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Sample Lesson Plan Grade 1-2 Symmetry

The discrete and continuous symmetry machine (2-3 lessons)

Main activity Students interact with on screen symmetric figures on the projector screen (or an interactive whiteboard) using pre-designed digital pages to explore vertical, horizontal, and oblique symmetry.

Grade level Grade 1, Grade 2, or Grade 1/2 split class

Overall objective/goals To build on students’ knowledge about line symmetry and develop students’ reasoning with properties of symmetry

To tap on students’ embodied experience and dynamic thinking in the learning of reflectional symmetry, i.e. what you do on one side, you do on the other

To develop students’ language related to spatial thinking and reflectional symmetry, i.e. moving along, towards, and away from the line of symmetry

Summary of tasks

Computer tasks Paper-and-pencil tasks

Materials Discrete symmetry machine (Geometer’s Sketchpad file) Continuous symmetry machine (Geometer’s Sketchpad file) Computer connected to a projector Colour crayons

Observation guides Student use of math language Student use of gesture Student use of diagrams and drawings Student approaches to tasks

Key Questions How do you know? What helped you? Why did you say that?


Detailed Plan of Lesson 1

Suggested Time: 30 minutes

Computer task: Exploring vertical symmetry with the discrete symmetry machine

After an initial survey of the children’s understanding of the word ‘symmetry’, the teacher introduces the “discrete symmetry machine”:

The teacher asks the children to observe and describe what they notice about how the symmetry machine works.

The children are invited to explain what will happen by coming up to the screen and showing their predictions.

The teacher uses the children’s descriptions and predictions to emphasise the motion of the squares in relation to the line of symmetry (the square moves along, away from or toward the line).


Talking about symmetry: Class discussion Using large cardboard diagrams of various symmetric and non-symmetric configurations (see below), the teacher asks the children to re-create the designs or explain why they symmetry machine could not have created the design. With the latter designs, the teacher encourage the children to talk about the relationships that should be present in order for a design to be symmetric.

Figure: (a) Vertical symmetry; (b) Vertical symmetry; (c) Not symmetric; (d) Horizontal symmetry; (e) Oblique symmetry

(a) (b) (c) (d) (e)


Paper-and-Pencil Task: Drawing symmetric figures The children complete some seated work in which they are to make drawing of configurations that the symmetry machine could produce.




Computer task: Exploring horizontal and oblique symmetry

Using the discrete symmetry machine from previous lesson, the teacher invites the children to explore the discrete symmetry machine with a horizontal then oblique line of symmetry. The teacher encourages the use of the same language developed in the first lesson so that the children describe how the squares moves along, away or toward the line of symmetry.


The broken symmetry machine: Reasoning with properties of symmetry The teacher opens a new page where only one side of the line of symmetry is shown; the children are told that the symmetry machine is broken and they must thus predict what the other side of the line should look like.

The sketch includes different pages, each of which has a broken symmetry machine with a different type of line of symmetry (see below).

The children are expected to use the relationships they had discussed in the previous lesson to help them decide how to create these symmetric designs.

Figure: (a) Broken horizontal machine; (b) Broken vertical machine; (c) Broken oblique machine.

(a)

(b)

(c)


Paper-and-Pencil Task: Reasoning with properties of symmetry The children are then move to the tables and are given two tasks:

The first contained two parts, each asking the children to describe how an asymmetric diagram could be symmetric—one involving a horizontal line of symmetry and one with an oblique one. (see Appendix 1)

In the second task, the children are asked to create their own symmetric designs, one having a horizontal line of symmetry and the other an oblique one.




Computer task: Exploring the continuous symmetry machine The teacher introduces the “continuous symmetry machine”, and asks the children to observe and describe what happens when one point is dragged on the screen. Note: Since there are only two dots on the screen, it is less obvious what the sketch is meant to do and whether or not vertical symmetry is involved.


Computer task: Using the continuous symmetry machine The teacher invites the children to draw particular symmetric shapes, which they must identify before they begin dragging. For example: Before drawing the shape of a heart or a house on the screen, the student must identify what they are about to draw.

Extension: The teacher asks the children, “where do you think that the blue point and the red point will meet?” A few children come up to the screen to answer the question by pointing. Then, the teacher asks, “how many places do you think that the two points will meet?” Through this extension activity, the children may learn that the line of symmetry can be constructed as a set of overlapping blue and red points.


The teacher gives a paper task in which the children are to draw symmetric figures that the continuous symmetry machine could make in their mathematics journals at the end of the lesson.


Appendix 1

Why is this square in the Why is this square in the

wrong place for symmetry? wrong place for symmetry?

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