, including a few that were edited by the awesome Desmos Teaching Faculty.  More Desmos activities are available at teacher.desmos.com and also at the Desmos Bank.

Algebra 1 Eureka Math/Engage NY Module 1

Lessons 1-3 Graphing Stories

Lesson 12 Solving Equations with Number Properties

Lesson 14 Solving Inequalities with Number Properties

Lesson 19 Rewrite Equations of Lines in Slope-Intercept Form
Lesson 20 Linear Equations in Standard Form

Lesson 20 Applications of Linear Equations 

Lesson 21 Linear Inequalities in Standard Form

Lesson 23 Introduction to the Elimination Method for Solving Systems of Equations

Algebra 1 Eureka Math/Engage NY Module 2
Lesson 12 Relationships Between Two Numerical Variables
Lesson 13 Comparing Linear, Exponential, and Quadratic Relationships
Lesson 14 Day 1 Modeling Relationships with a Line
Lesson 14 Day 2 Modeling Relationships with a Line
Lesson 15 (teaching tool) Interpreting Residuals from a Line

Algebra 1 Eureka Math/Engage NY Module 3
Lesson 1 Integer Sequences
Lesson 1 Part B Integer Sequences
Lesson 3 Version A Geometric Sequences
Lesson 3 Version B Geometric Sequences
Lesson 11 The Graph of a Function

Algebra
Hearts: Practice transformations with function notation
Broken Parabolas (Intro to symmetry in parabolas)
1-3-5-7 Parabola Challenges (all with a=1)

Geometry
Linear Equations in Standard Form (can also be used in Algebra)

G-GPE: Write equations of parabolas given focus and directrix

Algebra 2
Practice with Factoring and Connecting to Graphs
Roots of Quadratic Functions: Some Special Cases
Parabolas and the number d
Discriminants of Quadratic Functions
Polygraph: Intro to Absolute Value Graphing
Introduction to Polynomial Graphing
Practice with Inverses
Transformations of Square Root and Cube Root Functions 

Trig/Math Analysis
Graphing the Sine Function using Amplitude, Period, and Vertical Shift

Calculus
Modeling Exponential Growth and Decay (can be used with Math Analysis as well)

Google Docs in Math: Error Analysis

Looking for ways to incorporate more communicating reasoning problems into your curriculum?  Error analysis problems provide students with an opportunity to communicate their reasoning and focus on the Math Practice Standards "attend to precision" and "construct viable arguments and critique the reasoning of others."

A screenshot of my first digital error analysis assignment is below.  I made this on a Google Doc by adding pictures of the problems worked out in my own handwriting.  You can make a copy at this link.

There are many ways to get images into a Google Doc.  One way is to open Google Drive on your phone, navigate to the file that you want you image to be in, and then add an image by pressing the plus sign and taking your photo.  From your Google Doc you will locate and insert the image, and crop as needed.

I used Google Classroom to distribute this assignment to students.  We talked through the first problem together.  Then color coded each error according to its type.  I provided the following key at the bottom of the assignment.

This entire process took about 10 minutes.  With just a few minutes to spare before the end of class, students got started on the second problem and submitted their assignment.  Below are some of the results.

You'll notice that we didn't always agree on the type of error represented in the problem.  This was our first try at this type of assignment, and over time we'll continue to discuss the types of errors that we are making and hopefully have more agreement.  The amount of writing and discussion that took place in just 10 minutes was impressive, and I can see the results of this type of assignment improving over time.

Reflections on Desmos Activities

We've been in school now for a month and a half, and I've managed to make it out to number of classes to try and observe Desmos activities on Activity Builder.  We've had some hits and misses (though more hits!), and I find myself making tweaks as I go.  It's been helpful to reflect on the lessons with each teacher, and I recently got some feedback from an administrator as well.

I wanted to record a few reflection points, mostly so I don't forget, and also in case it is helpful for others.  

• Open up the teacher dashboard on an iPad or tablet so that you can monitor student work as you circulate the class.  During my last lesson I also kept a post-it note with me so I could take down names of student work to share with the class during debrief time. Doing this also helped me decide when we should debrief and keep track of time.
• One-to-one tends to lead to students working in isolation.  We started noticing this last year in our classes, and we've seen the same thing on Activity Builder.  Two students per one device might work better.
• If you are using Desmos as part of the instruction, consider pacing as well as where to stop for additional instruction.  If you have an exploration screen, allow students plenty of time to explore, discuss, and share out, and then bring the class together for some explicit instruction.  Consider going back to an exploration screen for students to use during a warmup or problem set the next day.  This might be the biggest reflection point of all for me, as it is helping me be more thoughtful about what the objective is for each lesson and how I can help students meet that objective.
• For what it's worth, nearly all of the activities that I have ever done with technology in a math class take way longer than I thought they would.

That's it for now.  Any thoughts on this?  Anything to add?

Desmos and Piecewise Functions

We are about to start functions and transformations in trig/math analysis, so I made some piecewise functions in Desmos to use for the intro.

The above function is named f(x).  Below is what I entered to graph the function.  

Then we can view transformations of f by typing the transformation on an input line to the left of the graph.

You can show or hide each graph by clicking on the colored circle to the left of the equation.  Below is 2f(x).

And f(2x).

Here are the links to the Desmos graphs.  Graphs 3 and 4 include questions for students to answer.   Hope some of you can use them!

Piecewise 1

Piecewise 2

Piecewise 3

Piecewise 4 

All of these functions were taken from Calculus AB free response questions, hence the link back to the website.  I also made a table of values to use for by-hand practice.

Watch this video by Meg Craig for a fantastic demo of how to use the table above.  Scroll down about halfway in her blogpost to watch the video.

Visual Introduction to the Definition of the Derivative

One of the new teachers I will be working with this year will be teaching Calculus, and this has got me thinking about some of the more successful strategies that I used the last time that I taught this course. A bunch of ideas come to mind, but one that sticks out from the others is the visual intro to definition of derivative that I stumbled upon the second year that I taught Calculus.  The first time I taught the course students struggled with this concept.  Using dynamic geometry software made all the difference for helping students learn this concept the next time I taught it.

To demonstrate, say you want to use the defintion of derviative to find the value of the derivative of f(x)=x^2 at x=-2.  Use the diagram below:

I've added a couple of objects to my diagram to help out with this explanation.  First, we note that we are really looking to find the slope of the tangent line of the function f(x)=x^2 at x=-2.  I don't tell students that my software can simply graph this tangent line and give me the slope, nor do I tell them that there are formulas to find the derivative of a function that we can use to find the slope of the tangent line.  That all comes in time.  For now my fixed point, a moving point attached to f(x), and a secant line between these points is all we need.

The next step is a reminder of what a tangent line is.  I let students discuss with a partner and then tell the class what we are looking at.  If the diagram above with a secant line is provided, I can ask students what to do to the moving point to make my dashed line become a tangent line.  I start dragging the moving point towards the fixed points and ask students to tell me when to stop.  If they tell me to stop too soon, I ask them if we can move the blue point closer to the fixed point.  We are visually developing the idea of using a limit to find the slope of a tangent line by physically moving one point as close to another point as possible.  Eventually we put the moving point on the fixed point.

Students notice right away that the secant line is no longer present.  Since you can't turn a secant line into a tangent line using a fixed point and moving point, we will do the best that we can.  And the best that we can do is to move the moving point as close to the fixed point as possible, and use these coordinates to estimate the slope of the tangent line.  I ask students to write this symbolically.  We introduce the following notation:

Fixed Point: (a, f(a))
Moving Point: (x, f(x))

Then the slope of the secant line is

We practice finding the value of the derivative by dragging the moving point as close to the fixed point as possible, and then finding the slope of the secant line.  When we introduce the definition of the derivative of a function at a given value, we use similar language.  Students can tell you the following about the slope of the tangent line with little help:

The slope of the tangent line can be found by taking the limit of the slope of the secant line as the moving point approaches the fixed point.  When we have had this conversation, it is not such a big leap to 

With the visual introduction, students can interpret the parts of this formula and feel empowered when the formula yields the same slope as our estimations did. 

My school district has open enrollment for AP and honors courses, and because of this the Calculus AB classes are very heterogeneous.  There is a nice split between students that have taken all honors math courses, students that are choosing AP Calculus AB as their first honors math course, and students that have never taken a honors/AP course in any subject.  Because of this I chose to keep the functions simple when we were finding derivatives using the definition.  This allowed for a greater focus on the conceptual understanding of derivative, and I believe that the visual introduction using dynamic geometry software and the extra conversations around the topic helped students ace this topic on the following test.  

You can use this premade presentation to introduce the definition of derivative in your own class.  This tool allows you to enter a function as well as coordinates for your fixed point and moving point.  A smaller version of the tool is below, and you can try this out by dragging the moving point.  

You can also use this presentation when talking about when a function is not differentiable, because it is easy to see that the slope of the tangent line will not approach the same value on either side of the cusp.

#July2014Challenge: Sketchpad Presentations from Key Curriculum Press

One of my favorite blog finds this past year was Sine of the Times by Key Curriculum Press.  Several bloggers write for this blog, and what I appreciate most from them is how they present math topics in new ways using Geometers Sketchpad.  

The latest post is Dilations Challenges.  The tool embedded on the webpage took me a couple of minutes to figure out, but this was time well spent.  If you have a few minutes to spare, I definitely recommend checking out this post as well as those below.  

Some other great posts from 2014:

CREATE PARAMETRIC CURVES GRAPHICALLY AND KINESTHETICALLY

ITERATION IN THE COMPLEX PLANE

SIMULTANEOUS EQUATIONS IN ELEMENTARY SCHOOL? YOU BET!

PI DAY 2014

What blogposts have you seen this year that present material in new and interesting ways?  Please feel free to share!

#JulyChallenge2014: Modeling With Trig Functions

Link to Geogebra Book with all 4 applets

Last year was the first year we taught trig graphing in Algebra II, and so it was a brand new teaching topic for a couple of our teachers.  Perfect opportunity for collaboration!

We decided to introduce the topic using Dan Meyer's Ferris Wheel.  This introduction built on intuition and gave students a day to practice reasoning with a context that involved sine and cosine graphs.  The equation for a sine graph was introduced at the end of the lesson, and students used sliders in Geogebra to fit the sine graph to the ferris wheel data of time versus height.

Towards the end of this unit students were asked to model real world situations using trigonometric functions.  We picked a few problems involving tides and ended with a problem from Illustrative Mathematics called Foxes and Rabbits 2.  We used a series of scaffolded Geogebra presentations to help students get started.  The first presentation is below, and is an embedded applet that you can play with.  Type a function into the f(x) input bar and press enter to see it on the graph.  You should try this right now. It is fun! The goal is to get the sine graph to pass through all of the data points.  



We introduced this to students by first talking about the data and how tides are measured.  You can talk about how the moon impacts tides and how the data is roughly periodic.  At this point students should know the amplitude and period for y=sin(x). Next, have a class conversation about how to transform this graph to pass through the given points.  The power of a premade interactive model is that you can pause during the conversation to allow students time to process.  I make use of the think-pair-share structure with the expectation that students may be called on to explain what they know or discussed with a partner.   One of the teachers on the Algebra II team started writing and sharing the questions that she used with these presentations, and the other teachers found this to be very helpful.  Below is a list of questions that can be used with this presentation after the initial conversation about the data.  Feedback  on this list of questions would be great!

1. What is the midline for the Santa Cruz Tides data? (Discuss first, then reveal the midline by selecting the midline box.)

2.  How can I change (transform) the function f(x)=sin(x) so that it has this midline? (Discuss, then type in the correct function and reveal the change in the graph.)

3.  What is the maximum value of this function?  What does it represent with respect to the tides?  Find the minimum value as well.  Discuss and then reveal the max and min lines by selecting the appropriate box.

4.  What is the difference between the highest and lowest tide measurements?  Does this help me find the amplitude, period, or vertical shift of my function? 

5. Now that I know that the amplitude is 1.5, how can I change my function f(x)=sin(x)+2.5 to account for an amplitude that is not 1?

6.  Discuss with your partner what one period of y=sin(x) looks like.  My current graph has been shifted horizontally from the parent graph y=sin(x).  Can you find a new starting point?  How can we change our function y=1.5sin(x)+2.5 so that it has been shifted horizontally to your new starting point? (There are multiple answers here, which can be discussed now or later depending time.)

7.  What about the period?  Note: Most classes will have a formula to use to account for a change in period.  I haven't taught trig in years, so I just use horizontal stretch/shrink reasoning.  y=sin(x) has a period of 2pi, and Santa Cruz tides has a period of 12.  Since 12 is larger than 2pi, I will multiply x by a factor of (2pi)/12.  My new function is f(x)=1.5sin(2pi/12(x-9))+2.5.

One of the teachers from this team made a worksheet for students to use as we modeled the thinking.  I find this to be an important step so that students can refer back as they practice and study.  Please let me know if you are interested in having this worksheet, and I can get you a copy.  

Below is a list of all the tide problems that students worked on.  

Santa Cruz Tides
San Mateo Bridge Tides
Bay of Fundy Tides

Students also worked on Foxes and Rabbits from Illustrative Mathematics.

Illustrative Mathematics Foxes and Rabbits 2 Problem
Illustrative Mathematics Foxes and Rabbits Geogebra Tool

#July2014Challenge: Tech Thursday and Community Building

There are plenty of ways to collect data about student interests that do not require technology, but most of them involve lots of little slips of paper, which I personally don't deal well with.  For this Tech Thursday I wanted to write about using Google Forms to collect data as you build community in your classroom.

One of the most important parts of a positive classroom culture is safety.  Students need to feel safe to participate, to fail, to ask questions, etc..  One of the first surveys I send out to students each year asks students who they can work well with and where they prefer to sit.  Getting student feedback on these two items can help alleviate some of the anxiety caused by all of the changes a new school year can bring. This is also a good time to ask about vision and hearing impairment.  While most students will let you know if they need to sit near the front, there will always be a few that are too shy to speak up.  I let students know that all seating arrangements are tentative, and that changes will be made if needed to support the learning of each individual and the class as a whole.

The screenshot below is from a Google form that I have sent out to students in the past.  There are plenty of programs that make surveys, but I prefer Google forms because the results live in my Google Drive so it is easy to refer back to later in the year.

Setting up group norms is also key in successful groupwork.  I like to brainstorm class norms for groupwork with each class, and use these lists as a starting point to agree on a final list for all of my classes.  I start with a prompt such as, "What do you think are the three most important rules for working in groups?" .  Give students a few minutes to make their own list, then narrow down the list in pairs or groups, then share out with the class (Think-write-pair-share).  We pick four or five for the class, and then after doing this with all 5 classes I will pick 5 common ones to post.  I will also add in important norms that students may have overlooked, but generally high school students do a good job of generating them through this process.  Google forms is also great for collecting input during a brainstorming process, though I haven't specifically used it during the group and classroom norms process.

After we start working in groups I will send out surveys to help students self assess how well they are working in the group, and whether or not there are any issues with the group.  Getting feedback on group set-up and progress helps students feel safe, and gives them a voice.

Another use of surveys for community building is a quick beginning of class icebreaker (favorite movie, favorite breakfast food, favorite song, etc.).  Icebreakers can be done without technology of course, but if you have access to technology for each student then it is a quick process, and a great way to help students get to know each other.  If you are not familiar with Google forms, there are online tutorials and videos to get you started.  Socrative is a another program that works well for this type of activity, and definitely worth checking into.

What types of activities/supports do you implement during the first week of school to help build community in your classroom?  Please share!

#July2014 Challenge: 5 Things

5 Things I can't live without in my classroom

Seating Charts

In 2014, this method feels pretty low tech, but it soooo works for me.  I made these seating charts in excel about 10 years ago, and I use them every year.  I make copies for the entire semester at the beginning, staple them together, and take a new packet out each Monday.  I can record attendance, classwork, and homework scores in the same place, and there is space in the margins to write notes about late work.  

Computer paper in different colors  
I haven’t tried interactive notebooks yet, but we make foldables in my class at least once per chapter.   Sometimes we will make a sophisticated foldable such as a flipbook, and other times we’ll just fold the paper into fourths or eighths and put a problem in each box.  Students like foldables for warmups because they can easily find the paper at the beginning of each day, and if you spiral the problems from the chapter it can help students study.

Flipbook Envelopes 
Not sure where I got this idea from, but I have used these envelopes for many tasks.  I keep a set of index cards in one of these with group progress grades to place on tables during group work (though I’m seriously considering changing to red-yellow-green cards after reading several posts this month).  Another is for name cards organized by period so I can randomly call on students.  A third is for sets of problems to use during groupwork activities.  

To make a flipbook envelope you first make a flipbook. Take several sheets of paper, and align as shown in the picture below.

Fold all the sheets over so that your papers look like the picture below.  If you want a flipbook you put three staples across the top.

If you want a flipbook envelop (mini-filer) rotate 180 degrees and staple along the sides.  

My smartphone  
This device replaces many of my must have tools from a decade ago.  I use the timer, the camera, name picking apps, just to name a few.  I even made a Google form to use as a to do list, and I put the icon on the front page of my cell phone.  The results of the Google form are recorded in a spreadsheet, which makes it easy to edit and prioritize at a later point in time. I can also open the spreadsheet from any computer or device, making it easy to keep up with all of the little items

Geogebra 
Need I say more?  I use this as a demonstration tool, and also to make lots and lots of diagrams for worksheets and class activities.  Having access to quick visuals really gets the students talking, and helps me to check for understanding.  One of my favorite discoveries was that you can take the tick marks and numbers off of the axes.  I’ll do this and graph several functions of the same type, such as parabolas.  Then I’ll write the equations for the functions on the whiteboard and ask students to match equations to graphs.  Without numbers on the axes the conversations tend to be richer, and we can generalize by naming other functions that could potentially represent those on the graph.

Definitely looking forward to reading more of these 5 things we can't live without posts, AND taking more notes on my reading so that I don't forget.

Some Things I Wish I Knew When I Started Using Geogebra

Using Geogebra as a demonstration tool for teaching concepts such as graphing and transformations can be amazing, but there is so much that can go wrong during the lesson.  After some pretty intensive play sessions with Geogebra and reading through a few tutorials such as this one by Gerrit Stols I was ready to try a demo in my class.

One of the first concepts I showed to students on Geogebra was how the factors of a polynomial function are related to its roots.  I typed in the function f(x)=x(x+2)(x-7) into the input bar at the bottom of the screen, hit enter, and below is what we see.

Not so great.  If I want my students to understand the nature of cubic functions, this is definitely not  what I want them to see.  Select "Move Graphics View" from the toolbar near the top of the screen, and then drag on either axis to rescale.  Drag in any quadrant to recenter.  When you are done, select the "Move" tool from the toolbar so you can select or move object.

The graph below looks better, but the students in the back still can't see the numbers on the axes.  The function will be hard to see on worksheets, so changing the line thickness can help as well.

To change the font size, select "Options" from the top of the page, then font size, then 24.

To change the line thickness right click on the function and select "object properties".  Select the "style" tab to change the line thickness.

The modified graph is much easier to see (and definitely appeals more to my inner interior designer).  There is also a tab for color under the object properties, which is especially nice if you want to build a graph matching activity.

One final must-have tip is to use a text box to display the equation for the function.  Select the "text" tool from the toolbar, click in the graphics view, type f(x)= and then from the objects menu select your function f.

Select the "move" tool and then drag the text box to a good location.

I made this document for a presentation to a math department that described themselves as low tech. Our focus for the day was transformations of functions, and so we focused on tools and settings that would apply to these presentations and images for worksheeets.  We walked through the steps on the document together, and I made screencasts for later use.  You can check out the screencasts below, though I'll give a fair warning that they were made at about 5am, pre-caffeine.

GeoGebra Tutorial: General Tools

Modify the axes and grid

Modify a point

Modify a function

Link to premade demonstrations organized by topic and course. 
This is the same list as the Geogebra Tools list from the top of the blog.  A summer project I am looking forward to is to write a few blogposts about how to use some of these tools.  If you are into Geogebra, please check back soon!