Transformations Lesson 1
Develop an understanding of translations in the coordinate plane and determine general rules for translations through exploration.
Prepare students to use the visual thinking strategy by providing the “I see, I think, I wonder” map on the board. Ask them to observe your actions and note their thinking. Demonstrate translation by picking up an object and physically moving it to a new location. Repeat if needed. Students should notice that each translation’s orientation, size, and shape are preserved. The only change with translations is location.
Possible guiding questions include:
[Possible student responses: the shape stayed the same, the object is not in the same spot, the object changed direction]
[Possible student responses: nothing about the object is different, it is just in a new place]
[Possible student responses: the shape always moves location but does not change in size]
[Possible student responses: they always change ]
Have students work with their partner on Part I of the Translations Activity Sheet (download from Materials section above) to generalize a rule for each translation using x and y notation.
After a few minutes, bring students back together to share student generalizations. Expand on student thinking to connect to the general translation rules using x and y notation. For example, (x +2, y-3) for a translation of a point 2 units to the right and 3 units down.
Have students continue to work in partners to complete Part II Exploring Properties of Translations. For this part of the activity, students should be able to understand and apply a translation rule to a given image.
As a whole class, have partners share their observations.
Possible guiding questions:
[Possible student responses: The combination of these translations moved the image diagonally.]
[Possible student responses: They are the same distance apart, just moved down.]
[Possible student responses: All of the points on the shape are still the same distance away from each other.]
After students have completed the second part of the worksheet, work as a class to summarize rules for performing a translation. Teachers may want to post the rules for translation on a classroom chart for future reference.
Students should recognize the orientation, size, and shape are preserved in translations; that is, the resulting figure will have the same side lengths and interior angle measures as the original figure.
Examples of rules include:
Leave your thoughts in the comments below.
Develop an understanding of reflections in the coordinate plane, and determine general rules for reflections through exploration.
Explore rotations on a coordinate plane where (0,0) is the center; determine general rules for rotations.
Students will develop an understanding of dilations on the coordinate plane and general rules for dilating an image through exploration.
CCSS, Content Standards to specific grade/standard
CCSS, Standards for Mathematical Practices
PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS