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.

Pi Day Fun 03.14 15

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?