Learning Transformations Through Dance

I am wrapping up our first unit in Grade 7 with our Data Management unit and our infographics of Who Are We. Every year this intro unit doesn't reach the level of design I want it to, but we do reach a great level of understanding in middle school organization expectations, homework management, class routines and friendships. I always need to remind myself that I purposefully do this unit first since it allows my students to focus on these other areas and not be stressed about the mathematical concepts.

Moving forward, I can now challenge them in their thinking in the classroom. My next term is a combination of geometry, algebra, number sense and measurement. To start we are going to be looking at transformations using dance as a way to introduce the vocabulary. I was inspired by a video I saw about a year ago from Math in Your Feet of a teacher doing the activity. Here is the video and below are my outline and goals.


Step 1: Dance Creation
Students are divided into pairs. Students stand an arms length away from each other and each within a 50 x 50 cm square. In this square, the two students create a short dance that includes foot, hand and body movement. They practice this until they both know the moves and can do it in synchronization.

Step 2: Vocabulary
Students are then slowly introduced to the vocabulary of origin, translation, dilation, rotation and reflection. One person in their box is told they are the origin. The other person is the translation or reflection. After an explanation of what there terms mean, the students then dance their dance in both situations. For the translation, nothing changes. Students see the movements are the same, but just not in the same box. However, when a reflection occurs, the origin does the original, while the other student completes the reflection. You can probably picture what happens with the others as well. Students practice each of these, switching who is the origin.

Step 3: Combination and Share
Students are partnered up with another group. The teacher calls out one or two terms. The students must dance their dance with these transformations. The other group is watching to see if they make a mistake and provide feedback. The teacher may say "translate, rotate 90 degrees and reflect". Students must understand what this means and preform.

Step 4: Music video analysis
As a possible homework activity, students watch a short segment of a popular music video and analyze the dance moves. They given the moves the transformation terms. They can also then identify who is the origin and also which types of moves occur more frequently. As a comparison, different people could get music videos from different countries to see what kind of transformations are more population there.

I am looking forward to trying this out. I am hoping it will take 2 periods and the homework to complete. After this, and they have the vocabulary down, we move onto geometric shapes on paper.

If you have any ideas of recommendations of how to make this better please let me know. 

Toronto Resources: My favourite sites to use in my classroom

With the upcoming Toronto election, I wanted to share the online resources that I have used with students to learn about the election, but also about Toronto as a city. So far this is my list. Please let me know if you have any others that can be added.

Great Election Sites:

• www.pollenize.org/toronto - Get to know your mayoral candidates with this clearly laid out website. The site takes information directly from each candidates platform and presents it in a visual and simplified manner. 
• FOR MATH: We have been discussing bias in data collection. We have also extended this into the election and how it can be challenging to gain an unbiased opinion of a candidate when reading an article in the paper as the author could have an opinion. This website has a disclaimer at the bottom of each page explaining how they attempt to provide unbiased and correct information. 

Great Toronto Data Sites:

• www.http://map.toronto.ca/wellbeing/ - Using Toronto Open Data, this website organizes many different indicators into various neighbourhoods of the city. Click on a neighbourhood and you get the 2011 census data.
• FOR MATH: Students are able to calculate percentages from the data. They can then compare various neighbourhoods and their populations or different indicators given. With the election in play, they can also consider what platform topics the neighbourhood could be most concerned with based on the indicators. 
• Open Data Toronto: This is a great site providing direct access to all the data that has been collected in the city. 
• FOR MATH: I have used this in my class many times from analyzing tables to creating infographics to display the data clearly. I have used the Food Bank attendance as well as Bike data. This raw data is easily accessible and related directly to Toronto students. 
• Toronto Demographics: This site is where the analyzed data from Open Data Toronto is placed. I have used this site for the Ward reports. 
• FOR MATH: I have used the reports here with students to complete a "If Ward 11 went to my school" or "If Toronto went to my school" project, which runs just like the "If the world was 100 people". The difference with this project is that students can think about the data and consider if they feel our classroom reflects Toronto. This can start great conversations about diversity, civic responsibility and who are we in our community.

Great Toronto Article Sites:

• Spacing Toronto: I am a big fan of this magazine, especially for articles for Middle School students to read. The focus of this magazine is how design is important in the creation and sustainability of a city. Articles are short and can be a good way to start a conversation about a topic or Toronto issue. 
• BlogTO: I use this site to become aware of great activities and events that are occurring in Toronto. I believe that if I want my students to be active citizens, than I must explore the city as well. The events section outlines great events each day and weekend.

Creating Equations: Starting with Rates, Ratios and Percentages

Determining how to launch a middle school math class was a challenge for me. Having students coming in from various schools and backgrounds, I had no idea what baggage, good or bad, they were bringing with them. It is a great challenge to learn about each student, their learning styles as well as background while trying to teach them something new. For the month of September, I like my students of all levels, to feel successful in our math class. This helps create a positive feeling over the subject and also helps create a sense of community where we can all learn.

For the past two years I have started with percentages, rates and ratios. For some students this is an area of confidence, but for others it challenging due to confusing word problems and mechanical calculations that can become confusing. The goal is that we move from this into creating and balancing equations. Deeply understanding equality is very important for the start of algebra and balancing equations, and I felt that we could introduce this with percentages, rates and ratios.

To do this, our class focused on equivalent fractions. To solve each of their problems from rates, ratios or percentages, students created equivalent fractions. Identifying what is the part and whole in the problems and how they are equal to another part and whole.

It took two weeks, and three classes a week for the students to really grasp the idea. However, what I found was that students were reading the questions, analyzing the values and thinking about equality more than when we learned how to solve each of the problems in the traditional "divide the numbers and multiply by 100". Those students that came into the class with these calculation methods and didn't understand why they worked, found the equivalent fractions a longer thing to do, but they understood why they were doing these calculations.

Most importantly, students are identifying that what is on one side of the equal sign is equivalent to the other. They use the term equivalent in their explanations and when they are working on a problem. I know that this will be very helpful as we move forward to making one step equations where students rebel at the idea of writing an equation and just want to solve. So far it has helped those that are struggling, and given a new challenge to those students that already feel confident with their rates, ratios and percentages.

I have attached some questions that we did as a class later on to see how we set up and solve our fractions.