# Perspective on Picasso

Purpose

In this unit students develop a further understanding of two-dimensional representations of three-dimensional shapes through creating drawings and artworks that explore shapes from different viewpoints.

Achievement Objectives
GM3-3: Classify plane shapes and prisms by their spatial features.
GM3-4: Represent objects with drawings and models.
Specific Learning Outcomes
• List the features of common three-dimensional shapes.
• Recognise that the faces of 3D shapes are 2D plane shapes.
• Explore and understand the defining features of a prism.
• Draw (freehand) common 3D shapes from different viewpoints.
• Represent different viewpoints of the constructions with drawings on isometric paper.
• Create cube constructions from viewpoint drawings made by another student.
• Become familiar with and describe the features of a Picasso portrait and of cubism.
• Create a portrait in the Picasso style.
• Appreciate and write about their own artwork and that of one other student, recognising the influence of shape and viewpoint (or perspective).
Description of Mathematics

In level two, students have been learning what is meant by ‘dimension, and coming to understand that three-dimensional shapes, called polyhedra, are bounded by flat (planar) shapes that have two dimensions. The language associated with the features of 2D and 3D shapes is becoming familiar, such as side, vertex (corner), edge, face.

At level three, students are developing more depth in their understanding of the properties of 2D and 3D shapes, including prisms. Prisms are three dimensional solids with a constant cross-section, and are named after that cross-section. For example, a triangular prism can be cut into parallel cross-sections that are triangles. Other classes of solids, such as pyramids or curved surfaces, have variable cross sections.

As they consolidate their understanding of polyhedra, students recognise that the faces are polygons (bounded planar shapes), and that the properties of those faces contribute to the properties of the polyhedron. Although dynamic computer software enables more helpful representations of three dimensional shapes, the images are still flat, that is in two dimensions. Such flat representations depict limited information about the three dimensional shape they represent. Through representing three dimensional shapes from different perspectives, student learn to focus on different attributes of the shapes and recognise that representations of the same shape can look very different.

In this unit of work, these understandings combine to inform the student’s appreciation at a simple level, of some of the features of Picasso’s portraits and of his defining art style, cubism. The development of cubism marked a pronounced shift in artists' interpretation of real-world objects. Picasso, and Braque, attempted to capture the characteristics of three dimensional shapes in a single two-dimensional image.

Associated Achievement Objectives

Art
Visual Arts

• Explore some art-making conventions, applying knowledge of elements and selected principles through the use of materials and processes.
• Develop and revisit visual ideas, in response to a variety of motivations, observation, and imagination, supported by the study of artists’ works.
• Describe the ideas their own and other’s objects and images communicate.

The learning opportunities in this unit can be differentiated by providing or removing support to students, by varying the task requirements. Ways to support students include:

• providing physical materials, such as models of three dimensional solids, so students can move themselves in relation to those objects
• providing access to sculpting materials, such as plasticine, so students can create their own three dimensional models, and cut cross sections
• orientating cube models so the viewpoint matches the orientation of isometric paper
• explicitly modelling drawing from various viewpoints, including the use of digital cameras, so students appreciate the minimal requirements of plan views.

Tasks can be varied in many ways including:

• manipulating the complexity of the three dimensional objects the students represent
• scaffolding the process of representational drawing into a sequence of steps.

The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. Capitalise on the interests of your students. Cubism is one form of artistic representation. Other forms might be more appropriate to the cultural background and interests of your students. Modern art marries traditional aspects of Māori and Polynesian art with modern techniques and media. Students may want to study how modern New Zealand artists represent their subjects to convey meaning and feelings.

Required Resource Materials
• Three-dimensional solid shapes: sphere, cylinder, cone, cube, cuboid, hexagonal prism, triangular prism, square based pyramid
• Small plain cubes
• Play dough
• Plastic knives
• Paper
• Pencils
• Copymasters One, Two and Three
• Chart paper
• Art paper
• Pastels
Activity

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 familiar with the defining features of common three-dimensional shapes and representing these shapes with freehand drawings from different viewpoints.

SLOs:

• List the features of common three-dimensional shapes.
• Recognise that the faces of 3D shapes are 2D plane shapes.
• Explore and understand the defining features of a prism.
• Draw (freehand) common 3D shapes from different viewpoints.

Activity 1

1. Make available pencils and paper.
Draw a diagram of a circle.
Give student pairs 1 minute to write some of the objects that this circle could represent.
Have student pairs share their ideas with the class.

2. Display solid sphere, cylinder and cone shapes.

Ask, “Could this (circle) be a drawing of a sphere or a cone or a cylinder?” Have students discuss this and reach agreement that this could be a bird’s eye view of a sphere or a cylinder or a view of a cone looking at it from underneath, (or perhaps from the top if the point were very fine).
Write ‘viewpoint’ on the class chart, agree on a definition that a viewpoint is a perspective of an object from a specific location.  Discuss and identify other possible drawings of the three objects. Ask students to be specific about the viewpoint each picture is taken from. For example, a cone appears as a triangle from side on, and a cylinder looks like a rectangle from side on.
3. Does a sphere always look like a circle, no matter the viewpoint?
4. Note that many students want to behave like cubist artists, and convey the curvature of surfaces in their drawings. For example, they might draw a side view of a cone with a curved base. Taking and displaying digital photographs of the solids can support students to accept the loss of information in a two dimensional drawing.

Activity 2

1. Add to the solid shape display, a cube, a cuboid, a hexagonal prism, a triangular prism, and a square based pyramid.
2. Create a chart, writing on it the names of each of the shapes and the headings, faces, edges and vertices. Define the meaning of each feature of the shapes. For example, a face is a polygon that is part of the boundary of a solid.  Model and record the features of at least 2 of the shapes. Note that a sphere is a curved surface and has no faces. A cone also has a curved surface.
 Shape Faces Edges Vertices Sphere 0 0 0 Cube 6 12 8 Cylinder Cone Cuboid Triangular prism
3. If you do not have enough models of the shapes available, provide play dough and plastic knives so students can sculpt the shapes.
4. Ask students to create and complete their own chart (individually or in pairs), making models of each shape with play dough as required, to explore and confirm their features.
5. Discuss the strategies the students used to count the number of faces, edges and vertices for each solid. Their strategies typically include counting top and bottom of a solid then counting the remaining faces, edges, or vertices.
6. Discuss what a cylinder, cone and sphere have no edges or vertices. That is because edges and vertices are formed where faces, polygons, meet.
How many faces meet at an edge? (Two – this is an important generalisation)
How many corners meet at a vertex? (That number depends on the number of faces surrounding each vertex. For a cuboid the number is three)
7. What do students notice about the number of faces, edges and vertices of a cuboid? (the same)
Why does that happen? (A cube is a type of cuboid)

Activity 3

Have each student choose at least two of the shapes that they have made, and make freehand drawings of each, from at least two different viewpoints. Have students share their drawings with a partner, and talk about what they have done, using the language of faces, edges and vertices.

In the follow up discussion ask one student at a time to show just two viewpoints of the same solid.
Can you identify which solid these viewpoints represent?
Do you need more viewpoints or less to make a specific identification? Why?

Activity 4

1. Invite students to visualise straight (planar) cuts of a square based pyramid and a cuboid (rectangular prism), parallel to the base. You might use the analogy of slicing loaves of bread.
What shape will the cross sections be? (squares for the pyramid, rectangles for the prism)
Will the cross sections be exactly the same? Students should notice that cross sections of the pyramid vary in size, while the prism has constant cross section.
Alternatively students can make a pyramid and rectangular prism from play dough, plasticine, or cheap vegetables such as potatoes, pumpkin, or carrot (Make a vegetable soup for lunch afterwards). They can make cuts through each shape.

2. Discuss the results, eliciting the explanation that the faces of the cuts of the pyramid change, whilst the prism faces remain unchanged.
Does the property of constant cross section also apply to other types of prism? (Yes)

3. You might explore the idea by slicing other prisms. Agree on a definition of a prism.

Activity 5

Conclude the session by having students draw any prism from at least two viewpoints. Ask them to record their work, using the language of faces, edges and vertices, and to write their own definition of a prism.

Is a prism easy to identify by its viewpoints? Why?

#### Session 2

This session is about exploring cube constructions, representing those constructions from different viewpoints on isometric paper, and interpreting the drawings of others.

SLOs:

• Make simple constructions using interlocking cubes.
• Represent different viewpoints of the constructions with drawings on isometric paper.
• Create cube constructions from viewpoint drawings made by another student.

Activity 1

1. Begin by having students share their work from Session 1, Activity 5.
2. Explain that they will use isometric paper to to reduce the need to measure, and to make their drawings more precise.
3. Introduce the task by showing a cube, selecting a viewpoint, and modelling how to represent a single cube on isometric paper.

Notice that the cube has a leading edge, marked by the central vertical line. To faces that meet at the edges are drawn as rhombi rather than as squares. The top face is also drawn as a rhombus.
4. Make cubes and isometric paper (Copymaster 1) available to each student.
5. Walk students through the steps of drawing a single cube then try joining additional cubes back, and below, from it.
The drawing above shows a large cube. Discuss any challenges that arise.
What is the smallest cube you could draw?

Activity 2

1. Make available isometric paper and interlocking cubes, sufficient for each student to have nine. Have students join the cubes to make a shape of interest, then draw this shape from at least two viewpoints. It is important that the faces of the cubes meet exactly.
2. If students have difficulty drawing the shapes hold art class.
• First, get students to tilt their model so there is a leading edge, and the top faces are visible from their viewpoint as rhombi.
• Second, draw the leading edge vertically on the isometric paper. That edge might be several little cube edges joined.
• Third, draw the lateral faces coming back from that edge.
• Finally, complete the whole shape, including the top.

Activity 3

Ask students to display their models on a table top, and pass in their isometric drawings. Mix-up the drawings and redistribute them randomly amongst the students. Each student must then locate the model that matches the drawing that they have been given. Confirm their matches.

How do you know that this is the correct model? (Viewpoint matches)
What strategies did you use to locate the model?
Is it possible to have different isometric drawings of the same model? Why?
Is it possible to have several models that match a single drawing? Why?

This discussion helps students appreciate the loss of information about a three dimensional object when it is represented in a two dimensional drawing.

Activity 4

Have students dismantle their shapes into single cubes. Collect in the drawings once more, shuffle these and redistribute them. Have students construct the model shape from another student’s isometric drawing.

Activity 5

Conclude the session by discussing the process, having students talk about the representation of shapes from different viewpoints and highlighting the geometric language, e.g. faces, edges, vertices.

#### Session 3

This session is about exploring a selection of Picasso portraits, identifying some distinguishing stylistic characteristics.

SLOs:

• Become familiar with and describe the characterising features of a Picasso portrait.
• Understand some of the defining features of cubism.
• Write a description of the influence of geometry in a Picasso portrait.

Activity 1

1. Write Pablo Picasso on the class chart. Brainstorm and record student knowledge of the artist. Show his picture, and share the information in Copymaster 2, or set a short time limit and have the students research pertinent information about the artist online.
I wonder why his style is known as cubism?
2. Discuss how Picasso tried to depict three dimensional features of his subject on a two dimensional surface. Isometric drawing belongs in the perspective methods of realist artists before Picasso.

Activity 2

1. Make available to students in pairs, one of the pictures in Copymaster 3, paper and pencils. Have students discuss their Picasso portrait, and record all the things that they feel and notice about it.
What was Picasso trying to represent about his subject?
How did he alter what can really be seen from one viewpoint?
2. Have students pair share their feelings, and observations and agree on common features.
3. As a class, discuss their feelings about the artworks. Record these responses, (like because….., dislike because….., puzzled because…., etc.)
4. Discuss and record on the class chart the features that they notice about the artworks.
These are likely to include:
• You can see the person from a front viewpoint and a side viewpoint (profile) in the same picture
• There are geometric shapes in the pictures
• There are many light and dark contrasts (chiaroscuro is the arrangement of light and dark elements in a pictorial work of art, also known as positive and negative space)
• Black is used to outline shapes and to draw features
• The pictures are not realistic – they are not how people really look
• The pictures appear to be fragmented, or broken up into parts
• They are a combination of two-dimensional flat plane shapes and some realistic rounded and shaded three-dimensional images.

Activity 3

1. Write ‘cubism’ on the class chart and have students share their knowledge of this art form. Agree that many of the features they have identified in 2 (above) are defining features of cubism. Explain that Pablo Picasso and Georges Braque began their innovative, new art movement, cubism, in the early 20th century (the 1900s).
What did art look like before that time?
(Some students may know about impressionists such as Van Gogh and Monet who were instrumental in the movement towards conveying feelings about a subject, rather than just capturing a realistic image).
2. Make a copy of one of the pictures from Copymaster 3 available to each student. Have them write a description on the picture and the artist, synthesising the information that has been presented so far about both and including references to geometry and viewpoints.

Activity 4

1. Display both photographs of Picasso (Copymaster 2).
2. Explain that in the next session, each student will be choosing one of the photographs and creating their own portrait of Picasso based upon the photograph. The portrait will be in the cubist style.
3. Have students begin a draft design of their Picasso portrait.

Activity 5

Conclude the session by having students share their work.
Ask each student to bring to the next session a photograph of a familiar person or pet that they would like to use as the subject of an artwork.

#### Session 4

This session is about using the style of cubism to create a portrait of Picasso, and begin an artwork of a person or pet significant to the student.

SLOs:

• Create at least one portrait in the Picasso style.
• Give feedback to other students on the cubist influence evident in their artworks.

Activity 1

1. Begin the session by reviewing the features of cubism listed in Session 3, Activity 2, Step 4.
2. Display both pictures of Picasso (Copymaster 2).
3. Students  select one of the pictures of Pablo Picasso, and create a draft cubist portrait.
4. Have students share the progress on their draft portraits of Picasso.
What viewpoints did you imagine?
How did you represent how Picasso would look from each viewpoint?
What geometric shapes did you use? Why?

Activity 2

1. Make available art paper and pastels. Students choose their own subject. Picasso tended to paint people (women mainly), though animals were another common subject.
2. Let students begin their Picasso works in a pastel medium. Insist they sketch the work first in pencil. Art takes careful planning, like other forms of design. Stop at significant points to review progress, checking against the listed cubist criteria.

Activity 3

As students complete their works, have them self-check and peer evaluate the works, referring to the cubist features.

Activity 4

Conclude the session with a gallery walk for the students to appreciate and give feedback on each other’s Picasso portrait artworks.
As a class, recognise those artworks that successfully and strongly show the influence of cubism. Look, in particular for representations from different viewpoints and the use of shapes in the fragmented (or disjointed) forms. Have each student identify improvements they might make to their own artwork.

#### Session 5

This session is about using self-evaluation and peer feedback to inform a second artwork in the cubist style.

SLO:

• Appreciate and write about their own artwork and that of one other student, recognising the influence of shape and viewpoint (or perspective).

Activity 1

1. Begin this session by having students review feedback and self-evaluation, using this to inform their design of their second artwork of the person or pet that is significant to them personally.
2. Stop at significant points to review progress, checking against the listed criteria and against their identified intended improvements. As students complete their works, have them self-check and peer evaluate the works.

Activity 2

Upon completion of the second artwork, have each student write a statement about the way in which the work has been created with reference to the cubist features, and whether the final work has captured the character of the special subject (the person or the pet), and if so, how.

Activity 3

1. Conclude the session by discussing the ‘geometry’ in their art and in the art of Picasso, referring to the learning in Sessions 1 to 3.
2. Discuss how artists like Picasso might represent a triangular prism or square based pyramid as a single two dimensional drawing. Let students choose a solid model and ‘Picasso’ it.
Can you capture the ‘feel’ of the solid as well as it’s appearance?
From this cubist drawing can you tell what solid has been used?
Would you ever see a picture like this is real life?