MACC.4.G.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.

Mathematical Practice #7 Look for and make use of structure

Meredith is making greeting cards for her friends Meredith is making greeting cards for her friends. She wants to make each friend a different shaped card. For each figure, find all the lines of symmetry so she can decide how to fold her cards before giving them to her friends.

Look for and make use of structure Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular and non-regular shapes. Folding cut-out figures will help students determine whether a figure has one or more lines of symmetry. This standard only includes line symmetry not rotational symmetry.

To look for and make use of structure, it is important to relate this skill to students background knowledge. In prior grades, they have learned about two-dimensional shapes. Pattern blocks are manipulatives that students have already been introduced to as well. They are a great way to introduce symmetry. Pattern blocks, such as the blue rhombus and yellow hexagon, can be divided into two congruent and equal pieces that show symmetry. Thus, this encourages students to look closely to discern a pattern of structure. For instance, when two green triangles are placed on top of a blue rhombus, the line of symmetry is evident.  

Continued… Students have also learned about fractions and cutting portions in half. By looking for and making use of structure, students understand that each half of a figure is a mirror image of the other half. Students may demonstrate this understanding by folding a figure along the line of symmetry to see the figures reflection. Students may also use a transparent mirror by placing the beveled edge along the line of symmetry to see the figures reflection.

Symmetry While students are exploring the symmetry of these various shapes, use questioning to guide their thinking. Ask, “How do you know there is a line of symmetry?” or “How can you prove that the shape is symmetrical?” Student proficient in this practice see complicated things as single objects or being composed of several objects.

The Solution Solution: The isosceles trapezoid has one line of symmetry, the perpendicular bisector of the base. The scalene triangle has no lines of symmetry. The isosceles triangle has one line of symmetry, the perpendicular bisector of the base. The ellipse has two lines of symmetry, one along the major and one along the minor axis. The rectangle has two lines of symmetry, the perpendicular bisector of the longer sides, and the perpendicular bisector of the shorter sides. The circle has infinitely many lines of symmetry, any line going through the center. (Any diameter is a line of symmetry.) The parallelogram has no lines of symmetry. Neither does the trapezoid.

To answer the question: Images below show how Meredith can fold each shape.

Real World It is also important to allow students to see that symmetry is found all around them in nature…

Real World Images