Math Background

Lesson: Transformations
Developing the Concept

Students have learned how to perform translations, rotations, and reflections. Now they will practice what they have learned.

Materials: overhead transparencies with coordinate grids on them, overhead washable pen, ruler; graph paper, ruler, and pencil for each student

Preparation: Four overhead grid transparencies with a trapezoid, a scalene triangle, a rectangle, and any other quadrilateral drawn on one of the five transparencies.

Prerequisite Skills and Background: Students should be familiar with various types of triangles and quadrilaterals. They should also have some familiarity with graphing points on a coordinate grid. Students should know the various types of angles and have an ability to use a ruler and protractor. They should also have knowledge of translations, rotations, and reflections.

  • Say: Yesterday we learned about three transformations called translations, rotations, and reflections. Who can tell us what a translation does? (It moves figures along a straight line in one direction.)
    Display an overhead grid transparency with a trapezoid drawn on it.
  • Say: Yes, that's right. Who can tell us what kind of figure this is? (a trapezoid) Good, now who wants to show us how to translate this figure so that it moves three units to the right and four units down?
    Have a volunteer do the translation on the overhead for the class to see.
  • Say: That's great. What happens when we do a rotation? (We turn a figure about a given point.)
  • Say: Let's try rotating a figure. Draw an isosceles triangle so that the non-congruent side is parallel to the bottom of the graph paper. (Give students a few minutes to make their drawings.) Label the triangle ABC with side AB parallel to the bottom of the paper and sides AC and BC the congruent sides. Now move two units to the left of point A and call that point P. Rotate the triangle 180 degrees counterclockwise about point P.
  • Ask: What does your triangle look like?
    It is upside down from the original triangle, but it is still congruent to the original triangle.
  • Say: Now who would like to come up and rotate this triangle about point X through an angle of 90 degrees clockwise?
    Have a volunteer come up front and explain how to do it.
  • Say: Now let's try a reflection. On your graph paper, draw any quadrilateral you'd like. Now draw a line that is below your quadrilateral and reflect it about that line. I'll come around to help you if you need it. You can reflect it using paper folding or by counting on a grid. If you do it one way, use the other way to check to see if you did it correctly.

Wrap-Up and Assessment Hints
One way to informally assess your students about their understanding of these transformations is to ask them to find examples of them in the classroom, around the school, or at home. For example, tiles on a floor can be used to illustrate translations.

Houghton Mifflin Math Grade 6