The Transformations of Spring

Purpose

The purpose of this unit of five sessions is to have students investigate transformation elements of geometry in spring flowers and use these elements to create their own artworks.

Specific Learning Outcomes
  • Develop and use attribute language.
  • Sort flowers by their appearance, explaining and justifying their grouping.
  • Explain reflection using their own language.
  • Recognise and show understanding of symmetry.
  • Apply understandings of reflection/symmetry to a practical task.
  • Recognise that a shape can turn around a point.
  • Apply understanding of rotation to a practical task.
  • Recognise that a shape can be translated.
  • Apply understanding of translation to a practical task.
  • Make an artwork in which elements of transformation are evident.
Description of Mathematics

This series of lessons begins with students sorting a selection of spring flowers by their characteristics. As they sort, the students explain and justify their grouping and in doing so, use and develop important the attribute language: they may talk about the flowers’ colour, size, shape, texture, whether or not they have a fragrance, their weight, the number of flowers on one stem and so on. Sometimes they will offer their own unique rationale for their grouping. Students should be encouraged to develop increasingly sophisticated classifications.

In working closely with a range of flowers the students will notice that they are comprised of interesting shapes that, in many flowers, are arranged in patterns. These flower patterns often involve reflections and rotations in particular, but students may also suggest that leaves, for example, ‘shift along a line’ (the stem). These are translations. To understand reflection, students benefit from working with mirrors and talking about the reflected image. It is important that students understand that the reflection is not a translated copy, but a ‘flipped reverse’ image. To develop this understanding, it is helpful to talk about the way the image is ‘flipped’, and to describe the image from the line of symmetry outwards.

Students need to understand that a rotation is when an object turns around a point. In the case of some flowers, the turns made by petals are part turns, sometimes half and quarter turns, which, when repeated, complete one full turn or rotation. Students should have many opportunities to model these actions.

As students work with translation, the focus is on the absence of turns and flips. Rather the only movement is a ‘slide’ along a plane.

These transformations are three distinct actions, most often referred to as ‘flip, turn, slide.’

Crosscurricular links (The Arts)

As students work with the flowers, an appreciation of their aesthetic qualities is developed. Flowers have inspired artworks and have been appreciated for their beauty throughout history. As students view the results of their own and each other’s practical creative tasks, it is important that they are given opportunities to express the feelings and responses.

Associated Achievement Objectives

Visual Arts, level 1

  • Explore a variety of materials and tools and discover elements and selected principles.
  • Investigate visual ideas in response to a variety of motivations, observation and imagination.
  • Share the ideas, feelings and stories communicated by their own and others’ objects and images.
Required Resource Materials
  • A selection of spring flowers
  • Pictures of spring flowers
  • Paper
  • Pencils and erasers
  • Coloured felts/crayons/pastels
  • Saucers/dishes
  • Sand
  • Cardboard
  • Scissors
  • A large selection of small flowers and leaves
  • A set of rectangular hand mirrors
  • One mirror (approx. A4 size)
Activity

Learning activities
Whilst this unit is presented as sequence of five sessions, more sessions than this may be required. It is also expected that any session may extend beyond one teaching period.

Session 1

This session is about students becoming aware of the attributes of flowers, using the language of attributes, sorting flowers and justifying their groupings.

SLOs:

  • Develop and use attribute language (to describe spring flowers).
  • Sort flowers by their appearance.
  • Explain and justify their grouping.

Activity 1

Begin the session by writing Spring on the class chart.
Have students talk to a buddy to tell them what they know about Spring. Share and record their ideas on the chart, including the fact that many beautiful flowers appear in Spring.

Activity 2

Explain that the class is going for a spring walk about the school/neighbourhood and that it is the job of everyone in the class to ‘spot spring flowers’ and to return to class with ‘wonderful words’ to describe the spring flowers that they notice.
Complete the walk. Brainstorm and record the spring flower words. Read these together.

Activity 3

Make available a selection of spring flowers.

  1. Have students work in pairs. Explain that together they are to sort their pile of flowers into groups of different kinds, and that they must be ready to tell another group about what they have done.
     
  2. Have students complete the sorting and pair share task several times. As the students complete the task, photograph the groupings for use in session 2.
     
  3. As a class, share some of the grouping results and discuss.

Activity 4

  1. Conclude the session by displaying the pictures in Attachment 1,
    Explain that:
    Vincent Van Gogh was an artist who usually wrote his name, Vincent, on his artworks.
    He was born in the Netherlands and lived for some of his life in France.
    In ten years Van Gogh made about 900 paintings.
    He only sold one painting during his lifetime.
    He only became famous after he died, which was over 120 years ago.
    One thing he loved to paint was sunflowers.


    The first picture in Attachment 1 is one of many pictures that he painted of sunflowers. Notice his signature.
    The second is a painting that someone has made, like Van Gogh’s art.
    (Sunflowers are not spring flowers because they grow from seed through the spring and summer and reach maturity in late summer.)
    Ask the students what they notice about the flowers in artwork and add appropriate attribute language to the list already begun on the class chart.
     
  2. Explain to the students that in another session, they will be making some flower art works too.

Session 2

This session is about students understanding the symmetry of reflection, explaining this using their own words, and using this knowledge.

SLOs:

  • Explain reflection using their own language.
  • Recognise and show understanding of symmetry.

Activity 1

Begin by distributing photos from Session 1 mounted on paper.
Make available the attribute word list from Session 1 and pencils.
Have individual students name their work and write an explanation for their grouping of the flowers.

Activity 2

Make available individual copies of the photographs of flowers (Attachment 2).

  1. Have each student select 2 or three photos of their choice and ask them what is the same about the flowers they have selected.
    Accept all appropriate answers. Guide the discussion to the shape of the flowers and to the fact that if they look at their flower from each side of the photo, flower looks much the same.
     
  2. Make available a set of small rectangular hand mirrors.
    Have each student carefully fold in half one of their photos then locate the mirror along the fold. Have them talk about what they see. Have students notice and describe the parts of the flower closest to the fold (line of symmetry), and identify the parts that are farthest away.
     
  3. Record their ideas on the class chart. For example: ‘I can see the whole flower again’, ‘It just looks like the flower in the picture’, ‘It’s like the opposite from the middle out-ways.’
    Introduce and write the words ‘reflection’, and ‘symmetrical’. Introduce the word flip and demonstrate folding, then ‘flipping’ open.
     
  4. Have the students apply the mirror to another of their photos and describe to a buddy/to the group what they see, using the words ‘reflection’, and ‘symmetrical’.
    Again, have students notice and describe the parts of the flower closest to the mirror line of symmetry, and identify the parts that are farthest away.
    Write line of symmetry, discuss and demonstrate.

Activity 3

Make available to each student, Attachment 3.

  1. Demonstrate how to complete one of the flowers. Show how to begin at the line of symmetry and to work out, thinking about which parts are close to the ‘centre’ and which are far away.
     
  2. Have each student ‘complete’ each flower using the mirror first, then by drawing the ‘reflection’ and colouring it appropriately.
     
  3. Have the students check their own drawings by, once again, applying the mirror (to the line of symmetry).

Activity 4

Display the copy sunflower picture. Show the bigger (A4 size) mirror.
Ask individual students to demonstrate how they would check if this picture is symmetrical.
Have students place the mirror in both vertical and horizontal positions, demonstrating that only the vertical placement produces a complete picture that is like, but not exactly the same as, the whole original picture.
Draw a pencil line of symmetry vertically down the centre of the picture. Discuss that the sides are not exactly the same and, if something is truly symmetrical, it would be an exact flip. Check to see if just the vase is symmetrical.

Activity 5

Explain that in the next session they are going to make a symmetrical and unusual work of art.

Session 3

This session is about students applying their understanding of symmetry as they create a sand-saucer flower design.

SLO:

  • Apply understandings of reflection/symmetry to a practical task.

Activity 1

  1. Display the class chart and the words, ‘symmetry’ and ‘line of symmetry’.
    Review some examples of student work from Session 2, Activity 3.
     
  2. Display several of the flower pictures from Attachment 2 and have individual students show how to draw a line of symmetry down the middle of the picture and describe the reflection using language developed in Session 2.

Activity 2

Make available, saucers, damp sand, a selection of small flowers and leaves, small pieces of card, rectangular hand mirrors.
Explain that each person in the class is going to make an artwork for display. Suggest that other classes of students and parents may be invited to the Room x Art Gallery when the artworks are complete.

Activity 3

  1. Demonstrate how to fill a saucer with damp sand, pat it down firm and flat, take a piece of card and score a line of symmetry down the centre of the sand, and carefully arrange chosen flowers in an ‘artistic’ way on one side only of the line.

    Emphasise the importance of covering all the sand in this half (not having any sand showing).
  2. Give students ample time to complete Step 1. Now demonstrate how to complete the sand-saucer making the other half a reflection of the half just completed. Emphasise once again how to begin at the line of symmetry and to work out from this line.
     
  3. As each student completes their ‘artworks’ have them check their symmetry with the hand mirror. iv. Have them write their name on the small piece of card and display their named work.

Activity 4

  1. When all floral artworks are completed and displayed, complete a silent art-walk, asking students to notice the artworks in which there is ‘ a good reflection.’ Discuss.
     
  2. Have student talk about the process of creating the sandsaucers. Have them evaluate their own work by telling and showing a buddy what in particular they did well/could improve in their artwork.
     
  3. Have students photograph their work.

Session 4

This session is about understanding that rotation is turning around a point.

SLOs:

  • Recognise that a shape can turn around a point.
  • Apply understanding of rotation to a practical task.

Activity 1

Review the process for making the symmetrical reflecting artworks.

Activity 2

  1. Display the class chart and with a felt pen draw a large dot in its centre. Show the picture of the frangipani flower.

    Make available to class members, a felt pen and a cardboard template of the shape of one of the petals.
    Ask: ‘Can someone show the class how to use the felt pen and this cardboard cut out petal to make a frangipani flower on the class chart?’

    After demonstrations and discussion, agree that it is possible to place one end of the template at the large dot, draw around the template, then turn the template to another place, keeping the end on the black dot.
          
     
  2. Write ‘turn’ on the class chart and make a list of ‘things that turn.
    Ask the students if they know another word for turn. Introduce and record the words ‘rotate’ and ‘rotation’.
     
  3. Ask how many turns have to be made to make to complete a whole flower. Explain that the turns that are being made are parts of turns.
    Model one complete turn, a half turn and a quarter turn.
    Draw the analogy with an analogue clock: a quarter past, half past and o’clock.
    Have students take turns with the cardboard petal template, to model a quarter turn and a half turn.
    Draw a flower using 4 quarter turns and count the 4 petals.
    Draw a flower with half turns and notice that it has just 2 petals.

Activity 3

  1. Explain that each student will make a artwork using ‘turning’ to help them.
    Make available, pencils, erasers, paper, cardboard templates of petals of different shapes, crayons or pastels, spare pieces of cardboard.
    Have each student make their own flower, or several flowers, using the process that has been modeled with a petal shape of their choice. Have them colour their completed flower/s.
     
  2. Have students draw and cut out a template of their own and repeat the process with their own ‘unique’ petal shape, including making one flower using quarter turns (four petals).

Activity 4

Conclude the session by having individual student explain aloud how they made their flowers. Record key words, including ‘half, quarter, turn, dot/point, middle, petal, flower’.
Have each student write a short explanation of how they made their picture, using words from the list. Attach these to the flower pictures for display.

Session 5

This session is about developing the understanding that when a shape is translated, it slides, without turning or flipping, in one direction along a plane.

SLOs:

  • Recognise that a shape can be translated.
  • Apply understanding of translation to a practical task.
  • Make an artwork in which elements of transformation are evident.

Activity 1

Display Van Gogh’s Sunflowers once again. Begin by having students review and explain reflection and rotation in their own words with reference to their own work and to the picture. (Notice that the vase is symmetrical, and that the sunflower petals rotate around a very large point)

Activity 2

  1. Show the students a daisy chain length and talk about the fact that the daisies are in a line (and linked by their stems).
     
  2. Explain to the students that they will make another artwork today, a bit like the daisy chain. They will not be ‘reflecting’ and they will not be ‘turning’ (rotating).
    Ask for suggestions of other kinds of movements. Look at the line of daisies.
    With discussion, agree and emphasise that another action or transformation could be to slide along a line (translation).

Activity 3

  1. Make available sheets of coloured paper, lengths of white paper, pencils, scissors, glue, crayons/pastels.
    Demonstrate the following:
    • Fold the paper into four (in half twice).
    • Keep the paper folded and draw a simple flower (daisy) shape on the visible quarter.
    • Cut around the flower shape, cutting through 4 layers of paper (ensuring that 4 identical flower shapes are cut out).
    • Keep the flowers in the pile.
    • Place the pile of 4 at one end of a length of white paper.
    • Slide each paper daisy, one at a time off the pile and along the paper strip till there are four daisies in a row.
    • Emphasise that the daisies are not turned at all. The only thing they do is slide.
    • Glue each flower carefully into place.
    • Connect each flower with a green line (daisy stems)
    Emphasise that there are no flips (reflection), no turns (rotation) only sliding (which is called translation).
     
  2. Have students complete the task, with support as appropriate.

     
  3. Students can repeat the process to add extra details to their flowers or to extend their daisy chain.
         
     
  4. Display the artworks and together, write a class explanation about the ‘daisy chain process’ using sliding, with no turning or flipping.
     
  5. As a class, reflect on the mathematical ‘flip, turn, slide’ actions used to make each of the class artworks.
    Take an ‘art-walk’ and have students notice where these actions have been accomplished well.
     
  6. Highlight the fact that, just as Van Gogh really liked to make art about flowers, and about sunflowers in particular, the class has enjoyed making art with spring flowers.
    Consider also, displaying a vase of spring flowers and having students create their own painting/pastel artwork called Spring-flowers.

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