MFM1P – Oh the Sugar… Ratios and Proportional Reasoning

Today in our period B MFM1P class we started investigating ratios and proportional reasoning.

We started using Dan Meyers 3-Act Math problem “Sugar Packets”. After watching the video, students were engaged and grossed out at the thought. Then, they were each given a different size of beverage (juice boxes, chocolate milk, small soda cans, large soda bottles, iced coffee, iced tea, gatorade and lower sugar gatorade, powerade, snapple, vitamin water, etc.). Groups had to figure out how many sugar packets were in each beverage container.

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After collecting all that data, we talked about if this was a fair comparison to base our decisions on. Students decided that it was not fair because each container was a different size. Groups then began the difficult work of figuring out how to find the number of sugar packets in a 591 mL sized bottle of their beverage.

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Some groups found a unit rate (number of sugar packets in 1 mL and then multiplied by 591 mL), some groups found out how many “times” larger the 591 mL bottle was and then multiplied the number of sugar packets by the same. Lastly, one group used an additive method to figure out how many of the smaller containers were in the larger one and then did the same thing to the sugar packets.

We consolidated by setting up ratios and then comparing a few different algebraic methods for solving it. We ended up with a great discussion on types of beverages, types of sugar (fruit sugar, liquid sugar, corn syrup) and ratios.


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MFM1P Proportional Reasoning Task: 3D printing, Minecraft and Art

We started talking about our Proportional Reasoning Task #1 in class today. Students will create scale models or drawings (and explain how they did it) to demonstrate their understanding of ratios. They were given three options:

  1. Minecraft scale model – create a scale, find or measure the dimensions of an object or room and build a scale model in Minecraft
  2. Art enlargement – find or create a small image and enlarge it using a scale created by the student
  3. 3D Printed scale model – create a scale, find or measure the dimensions of an object and design a scale model of it. Then print using one of our 3D printers.

Of course, my very creative students pushed me to offer even more options. “Could we create a Lego scale model?”. Well, yes… that would be spectacular. Anything to show me that you understand ratios.

Much to my dismay, we have limited time to do this task. If we had my way, I’d do creative projects like this all semester and go really very deep. However, we have an amazing final task planned for this class which will relate back to this task. It will let us go much deeper. We will only have 2-3 periods to work on this one.

As teachers, we are moving so very far out of our comfort zones on this one. I had never played Minecraft before. Thanks to an OTF Co-op Ministry grant, I now have a server set up through the folks at Minecraft EDU and a world with 10 really neat workspaces for groups. I now know what it means to “teleport to spawn location”. Yikes.  I’m much more comfortable with the 3D Printer, but to be honest the design aspect is still very new to me. I have not spent much time learning how different design programs work. My students in previous classes figured out what they need to design what they wanted. I spent the time troubleshooting the file types and 3D printer itself.

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Some students in our class were worried because they bring their own tablets to class (not laptops) and the 3D design program I showed off works on laptops best. We solved that problem too. Students are pretty excited. About half chose Minecraft and half 3D printing. Only 1 or 2 chose the art task, which surprised me.

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Our assessment will ultimately bebased on the presentation and explanation of how they chose their scale, and how they set up and solved ratios to determine 3 or 4 dimensions of their model. This may be done in Educreations, using a cell phone video camera, Explain Everything, using Camtasia screen capture on a laptop, conferencing with students or a presentation to the class.

The next couple of days are going to be crazy, insane and totally out of my comfort zone. If you have any tips or tricks for us, we’d greatly appreciate it. My fingers are crossed that this works out!

Cross-Curricular Collaborations in Grade 9 Applied Mathematics

Since I weaselled my way back into the classroom a few years ago (after many years as a Student Success Teacher and ICT Consultant), I’ve taught all my classes with the help of others. Basing my courses around large, themed global collaborations and smaller class-to-class collaborations has brought energy, engagement, authentic learning and excitement to all my courses. Some examples are:

– participating in a global project looking at deforestation in Borneo (Deforestaction and Earthwatchers) in grade 9 and 10 science

– Google Hangouts, twitter chats and web conferences with Chris Hadfield, the ISS and other astronauts in grade 9 science while we compared neutron radiation all over Canada and on the ISS

– global malaria projects in grade 12 science

collaborative music creating projects with students from all around the world with the Seventh Fire alternative program

– web conferences and Skypeing with other classes and former child soldiers in learning strategies

– video conferences with classes and scientists on Tundra buggy’s in the arctic with learning strategies and geography

– co-creating videos with classes from local elementary classes through video conference and Edmodo in grade 10 science

– teaching elementary classes about scientific concepts and learning from them in grade 10 science

– creating radio shows with twitter questioning for elementary students in learning strategies


This semester I am teaching math. I have been very focused on supporting the development of creativity and critical thinking through teaching through problem solving in Grade 9 Applied Mathematics along with the impact of different forms of feedback. I have struggled over and over again to find global or cross-curricular projects that will work for our rushed timelines in MFM1P. We have plenty of excellent, thought-provoking activities in class using tools such as ClassFlow, OneNote, Knowledgehook, DragonBoxEDU, PearDeck, Minecraft and Turtle Art. We have many real-world connected problems to use for context using popcorn, video, really big gummy bears, chocolate milk, etc. I still struggled to find ways to connect beyond our four walls. It has bothered me all semester. I know how engaging and organic the learning stemming from integrated projects can be and was stretching to find something (anything) that fit with MFM1P.

Heather Theijsmeijer (@HTheijsmeijer) broke my “collaboration block” (similar to writers block). Her Grade 9 Academic Science class sent a survey out to the world via twitter collecting data about energy use, home heating and internet use in households. She describes the science project here. When we accessed the spreadsheet of results this week there were over 600 responses, from all corners of the world.

My math class took the spreadsheet of data and calculated percentages. What percent of participants from the UK heat with wood? What percent of participants from New Zealand heat with oil? We also calculated the average daily TV and internet use approximated by participants from different countries. What resulted were great conversations in data collection, bias, statistics and geography. The class created a list of questions and sent them to the science class. Today we Skyped with them and got to hear the thoughts and ideas that they’ve formulated from their research into energy use and production in various countries. 

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My math class got to see how math connects to other subject areas such as geography and science. They became masters of converting between fractions, decimals and percent. They started developing some proportional reasoning skills. We will be able to use this data when studying relationships and scatter plots as well as proportional reasoning. What a great opportunity to learn about another area of Ontario and share our work with others. We will share data and visual representations we create with the data to Heather’s class so that they can use them in their projects if helpful. They have taught us about energy use and production in countries all over the world.

THANK YOU Heather. I live for collaborative projects and student learning is always so much richer, authentic, organic and deeper when our projects take us beyond our own four walls. EVEN IN MATH 🙂


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Assessment in Grade 9 Applied Math

Yesterday a student asked me a question that made me stop and think. After squelching my initial reaction, I gave it some thought.

The students’ question was “do I really have to do all these practice questions? I know how to solve two and three-step equations with like terms on each side of the equation”. The old teacher in me would have stressed the importance of practice. I would have thought that I knew best and that all students should do the work that I chose and assigned. After some thought, I realized that this students’ question is an indicator of great things happening in our math class.

We are assessing by standards in our math class. This means that we have broken up the course into 22 learning goals and we measure student ability to do these things instead of measuring achievement on “stuff” (assignments, tests, tasks, etc.). At the end of the day, I need to know if a student can add and subtract polynomials. If they show me this through a task, a test or a video is inconsequential. I just need to know if they can do it.

I have assessed like this for years and remember the excitement when my science students finally understood how the assessment was working and began to advocate for themselves and what they needed to meet learning goals. I always worry that in math, I may not be able to ensure students fully understand how they are being assessed. I stress about how to empower them to come up with ways to demonstrate understanding that works for them. I’m more confident in science assessment.

So, after catching myself and thinking through this students request I responded to him by telling him to “archive your learning and move on”. We can archive our learning in our math class using the Sesame Snap app (thank you Min Min for sharing this tool with me). Each student has a digital math portfolio. We often roam class with our phones and take pictures, videos or notes of student work. These can be used in our assessment.

This students’ question ended up making my day because it showed me that he understood how he was being assessed. He knew that he was not being marked on “stuff”, but that he was being marked on his ability to solve a multi-step equation with like terms on both sides of the equation. He knew that he could better use his time revisiting the concept of multiplying polynomials, because he wanted to improve his mark on that learning goal.

A few of the boys in our class have “gamified” our math class. They have decided that they want to continuously improve and do better on the learning goals, so they are motivated to figure out how to get better and better at the concepts. A couple of these guys have learning disabilities and the ability to show a concept in a different way than the bulk of students have, or the ability to take some more time and reassess it later has really helped with engagement and of course achievement.

I’d love to hear more about how other math teachers view and manage assessment.


Desmos Central Park Activity in Grade 9 Math

Today in class the grade 9’s worked through an activity created and shared by Desmos Teacher. Desmos is a free online graphing calculator that many, many math teachers and students make use of. It is available on all types of devices and pretty straight forward to use.

To help support classroom learning even further, Desmos has a “teacher” section with some pre-created activities. One of these activities is Central Park. Central Park helps students transition from from the place where they can look at an equation and determine what value of “x” works to create balance, to a place where they have a deeper understanding of how variables can be used to create equations that model complex situations.

The activity starts by drawing on students intuitive understanding of parking lots and balance. It then begins to use mathematical calculations. Lastly, it has students developing equations that work in a variety of situations by inputing the values specific to that occasion. This is where students really begin to stress as they expand their understanding of what equations and variables really are. During consolidation at the end of the activity, most students in the class understood the new concepts. We will conference with students who could use a quick 1:1 to revisit the idea on Monday.

These desmos activities work well in our environment because they are quick to set  up (2 minutes) and work on any devices. The teacher simply “starts activity” and then provides students with the code given. They do not require accounts, students just use the code at to start the activity. The teacher can monitor student work and we identified students struggling and worked to get them on track or paired up with another student to help.

The next activity I think we will try will be the Polygraph Line activity. Students pair up and ask questions to their partners about their line (slope, intercept, etc.). As they ask more questions they eliminate some of the possible graphs to determine which one it is. It looks like a fun game to practice the vocabulary involved with linear equations.

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DragonBoxEDU in Grade 9 Applied Mathematics

Today in class we made explicit connections between a game we’ve been trying (DragonBoxEDU) and “the math”. Myself and the other teacher took a risk and had kids playing DragonBoxEDU for a portion of every class over a couple weeks. I had piloted it in a learning strategies course the semester before and knew that some students really enjoyed it. This proved the same in Grade 9 Applied Mathematics. Most of the students really enjoyed it, so it was more difficult to convince them to get OFF the game while we did other things than it was to get them to play. Students even came in after March break excited about how far they had gone in the game. The game can be played on a laptop or iOS device. The teacher signs up and creates a class and then the access for students is free. The game does not look like math. Students “discover” algebra rules while trying to isolate a box and grow a dragon. Sounds crazy ‘eh? Its not a drill and kill type game where they are practicing solving math equations. They are actually doing something that appears totally unrelated and acquiring skills as they go.

I’ll be honest, I was very worried at my ability to help students make the connections between the game and traditional-looking algebra questions. I worried that we had “wasted” all that time on the game. However, today we started solving equations and students were totally engaged. They watched me do a few questions in the game (and laughed at me while I messed up and then showed me the “short cuts”). Then the dreaded moment – I put a traditional looking question on the board (in ClassFlow where students can write on their own screen and send it to the front board for us to discuss). They made the connection immediately. They talked excitedly about equations.

I struggle to teach algebra “through problem solving”. I can find a way to introduce every other concept through investigation or problem solving. Algebra however, I struggle with. I can provide multiple ways to solve algebra problems using manipulatives and tools, but I struggle to pose a rich problem for students to solve that leads us to rich discussion of the skills we need for solving equations. While playing DragonBoxEDU may not be a real investigation or actual problem solving, it sure did allow students to construct their own meaning and understanding of equations and balancing. It gave us a great context for our discussion about algebra today. Students who regularly struggle in class were the first to jump up and show us how to go about attacking a problem. They just “got it”.

I’m hoping that they continue to make the connections to strategies discovered in DragonBoxEDU as we get to more complex, multi-step equations. I’d love to hear from others who have found engaging ways for students to approach the algebra content in grade 9.

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Today in math class (MFM1P) we decided to celebrate #PiDay seeing as we would not be together on the real Pi Day this year.

Of course it wouldn’t be fun if the teacher didn’t get to torment everyone just a bit. We listened to this song in the background all period –

We started by brainstorming what we already knew about pi. We decided to measure all the circular objects that we could and see if we could measure accurately enough to get to pi. Lots of great discussion around significant numbers and place value. I may have sweetened the pot by providing lots of circular treats (cookies, crackers, candies, chocolate, etc.).

Using a google form and spreadsheet, we collected all our measurements and averaged them all. Even including our obvious measurement or calculation mistakes, we ended up with a number pretty close to pi.

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Later we talked about what a ratio was and decided that pi was a ratio. We used this ratio and our new skill of solving equations to predict the circumference of objects such as the big nickel in Sudbury (we pretended it was a real circle).

After all was said and done we pulled out our EQAO formula sheet and described everything we now understood about the C=?d or C=2?r formulas.

Their homework is to consider what the graph of C=?d might look like.


Mindomo to create collaborative mind maps in math

Today in Grade 9 Applied Math class we were reviewing our first topics of study. Students created collaborative mindmaps using all the vocabulary, shapes (visuals) and formulas we’ve used so far. What a great way to consolidate our three main learning goals so far;

– I can solve problems involving area and perimeter of composite 2D shapes

– I can solve problems involving volume of 3D shapes (prisms, pyramids, spheres)

– I can solve problems involving pythagorean theorem


Setting up an assignment on Mindomo is super easy. I could pre-populate a mindmap with some of the basic vocabulary to save students time. Having groups of 2 or 3 each access their collaborative mindmap from their own computers was helpful to ensure all were on task and contributing. It also forced discussions around the vocabulary and characteristics to determine how they would structure/organize their mindmap. Some excellent math talk happened today. I find mindmaps can help students see the big picture and how all the concepts fit together. This holistic view is important for many learners (and is highlighted as a research-based method of high success for First Nation learners).

Many students enjoyed adding in images and links to examples in addition to the basic vocabulary. Comparing how different groups organized their mindmaps added some rich discussion.

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YOU can learn how to use Mindomo (Ontario teachers) by attending OTF’s Connect webinar on April 9th.


Co-Teaching in Grade 9 Math

This semester I have been given the opportunity to co-teach a couple grade 9 applied mathematics classes. I am officially the teacher for one of the classes and I am a math SERT (special education resource teacher) in the other class. However, both of our classes are following a co-teach model. We are alternating who is instructing or “running the show” while the other is conferencing with, supporting specific learning needs and observing students. The students think we are just both their teachers. They see no difference between our roles.

Unlike most teachers, I’ve personally had many opportunities to co-teach, co-plan and observe others teach. After only a week, I am already realizing how it is even richer to watch how YOUR students respond, behave and learn during lessons. The ability to step back in your own classroom and observe students is something we rarely have the opportunity to do. After only a few days, I feel as though I already have a better handle on my students and their needs than I would have after a month of teaching on my own.

We always talk about providing students with ongoing, timely feedback, and yet as teachers we rarely get feedback on our work. When you work to continuously co-plan and co-teach with another teacher the professional dialogue is integrated into your day. The 5-10 minute check in before school starts, the time during our prep period, the quick check-in over lunch hour and then the 10 minutes after class. This immediate dialogue and feedback is authentic, focused on student learning and never obscured by any feeling of assessment or evaluation. We’re in it together. The discussion is simply on what we can do to improve student learning.

In both the grade 9 math classes we are building in a method for timely, descriptive feedback for students as well. With two teachers in the room, one can spend the time each day to conference with each student who struggled with yesterdays concepts. The goal being to ensure students never get further than that one concept behind. While all teachers try this, in a busy class, it often becomes impossible. We easily are able to do that when co-teaching.

I have never been more excited to teach. I have a whole host of crazy things I want to try with my grade 9 applied mathematics class including;

  • OneNote class notebook with Wacom writing tablets (plug into laptops like a mouse to allow writing) for ongoing assessments and portfolios (we have a BYOD program where all students bring their own laptops)
  • ClassFlow with Wacom tablets for interactive math lessons
  • a classroom culture supporting a growth mindset and resilience
  • learning through inquiry for most, if not all concepts
  • integrating a couple games (Minecraft and DragonBox) to investigate mathematical concepts through
  • integrating some First Nation culture and outdoor education by completing some investigations into the math found in dreamcatchers and archery
  • integrating some art into mathematics by providing choices for inquiry that include connections to art (TurtleArt, visual arts, music)

With a full class of 24 students and 12 of these students with individual education plans, I was very worried about my ability to try these new things in addition to providing enough opportunities and entry points for all students in the class to access the content. Having two teachers in the room and the embedded professional support this provides has given me the confidence to try many new things in one semester.

What a great opportunity! Have you ever had the opportunity to co-teach an entire semester or extended period of time? If so, do you have any tips and tricks to provide for us?


Mind Mapping Study Notes using Mindomo

Yesterday for our last Learning Strategies class we used the new provincially supported (OSAPAC) tool Mindomo. It let students in my class work together collaboratively with those who shared a course with them (science, geography, French, English). Students were able to reflect on the course and tease out the big ideas or concepts and then start adding in details together. Listening to the conversation among students as they created mind maps of their entire courses was great. Some very rich discussion about which concepts fell under which big ideas. They also could add in links, images, etc. to help each other study.

It was a great way to end the semester! Lots of collaboration and lots of learning.

Today, for their final “exam”, students completed reflection sheets (Google Forms) on the learning skills required by their peers as they watch videos about their personal learning projects. At first I was worried about everything running smoothly, having all students streaming videos and bouncing back and forth between forms. It worked wonderfully and I was able to keep track of how many reflection sheets they completed (they did five each) as we worked through the period.

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