Oakland Terrace Math Grade 3

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Grade 2 Unit 2/Grade 3 Unit 4 ~ Symmetry/Reflections

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Symmetry/Reflections
Students explore symmetry and reflections by creating designs that are symmetrical in which they reflect along a line of symmetry. Students must be able to identify lines of symmetry and to construct symmetrical designs.

Student work showing a symmetrical design using pattern blocks

In this activity, students create a design using pattern blocks along a line of reflection. Then, the same student or a different student reflects the design, creating a picture with one line of symmetry. Students should be able to communicate why it is a symmetrical design. They should be able to identify the line of symmetry. And, they should point out the transformations of some of the shapes. For instance, a student might identify that the green triangles are all flipped (or reflected).

In this activity, students first create a line of symmetry on the geoboard. They then create a design on one side of the line of symmetry that they reflect onto the other half of the geoboard. Some students will need strategies for reflecting the design. Struggling students should use a strategy such as counting the number of pegs from the line of symmetry. If a point on the design is one peg left of the line of symmetry, there must be a point one peg right of the line of symmetry.

This activity not only connects reflections and symmetry; it also connects to congruence. A design with one line of symmetry is congruent on either side of the line of symmetry. On the designs, the student has marked the area of each side of the design. Not only has the design been reflected; each half of the design occupies the same area. Discussing the specific area of the halves of the designs broadens the students' understanding of congruence to mean more than simply the design can be folded. Or that the halves have the same size and shape.

Student work showing symmetrical designs drawn on geo-dot paper


$Download Geodot Paper$ Download Geodot Paper	$Online Geoboard$ Online Geoboard	Indicators 2.2.4.1 identify and model symmetry with concrete materials and drawings. 2.2.4.2 identify the line of symmetry in figures and objects with symmetry. 2.2.5.1 identify and model congruence with concrete materials and drawings. 2.3.4.2 identify, describe, and represent symmetry of geometric figures and real-world objects. 2.3.5.1 identify, describe, and represent congruency of geometric figures and real-world objects. 2.3.4.1 describe and represent slides, flips, and turns using pictures and simple objects.

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