Category: investigation

Problem(s) with Triangles

My provincial curriculum scatters trigonometry throughout several high school courses. Right-angled trig appears first as an isolated experience at the Grade 10 level. From there, the two pathways in Grade 11 cover the Sine and Cosine laws, but only one stream (Pre-calculus) continues into the idea of the unit circle and eventually the connections between the …

Experiencing Scale in Higher Dimensions

A colleague and I have often bemoaned our attempts to teach the concept of scale factor in higher dimensions. A topic that has such beautiful and elegant patterns and symmetries between the scale factors consistently seems to sail directly past the experience of our students. I have tried enacting several tasks with the students including …

Problem Posing with Pills

My class always welcomes conjectures. This is made explicit on the very first day of the semester. This goes for everything from grade nine to grade twelve. As the grades advance, the topics have us venturing into increasingly abstract concepts, but conjectures are always honoured.  Certain class structures promote conjecturing more than others. Students offer …

Algorithms and Flexibility

I was given a section of enriched grade nine students this semester. I decided very early on that the proper way to enrich a group of gifted students is not through speed and fractions. They came to me almost done the entire course in half the allotted time. This essentially alleviated all issues of time pressure. …

The Discourse Effect

This semester, I’ve been attempting to infuse my courses with more opportunities for students to collaborate while solving problems. This post is designed to examine the shift in student disposition throughout the process. I have noticed an increased conceptual understanding almost across the board and this is reflected in the differing solutions on summative assessments. …

Sorting Set(s)

Set Theory, Counting Methods, and Probability are probably my three favourite topics to teach. For the first time under our new curricular framework, I got to teach these topics to a group of seniors. I decided to build up large themes and understandings through introductory tasks; my goal was to create an “unflippable” entry point …

Pythagorean Triples Part 1: Student Strategies

The school year is winding down for me and my project-based grade ten classes. I have found myself looking at the curriculum more and more as the final day approaches. I was told by many that content coverage would be impossible in a project-based setting; this only made me more anxious. Compounding this problem, I …

Using Real-Time Graphs

I have a class of grade nine students this semester that are part of a stretch program. This essentially means that they get 160 hours to complete a 120 hour course. The class is designed to accommodate the transition from elementary school (Grades 1-8) into high school (Grades 9-12) for those students who feel uncomfortable with …

Soft Drink Project Part 3: The Design

This post is the third in a series of posts detailing the happenings of a math project. To better understand the whole story, please start reading at the beginning: Soft Drink Project Part 1: The Framework The next few classes after the brainstorming class were a blur. Students would come into class, grab their previous …