Math: Geometry

Pre-K-8: Instructional programs from Pre-Kindergarten through grade 12 should enable all students to use and apply transformations and use symmetry to analyze mathematical situations.

• In Pre-Kindergarten through grade 2, all students should recognize and create shapes that have symmetry.
• In grades 3-5, all students should identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs.
• In grades 6-8, all students should examine the congruence, similarity and line or rotational symmetry of objects using transformations.

Pre-K-8: Instructional programs from Pre-Kindergarten through grade 12 should enable all students to use visualization, spatial reasoning and geometric modeling to solve problems.

• In Pre-Kindergarten through grade 2, all students should recognize and represent shapes from different perspectives.
• In grades 3-5, all students should build and draw geometric objects.
• In grades 6-8, all students should recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science and everyday life.

Standards are listed with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments.

Source:Principles and Standards for School Mathematics

The teacher can explore the concept of symmetry and check for student understanding through identification of symmetrical objects in the classroom. Students recognize symmetry, explore lines of symmetry, examine congruence and find similarities.

Figure A

Figure B

Figure C

Figure D

Figure E

Supplies Used: Construction Paper, Glue, Scissors, Adhesive Letters

The teacher will die-cut the materials for student use prior to the lesson.

Symmetry Poster

1. Cut a 20" x 16" sheet of yellow cardstock or poster board for poster.
2. Die-cut the title for the poster using 3" Lollipop Alphabet Capital Letter Set from black cardstock or construction paper. Adhere the letters at the top of the poster (see Main Photo).
3. Die-cut various geometric shapes from cardstock or construction paper and adhere to the poster. Follow the Main Photo or create other samples showing Mirror Symmetry (Figure A), Rotational Symmetry (Figure B) and Asymmetry (Figure C),
4. Hand print or use adhesive letters to title each of the areas (see Main Photo).
5. Cut two 4 1/2" squares from black paper for the Dodecagon Puzzles. Die-cut various geometric shapes from paper and adhere to the black squares for Mirror Symmetry (Figure D) and Rotational Symmetry (Figure E). Hand print or use adhesive letters to label each area (see Main Photo).

Dodecagon Puzzle

1. Die-cut a LG Dodecagon for each student from black paper.
2. Die-cut various Pattern Block Multiple shapes from different colors of paper and give a packet to each student.
3. Students create different Dodecagons by placing the Pattern Block Multiple shapes on top of the black Dodecagons. Over 300 different Dodecagon designs are possible.
4. Have students identify if the pattern created will tessellate, if it is a mirror image, if it will rotate or if it is asymmetrical.
5. If the first pattern will tessellate, have the student create a pattern that does not tessellate. If the pattern does not rotate, have the student create one that will, etc.