Friday, December 8, 2017

Inquiry Math

As an educator, I found teaching math to students within the grades of 7-12 somewhat difficult to make engaging and interactive for the students involved; and we all know how much they emphasize making our lessons engaging and interactive during teachers college. By the end of it, our professors and associate teachers may sound like broken records.

I spent a lot of my time looking through many math resource websites, trying to find methods of teaching that spend more time engaging students in the learning process, and less time dictating notes from the board/projector. So when I started teaching full time in my first year after teachers college, and struggled to engage my students in math, I tried using Inquiry Based Learning techniques to the math concepts being taught.

From a student point-of-view, inquiry-based learning focuses on investigating an open question or problem. They must use evidence-based reasoning and creative problem-solving to reach a conclusion, which they must defend or present.

It is great tool in any classroom because most inquiry based tasks can be designed to accommodate students with learning disabilities, and students who have identified multiple intelligences. It allows students to work together/independently to draw conclusions to questions presented to them, base don their prior knowledge and understanding, and challenges them to build on what they know but making predictions or inferences regarding what they are learning. This website is a great resource that has inquiry based learning activities, prompts, assessments, lessons, and games that can be used to engage your students in the learning process, and make math class more enjoyable! 

Find the link to the website here:


What Are The Chances?

Here is an interesting question that I found in a New York Times article. It only took a 13 yera old boy seconds to answer this question correctly:

In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or right. What is the expected number of unpecked chicks?

Comment your responses below and follow the link in the article to find out what the correct answer is!

This is a great math problem that can be applied into a class of grade 7-9 students. It ties into the curriculum expectation of both fraction and probability of an event occurring. I would definitely use this as a riddle that students would be given the chance to respond to for approximately one week, to earn bonus marks on upcoming assessments. It is a challenging question, but I think students would be able to come up with a response if they apply the concepts they have learned or are learning at the time. 

How many chicks do you expect to be unpecked? Show your work! :)


Thursday, December 7, 2017

Technology, Use it, Don’t depend on it

I know the title to this blog post might be confusing some of you but I assure you it will make sense as you continue to read. I am a strong believer to incorporating technology into the classroom. I believe there are many pro’s for it however I also believe that there are quite a few con’s and therefore DO NOT DEPEND ON TECHNOLOGY.

First off on an overall note, technology is great, it allows students and teachers to remain in contact through applications like google classroom or remind. It also allows teachers to use different techniques to help students understand the content (gizmos, desmos, youtube, and etc.). In a mathematics setting I think it is helpful for students to be able to explore using geometric softwares, gizmos and watch youtube videos while completing homework to understand something that they are confused about. I also think it makes learning interesting for students. This is why I encourage the use of technology into the classroom. Now as to why is say don’t depend on it. My reasoning behind this is because first off technology can crash. I have been in many situations where I plan to use a powerpoint and it isn’t loading or the wifi is down, or google classroom isn’t working properly and therefore I need to have another option prepared in case this happens. If you depend on technology then when a situation arises you would have a back up or know what to do next and you will waste a period of student learning. Another problem for technology is that it can be distracting if not used properly and therefore constant circulation is important. Lastly, technology in certain situations takes time out of a lesson. Students turn on the laptops and one of them is dead, turns on the other and it is completing a configuration. By this point class is half way done. Therefore have option B; for example if the class is supposed to complete a gizmo print copies of the student exploration sheet so that they can start to work on it while their computer is loading if they are having difficulties with technology. Always be prepared for any situation that could arise to maximize student learning. Thus I am going to say it again, integrate technology, use technology in the classroom it is beneficial for student learning albeit, DON’T DEPEND ON IT or else you may be like this guy:



21st Century Literacies, HOW do we accomplish this?

As displayed in the image above there are many aspects to 21st century literacies. 21st century literacies were introduced into education in order to prepare students to develop into young adults and face the real world that we live in today. One thing that I have come to notice within the 21st century literacies and incorporating them into a mathematics classroom is that for the most part you can integrate each of these into examples and activity topics as real world scenarios to target student interests as well as prepare them for becoming an adult in society.  Literacies like financial literacy, technology literacy, environmental literacy, global literacy and multicultural literacy can be integrated into the mathematics classroom easier than the  others because they are great topics to use for examples, activities or question topics. Media literacy can be integrated as well by talking about medias portrayal of sales, and consumerism, advertisements integrating this then into financial literacy and mathematics. Mental health literacy and moral literacy are a little more challenging for me however these might be brought into play with classroom rules and expectations as well as living skills within the mathematics classroom. If anyone has other ideas for incorporating these into the math class please leave a comment on this blog as I would love to hear them.



Treating everyone with Equity Dignity and Respect!

Here is a blog post I created not too long ago that I thought would be very knowledgeable for us as we are entering the mathematics classroom. Please let me know your input on it. When I started my University degree under the Concurrent Education program, I never actually thought about the importance of and need for integrating multicultural learning into all subjects (i.e. Math, Physical Education) as opposed to only subjects like the Social Studies and English's. I knew the importance of understanding the diverse cultures of the students within your classroom in order to gain a positive relationship with them but never considered the importance of teaching about and to these cultures in specific.  Banks and Tucker discusses how a math teacher said to banks after his Multicultural Education presentation that "What you said is fine for social studies, but it has nothing to do with me." He then discusses how teachers within the subjects of the maths and sciences must think that multicultural education was simply content integration and therefore he developed the


Retrieved from
According to Banks and Tucker the First Dimension is where it all started. By putting African Americans in the curriculum, then Mexican Americans in the curriculum, and then Asian Americans in the curriculum we began with the content integration. Content integration is important for multicultural education however Banks states "with content integration, language arts and social studies teachers can do more than the physics teacher" and that a physics teacher may be able to create a poster with famous female physicists or a minority physicists however this is not what we are trying to teach through Multicultural Education. Therefore the first dimension of content integration is important however you will notice that as I discuss the other 4 dimensions discussed by Banks and Tucker they allow for more teachers like the math and science teachers to get involved and be a part of multicultural education. 

Retrieved from
The Second dimension focuses on Knowledge construction. Within this dimension Banks and Tucker discusses that the teacher should guide the students learning in order to help them "understand, investigate and determine the implicit cultural assumptions and frames of reference and perspectives of the discipline they're teaching" and therefore help kids with the learning process. It is knowledge construction that helps students become critical thinkers and readers and therefore causes students to think about the content that they are reading about and writing about in order to better understand the content. 

Teachers are to change their teaching methods in order to provide students from diverse racial groups and of any gender with a positive learning environment to achieve. Changing these methods for the diverse racial groups and different genders is known as equity pedagogy and is the third dimension discussed by Banks and Tucker. As Discussed above Content integration is when a physics teachers creates a poster of famous female or minority physicists and therefore equity pedagogy would be a physics teacher changing his or her way of teaching in order to provide an environment for the female student and the African American student to learn physics more effectively. Therefore equity pedagogy focuses on providing different teaching methods within the classroom to meet the needs of the diverse students and allowing them to succeed. 

Retrieved from
According to Banks and Tucker the fourth dimension of their multicultural education is prejudice reduction. The third and fourth dimension is where all the teachers no matter the subject are able to be involved. Within this dimension teachers are to work within their classroom in order to reduce prejudice in the classroom. "All educators should use methods to help kids develop more positive racial attitudes (Banks and Tucker). 

Retrieved from

Retrieved from

The fifth dimension goes outside of individual classrooms within the school and focuses on school wide culture and social structure. The goal within this dimension is to make the entire school culture more equitable and knowledgeable. It is about take the four other dimensions and growing them school wide. Within this dimension Banks and Tucker look at student groupings, teacher groupings, participation on sports teams and many other aspects of the school structure. Therefore the fifth dimension is about empowering school culture and social structure in order to allow every student and staff member to feel included and welcomed. 

As I discussed at the beginning of this post, I always considered learning about the students cultures within my classroom in order to gain a better relationship within them and ultimately promoting a more comfortable and inviting learning environment. However, after reading this article and learning about multicultural education into more detail I have learnt that it is more than this, it involved meeting all 5 dimensions that will ultimately provide each and every student with the opportunity to succeed. 


Banks, James A. and Michelle Tucker. “Multiculturalism’s Five Dimensions.” NEA Today Online. Retrieved from: 



Friday, December 1, 2017

Math isn't hard, it's a language!

This is a great TedTalk that talks about improving the amount of high school graduating students who are proficient in math. It talks about how math is actually a language, but we teach it in the most dehumanized manner, within many of our curriculums. It is a great video that shows us how we can teach math in a way, where students will understand the concepts and more importantly, what the question is asking of them. Using real world examples and relating math to the knowledge of their real life is one of the major keys to helping students become more proficient in mathematics. Enjoy!

Tuesday, November 21, 2017

Broken EQAO Record

Good evening all,

Now that I have this Blog thing figured out, I am able to fire out some work that I have head sitting in wait. The title might seem fitting to my next blog as again, it is about the EQAO.

Recently, I read about the Peel Board's decision to suspend EQAO testing due to catastrophic math results (CBC). It would seem as though the board has "no confidence" in the test, reasoning a "strong discrepancy" when comparing EQAO and report card results. The PDSB Chair, Janet McDougald, is suggesting that because the Ontario government is reviewing the test, that there is a "problem with the test and curriculum". I find this rhetoric to be short-sighted and self-serving.

The EQAO is an external organization, specializing in the assessment of curricular expectations. Their job is to "assesses how well Ontario’s public education system is developing students’ reading, writing and math skills. EQAO provides reliable and useful information that is used to help improve student achievement and ensure the accountability of school boards." (EQAO Website) What I find comical is that the very organization that is keeping our school system accountable is now under attack for producing an assessment that rigorously assesses and accurately portrays student abilities. The EQAO gets nothing out of having low or high results, but it does put scrutiny on the individual boards with low results. Ask yourself this, would there be a heavy-handed push back if the test results showed a majority of passing students? I believe the boards would work in opposite to what we are seeing now, and try to protect the EQAO, in a self-serving agenda. The results, coming out of years of continual review and revision of these tests, show a trend to be more than a problematic test and the Peel Board's push to suspend EQAO testing is nothing short of putting the cart, before the horse. Maybe I watch too much HBO and Netflix TV series, but the more I watch, the more I agree that Art is an Imitation of Life: Swing first, put them on the defense.

Don Henley got it right, Dirty Laundry.

Peel Board CBC Article


EQAO Extended

Good evening all,

I've included my original post from the Course Website with additional comments below.

 Every student has a gap in their learning. Whether it be in their writing and the correct use of then or than, appropriate comma or colon use or just how to structure an article or letter, there are gaps. The same is true of mathematics, and the province is aware of it. The EQAO is focused on improving students' abilities by analyzing trends in cohort, province wide testing achievement. This analysis is showing a negative trend in achievement, and has since tracking began. So with all this attention being placed on province wide testing, why are students' abilities in decline? A simple answer is the data is not being analyzed and utilized correctly, but obviously there is always a few jacks in the deck and it can't be that simple. If you are a fan of George Clooney or Mark Wahlberg, you'll know of the Perfect Storm, and that is what I believe we are creating in our Province.

      I think the EQAO province wide testing could indicate why students have gaps, but I'm not seeing the attempt in their findings. I'm not an activist against the EQAO's province wide testing, in fact, I'm the complete opposite, I think the testing has great potential to right this ship, but I think it is being misused.  The current longitudinal study is only focusing on student achievement as pass/fail. The last time I checked, the Ontario Curriculum was not a pass/fail document, but a listing of skills that students should display by the end of each grade. If the EQAO would analyze and publish the skills expected by the end of the respective grades, and not just pass rates, a clearer picture of where students show weakness on a class, school, community, board and province wide could be viewed and used to reverse the increasing failure rates in mathematics.
       Now the EQAO does publish findings "linking EQAO assessments to 21-century skills," which is a fantastic idea, but these skills are not specific, clump together numerous expectations, and cloud the picture. They are not a waste of time, but they are not specifically assessed in the Ontario Mathematics Curriculum. I like the idea for preparing students for the future, but how about just preparing them for what's next. A great Australian comedian, Tim Minchin, gave an inspiring and thought-provoking graduation speech for the University of Western Australia wherein he said, "You don't have to have a dream... I advocate for passionate, dedication for the pursuit of short-term goals... If you focus too far in front of you, you wont see the shiny thing out the corner of your eye." Like Tim, I believe if you have a dream, great but it takes a million steps to get there. What about those steps? This is where I think the EQAO should shift the focus from pass/fail reports to an intricate analysis of the specific curricular expectations, published for the province to see.

Below is the extension to the original post.

        As seen in all the reports being published by EQAO, students who show math weaknesses early on in their education have a difficult time rebounding and achieving a passing grade on EQAO assessments. What I find the most troubling is the fact that this is well know and documented but still the number of Educational Assistants has been in decline, and in some areas drastically, over the last few years. In 2012, the Toronto District School Board cut 430 EA positions. Their reasoning, declining enrollments. Instead of looking at the number of bodies in a classroom, why not shift the focus onto something more pressing like the province wide testing results that show a steady decline in math scores. Instead of laying-off EAs why not provide them with specialized training to help rectify the more serious problem. Education is about the results, not the bodies in the seats, why else would Ontario worry itself with EQAO testing if were not true.
        In my board, EA positions have decline over the last 4 years. Continual cuts to classroom support undermine the very ideal of education in Ontario. The EQAO report bulletin from 2012, updated 2014, justifies the extra help for students, citing "Early and ongoing intervention to support students who are at risk in kindergarten or the primary or junior level can help them meet the provincial standard in mathematics in later grades." Why on Earth are we taking the very instruments that can apply the interventions, that would help students improve, out of the classroom? In one word, Money. To balance budgets, we are removing support that could help improve math scores. The old adage "You have to spend money, to make money" rings true. Nothing comes for free and I think it's time we stopped lying to ourselves and get some support in the classroom for these students, who are clearly in need.

Feel free to follow the bouncing ball through the information below. In my opinion, enlightening but aggravating.
21 Century Skills and the EQAO
Testing Review
What the EQAO is all about: Province Wide Testing
Student Achievement Reports
Longitudinal Study 3-6-9 Cohort 2012
Bulletin of Findings from Longitudinal Study
Gaps in Early Education
TDSB EA Layoffs 2012
Bluewater EA Layoffs 2015
Bluewater EA Layoffs 2016

Friday, November 17, 2017


Factile -

This is a website that assists teachers in creating quizzes for their classroom. It is helpful for making Jeopardy style online games that can be used to making teaching and learning more interactive and engaging for both teachers and educators. There are also online games that have been already made by other people that can be utilized as well.

Monday, November 13, 2017

Math Clips and ePractice is a great resource that I found for different math strands and topics from grades 7 - 12. The website provides various resources such as clips, activities, educational games, and tools. Both teachers and students can use this website for additional support or for various ideas.


ESPN is a great website that deals with numbers of all the sports around the world. What we can do as teachers is that we can have the students log onto this website and choose a sport that they are most interested in. When they do so, we can assign different questions that they need to answer depending on the sport they have chosen. For example, if a student picks basketball, they would have to go through all 15 games that were played. Questions that we can ask are: make a bar graph representing the scores of each team. Use intervals.

The reason why I chose this website is because each student can choose a sport they mostly like. By doing so, they are interested in what they will be doing no matter whether they understand the lesson or not. If they didn’t understand the lesson, by having them interested in what they are doing will definitely help with having them understand it. 

Tuesday, November 7, 2017

Who Invented 'Zero'?

Yet another link that comes from the NY Times website! This was a great read though, diving into who is responsible for the development of the concept of "zero". There is always such a weight placed on cross-curricular lessons, especially with literacy and math/science. It's nice to try and find articles that connect different subjects. With this example, we have Math, Literacy, and History and its tied to something we use every day. It is about a month old, but worth the read if you're sippin' coffee and doing some KenKen (ha.).

Cheers gang

Sunday, November 5, 2017

Yummy Math

Yummy Math is a great resource that I have found to have math activities that are related to current events. This website provides students and teachers with engaging real life math activities. This past week was Halloween, and there are so many different activities that we can use in our lessons.
So the activity I was looking at was about Holiday Candy Sales. We can start our lesson by asking the students:  
  • Which holidays are associated with candy?
  • For which of those holidays is the most candy sold?
  • What percents of annual candy sales does each holiday contribute?
We this activity, we can have students work on independent think time, then small group discussion, then whole group discussion as kids reason and estimate with these questions. We can have the students translate a pie chart of information on candy sales to actual dollars spent for Halloween, Easter, Christmas/Hanukka, and Valentine's Day. 
We can hand out some candy in the class to the students and ask them to look into the amount of money that is being spent every year on candy during this holiday.

Thursday, November 2, 2017

Growth Mindset and Math

I came across this video, I really liked it because it explains how all students can learn math at any level they want to.

I'm not sure if anyone is familiar with Growth Mindset theory, I've posted a chart below but basically it tells us that everyone has a mindset about their own learning beliefs and potential. People with a growth mindset believe anyone can learn and grow their mind through practice and hardwork. Those who do not share this mindset, having a fixed mindset, believe people are either smart or not and you cannot change who you are.


A little cheesy at times, but it is a great motivational video. It focuses on these main points:

  • Making mistakes is okay, even helps you learn
  • Speed is not important, take you time 
  • Most importantly, math is not about memorization, it is visual and creative

Task: Become a math rock star

Throughout our course we have been discussing ways of making math learning real for students, creating our own questions as well as the relative merits of different textbooks. Here’s an interesting teacher whose life story intertwined all these elements and more. 

James Stewart was a math professor at McMaster whose students were so impressed by his lecture notes that they convinced him to write his own textbook. It turns out that the students were on to something and the lucidity of his calculus textbooks garnered him millions of dollars in royalties. What would an eminent professor do with his earnings? Design a house that pays homage to his passion, of course. The result is the House that Math Built, an architectural marvel clinging to the edge of a Toronto ravine. 

Students may have already heard of mathletes, but I can think of classes that would also be interested in the idea of a math “rock star”. A quick virtual tour of this building could lead to conversations about the different math-related careers mentioned elsewhere on this blog (not to mention their potential remuneration). James Stewart has some interesting views on how textbooks should be crafted here. Who knows, maybe one of us will create our own math Xanadu one day.

Read more about James Stewart's life and career here.

Tuesday, October 31, 2017

Infographics in Math Class

I am a big fan of the infographic as a means of harnessing student attention. I think they can present entry points to all sorts of rich math discussions in class. They are visually interesting and often neatly summarise quite complex ideas or huge figures in a way which is easy to absorb. Below is one that recently caught my eye, listing the dizzying number of social media happenings in 1 minute (from This presents some obvious tie-ins with Number Sense or Data Management strands; students might survey and graph their own social media use after exploring the stats here, for example.  

On a similar theme, this interactive 3D graphic mapping global population is pretty fascinating too.

Students could be tasked with finding out the biggest population centres in each continent and creating their own graphs, but this would be a great hook to kick things off in the Data Management strand. There are lots more in a similar vein at

I’d be interested to hear if anyone else has any favourites.

Saturday, October 28, 2017

Mnemonics make math FUN!!!

Math Mnemonic
How many of us were not very interested in our math classes??? Many of us struggled due to finding difficulties memorizing those rules and mathematic formulas or stuck finding a motivated way to solving those equations.

There are many ways, which a teacher can utilize to engage his/her students and keep them motivated in learning math. I have discussed in my previous blog the integration of rap songs into math classes and it is noticeable affect on students’ success and elevating their interest in math. Today, I want to share some math mnemonics, which will make you the coolest and smartest teacher ever, in your students’ eyes, at least 😊
A mnemonic is a device, such as a formula or rhyme, used as an aid in remembering. Many students just remember the mnemonic, which could help them memorize orders of solving expressions or a formula to find an unknown during any assessment. This will uplift their academic performance along with increasing their enthusiasm level towards learning math.  
          Those mnemonic will add enjoyable mathematic environment in your classroom, when posted on the walls. It would be ideal, to prepare a visual representation, such as a poster, of each new mnemonic introduced to your students and display so students can easily access it whenever needed.

Some teachers provide their students with formula sheets to be used during tests or quizzes. Having those mnemonic posters in your classroom will save you time preparing formula sheets. Otherwise, you can put them down before a test, if you expect your students to know those formulas.

An example of mnemonic for measures of angles in right triangles:

·       SOH: Sine = Opposite leg divided by the Hypotenuse.
·       CAH: Cosine = Adjacent leg divided by the Hypotenuse.
·       TOA: Tangent = Opposite leg divided by the Adjacent leg.

Silly Old Harry Carried A Horse TOur Apartment.

Below is a full archive of many mathematical mnemonics, which surly you'll enjoy using in any future math class 😊

Friday, October 27, 2017

What's the Best Deal?

It might be a close race, but I think students might like their phones, tablets, and gaming consoles more than school. The enjoyment I see from kids at my part-time job (Best Buy) can SOMETIMES exceed the excitement I see when I'm teaching linear or quadratic relations...okay, all the time. Depending on the course you're teaching, it can be a good idea to incorporate a weekly flyer into your class, to discuss discounts and better deals. Around this time of the year, flyers at any retail store are going to be pretty thick, so you have many options to choose from to answer the question: "what is the better deal?".

I've used this activity in a MEL3E night class, where I grab a few flyers and have students work in partners or a group of 3. I ask specific groups to tell me what is the best deal with respect to percentage discount and not actual price. I'll give one group laptops, another televisions, appliances, etc. It serves the purpose of students practicing working with percents, and also lets me know what the solid deals are (and yet still procrastinate on my Christmas shopping). At this time last year, my students (many above the age of 30) were gearing up for Christmas, so having them use a real flyer, instead of a made up worksheet, made this assignment more appealing. I'm sure many teachers have done this. I can give credit to the customers that always...always...ask: "which is the better deal though?".

Have a great day gang.

Wednesday, October 25, 2017

Mathematical Rap Videos

Using Math Rap Videos

Senior mathematics can be very tough form many students to grasp and retain. Few teachers, like Ernesto Lara, write and produce their own mathematical rap songs/videos to share with students. Most of students find it easier to understand and retain geometry and calculus concepts through memorizing the beats and lyrics.

Using rap videos, especially those displaying pictures of the presented mathematical concept along with the written lyrics will allow students to learn math concepts in a more interactive way. Students will stay focused and pay attention to the video presented. Many students just remember the lyrics of the song, which helps them to sing it to themselves during a test and a quiz. This will elevate their academic performance along with increasing their motivation level towards learning math.  


          Since understanding the lyrics of the rap videos is an essential aspect for students to memorize the song and utilize it, teachers can provide students with the written lyrics before playing the song. So, if there are any students with special needs or ESL students who find some difficulties with decomposing the song lyrics, would have the chance to refer to the provided lyrics.


Ernesto Lara and his students’ feedback on rap song:


An example of how to solve quadratic equations:


Sunday, October 22, 2017

Virtual Reality Math

Wouldn't it be amazing if a student who has difficulty understanding 3-D trig questions use a virtual reality app to go to the great pyramids of Giza and find the angle of elevation of one of the pyramids? I learned about CoSpaces from the EdTech session ‘VR & STEAM education’ where I was able to create a pyramid in a virtual reality world and go inside it. Although the equipment I tried there was quite expensive and we are not likely to have it in our classroom (at least anytime soon), but I also learned that we could make a VR headset from scratch and create VR worlds using CoSpaces

This afternoon I worked on a VR headset with my daughter (I had promised her to make one together). After lunch we collected materials like cardboard, glues, lenses (you can use toy binocular lenses) and spent a couple of hours to build one. We used the following steps:

1.       Download the template 

2.       Cut the images out

3.       Trace them on cardboard
(I printed some on cardstock paper but cardboard is a lot stronger)

4.       Cut the traced lines 

5.       Assemble the pieces by glue/tape 

6.       Go to CoSpaces (download required) and choose a space or create one 

7.       Place your phone in the headset

8.       Explore the VR world

I thought about how this kind of experience could help students understand math (e.g. 3-D geometry) or science lessons.

What is Google Classroom? Wow it works with Quizizz too!!

I'm just starting to look into this since (


is also connect to it (see picture below for details)

Anyway, check out the "What is Google Classroom" below, I'm going to set it up with my math class, it looks just too easy and helpful in mark keeping!! 

Google Classroom is a blended learning platform developed by Google for schools that aims to simplify creating, distributing and grading assignments in a paperless way.