Reasoning With Interior Angles

Reasoning With Interior AnglesDownload In the previous post in this series I looked at different derivations for the sum of interior angles. This post focuses on using that information in different ways once a level of fluency has been attained. This generates a lot of discussion with pupils about symmetry, as some pupils spot that …

Interior Angle Sum Derivations

Interior Angle Sum DerivationsDownload There are pros and cons to every derivation we use for a formula - not every sequence of deduction will click at each stage with every kids. For interior angle sums, the derivation often shown in textbooks relies on drawing triangles from a single vertex. While this makes perfect sense to …

Concave Polygons

Concave Polygon ResourcesDownload When should we introduce directed angles? Bearings seems like an obvious place, but bearings is a hit and miss bit of content, and seems to be disconnected from the geometry pantheon in a lot of curriculum mappings I've worked with in the past. It's a component of A Level that pupils find …

Exterior Angles of Convex Polygons

Exterior Angles of Convex PolygonsDownload The next step in my sequencing of angle content is exterior angles. I really struggle with sequencing of content in angles because I find my opinion changes quickly and often. The biggest issue I have is where to put parallel line angles. If they come before angles in polygons you …

Filtering With Basic Angle Facts

Filtering With Basic Angle Facts ResourcesDownload In my previous post I discussed labelling angles and focusing on angles as a turn. In this post, all of the tasks are designed to encourage filtering. By filtering, I mean seeing and noticing the specific aspects of a geometrical figure one at a time. This is really difficult …

Understanding Angle Labels

Angle Labels (Animations, Tasks and Answers)Download Using Formal Notation (Slides and Notes)Download Using Formal Notation (Task and Answers)Download Labelling angles is difficult. Even asking kids what angles actually measure is difficult. Seeing a turn instead of a line or distance takes practice, and pupils need to be nudged to reckon with these differences. In the …

Perimeter Part 2: Overlearning

Perimeter Overlearning ResourcesDownload In part 1 I discussed "seeing" perimeters. The tasks in this post are designed to hone in on notation, without getting into properties of shapes. Dashes denoting equal lengths is isolated to begin with, and exaggerated to really hammer home how much information is implicit in mathematical diagrams. In the following questions, …

Perimeter Part 1: Seeing

Nibble PerimetersDownload Nibble Perimeters AnswersDownload Separating perimeter from area has a whole host of benefits in allaying misconceptions around dimensional differences between lengths and areas, but this often means that reasoning and teaching to greater depth with perimeter exclusively can be more challenging. This post, and the subsequent post, address two approaches I've taken. Firstly, …

Reasoning With Frequency Trees

Reasoning With Frequency TreesDownload I used to think frequency trees were naffmaths. No real mathematical stuff in there. A place mathematical reasoning goes to die. Internally, I'd be convinced I needed to grit my teeth and get through it before returning to something proper. No more! The resources linked at the top of this post …

What Bar Models Actually Are

Counters Into Bar ModelsDownload Reasoning With Lengths ResourceDownload Moving from concrete representations through pictorial representations and then to abstraction are not three distinct stages, but rather categories along a continuum. While bar models are useful representations for many things, pupils were struggling with the layers of abstraction between physical counters, counter diagrams and bar models. …