Organise content into an effective learning and teaching sequence.

Standard 2.2

The teacher helps students build rich coneptual knowledge and mastery of complex skills.

South Australian Teaching for Effective Learning Framework Guide

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Content area: Measurement and Geometry

The learner will:

• Recognise, understand, and use basic geometric properties and standard units of metric and customary measurement.
• Draw and classify polygons and polyhedrons (solid figures) using appropriate vocabularly: faces, angles, edges, and vertices. Describe rules for grouping.
• Identify and model symmetry and congruence with concrete materials and drawing.
• Recognise three-dimensional objects from different perspectives.
• Observe and describe geometry in the environment.

Unit Concepts and Generalisations

Structure

• There is structure in everything around us
• Structure helps us define and categorise objects in our world
• Structure is often based on patterns of parts that create a whole
• The structure of some objects can be explained in geometrical terms

Unit Objectives

As a result of this unit, the students will know:

• The attributes of points, lines, line segments, planes, rays, parallel lines, and perpendicular lines.
• Types of angles (right angle, acute angle, obtuse angle).
• The unique characteristics of circles and their related parts (radius, diameter, circumference, chord).
• What makes shapes and objects congruent and symmetrical.
• The distinguishing characteristics of the following polyhedrons: cone, cube, pyramid, rectangular prism, cylinder, and triangular prism.
• Different rules for grouping polygons and polyhedrons using the following terms: faces, angles, edges, and vertices.

As a result of this unit, the students will understand that:

• The shortest distance between two points is a straight line.
• Geometry and symmetry are found in nature.
• There is a structure to everything around us.
• Using geometric terms is one way to describe the structure of our environment.
• Geormetry is a very important part of the building industry and of architecture, art, science, astronomy, clothing design, farming, and many other professions.
• There is often a relationship between the shape of an object and its use.

As a result of this unit, the students will be able to:

• Describe, draw, compare, and classify geometric objects
• Communicate effectively using geometric terms
• Gather, analyse, and apply geometric information in problem solving
• Work cooperatively in pairs and small groups
• Establish a project plan, including time line, and follow it

Instructional strategies used include:

• Brainstorming
• Flexible grouping
• Independent projects with process logs and a scoring rubric
• RAFT activities
• Think-Pair-Share
• Differentiated writing prompts
• Gardner’s multiple intelligences
• Pre-assessment
• Small group collaborative activities
• Tiered assignments

Lesson 1: Introduction (1 class)

• Discussion in List-Group-Label format (20 minutes)
• Writing activity as pre-assessment (15-20 minutes)

Lesson 2: Points, lines, line segments, and rays (1 class)

• Discussion of definitions and examples (10-15 mintes)
• Small group problem solving (30 minutes)
• Whole group sharing for lesson closure (10 minutes)

Lesson 3: Angles (2-3 classes)

• Discussion of the types of angles and demonstration of angle measurement (15 minutes)
• Practice identifying and measuring angles in small, mixed-readiness groups (20 minutes)
• Discussion for lesson closure (5-10 minutes)

Lesson 4: Circles (1-2 classes)

• Reading assignment on circles and discussion (15-20 minutes)
• Partner discussions of circles (10 minutes)
• Discussion for lesson closure (5-10 minutes)

Lesson 5: Polygons (1 class)

• Discussion of the prefixes, names, and attributes of polygons (15 minutes)
• Geoboard activity (40 minutes)
• Discussion for lesson closure (5-10 minutes)

Lesson 6: Tangrams (2-3 classes)

• Presentation of basic tangram shapes (5 minutes)
• Reading and discussion of Grandfather Tang’s Story (20-30 minutes)
• Tiered tangram activities based on readiness (60 minutes)
• Product sharing and discussion for lesson closure (10-15 minutes)

Lesson 7: Symmetry and Congruence (1-2 classes)

• Discussion of an practice with finding lines of symmetry in classroom objects and in the alphabet (30 minutes)
• Small group practice with polygon symmetry (20 minutes)
• Introduction of congruent shapes using Geoboards (30 minutes)
• Exit card activity for lesson closure (5 minutes)

Lesson 8: Observing and Describing Geometry in Flags (1-2 classes)

• Round robin review in mixed-readiness groups (20 minutes)
• Discussion of shapes in state and country flags (15 minutes)
• Tiered task card activities based on readiness (40 minutes)
• Small and large group discussions for lesson closure (10-15 minutes)

Lesson 9: Polyhedrons (1-2 classes)

• Discussion of the attributes of polyhedrons (15 minutes)
• Think-Pair-Share: Is a sphere a polyhedron? (10 minutes)
• Small group activity with the vocabulary of polyhedrons (15 minutes)
• Self-selected application tasks based on Gardner’s multiple intelligences (40 minutes)
• Product sharing with partners (10 minutes)
• 3-2-1 exit card activity for lesson closure (5 minutes)

Lesson 10: Review and application (2-3 classes)

• Polyhedron review (10 minutes)
• Geometry scavenger hunt in mixed-readiness groups (40 minutes)
• Self-selected RAFT activities based on interest and learning style (45-60 minutes)

Lesson 11: Unit assessment (1-2 classes)

• Self-selected final products based on student interest and learning style