Reflections, Translations, & Rotations

The big idea

In short, students will trace half of a lion face three times onto tracing paper, cut out each traced image, perform a reflection, translation, or rotation with each, and glue each traced image in its place next to one of the three original half-face pictures. Before students begin, the teacher explains the three words using a previously constructed project as a reference. The traced half of each picture must be unattached so the teacher can demonstrate how flipping an image creates a reflection, sliding an image creates a translation, and turning an image creates a rotation.

Learning objectives

By the end of the lesson, students will be able to:

• Define reflection, translation, and rotation.
• Match flipping, sliding, and turning to those three terms.
• Perform each transformation on a traced image.
• Recognize that a transformation moves an image without changing its shape.

Common Core alignment

• CCSS.MATH.CONTENT.4.G.A.3

  Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

  Reflecting an image across a line is the same fold-into-matching-parts idea behind the symmetry standard at this grade.

• CCSS.MATH.CONTENT.8.G.A.3

  Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

  Performing reflection, translation, and rotation on the traced image is a concrete introduction to the formal transformation work this standard names.

Materials

• Pencils (1 per student)
• Background sheets, page 149 (1 per student)
• Lion sheets, page 150 (1 per student)
• Tracing paper (1 sheet per student)
• Scissors, a scotch tape dispenser, and glue sticks
• The completed project, prepared by the teacher before the lesson, with the traced half of each image not yet glued

The project

Students start by cutting their background sheet in half along the solid line, then gluing the two halves back together so that the word "top" appears three times along the top. Next, they cut out the three half-lions and glue them inside the three rectangles on the background sheet. They then trace each lion face, and it helps to give each student a small piece of tape to temporarily hold the tracing paper in place so neither it nor the sheet shifts.

Model how to trace before letting students try. Show them that they trace each picture's rectangular frame first, since they will cut along that rectangle. When tracing the lion face, tell students not to try to trace or color every detail: the important parts are the outline of the face, the nostrils, the eye, and the hood over the eye, plus a dozen wiggly lines for the mane and a few light lines for the whiskers. Students glue their traced cutouts only after conferencing with the teacher, and each student should manually perform all three operations for the teacher before gluing.

Common student mistakes

• Mixing up the three moves. Tie each firmly to a plain word: flip is a reflection, slide is a translation, turn is a rotation.
• Letting the tracing paper slip. A small piece of tape holds the paper and the sheet still so the traced image lines up.
• Trying to trace every detail. The face outline, eye, nostrils, hood, mane, and whiskers are enough; over-tracing bogs students down.