# Autograph Newsletter 11 – Constructions

 Welcome Welcome to the eleventh Autograph Newsletter! Each jam-packed edition looks at a specific topic in mathematics and how Autograph can help engage students and enable them to understand the key concepts better.
 Introduction Many students find constructions a difficult topic to grasp. Perhaps it is the addition of extra equipment (compasses, rulers, angle measurers), or the unstructured nature of some of the questions. Alternatively it could be the case that, like me, some students just find such visual topics tricky to master. Dynamic geometry software should never replace paper and pencil. Until exams are set on computers, there will always be a need for students to be able to do things by hand. Perhaps more importantly, as this is how the great mathematical discoveries were made, students should be given the opportunity to see their beauty. But dynamic geometry certainly does have a role to play. It allows us to look deeper at each construction; to instantly change variables, look at why something works, and take one step closer along the road to generalisation.
 Diagnostic Question Diagnostic questions are ideal to use at the start of the lesson to enable you to get a quick and accurate picture of your students’ levels of understanding. They are designed in such a way that common misconceptions that your students may hold should steer them to one of the incorrect answers, thus allowing you to learn where the problems lie from their responses. Typically I give my class 30 seconds thinking time and then ask them to hold up their fingers: 1 for A, 2 for B, etc.
 Free Online Autograph Activity Angle Bisector Have a look at this construction to create an angle bisector. Can you explain why it works? These Autograph activities do not require the full version of Autograph to run them. You just need to install the free Autograph Player (you will be guided through how to do this), which means you can use these activities in the classroom or set them for your students to do at home.
Ideas for Extension
The following ideas for extending this topic require the full version of Autograph.
Idea 1 – Perpendicular Bisector
The Autograph page shows a possible construction for the Perpendicular Bisector
 • Drag the nose of the vector to change the size of the circle arcs • Drag the circled points to change the angle of the line • Can you construct this on paper using compasses, ruler and pencil? • Can you make this construction from scratch on Autograph? • Can you explain why this construction works? • When does this construction not work? • Can you think of any other way to construct a perpendicular bisector?
The Autograph page shows six quadrilaterals cunningly disguised to look like squares
 • Experiment by dragging the corners of the shapes around to see how they change • Can you identify which quadrilateral each shape actually is? • What are the properties of each quadrilateral? • Can you construct these quadrilaterals on paper using compasses, ruler and pencil? • Can you make these constructions from scratch on Autograph? • Can you explain why these construction work? • Which are the most difficult to construct? • Can you do the same with different types of triangles? • Note: If you want to see the secrets behind how each of these shapes were constructed, go to Object > Unhide All.
Idea 3 – Alternative Angle Bisector