Let's Learn AbouT Symmetry

Expectations:

E1.3 construct and describe two-dimensional shapes and three-dimensional objects that have matching halves

Key Concepts

• If two shapes or objects match in every way, they are congruent. Shapes with matching halves have congruent halves.

• Congruent halves can be superimposed onto one another through a series of slides (translations), flips (reflections), or turns (rotations). This means that congruent halves are also symmetrical.

• Both three-dimensional objects and two-dimensional shapes can have matching, congruent, symmetrical halves.

Materials

• Symmetry cut out templates

• Masking tape to put on floor or table as a line of symmetry

• Plastic set of pentominoes for each student (different colour sets)

• Paper game board for each pair of students (grid template can be found here. You will have to print and tape the grids to form a 11x 12 rectangle and draw a line of symmetry down the middle to create two halves that are both 6 x 11 squares.)

Hold up a folded piece of paper that shows half of a heart drawn on one side. Ask children to predict what the shape will look like after it has been cut and unfolded: Look closely at this outline. (Use a finger to trace around the shape).

Key Questions:

What shape will I have if I cut on the line and then unfold it?

What makes you think it will be a heart?

Once children have guessed that the object is a heart, cut the outline of the half heart. With dramatic purpose, unfold the paper to reveal the heart. Ask questions such as: What do you notice about the heart? What do you notice about the two sides?

Now focus the children’s attention on the fold line (line of symmetry): Look at this line. (Move finger along the fold.) It has a special name. IT is called the line of symmetry. Now bring students attention back to the heart: The line of symmetry divides the heart in half. Are the two sides the same? How can we prove that? Allow children the chance to answer. Then use scissors to cut down the fold line. Invite students to come up and superimpose one half-heart onto the other to verify that they are exactly the same.

Repeat this process with other symmetric pre-drawn half shapes such as a star, crown, butterfly, pine tree, or other shapes that have a vertical line of symmetry.

(Click here for templates)

**Note whether all children are able to anticipate what the unfolded shape will be. This is an essential understanding that students will need to have as they begin their work on symmetry. Listen for students using vocabulary related to symmetry and transformations: half, same, reflect, mirror, flip, symmetry, line of symmetry.

Place a piece of tape on the floor or table to serve as a line of symmetry. Explain that students will pair up and each player will play only one side of the line of symmetry. Together, each pair will be making a symmetrical design. As you introduce the game, focus children’s attention on the line of symmetry that has been placed on the floor or table. Activate their prior experience with the line of symmetry, asking them what they remember about the line.

Model the rules of the game with the help of a student volunteer:

• Player one selects a pentomino and places it somewhere on his or her side of the floor or table so that it touches the line of symmetry.

• Player two looks for the matching pentomino from his or her set and places it on his or her side of the line so that it is symmetric to Player one’s piece.

• Now Player two takes the lead and selects a pentomino to place on his or her side of the line. From this point on, the pieces need to not touch the line of symmetry.

• Player one must try to create a mirror image.

• The game continues in this way until all of the pentominoes are used up.

Give each child a set of pentominoes. Divide the class into pairs, making sure that the members of each pair have different coloured sets of pentominoes.

Key questions:

• What do you remember about the line of symmetry?

• What will we need to think about when we place our pentominoes down in this game? How will the line help us know where to place our pentominoes?

• Do both sides look symmetrical? Are you sure all your pieces are facing the correct direction?

Next, provide students with a paper game board on 1 inch grid paper with an outline of a large rectangular 11x12 grid with a line of symmetry drawn down the centre (click here - you will have to tape two sheets together in order to create a 11x12 grid). Explain that this is a game of symmetry so the placement of the pentominoes on both sides of the line must be symmetric. Explain also that the pentominoes must stay in the squares.

Tell children that the rules of turn-taking are the same as the previous game:

• First, Player one places a pentomino on his or her side of the board so that it touches the line.

• Player two finds the same pentomino and places it on the other side of the board so that it is a mirror image of the first player’s piece.

• Then Player two takes a turn places a piece on her or his side of the line of symmetry. Pieces places after the first one need not touch the line.

• Player one creates the reflection using the same penomino on his or her side of the line.

An important consideration for this game is that all pieces must be placed directly on the squares provided on the game board and that they have to stay within the game board. The objective is to place as many pentominoes as possible within the space, keeping all shapes within the rectangular outline. The game ends when the board is so filled that no more pentominoes can be placed without going over the outer boundary.

**It is not necessary for a student to place all 12 pieces on his or her side of the line of symmetry (although this could be a fun challenge once they are familiar with the game).

As you circulate during the game consider some Key Questions:

• Are you sure that you are staying in the lines when you place your pentominoes?

• Do you think that you will fit all of your pieces on the game board or will you run out of space?

• Do you have a strategy to fit as many of your pieces as possible onto your side of the board?

• Do you need to rotate that piece in order to fit it more snugly into the squares so that you can fit more pentominoes on your side?

Prompts for whole group discussion:

• When it was your turn to place a pentomino on the grid, what did you try to do?

• What helped you to match up the correct pentomino?

• When you looked at the design you created with your partner, were you both sure that all the pentominoes were placed so that they design was symmetric?

• What was the trickiest part of this game for you?

• What do you like about the design you created?

• What do we know about the line of symmetry?

• Can you find anything else in the classroom that has a line of symmetry?

• Were some blocks harder to place than others? Why?

Notice students reasoning about the line of symmetry.

Notice how children play on the floor or table, notice how a child gauges the placement of the pentomino to match a piece that has been placed away from the line. Does the child try to match the distance of the first piece from the line? Does the child appear to be measuring by counting squares on the grid to ensure the placement is correct? How accurate is the child in gauging the correct distance from the line?

Listen to children’s language. Do they use the language of transformation as they talk with each other? For example, “No, that’s not rightl you have to flip it / rotate it!”

Notice whether children incorrectly place the pentomino on their side of the line of symmetry in the same orientation as the challenge piece rather than as a mirror image.

Notice whether students gesture actions as they reason.

SEL Self-Assessments and Teacher Rubric

Extension Activities:

• Super Source K-2 (Snap Cubes) - Page 42 “Mirrored Images”

  • • Children build a snap cube structure, place it along the fold of a piece of grid paper, trace around it, and cut out the shape to create symmetrical designs. Then they challenge their partner to create the mirrored image of their structure. In this activity, students have the opportunity to work with the line of symmetry, create a symmetrical design using folded paper, build a mirrored image of a design.

• Super Source K-2 (Pattern Blocks) - Page 26 “Copy Cat”

  • • Children use Pattern Blocks to create shapes that have reflective symmetry across a horizontal or vertical line. In this activity, children have the opportunity to create a symmetrical shape, piece by piece and decide whether or not a design has symmetry.

• Taking Shape - Symmetry - Page 65-100