In this unit students explore lines of symmetry in pictures, shapes and patterns and use their own words to describe the symmetry.
- Identify lines of symmetry in objects.
- Make patterns which have line symmetry.
- Describe line symmetry in their own words.
In this unit, the central idea is that of symmetry, specifically line symmetry. This is an introductory and exploratory unit on this topic. As such it sets the groundwork for a great deal of later mathematics. As far as geometry is concerned, symmetry is important in classifying shapes (regular polygons versus non-regular polygons), in working with patterns, tessellations, and later curves in co-ordinate geometry.
Symmetry is fundamental to mathematics, even those aspects that seem to have nothing to do with geometry. For instance, in algebra, symmetric functions deal with variables that are all treated in the same way. Because symmetry is part of a child's environment, both in mathematics and the rest of their life, it is important that students explore the ideas relating to symmetry from an early age.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
- providing squares and circles of many sizes so that students can work with shapes that have multiple options for the “folding line”
- providing additional support to draw a line on the fold and to position the mirror so that they can see the reflected side of the shape.
The context for this unit can be adapted to suit the interests and experiences of your students. For example: look at the line symmetry in fruit and vegetables (apples, tomatoes, pineapple, strawberries) or in objects outside the classroom (leaves, butterflies, spider webs, flowers).
- Peg boards and pegs
- Magazine pictures
- Pictures to classify
- Mosaic tiles
- Attribute blocks
- Classroom objects
- Cuisenaire rods
- Bottle tops
- BSM 2-3-9, 2-3-87, 3-3-8, 3-3-51
- Ice block sticks
- Assorted craft materials
- Copymaster 1
In this session we explore shapes and pictures and classify these as having line symmetry and not having line symmetry. Students are encouraged to use their own language to describe objects and pictures that have symmetry.
- Gather students in a group and pass out a selection of paper shapes (Copymaster 1). Ask students to talk about the shapes and what they know about them. Ask students Can you find a way to fold your shape in half so both halves are exactly the same? Talk about which shapes are easy to do this with and which ones are more difficult (for example, compare the circle and the hexagon). Ask students to draw a line on the fold that they discovered. Demonstrate with a mirror how holding a mirror on the fold line creates an image of the whole shape. Then demonstrate how holding a mirror on other fold lines wouldn't (for example, across the heart shape can create a diamond or an bumpy cloud shape, or across a triangle can create a quadrilateral or a diamond). Explain that the fold line that creates exactly the same halves side by side is the special line we will be looking for this week.
- Have a collection of objects and pictures in the centre along with mirrors, straws, scissors, magazines and two pieces of chart paper.
We are going to look through these pictures and objects and find out if any have two sides that match exactly.
Ask students to explore the objects and pictures on the mat and to choose one that has a line of symmetry and one that doesn’t. The language of symmetry could be introduced to describe the matching shapes.
Why have you chosen that object?
Try using the mirror to see if the sides will be the same.
Can you put a straw down the line of symmetry? (folding line)
- Ask students to sort their shapes (those that have symmetry and those that don’t) onto the two pieces of chart paper and to state why they have placed them where they have. Ask students to check that each shape, object or picture is being placed on the appropriate piece of paper.
How can we tell for sure?
Encourage students to identify the line of symmetry and for some pictures to indicate if there is more than one line. The students can then contribute to captions to describe the two charts and how the objects have been classified.
- Let the students independently explore the idea by using magazines to locate a picture of something with a line of symmetry and something with no line of symmetry. Students can paste these pictures onto a piece of paper or into a maths book. They draw a line or paste a straw onto the symmetrical picture to show the line of symmetry and provide a caption for the two pictures.
Over the next few days students explore things that have line symmetry (or reflection symmetry) as they complete a variety of activities using shapes, familiar objects, pictures, patterns. The students could be organised into small groups and rotated through the activities or they could work independently choosing from a range of activities or marking off completed activities on a contract. As you are monitoring the activities, encourage the use of the vocabulary related to symmetry: reflection, line, half, match, etc
- Pattern Match
Templates showing a pattern made with mosaic tiles are provided for the students. Each pattern stops at a line.
Students use mosaic tiles to complete the pattern so that it matches on each side of the line. The line is a line of symmetry.
Templates could be made by drawing around mosaic tiles or setting up a pattern using the tiles and photocopying it. BSM 2-3-87 has some of these cards.
- Symmetrical Patterns BSM 2-3-9
Students use the cards showing reflective symmetrical patterns, which they copy using concrete materials.
Students can locate the line of symmetry using a mirror or placing a straw (string, skewer, pencil, ice-block stick) along the line.
- Splodge Pictures
Provide the students with pre-folded A4 paper or with a line down the middle.
Students paint splodges and patterns on one side of the paper.
The paper is then folded to create the matching pattern on the other side of the paper.
Students provide a caption about their picture either to describe how both sides are the same or to say something about the process for making the picture.
- Place Mats
Students fold a half A4 piece of paper in half one way and then the other.
They cut out shapes on the folds.
Unfold the shapes and mount them on paper with a contrasting colour.
Students identify the lines of symmetry by drawing them in with a coloured pen.
Some students may want to use more folds and so create a more complicated pattern.
- Leaf Lines
Students collect leaves and explore the symmetry or lack there of in different species. They can create a tray displaying different leaves and use straws or string to show the lines of symmetry found.
- Pegboard Patterns (BSM 3-3-8)
Students use the pattern cards; they copy the patterns onto the pegboards.
Students locate the line/lines of symmetry.
Students create their own symmetrical patterns and get a friend to locate the line of symmetry.
- Pegboard and Pattern "Snap" (BSM 3-3-51)
Students play as per the instructions in BSM booklet Cycle 3 Module 3 activity 51.
- Symmetrical Me
Students look in a mirror to see if both sides of their face look the same.
Students take an outline drawing of a person and fold it in half to show a line of symmetry.
They add details to the person to make it a picture of themselves, for example, clothing, facial features, hair.
Students provide a caption about being the same on both sides.
In this session we review the activities that have been completed over the last few days and revisit the class charts and individual charts made in the initial activity. The students are provided with opportunities to demonstrate their understanding of symmetry, to find examples of line symmetry within the classroom, and to create a symmetrical pattern to contribute to a class book.
- Gather the students on the mat and get them to describe the sorts of activities they have been involved in over the week. Encourage them to talk about patterns that match and about lines of symmetry.
What was special about the patterns we made with the pegboards?
Why did we put a line down the pictures of ourselves?
- Revisit the charts made in the initial session and talk about the way the objects have been grouped.
Why was this picture of a house put on this chart?
Can you find the line of symmetry in this picture?
- Get students to look at large objects in the classroom and to think about line symmetry, for example, the door, tables, chairs, the board. With a partner, get the students to find three things in the classroom that have line symmetry and to identify the line.
- Gather the students back on the mat and show them a range of craft materials; coloured ice block sticks, pom poms, stickers, ink stamps, coloured toothpicks, pipe cleaners.
- Give each student a piece of paper and get them to fold it down the middle.
- Get the students to create a pattern by sticking on the craft materials on one side of the paper and then to mirror it on the other.
- Get each student to provide a caption and to draw in the line of symmetry.