Highlight your correct answers in Geogebra

I've led a number of sessions over the past few months introducing teachers to Geogebra and Desmos. My general outline for presentation is to show the basics of what you can do with these programs, as well as to share some of the great pre-made resources that are available online, namely at geogebratube.org.  After this we aim to have some playtime, during which teachers always ask me how to make the presentation below:



For this particular presentation, we asked students to perform a specific transformation of the graph of y=x^2.  You move the 5 points according to the description, then you input the equation for the transformed graph and check your answer.  The blue dashed graph turns green to let you know that you are correct, and a textbox appears saying "you got it!".  I've been promising a how-to blogpost on this topic.  Hope it is helpful!  Follow the steps below to create a modified version of what you see in the above video, and please let me know if you have questions.

Stage 1:  Create your objects

1. Type into the input bar g(x)=x^2 and f(x)=0.  Press enter after each entry.  (Note: I only use a function for g(x) if covering transformations.  No g(x) needed if you just want students to write the equation that goes through the 3 points).
2. Use the add a point tool to add 3 points to the grid.  Be careful not to put them on the axes or on an object.  This will attach them to an object, and we need them to be movable.  At this point in time I start changing the color and style of the objects.
right click-->object properties-->color (or style).

3.  Add an input box.  The caption should be "f(x)", and we attach it to object f. 

4.  Add a text box.  I chose the "You got it!" as my text.  Drag your textbox and input box to an appropriate location.   

Stage 2:  Boolean Variable and Conditions to Show

5.  Add a boolean variable.  My boolean variable is called sameGraph.  It is true if function f goes through points A, B, and C.  Otherwise it is false.  You add the variable by typing into the input bar.

6.  Type fcorrect=f into the input bar and press enter.  This creates a new function called fcorrect(x) that is exactly the same as f(x).

7.  Right click on function f and select object properties.  From here you can change the color and style.  I chose blue dashed.  Under the Advanced tab we will type !sameGraph into the "conditions to show object" box.  This means that function f will only show when our boolean variable sameGraph is false.  This means function f will only show when points A, B, and C are not on f.

8.  Right click on function fcorrect and select object properties.  From here you can change the color and style.  I chose green.  Under the Advanced tab we will type sameGraph into the "conditions to show object" box.  This means that function fcorrect will only show when our boolean variable sameGraph is true.  This means function f will only show when points A, B, and C are on f.

 9.  I also want my "you got it" textbox to show only when A, B, and C are on f.  The steps are the same as those above.  The tricky part is that your textbox may not be showing on the screen, so you can't right click on it.  If this is the case, right click on another object, select object properties, and then find your textbox in the objects list.

Below is what your final product will look like when you have a correct answer.  For this example, we transformed the points on y=x^2 three units right and one unit up.  Then we typed in the correct function into the input box.

Side note:  If I intend for students to interact with my presentation, I always change the point capturing to "fixed to grid".  This saves valuable class time, as points will automatically go to the nearest point with integer coordinates (or where gridlines cross, depends on your settings).  I haven't found this feature yet in Geogebra 5, so I use Geogebra 4 for these types of presentations.

Preparing for the new Common Core Test Part II

Links:
Assignment (Google Doc)
SBAC High School Calculator
Desmos

Students were required to have two windows open, each taking up half the screen.  This mimics the setup of the performance tasks on the SBAC test (You can log on to the practice test here. Be sure to select 11th grade, and math performance task).  We asked students to download the Chrome extensions Tab Scissors and Tab Glue if their computers didn't automatically create half size windows.

In this task a group of 11th graders was being introduced to regression for the first time.  The problems on the Google doc are modified from the textbook for this class.  The mathematical goal for this day was to find the equation of a linear regression and use the equation to make predictions.  The technology goal was to find needed information and solve problems by navigating between various windows.  Below is one of the problem sets we asked students to work on.

We had students open a separate link to access data so that they could easily copy and paste the data into Desmos in order to find the regression equation.  Below is a snapshot of the data stored in a Google Sheet.

After you copy the data from a spreadsheet, you can go to the first input line in a Desmos sheet and paste the data.  It's as simple as control-C and control-V copy and pasting.  In line 2 you type y1~ax1+b.  Desmos automatically makes the subscripts for you.  Note that we use "~" instead of "=" when finding a regression equation.  See the regression parameters on line 2.

You might be asking why we used Desmos for regression when SBAC has its own regression calculator.  The answer is that Desmos makes regresssion sooooo easy, and it also automatically scales your graph to fit the data (see below).  We didn't want students to be focusing on too many new technology skills for this lesson, so we stuck to Desmos for the regression piece.

Once students found the regression equation, they needed to use the equation to make predictions/answer the questions on the worksheet.  This is the part when we required students to have two windows open side by side (so use tab-scissors and Tab-Glue Chrome extensions or similar.  Some computers/browsers have this feature built in).  The reason we found this step to be so important is that students needed to transfer information between various windows in order to make calculations.  Below are the transfer steps:

1.  Transfer regression equation from Desmos to worksheet.  Desmos only gives regression parameters, so this is not a copy-paste step.

2. Transfer expression from worksheet to calculator.

3. Transfer answer from calculator to worksheet.

We also found that some students weren't able to paste expressions into the SBAC calculator, which further frustrated them if they didn't have two side-by-side windows open.  Below is a screenshot of what students see when they are working with the SBAC calculator to answer questions 9 and 10.

Many students really-really-really wanted to pull out the paper and pencil to do this work.  I don't blame them.  I've never shown my work for a math problem on the computer until I made this activity for students.  Since students will need to show their work on the computer when they take the SBAC test, we need to have some practice doing so in the months leading up to the test.  In scanning student work, the teachers saw that many students did not show their work on the computer, despite explicit modeling at the beginning of the lesson.  For our next activity, we will definitely have some exemplars to share with students as well.  Below is an exemplar for problem 9.

So far we've competed this lesson in 7 classes, and it has gone well with the exception of students not showing their work on the computer.  

A few pieces of background info (in case it is helpful):

-This particular school is a BYOD (bring your own device) school, where most of the English and Social Science classes have been using Google Drive for this school year. 

-We used Doctopus to distribute the worksheet to students. 

Preparing for the new Common Core Test

This is a post about the not-so-glamorous-but-necessary part of teachers job that is the task of preparing students for standardized testing.  This is also part I of a series of posts that I intend to write about the work we are doing in our district to prepare for our new standardized test.   In California, this means the SBAC test (Smarter Balanced Assessment Consortium), which replaces the STAR test.

Many schools in California took the SBAC field test last school year, but for both of the high schools that I work with this will be the first time that we are taking the test.  Naturally there is a certain amount of anxiety, as this is the first time that students will be taking a math test entirely online.

So the big question is how do you prepare for such a test?  Teachers have spent countless hours during the past couple of years to adjust course maps, curriculum, and teaching strategies in our transition to the Common Core. But what about the big test?  How ready are we for the Common Core test?

After some conversation, we've identified a few focus areas:

-Content: There are a some content standards that our books don't cover
-Depth of knowledge: Students haven't necessarily worked on performance tasks in math class
-Technology.: This is the big one.  Students need to practice with the SBAC tools, specifically with the SBAC calculator and entering answers using the SBAC equation editor.  Another big item is navigating between different tabs or windows to access all needed information.

Identifying the areas above has helped in developing a plan to address the focus areas and get ready for the SBAC test. No doubt we will make sure that 11th graders have taken the Interim Block Assessments that SBAC has released.  Other than this a bulk of the test prep work will involve doing in class practice activities and homework assignments that involve students showing their work and explaining their thinking on the computer.  In this series of blogposts I will share some of the specific activities that we are using, all of which are housed in Google Drive.  Hope you will find them useful!  And if there is a similar resource out there that I have missed, please feel free to share.