# Patterns in Nature, Maths and Art

F-10 | Mathematics, Art.

This Numeracy unit on Geometric Reasoning and Space (angles, location, shape and symmetry) was created with the aim of meaningfully linking the content descriptors of Art, HASS Celebrations, Dance and Mathematics through the theme: ‘Patterns in Nature, Maths and Art’.

### 1. Overview

Description
This unit will investigate

Teaching Method: Inquiry-Based Maths.

Teaching Model: 5Es, HITTS, Launch, Explore, Discuss.

Teaching Strategy: Representations.

Skills: Metacognitive thinking.

F-10 | Year 2/3

Mathematics:

• Explore and describe patterns resulting from performing multiplication (ACNA081).
• Compare and describe 2D shapes that result from combining and splitting common shapes, create 2D shapes from written or verbal instructions (ACMMG088).
• Make models of 3D objects and describe key features.
• Describe number patterns resulting from multiplication (ACMMG063).
• Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091).
• Identify symmetry in the environment (ACMMG066).

Art:

• Use materials, techniques, and processes to explore visual connections when making artworks (ACAVAM111).

HASS (Celebrations):

• Celebrations and commemorations in places around the world (ACHASSK065).

### 3. Teaching and Learning Sequence

##### 1. Geometry

Teaching Strategy: Engage, Questioning, Feedback.

Learning Concepts:

• What do you know?

Teaching Input:

• Teacher identifies students prior knowledge on the subject, including misconceptions.

Student Activity:

• Place name on SOLO chart.
• Students write all that they know about shapes.

Student Examples:

##### 2. Fibonacci sequence

Teaching Strategy: Engage, explore, multiple exposures.

Learning Concepts:

• Understand connection between the number sequence and spiral shape

Teaching Input:

• Teacher guides short discussion on number sequences and art.

Resources:

Student Activity:

• Students create their own Fibonacci Sequence artwork.

Student examples:

##### 3. 2D shapes

Teaching Strategy: Explore, Explain, Multiple exposures, Collaborative learning.

Learning Concepts:

• Identify 2D shapes from verbal instructions (fluency).

Teaching Input:

• Teacher leads discussions and shape bingo.
• Teacher assists students at their tables to construct the 2D shapes table, working closer with students who need extra assistance.

Student Activity:

• Students create and use a 2D shape chatterbox
• Students play 2D shape bingo
• Students create table of 2D shape properties.

Resources:

##### 4. 3D shapes

Teaching Strategies: Explore, Elaborate, metacognitive strategies.

Learning Concepts:

• Identify features of 3D shapes (edges, faces, vertices). Name shape using 2D base shape (fluency, reasoning, problem-solving).

Teaching Input:

• Teacher directed discussion at end of activity.

Resources:

Student Activity:

• Table of 3D properties, discussion of number patterns.

Student Examples:

##### 5. Perspective drawing

Learning Concepts:

• Create realistic and proportionate 3D world (shape and perspective).

Teaching Input:

• Teacher demonstration of how to draw 3D perspective art.

Student Activity:

• Student draws a creative 3D art piece.

Student Examples:

##### 6. Symmetry

Teaching strategy: Engage, Questioning, Collaborative learning.

Learning Concepts:

• Draws symmetrical objects and simple transformations from verbal instructions (fluency).
• Understand that there is more than one type of symmetry, identify number of symmetries.

Teaching Input:

• Give feedback to students as they work collaboratively.

Student Activity:

• Use manipulatives to identify rotational and reflective symmetry.

Student Work:

##### 8. Rangoli artwork

Teaching Strategies: Elaborate, Worked examples, Structuring lessons.

Learning Concepts:

• Apply knowledge of symmetry to creating Rangoli Patterns (problem solving).

Teaching Input:

• Give feedback on drawings.

Student Activity:

• Create Rangoli Pattern artwork piece.

Student Examples:

##### 9. Math games

Teaching Strategies: Evaluate, Metacognitive strategies, Multiple exposures.

Learning Concepts:

• Recall mathematical names/concepts in new context. Ext.: define quadrilaterals using relational properties

Teaching Input:

• Participate in games!

Student Activity:

• LEGO, Rangoli pattern challenge, Swamp hunt, measuring angles, ext.: properties of quadrilaterals.

Student Examples:

### 4. Why this activity?

van Hiele argued that children need to be exposed to five scaffolded levels of geometric understanding through deliberate instruction appropriate for their development. Students move from a visual-based system (they are the same shape because they look the same) to a property-based system (a square is a four-sided shape) through to a relational system (if shape has property X it also has property Y).

The integration of maths and art allows students to see connections between shape and form and move into the higher van Hiele levels. This is especially evident in the link between the ‘Fibbonici Number Sequence’ and the relational properties of 2D and 3D shapes.