In the garden

Purpose

This unit uses the context of a garden to explore Level 2 symmetry and transformation concepts (translation, reflection and rotation). 

Achievement Objectives
GM2-7: Predict and communicate the results of translations, reflections, and rotations on plane shapes.
Specific Learning Outcomes
  • Investigate shapes that tessellate.
  • Make geometric patterns by translating, reflecting and rotating shapes.
Description of Mathematics

Three important ideas about symmetry are covered in this unit:

  • A shape has reflective symmetry when it contains at least one line of symmetry. A line of symmetry is often described as a mirror line.
  • A shape has rotational symmetry when it can be rotated by less than a full turn around a central point and look the same. 
  • A tessellation is the covering of a plane surface with one or more shapes, with no gaps or overlaps.
Opportunities for Adaptation and Differentiation

This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

  • Provide templates that students can use to create symmetrical butterflies. Templates could be one half of a butterfly with students needing to draw in the other half, or a full butterfly for students to colour or decorate symmetrically. Templates for bugs and flowers might also be helpful.
  • Provide students with a range of A4 sheets of tessellating patterns that students can use to create garden paths.
  • Have students use mirrors to help them draw symmetrical butterflies and other items.

The context in this unit can be adapted to recognise diversity and student interests to encourage engagement. For example create a classroom display of a skate park instead of a garden. Symmetrical people, dogs, and skateboards could be created, and tessellating paths and walls drawn.

Required Resource Materials
  • Paper
  • Scissors
  • Paste
  • Mosaic pattern blocks
  • Coloured paper
  • Rulers
  • Split pins
  • Blue tack
  • Sticks
  • Crayons
  • Butterfly pictures
  • School Journal Part One, Number 5, 1995, The Shapes of Leaves.
Activity

It would be helpful to introduce this work by reading a book to the students that includes a garden setting. The overall aim of the unit is to make a classroom display about a garden using the activities as starting points. Be as creative as you can! 

Session 1: Up the garden path

In this session students will explore shapes that tessellate or repeat to cover the plane without gaps or overlaps. Although the students will only be covering a strip (path) any covering of a path can be used to tessellate the plane simply by putting paths together.

  1. Explain to the students that they have the task of building a garden path. Show them examples of cobblestones and other garden paths, using online images if no real-world examples are available. 
  2. Give them the mosaic pattern blocks and ask them to build a path using the pattern blocks as cobblestones. All the cobblestones must fit together without any gaps. Students are to select 1 or 2 shapes to build their path. The path needs to have at least 3 or 4 rows of blocks. Ask them to experiment with the mosaic pattern shapes to design their path.
  3. Students draw their path shapes and present them to the class describing the shapes that they have selected.
  4. Create garden designs around the paths. 
    paths

Session 2: Bugs, Beetles and Butterflies

In this session students will be investigating line symmetry by making butterflies out of coloured paper.

  1. Show pictures of butterflies. Look at the wings and discuss reflective symmetry.
  2. Ask students to make their own butterflies by folding and cutting.
  3. Encourage them to cut out pieces in the wings to add detail.
  4. Ask students to share their work and talk about the reflective symmetry it contains.
  5. Extend the activity to making other bugs and beetles by folding and cutting.

Session 3: Butterfly Painting

In this session students will make symmetrical butterflies with paint.

  1. Fold a piece of paper in half. On one half draw the outline of half of a butterfly. Create designs on this half of the wings with paint. Carefully fold the other half of the paper onto the wet paint. Unfold it to get a symmetrical pattern.
  2. Ask students to share their work and talk about the reflective symmetry it contains.
  3. Students could then make other bugs and beetles for the garden using the same technique.

Session 4: The Flower Garden

In this session students will be introduced to making symmetrical patterns with shape blocks. The theme for this lesson is flowers for the garden. Sunflowers would be a great example of this. Show students pictures of sunflowers or read the story "The Sunflower That Went Flop" by Joy Cowley) which can be accessed on YouTube if it is not readily available.

  1.  Give students a piece of paper with a line drawn down the middle.
  2. Students use mosaic pattern blocks to make half of a flower pattern on one side of the line. They give this pattern to a partner who has to then repeat the pattern on the other side of the line making sure that it is symmetrical.
    Symmetrical flower
  3. Ask students to trace around the mosaic shapes to make the petal shapes. This can be done with coloured paper. Glue the petals onto the paper to make symmetrical flowers.
  4. This activity could be extended by encouraging students to create their own symmetrical designs. They could experiment with cutting the paper shapes in half to create other pieces for their designs.
  5. These could then be displayed alongside the path designs from Session 1.

Session 5: The Garden Wall

In this session introduce students to the idea of translation. Students will be making tiles for the garden wall. Introduce the activity by showing them examples of some wall tiles.

  1. Give each student a piece of square grid paper, for example a 4x4 grid. Students are to draw a design by colouring in the squares to make a pattern.
  2. They make 3 or 4 copies of this pattern.
  3. Stick these in a row to make a row of tiles with repeating patterns.
  4. These could then be displayed above the flowers made in the activity from Session 4.

Session 6: Wind Catcher in the Garden

In this session students will make a wind catcher, which illustrates rotation, as an ornament for the garden .

  1. Give each student a square piece of paper.
  2. Fold the square along its diagonals.
  3. Make cuts along the diagonals leaving about 1 cm uncut at the centre of the square.
  4. Take one of the cut ends at each corner and fold into the centre.
  5. Repeat this at each corner.
  6. Pin the folded pieces together with a split pin.
  7. Put a little piece of blue tack onto the back of the pin to hold the pieces in place.
  8. Attach the pin to a stick.
  9. Blow to watch it rotate.
    wind catcher
    Cut along lines in first image

Teaching Notes:

The wind catcher has rotational symmetry but not reflective symmetry. This is because it can be rotated around onto itself but it doesn't have a line of symmetry in the plane.

Session 7: Making Scarecrows

Ask students to draw a scarecrow on a piece of paper. Fold the piece of paper down the middle of the scarecrow. Cut down this middle line. Students then give their scarecrow to a buddy who has to draw the other half of the scarecrow making sure that the drawing is symmetrical. Stick one half of the scarecrow onto a piece of paper. A buddy draws on the other half. Finished scarecrows could be stuck onto sticks and displayed in the garden.

Other Ideas

  • Make designs for a dinner set for a picnic in the garden. Students could design a pattern for the pieces in the dinner set. The Willow Pattern story and plates could be used as motivation for this. Patterns around the edges of the plates would need to be repeating patterns.
  • Paint patterns around the rim of pots. Plants could be planted in these pots.
  • Make a patchwork picnic cloth with designs in each patch piece. This could be made out of paper or fabric. The patch pieces could show a tessellation or reflective symmetry.
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Level Two