Flipped Intro to Quadrilaterals with Edpuzzle and Google Forms

The Common Core standards have brought us many changes to our Geometry curriculum, including less of an emphasis on special quadrilaterals and their properties.  We used to spend an entire chapter talking about parallelograms, rectangles, rhombuses, kites, and trapezoids.  Some of the newer curriculums such as Engage NY give this topic a couple of lessons worth of attention, with the focus being on proving properties of parallelograms.  The Common Core Standard here is G-CO-11, which states:

Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

With the emphasis being on proving the properties/theorems, I am rethinking the way that I approach this material.  Below is an Edpuzzle video that students can watch before we begin talking about parallelograms.  

My hope here is to get students to review vocabulary related to quadrilaterals such as sides, angles, and diagonals, and to make some observations about what is happening with the parallelogram in the video as it is being transformed.

The video above gives concrete measures for both angles and segment lengths, so to transition to abstract thinking I've made a few more videos for students to take a look at.  Below is a Google Form that students can go through to both watch introductory videos and to answer some questions before we launch into a class conversation.  There are additional videos on pages 2-3 of this form, and I will post the videos below so that you don't have to input answers into the form in order to proceed to the next page. If you want to fill out the form just for fun go right ahead, as this is a copy of my original form.



Video 2:

After this video the Google Form asks students to identify the pair of congruent angles that justifies why the marked pair of sides are parallel.

Video 3:

This video asks students to recall what a diagonal is, and also asks students to make an observation about congruences formed by intersecting diagonals.

These videos may need a bit more context, but basically I am hoping to show students how to see that all parallelograms are formed by rotating a triangle 180 degrees about the midpoint of one of its sides.  From here, corresponding parts are congruent, and we begin to see why many of the parallelogram properties are true.  Between the Edpuzzle video and the google form, I am asking students to make some of the observations about congruent parts of parallelograms that we will later prove.  I'll note that this is still in draft form and my first attempt at flipping, so any feedback is welcomed.

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.  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.
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.

SBAC Calculators

Basic Calculator
This is the calculator that is embedded into the practice problems released by SBAC.  Students can work through the tutorial to learn how to enter fractions, exponents, etc.

Graphing and Regression Calculator
Here you will find the calculator that is embedded more so into the performance tasks.

There will be opportunities to learn more about these calculators soon, as well as class activities.

LAHS Geogebra Training 1-6-2015

Please sign in, then fill out this quick form to help us guide our time together.

Vision: Teachers and students will be proficient at using Geogebra to demonstrate thinking and to solve problems.

Goals:
-Learn about support available for integrating Geogebra into your class
-Learn how to locate and use pre-made Geogebra presentations
-Learn some basics for using Geogebra

Basics Tutorial
Screencasts
Functions
Geogebra Tools Page

Piecewise Functions for Trig/Math Analysis

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 to the embedded video to view.

SBAC Test Resources 2015

Updated links.  Also available on the mvla website under the common core tab, as well as on our common core resources page from 2013-2014.

Smarter Balanced Question Types

Smarter Balanced Practice and Training Tests

Smarter Balanced Practice Test Scoring Guides

SBAC Grade 11 Released Items

SBAC Grade 8 Released Items

Clovis Unified School District SBAC Page.  Organized by claim for easy navigation.

SBAC Calculator

Square Root and Cube Root Graphing: Alg2 Section 6-5

Yep, it's that time again.  We are back to graphing, and we are back to transformations.  The book that we use for Algebra II starts in Chapter 2 with transformations of the absolute value function. Chapter 4 includes quadratics, Chapter 5 is cubics, and now in chapter 6 it is square root and cube root functions.  

Since I won't be able to help out in all of the classes this time around, I am hoping this blogpost can be helpful in getting ready for the lesson (which I taught in Jennifer C's class).  

I began the lesson by looking back at the Desmos pre-made sheet for parabolas in vertex form for a reminder of how a, h, and k transform a graph.

 I decided to take a different approach for the intro to 6-5.  Instead of starting with functions and table of values, I started with a transformation given in words.

I showed the Geogebra applet below.  Directions are to move points A, B, and C so they are first ON the square root graph, then shift each point up from the parent graph by two.  Students could pick which of the points from the parent graph to look at, as long as A, B, and C are two units up from a point on the parent graph of y=sqrt(x).

 Step 1:

Step 2:

Next I typed the y=a*sqrt(x-h)+k into the input bar, and we talked through the transformations that had taken place.  I changed a, h, and k as we decided on values.  For this example a=1, h=0 and k=2.

If you have entered the correct function into the input bar (hit enter when finished), the transformed function will turn green if correct.

Students practiced a few problems with both horizontal and vertical translations, and then problem 5 asked students to reflect y=sqrt(x) about the x-axis.  About 90% of students were able to move points A, B, and C to the correct location, and about 50% correctly guessed that the correct transformed function was y=-sqrt(x).  This was with NO direct instruction for this part of the lesson.  I was hoping for this moment, as one of my goals for this approach was for students to think about how we were transforming a set of points, and specifically to think about what happens to a set of points before we think about the transformed function.  I did call the class back together to finish up problem 5.  I also walked them through problem 14 so that they would get a chance to see a cube root transformation modeled by teacher.

You can access the problem set here, as well as from the email attachment.  There is space to record transformed points and the transformed function.  Answers can be checked using the applet, which is set up to indicate a correct answer as long as your transformed function went through points A, B, and C.  Since students were checking their own answers, I got to walk around and asked questions to check for understanding.  No doubt it is too many problems, and would have been much better on a block day, but it still was a great experience for students.  Overall, I like this approach for introduction to graphing a new type of function in Algebra II, and I can see adapting this lesson for the other function types (with tweeks of course!).

One last note is that it is possible for students to get the wrong "answer" using this applet.  The floating points A, B, and C begin at (1,4), (4,4) and (7,4), so if a student enters the function f(x)=4 the applet will indicate that they are correct.  This has happened a few times since I started using applets like this one, and it's made for great conversation and reinforces the need to check the reasonableness of an answer.