## Wednesday, February 13, 2013

### Valentine Symmetry

Since tomorrow is Valentine's Day, we thought it would be fun to take a look at symmetry as it relates to hearts, valentines, and other fun graphics. Help your students learn about symmetry as they cut out valentines and eat heart-shaped cookies. Let's start with the definition of "a line of symmetry":
A line of symmetry is an imaginary line that divides a figure in half. If you were to fold the figure along the line of symmetry, the sides would line up exactly, and the two halves would be mirror images of each other.
Download this math worksheet and copy it for each of your students (the second page includes the answers). You can copy it in color or in black and white. Talk about the definition of symmetry shown at the top: Excel Math Symmetry WorksheetClick here to download the PDF file.
Give each student a pencil. Have the students turn over the worksheet and draw a straight line diagonally from one corner to the opposite corner. Have a student (or you) read the definition of a "line of symmetry" aloud. Ask the students if they think the line they each have drawn is a line of symmetry. To check, have the students fold their papers along the pencil lines. They will discover that these are not lines of symmetry because even though the two halves are the same size, one is not the mirror image of the other.

Now give each student a square piece of paper. Ask them if they draw a line from one corner of the square to the other, would the diagonal line be a line of symmetry? Yes, this time the line will be a line of symmetry. Let each student fold the paper in half along the diagonal to check. This time the two halves are mirror images of each other.

Now have your students turn their worksheets face up. Talk about the figures shown on the top row and how they show symmetry:

Point out that these figures show one or more lines of symmetry. For some of these figures, more than one line of symmetry can be drawn:
If we fold each of these figures in half along the arrow, the sides would line up exactly, and the two halves would be mirror images of each other. The arrows show the lines of symmetry. Two of the figures have more than one line of symmetry.

These figures do not show a line of symmetry:

If we folded each of these figures in half along the arrow (or along any other dividing line), the sides would not line up, and the two halves would not be mirror images of each other. At the bottom of the worksheet, let your students draw all possible lines of symmetry for each figure. Talk about the answers as a class when the students have finished.

Hand out red paper and let each student fold it in half. Some of your students may have cut valentines from a folded sheet of paper. If so, let them demonstrate for the rest of the class. Point out that these valentines are symmetrical. When they are folded in half, the two halves are mirror images of each other, since they were cut together. Provide red and white doilies and markers for the students to use to decorate valentines for your school staff, nursing home residents, hospital patients, or for military families in your area. If you have time, bake some heart cookies and bring them for your students to decorate with symmetrical patterns. Then let each student eat half a cookie along the line of symmetry. After taking a picture of each child (or the entire class) holding the "line of symmetry" cookies, serve juice to wash down the other halves of the cookies. Let each student decorate additional cookies to give to others along with the cards.

Symmetry is now part of the Common Core (CCS) geometry requirements for Grade 4. In Excel Math, we begin teaching students about the line of symmetry in Grades 1, 2 and 3. Download the Excel Math correlations to your state standards: Excel Math Correlations