Transformations Review Activity

LINK TO GEOGEBRATUBE BOOK WITH ALL 5 REVIEW PROBLEMS

Below is the Geogebra applet for problem 1 showing three line segments.  One of the segments is independent and the position of the other two depends on the first.  Which line segment is independent from the others?  You can drag line segments or points in the applet below.

For this diagram the blue segment maps to the orange segment (reflection about the y-axis), and the orange segment maps to the purple segment (translation right 3 and up 2).  We can also think about which points are independent/dependent, and about the mapping between the points.  Point A maps to point F, which is then mapped to point D.  The type of transformation that maps the points is the same as the transformation that maps the segments (reflection then translation).

The objectives for student use of this lesson are to identify the types of transformations for each problem (2 per problem), write the coordinate rule for each transformation, find the image of a point given the pre-image, or find the pre-image of a point given the image.  Since there are two tranformations per problem, vocabulary might get in the way of understanding.  The organizer below can facilitate conversations about the objectives, and can help students organize their thinking.  I would model the thinking and fill out this entire organizer with students before they get started with practice on their own.

Completed Organizer for problem 1:

This activity is still in the draft stage, but my plan is to have students use the exact same organizer for each problem.  I suspect that rotations might be hard for students to see, so I might model problem 2 as well so we can do the first problem with rotations together.  

There is no answer key yet, but the transformations for each problem are:

1.  Reflect about y-axis, then translate 3 units right and 2 units up. Begin with segment AB.

2.  Translate two units left and 5 units down, then rotate 90 degrees counterclockwise about origin.  Begin with segment CF.

3. Rotate 180 degrees counterclockwise about the origin, then translate 7 units left and 3 units up. Begin with segment BD.

4.  Translate 6 units left and 10 units down, then reflect about the x-axis.  Begin with segment AF.

5.  (This is supposed to be problem 6, looks like I missed an upload).  Dilate by a factor of 3 with center at origin, then translate 8 units left.  Begin with segment BF.

LINK TO GEOGEBRATUBE BOOK WITH ALL 5 REVIEW PROBLEMS

Translations with Geogebra

Unit planning for transformations is almost complete.  We have a set of notes/practice worksheets from the county office of ed (really great!), an FAL (Transforming 2d figures), and a common test.  The next step is thinking about how to use Geogebra to help with demonstrating the concepts and with practice.

There are a few different ways you can use Geogebra to look at translations.  The first way is to use a vector to translate a point or a figure.  The diagram below has a point and a polygon, so my next step will be to add a translation vector anywhere on the screen.  It doesn't matter where you put the vector.  You can find the vector tool under the dropdown menu for lines.

 For this example I'll use a vector to translate my point/figure 3 units right and 2 units down.  You can see the vector below, at the origin.

It might make more sense for students to see the vector starting at the point that will be translated, but then you need to construct a new vector each time if you want to stay consistent.  If I put the vector away from my diagram, I can use it each time I want to translate an object, and explain to students that the translate tool works by selecting the object first, then the vector that describes its translation (see pic below, located in a dropdown menu).

The diagram below shows my point and my polygon after translation.  Notice how the program automatically names the points in the image using the prime notation.

If you want students to focus on using the coordinate rule (x,y) -> (x+3,y-2), then you can do the transformations without using a vector by making use of the coordinates of your pre-image point(s). Before you give this a try, it is best to open a new window and add point A.  The way Geogebra names the coordinates of point A is (x(A),y(A)).  To translate point A 3 units right and 2 units down, create a point with coordinates (x(A)+3,y(A)-2).  Create this point by typing into the input bar at the bottom of the screen.  Better yet, give this new point the name A'.

Select the "move" tool, then drag point A around and watch how point A' moves.  Another helpful strategy is to turn the trace feature on for both points.  Do this by right clicking on the point and selecting "trace on".

Make sure the "move" tool is selected, then drag point A and watch as point A' follows along and traces out a figure that is congruent but translated 3 units right and 2 units down.  To clear the traces from the screen, type ZoomIn[1] into the input bar at the bottom of the screen.  (This command zooms in your screen, making it 1 times as large as it was before.  Clever trick to get the traces off the screen).

Geometers Sketchpad has lots of presentations on transformations that can be viewed on the Dynamic Number Project website.  My understanding is that students can access these presentations with the Sketchpad Viewer on an iPad.  I haven't thought too much yet about how I can use these in my class.  We don't have Sketchpad, and we also don't have ipads for each student.  For now I am trying some of their ideas on Geogebra, though I have to admit the experience isn't as smooth.  One strategy that Sketchpad uses is to attach a point to the perimeter of an object.  Geogebra has a similar tool, which is an option in the dropdown menu under polygons.  Make sure you have the object and a point created first.  Then when you select the "attach/detach point" tool select the point first, then the object to attach it too.  I found out the hard way to select the interior of the object.  By selecting the perimeter of a polygon, the point was confined to the line segment that created that side only.  

Once I had point A attached to the polygon below, I dragged point A to the edge and around the perimeter.  This created a congruent the congruent shape in orange traced out by point A'.

More to come on transformations with Geogebra as I prepare for a Thursday meeting.

Links you may find useful:

Geogebra Tools from Making Math Visual blog.
Geogebra Wiki.  Includes tutorials on how to get started with Geogebra.
Some Things I Wish I Knew When I Started Using Geogebra.
More practice with Transformations

#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!

Coordinate Fun

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Part I of this activity is called Crown Transformations,which I have tried many times in my Geometry classes.  It is always a big hit.  I usually have students fold a colored sheet of computer paper into eighths, and show the work on the paper.  You can use this graphic organizer if preferred.  We use colors to graph the different transformations of the crowns, which helps me assess understanding both during and after the activity.  My finished product is below, and I will project this and call on students at random to tell what type of transformation was performed on the original crown (in red) to get to on of the other crowns.  This activity will take about one 45-50 minute class period.

 

Parts II and IIIhttps://drive.google.com/file/d/0B8lXOcLLfHgvTF9KaXRWYjgySlU/edit?usp=sharing of this activity are new, and I haven't tried this yet with students.  Follow the directions in the worksheet to learn how to transform points using GeoGebra, then turn on the trace function and create diagrams like the one below.  Depending on student familiarity with GeoGebra, this activity with the final product should be doable during a 90 minute class period.  I would ask for students to upload their diagram to Edmodo so that I could use the diagrams at a later time for review.  Plus I like to fill my walls with student art.

                               
Unfamiliar with GeoGebra?  This tool can be used for teacher demonstration and student practice.