I Spy II: Class Activity

This post gives a few samples from the follow up activity for the I Spy introduction to congruent triangles activity.  The directions that will be given to students are:

I Spy

Directions: Each diagram has a pair of triangles.  One triangle has been either translated, reflected, or rotated to create the second triangle.  As you view each diagram, see how many of the following objects you can find.

-Angle Bisector

-Midpoint

-Isosceles Triangle

-Parallel Lines (or parallel segments)

-Right Angles

Team Directions:  Each team member should use a different color marker to record responses to the problems.  Switch roles for each problem.

There are 6 problems to total to give the groups.  The first two are easier than those shown below, with only one conclusion (I spy item) to make from the diagram.  The photos below are provided as a preview for this activity.  The full problem set with directions is available here.

I Spy: Introduction to Congruent Triangles

Below is an introduction to congruent triangles that makes use of student prior knowledge of transformations.  It also encourages students to deduce information from a diagram and to justify their reasoning. 

Show students the following diagram, and go through the steps below.  Some questions/prompts are shown in blue.

1.  What type of transformation is shown in this diagram?

2.  Reveal the measures of ABC.  Ask students, “Who thinks they know another measure in the diagram?  Be ready to explain your answer.  Show me ONE other measure that you know, and hold up your whiteboard when you are ready.”  Teacher can show answers from students that used notation correctly.  Reveal the measures of AFE.

3. Show students the statement below.

Ask them how we might fill in the blank, and why.

4.  Move point C to the horizontal line (you can do this in the Geogebra applet).  

Leaving the measurements showing, ask students to tell you what they “spy”.  They can write on their whiteboards, “I spy __________________.”  Answers must be defended.  Make sure to have the list of possible answers written on the whiteboard.  

The choices are angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.

3.  Move point B to F. Move point A down the vertical line so your diagram looks like the one below.

Leaving the measurements showing, ask student to tell you what they “spy”.  They can write on their whiteboards, “I spy __________________.”  Answers must be defended.

I SPY CHOICES:  angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.

4.  Turn the measurements off.  Move point A back up to the horizontal line, and make sure point B is on point F.  Ask student to tell you what they “spy”.  They can write on their whiteboards, “I spy __________________.”  Answers must be defended.

I SPY CHOICES:  angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.

Extension if there is time:  Since we haven’t seen parallel lines yet in this dynamic diagram, ask students how we can modify the diagram to form parallel lines (and explain why).

There is a second page in the Geogebra Book that has a triangle rotated around a vertex by 180 degrees to form the second triangle.  

Part II will have the I Spy Class Activity if you have time for it.

Symmetry Artist

I was observing a teacher today, and one of the lesson resources was Symmetry Artist from Mathisfun.com.  I was so excited by this resource that I could hardly focus on the lesson.  If you've never seen this resource before, it looks like the screenshot below:

 My five year old created the drawing above.  When she was finished I told her to pick a different number of "petals", and she chose 9 (shown below).

What an amazing resource!

Pierce, Rod. "Maths is Fun - Privacy Statement" Math Is Fun. Ed. Rod Pierce. 27 Feb 2012. 20 Oct 2014 <http://www.mathsisfun.com/Privacy.htm>

9-5 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

Transformations with Geogebra

Use this Geogebra Book to help demonstrate translations and reflections.

Use this Geogebra Book by Jed Butler to demonstrate rotations.

An organizer used during a Geogebra presentation can help students organize their thinking and study later on.  Follow this Dropbox link to download one that can be used for section 4-8.  Below is a sample of what is on the organizer:

Geometry: Slogan Project

Below are two examples from MVHS Geometry Slogan Project.  This project almost speaks for itself, but I will post a link to the directions soon to clarify directions/scoring.  Student posters were presented in class at the end of the project.

Math Problems from Exeter

If you ever want to do math problems in your spare time, or are looking for inspiration, check out the math curriculum from Phillips Exeter Academy.  The math program is integrated, and the problems spiral like CPM.  They do a great job of developing concepts through problem sets.