## Pattern Matching

Purpose

In this unit students explore lines of symmetry in pictures, shapes and patterns and use their own words to describe the symmetry.

Achievement Objectives
GM1-5: Communicate and record the results of translations, reflections, and rotations on plane shapes.
Specific Learning Outcomes
• Identify lines of symmetry in objects.
• Make patterns which have line symmetry.
• Describe line symmetry in their own words.
Description of Mathematics

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 coordinate 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 recognise diversity and student interests to encourage engagement. For example:

• looking at the line symmetry in Māori or Pasifika designs, carvings and faces
• using objects from the outside environment (leaves, butterflies, spider webs, flowers)
• Te reo Māori that could be introduced in this session includes that of shapes such as square (tapawhā), circle (porowhita), triangle (tapatoru) and line symmetry (hangarite whakaata).
Required Resource Materials
• Peg boards and pegs
• Geoboards
• Play-dough
• Magazine pictures
• Pictures to classify
• Mirrors
• Mosaic tiles
• Attribute blocks
• Classroom objects
• Cuisenaire rods
• Bottle tops
• Counters
• Cubes
• Ice block sticks
• Assorted craft materials
• Copymaster 1
Activity

#### Getting Started

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.

1. 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). Model how to fold some of the shapes in half, and encourage students to share their thinking with the class.

2. 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 a 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, called the line of symmetry, we will be looking for this week.

3. Have a collection of objects and pictures available and place them in the centre of the mat along with mirrors, straws, scissors, magazines and two pieces of chart paper. Explain to the students that we are going to use these objects to find out if any have two sides that match exactly.

4. 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)

5. Ask students to sort their shapes onto two pieces of chart paper, one for shapes that have symmetry and one for those that don't, and to state why they have placed them where they have. Ask the rest of the students to check that each shape, object or picture is being placed on the appropriate piece of paper.
How can we tell for sure?

6. Encourage students to identify the line of symmetry and for some pictures to indicate if there is more than one line. Ask the students to then offer two sentences to describe the two charts and how the objects have been classified.

7. Let the students independently continue to explore this 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 write a sentence to describe the two pictures.

#### Exploring

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 (whakaata), line (rārangi), half (haurua), match (tūhono), etc

1. 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.
Teaching Notes:
Templates could be made by drawing around mosaic tiles or setting up a pattern using the tiles and photocopying it.
2. Symmetrical Patterns
One student uses concrete materials to create a simple pattern showing a reflective symmetrical pattern.
Other students can locate the line of symmetry using a mirror or placing a straw (string, skewer, pencil, ice-block stick) along the line.
3. Splodge Butterfly Pictures
Provide the students with an outline of a butterfly on pre-folded A4 paper or with a line down the middle as well as images of native butterflies such as the Red Admiral (Kahukura) or Rauparaha's Copper to see the reflective symmetry on their wings.
Students paint splodges and patterns on one side of their butterfly.
The paper is then folded to create the matching pattern on the other side of the paper.
Students write a sentence about their picture either to describe how both sides are the same or to say something about the process for making the picture.
4. Place Mats
Students fold an A4 piece of paper in half one way and then the other.
They cut out shapes on the folds then 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 to create a more complicated pattern.
5. Leaf Lines
Students collect leaves and explore the symmetry or lack thereof in different species. They can create a tray displaying different leaves and use straws or string to show the lines of symmetry found.
6. Pegboard Patterns
Students create their own symmetrical patterns and get a friend to locate the line of symmetry.
7. Symmetrical Faces
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.

Outline drawings of tekoteko (carved, human-like figures) could also be used and symmetrical Māori designs such as koru could be added.
Students can write a sentence about their picture being the same on both sides.

#### Reflecting

In this session, 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.

1. 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 butterfly outline?
Why did we put a line down the pictures of ourselves (or the tekoteko)?
2. Revisit the charts made in the initial session and talk about the way the objects have been grouped.