Visual Patterns and Hotel Building Challenge

Many of you mentioned in your reflections how the use of imagery or graphical representations can increase the level of student engagement. I'm reminded of this web site visualpatterns.org created by a math educator in California, Fawn Nguyen. It is an excellent resource for teaching introductory algebra. 

Another of my favourite math activities from Fawn's site is Hotel Snap. Here is an example of my activity sheet. I simplified the problem to just 15 hotel rooms for a regular Math 8 class so that the activity could be completed in one class period. However, I have tried this activity with 30 or 50 hotel rooms and added a component of getting students to do the calculations using an Excel spreadsheet if I was able to book the school computer lab or laptop cart and had 2 to 3 class periods to spare.  

Topography Project

I have very much enjoyed the thoughtfulness and creativity in the Assignment 1 presentations! They've also been a great reminder to me of how using hands-on activities with tangible materials in math classrooms can be a powerful way to enhance learning and make abstract concepts more accessible, engaging, and meaningful to our students.

 

I am reminded of an activity by my former Math department head and a wonderful mentor, Maria Nicolidakis. She did a topography project with her Math 9 Enriched class. Students were given a portion of the map of Haida Gwaii and made a topological graph. Students engaged with estimating area and volume as well as finding the gradient of their assigned pieces. Teams worked together to construct the 3D modal as a class. Our district Indigenous resource teacher was invited to the class as a guest speaker.

Maria was also involved in developing a weaving math project, which was part of the Burnaby School District's initiative to develop more teaching resources to incorporate Indigenous content.

You can also find many hands-on activities from Math First Peoples developed by the FNESC (First Nations Education Steering Committee).

Janice Novakowski, a math consultant for the Richmond School District, often posts great resources as well.

FREE Virtual Math Ed Pro-D Event - Nov. 15-17

Here is a free, virtual Math Ed Pro-D event that may be of interest: 2024 Make Math Moments Virtual Summit. There are some high-profile math educators presenting at the event, such as Jo Boaler (Mathematical Mindset), Peter Liljedahl (Building Thinking Classroom), and Ben Orlin (Math with Bad Drawings), just to name a few. 

Make Math Moments is a popular math education podcast host by two Ontario math educators, Jon Orr and Kyle Pearce. Check out their work if you enjoy podcasts!

Dan Meyer's Three-Act Math

Last post today. There's just so much I could share when we're discussing word problems!

Saiya's good idea about using videos reminded me of Dan Meyer's Three-Act Math Tasks. I've learned over the years that if other colleagues have develop something that can be used, don't re-invent the wheels! I usually just access his spreadsheet directly. And if you do a search on "3 Act Math" you'll find many other math teachers have developed and shared their work. 

Inspired by Dan Meyer's Three-Act math tasks, I've also collected videos I could use in class. One of my favourites is this one about gummy bears. I heard about this video from another teacher at a BCAMT conference one year, and it's become an activity I'd do in Math 8 after students learn about ratios and rates. 

So the obvious question that students would come up with is: How many small gummy bear is equivalent to the world's largest gummy bear?

I'd bring a bag of gummy bears to class, show students the nutrition label which has information such as weight and calories, and ask students to do their estimates. Some groups want to use volume and would measure the size of the small gummy bears. (Remember to remind the students to measure first before eating it!) 

Math 10 Lab: Estimating Height

I look forward to hearing your thoughts on word problems through your blog entries!

As I mentioned, that Leaning Tower of Pisa word problem is still used in the trigonometry unit in Math 10. I actually had a good discussion with the students last year after watching this:

In an attempt to do something more hands-on in the trigonometry unit, I did a lab for estimating the height of a building using a simple clinometer. Here is the activity handout: Math 10 Lab Estimating Height. Feel free to use it and make it better!

For one class, it was raining, so I got the students to estimate the height of the classroom. (Always have a back-up plan in your lesson plan!)

I also challenged the students to get creative and find other ways to do the height estimate. One of my favourite solutions was from a group that took a picture of a classmate with the building and found the ratio of the student's height to the building height in the picture. Excellent use of proportional reasoning!

In a Small Town Called Mathville... The Create Your Own Business Project

I'm reflecting on my own comment in class today about making word problems more realistic. And then I was like... wait... maybe "realistic" isn't the right word, as I thought of this Math 8 project.

This blog post was originally written on April 15, 2018. 

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"In the small town called Mathville, you, the new business owners, decide to have your grand openings together at the new Wildcats Shopping Mall on Tuesday, Mar. 13. On this day, you will promote your shop to the residents, and you will offer discounts on five items from your shop to attract customers." 

It has been four years since I last gave a unit test on the percent unit in Math 8. I have been giving students the "Create Your Own Business" project as the summative assessment for the unit. I want to make math more relevant and, at the same time, to give students an opportunity to show their creativity. Students have to make advertisement posters, and on the "grand opening" day (i.e. presentation day), they have a chance to act as customers and shop owners. The presentation is done in a math fair/gallery walk format. Some students were really into it and even made coupons for their grand opening! During the presentation, I went around every shop and acted as a customer. I evaluate students' understanding of percent concepts: Do they apply the discounts and taxes correctly? Can they explain what percent means and how they do their calculations? We also had good discussions on things that weren't part of the textbook for this project. Is it better to apply a dollar-off coupon first or the percent discount first? What items are exempted from PST?

  

The students always amaze me with their creativity and imagination. My intention was to make math more practical, and what I envisioned in my mind were shops that sell sports goods, shoes, electronics, food, etc. However, not only do we have these shops, but we also have many imaginary shops. In the first year I did this project, some students asked me: Does it have to be real? Can we sell things that don't exist yet? And I didn't see why not.

So we ended up with a pet store with unicorns on sale for $150 each, and you can buy one and get a koala 25% off. We had a shop, Wizarding Wonderland, that sells the invisibility potion, magic wands, and flying broomsticks. We had a shop called "Planet N' Go" that sells different planets; their slogan is "the deal is out of this world!" 

 

Year after year, students tell me that this is one of their most memorable Math 8 assignments. The room is always buzzing on the presentation day, with great enthusiasm. The most important part for me is that I got some kids struggling in math to engage; I have had students who don't normally hand in assignments participate because they can create a shop to sell something they like. 

Why is x the unknown?

The question from Josh today reminds me of this video,  which I often show in Math 8 when introducing algebra: