Dimensions — AAMT

Opening the Top Drawer to Geometric Reasoning Module 3

Geometric proof

Duration: 75 minutes

Year levels: 10, 10, 10, 10, 10, 10, 7, 7, 7, 7, 7, 7

Category: Angles, Angles, Angles, Angles, Angles, Angles, Geometry, Geometry, Geometry, Geometry, Geometry, Geometry, Lines, Lines, Lines, Lines, Lines, Lines, Shapes, Shapes, Shapes, Shapes, Shapes, Shapes

Proficiency standards: Problem Solving, Problem Solving, Problem Solving, Problem Solving, Problem Solving, Problem Solving, Reasoning, Reasoning, Reasoning, Reasoning, Reasoning, Reasoning, Understanding, Understanding, Understanding, Understanding, Understanding, Understanding

AITSL standards: 1.2 Understand how students learn, 1.2 Understand how students learn, 1.2 Understand how students learn, 1.2 Understand how students learn, 1.2 Understand how students learn, 1.2 Understand how students learn, 2.1 Content and teaching strategies of the teaching area, 2.1 Content and teaching strategies of the teaching area, 2.1 Content and teaching strategies of the teaching area, 2.1 Content and teaching strategies of the teaching area, 2.1 Content and teaching strategies of the teaching area, 2.1 Content and teaching strategies of the teaching area, 2.2 Content selection and organisation, 2.2 Content selection and organisation, 2.2 Content selection and organisation, 2.2 Content selection and organisation, 2.2 Content selection and organisation, 2.2 Content selection and organisation, 3.4 Select and use resources, 3.4 Select and use resources, 3.4 Select and use resources, 3.4 Select and use resources, 3.4 Select and use resources, 3.4 Select and use resources, 6.1 Identify and plan professional learning needs, 6.1 Identify and plan professional learning needs, 6.1 Identify and plan professional learning needs, 6.1 Identify and plan professional learning needs, 6.1 Identify and plan professional learning needs, 6.1 Identify and plan professional learning needs, 6.2 Engage in professional learning and improve practice, 6.2 Engage in professional learning and improve practice, 6.2 Engage in professional learning and improve practice, 6.2 Engage in professional learning and improve practice, 6.2 Engage in professional learning and improve practice, 6.2 Engage in professional learning and improve practice

Use: Groups of Teachers, Groups of Teachers, Groups of Teachers, Groups of Teachers, Groups of Teachers, Groups of Teachers

Teaching practices: Engagement, Engagement, Engagement, Engagement, Engagement, Engagement, Group Work, Group Work, Group Work, Group Work, Group Work, Group Work, Student Learning, Student Learning, Student Learning, Student Learning, Student Learning, Student Learning, Technology, Technology, Technology, Technology, Technology, Technology

Understand the difference between experimental verification of geometrical statements and geometric proof and confidently scaffold the process of writing geometric proofs.

This module addresses the major big idea of geometric reasoning, that is geometric proof. It contains a number of activities, including; exploring the proof of angle sum of a triangle in several ways, progressing to proof of congruence and similarity. There is an emphasis on correctly and clearly identifying and naming angles and lengths, reinforcing the formality required for a deductive proof. Participants might further explore with Geogebra. Teachers will be able to reinforce their understanding of the often complex nature of writing formal geometric proofs.

This module is one of four modules on Geometric Reasoning; the others are: plane shapes, congruence and similarity, and circle geometry.

Reasoning about geometric proof is based on some of the material found in AAMT’s Top Drawer Teachers.

Videos

Video: Geometric proof: Demonstration of the angle sum of a triangle

The video provides evidence to conjecture that the angle sum of a triangle is 180°.

Downloads

Related modules