Welcome

Welcome to BHNmath, an Ontario Secondary Mathematics resource centre for students, parents and teachers.

Students

A variety of tools to supplement classroom learning, strengthen understanding and enrich mathematical experience.

Parents

Strategies and materials for parents to use while accompanying children on their journey through mathematics.

Teachers

Resources to support teachers in their instruction of the Ontario Secondary Mathematics Curriculum.

Growing in Mathematics Book for Grade 9

The Growing in Mathematics book is a collection of all the Check Your Understanding problems from the Mathematics, Grade 9 (MTH1W) lessons. 

For more options, see Check Your Understanding Resources in the Extras section of the MTH1W home page.

An ongoing video series that explores a variety of careers and the ways in which math plays a role in them. 

Do You Have a Math Question?

Browse the archive of answered questions in the Question and Answer Centre!

Subscribe to the Mailing List!

To receive email notices about content updates and other news, please subscribe to the BHNmath mailing list!

Resources for Grades 7 and 8

Visit the Grades 7 and 8 page for a collection of relevant teaching and learning resources!

BHNmath

NEWSLETTER | ISSUE 13 | JUNE 15, 2023

Written by Adam Gesjorskyj

BACK TO THE CLASSROOM

After four years in the System Teacher/Consultant role, I’m very excited to report that I’ll be heading back to the classroom in September! It has always been my plan to return to classroom teaching and my decision to do so next year comes after careful consideration of many factors. That said, it’s been a good run! Working in this role has allowed me to make substantial progress with the BHNmath website and I’m very pleased with the way it’s coming together! Traffic on the site is at an all-time high and I’m thrilled to frequently receive feedback about the effectiveness of its content. Serving in a central role has also provided me with numerous opportunities to participate in a variety of exciting projects and events. I’ve had a blast engaging in everything from K-12 classroom visits and extra-curricular math initiatives, to authoring projects and hands-on skilled trades sessions (thanks, Carmine!). One of the most enjoyable parts of the past four years has been connecting and collaborating with teachers across the province (and beyond) and it’s really opened my eyes to some of the amazing work that’s currently happening in mathematics education. I look forward to maintaining these relationships and building many new ones in the years to come. To say that I’ve learned a lot over the past four years is an understatement. I can’t wait to put it into practice with my students! 

THE FUTURE OF BHNmath

Despite my upcoming return to the classroom, the BHNmath website will continue to operate more or less as usual. I’ll keep adding new resources as I build them. The vast majority of these materials will support courses that I’m teaching at the time (likely a mix of Grade 9 and Grade 12 courses). I’ll also continue to provide updates on new content and other news via the BHNmath mailing list and Twitter. The Question and Answer Centre‘s archived answers will remain available for all to view, but I will only be responding to new question submissions from my own students. Finally, I’ll be removing the Resource Request Form from the site, but will still welcome ideas, suggestions, questions, and feedback through email or the General Contact Form. Although the need for a few other changes may arise as I learn to navigate the workflow of maintaining the site while carrying out teaching responsibilities, I don’t predict that any other significant adjustments will be necessary.

SOME THANK YOUS

During my time in this role, I’ve been very fortunate to work alongside many incredible teachers and administrators. I’d like to extend a warm thank you to Keri Calvesbert and Chris Rait, whose cherished friendship, contagious creativity, and refreshing sense of humour have kept me sane during some of the most trying periods of my professional life! Many thanks to my dear friends Rachel Vukelich, Dan Yakymyshyn, and Rob Todd for continually lending me their ears and never hesitating to provide honest and insightful input. This trio never ceases to inspire me with their unwavering dedication and overall brilliance. My sincere gratitude to Lorrie Temple and Chandra Portelli for their guidance, support, and faith in my work. I’m blessed to work with leaders of such high caliber. Lastly, thank you to all the teachers of the BHNCDSB and other boards who have provided feedback over the past four years. Your suggestions play a huge role in shaping BHNmath and your messages of gratitude mean more to me than you know! 

Congratulations, Rachel!

I’m very pleased to announce that Holy Trinity Catholic High School teacher Rachel Vukelich was selected as the 2022/2023 recipient of the BHN OECTA Innovation in Pedagogy Award! Through her unmatched creativity and skilful use of technology, Rachel continually pushes the boundaries of her practice to best serve her students. She has been an integral part of BHNmath since its beginning.

NEW TOOLS FOR ELEMENTARY MATH

Over the past few months, I’ve had the pleasure of delivering math lessons in several elementary classes. For a handful of these visits, I wanted to make use of digital math tools, but wasn’t quite satisfied with the options available at the time. I ended up creating my own, which you can access below (click the image). Each tool is accompanied by a brief tutorial video. These tools are also available via the Grades 7 and 8 page and through relevant MTH1W1 lessons.

A DAY OF MATH

At the end of March, I had an amazing opportunity to host a full-day math workshop with a group of students in Grades 7 and 8. Given that I had complete freedom over choosing the content and delivery, I wanted to design an event that would provide students with hands-on exposure to some of the captivating mathematics not usually seen in elementary and secondary classrooms, but which is still connected to the curriculum. I decided to centre the entire day around the beauty and power of math. Exploring everything from mathematical proofs to introductory topology, the workshop was aimed at giving students a sense of how beauty appears in mathematics and how its power extends far beyond utilitarian purposes. It was an incredibly enjoyable day and I hope to do it again soon! Below is an outline of how the session unfolded, along with links to several of the BHNmath digital tools we used.

We started the session off with a thinking classroom activity with students collaborating in random groups on a problem solving task at whiteboards. It was immediately evident that this group was ready for action and that an engaging day was ahead of us! Following the activity, we gathered to chat about how it was currently a very exciting time for mathematics… Within the previous two weeks, the first aperiodic monotile was discovered by Kaplan, Smith, Goodman-Strauss and Myers, and two high school students, Calcea Johnson and Ne’Kiya Jackson, proposed a valid proof of the Pythagoren Theorem that uses trigonometry

From there we dove into a deep discussion on beauty in general. When considering where we often see beauty, students referenced nature, people, relationships, and art. Using musical examples such as Beethoven’s Sonata Pathétique, we analyzed how tension and resolution evoke emotion. Visual art examples such as Loretta Gould’s Prayer for Our Future and Henry Ossawa Tanner’s The Banjo Lesson  provided powerful evidence of Colonel Chris Hadfield’s claim that “when we really want to communicate, we use art.”

The discussion soon turned to the question of how (or if) the qualities of beauty that we noted (evoking of emotions, internal interactions, tension and resolution, purity, truth, etc.) appear in mathematics. Back to the boards! Through a series of investigations in number theory emerged an appreciation and, in some cases, obsession with the concept of mathematical proof. Not only did students feel firsthand the satisfaction of expressing undeniable mathematical truths through the use of drawings and manipulatives, they also experienced the power of algebra in generalizing their results. The finale of this introduction to number theory was a proof using mathematical induction (yes, with Grade 7/8 students) that the sum of the first n odd numbers is n².

Our chat about square numbers led us to the world of 2-dimensional geometry, where we reviewed how the so-called Pythagorean Theorem is based on the areas of squares. This idea wasn’t new to anyone in the room, but instantly became more intriguing when we asked if it could be extended to three dimensions. Using a digital tool to explore, it was evident that the 3D version of theorem holds if rectangular prisms of equal depth are built off of the right triangle’s sides. Pondering if it worked for cubes led us directly to Fermat’s Last Theorem. Enter Andrew Wiles and his emotional journey to prove that age-old enigma.

Continuing our chat about squares took us to the Fibonacci spiral and its relation to the golden ratio. Afterall, how could we skip that when talking about beauty in math! We used a digital tool to explore the golden ratio/rectangle and another digital tool to construct and compare the Fibonacci spiral and the golden spiral. Of course, we also took a look at where such spirals appear in art and nature!

Our journey into topology began when we saw how the golden rectangle appears in regular dodecahedrons and icosahedrons. Students proved that there are only five Platonic solids before exploring Euler’s famous polyhedron formula. Finally, we extended this idea to nonrigid objects and concluded with a cheesy joke about how we spent a whole day showing why coffee and doughnuts go so well together (they have the same Euler number)! 

RESOURCE TYPES

Here are five other resources recently created for BHNmath:

Course: Mathematics, Grade 9 (MTH1W1)
Topic: EQAO Practice Test #1
Type: Interactive Practice Test
Target: Students
Location: EQAO Practice Material
Notes: An interactive practice test to prepare for the Grade 9 EQAO assessment. Designed to resemble the digital practice test provided by EQAO. Also available in document format.

Course: Mathematics, Grade 9 (MTH1W1)
Topic: EQAO Practice Test #2
Type: Interactive Practice Test
Target: Students
Location: EQAO Practice Material
Notes: An interactive practice test to prepare for the Grade 9 EQAO assessment. Designed to resemble the digital practice test provided by EQAO. Also available in document format.

Course: Mathematics, Grade 9 (MTH1W1)
Topic: EQAO Practice Test #3
Type: Interactive Practice Test
Target: Students
Location: EQAO Practice Material
Notes: An interactive practice test to prepare for the Grade 9 EQAO assessment. Designed to resemble the digital practice test provided by EQAO. Also available in document format.

Course: Mathematics, Grade 9 (MTH1W1)
Topic: ymxb Form for the Equation of a Line
Type: Interactive Applet
Target: Students
Location: How can we describe it?
Notes: An activity to practice finding the values of m and b in the y=mx+b equation of a line given its graph.

Course: Various Courses
Topic: Intersections of Lines/ Combinations of Functions
Type: Interactive Applet
Target: Teachers/Students
Location: Various Locations
Notes: Designed for a teacher in the Business Department, but applicable to topics in MTH1W1, MFM2P1, MPM2D1 and MHF4U1. An interactive applet for exploring break-even points.

WHAT'S NEXT FOR BHNmath?

  • Enjoying the summer and preparing for September!

Have a wonderful summer break!
– Adam