This type of activity is known as Demonstration. Please read the guidance notes here, where you will find useful information for running these types of activities with your students.

1. Demonstration

Please Note: I use this file for the area of any quadrilateral. By default it displays trapezia, but can be manipulated to display any pair of quadrilaterals. The key (for me, anyway!) is that initially the two shapes should be exactly the same so students can appreciate the variation when it happens.

• I display the Geogebra page in silence with all information revealed
• I ask students to pause and reflect on what the page shows
• I then hide the area calculation on the second diagram and then move Points F and G both down one square
• I ask students to reflect on what has changed and predict what will happen when I reveal the size of the area
• I continue the process, always changing one thing from the original diagram, and always giving students an opportunity to pause, reflect and predict
• At the end I ask students to discuss the rule with their partners, and then we have a class discussion

2. Possible variations

• Vary the position of each point
• Vary the orientation of the shapes
• Vary the type of quadrilateral
• Create two different shapes that have the same area

Click here to open sheet full screen in Geogebra