Combining Expectations: Integers, One Step Equations and Translation Vectors

When looking at my curriculum, as I think many other teachers do, thought "How am I going to cover all of this". However, when I started looking through the parts I thought of how each expectation didn't have to be taught separately, but that perhaps if they are taught and explored together they would provide great context and then also the time to think through each of them.

My first attempt at this is exploring translation vectors, integer addition/subtraction and one step equations all in one hit. By doing this, I feel that my students will have longer to look at each concept and also use their strengths in one area to help them in another. I have already seen that my visual students have grasped the addition and subtraction of integers through their translation vectors, better than they would have done if it was taught separately.

I have put below each days goal and the related handout that the students completed (if applicable). My classes next steps are to explore the rest of the transformations on a Cartesian Plane. Through this we will also be looking at composite areas, similar and congruent shapes and two step equations. If you have any ideas of how these can lead into each other please let me know. I have a plan but open to change.

Outline and Resources:

Previously to this we had already explored the transformation terms through dance. Please see the previous post about this exciting activity.

Day 1:

• Explore the Cartesian Plane and how coordinate points are communicated. Translation Vector Intro.
• Resources: Click Here. 

Day 2:

• Translation Vectors Review and Thinking -> Inquiry into integer addition and subtraction.
• Resources: Click Here and Click Here. 

Day 3:

• Determining Translation Vectors through One Step Equations
• All class handout: Click Here. 
• Challenge by Choice
• Green level: Click Here
• Blue Level: Click Here
• Black Level: Click Here

If you are interested in my challenge levels please read my blog post about it. Click Here. 

UPDATE: Dancing Through Transformations

So the transformation dancing is almost done (Click Here for the post). Things that I have learned from the experience are listed below as well as the documents that were given to the students:

Things that went well:

• Students were more open to risk taking since it was not done on paper. 
• It was a great activity to use for students to get to know a different member of the class. 
• Students helped each other.
• It illustrated that even though these terms have been learned before, they are not concrete in their heads. 
• Having them communicate the dance with the boxes on the ground was a good introduction to coordinate points and communicating a transformation. 
• Having the three different challenge levels allowed each groups to work on the dance for the same amount of time and with the same amount of attention to detail. 

Things that were a challenge:

• Time. It took longer than I previously thought.
• Music. Giving them music to dance to caused stress. 
• Assessment. Finding the right time/place to give formative feedback.

Things to do next time:

• No music, but indicate that they will use only 10 moves. 
• Have mini due dates for each day. Make sure that the students film their translation dance in class since the communication of it can be done at home. 
• Now that I have done this once, create a rubric that the students can refer to, and can be attached to their completed Google Doc by Goobric. 
• Determine a time when formative feedback will be given. This feedback will be on their ability to apply the terminology as well as if they are able to communicate specific steps. 

Documents:

This link is to the Google Drive folder for the class. In it are the handouts, as well as example videos for them to complete. This folder was used on the first day. Click Here. 

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.