Patent Laws, Areas of Shapes and Launching into Structures - June is on its way!

It is weird to think that May is already here and June is just around the corner. However, when I feel the energy in my classroom, it is evident that these Grade 7 students are ready to move and get going into action. This week the goal was to have a short launch into their activity and then send them loose to explore, try and play. The learning goals for this week were:

• Through understanding forces, we can prevent failure of a structure
• Understand area is the space taken up by a 2D object
• Explore the relationship between finding the area of a rectangle to the creation of a formula for the area of a triangle

Science:

This week was the wrap up of the solar oven project since we cooked our s'mores on Friday. With the twist of having students decide if they should make their results of experiments for public or private use, I wanted to take time to explore how this is applied in the world outside our classroom through patents. I decided to have a discussion period where students would understand and question how patents can motivate as well as make it difficult to innovate. 

To launch, I used the Poll Everywhere app to have the students share anonymously how they felt about making the results of their solar oven experiments for others to use. Through the different questions it was identified that:

• In this project, students made all of the experiments public for others to us, but if there was the option of charging their peers a chocolate bar to use their ideas they would have done so. 
• If they knew that not everyone in the class had a chocolate bar to spend, there was a slight shift to making it public but the majority still remained keeping it private and charging. 
• When asked what they think causes people to want to create inventions, the highest ranked choice was because they had a problem to solve, but also the idea of financial rewards appeared. 

After discussing the results of our class data, I walked them through the process of getting a patent and outlining the time and investment of money that is required. We searched on the international database of patents to see if an idea we had for our solar oven was already created. They found this challenging and time consuming. They also saw how inventions that are patented show how to make and produce the invention to everyone online, which they saw as a way to spark ideas in others...if others could find the patent. 

We then took time to ask why inventions had not been created to solve problems such as clean water, when we have made great improvements in cell phone technology. By talking through different world views, they were able to identify that the financial investment required to develop a product would then be gained back by selling the invention. However, if the people needing it have no money to pay, than the inventor would be at a loss of money.

I was really happy that we had this conversation as it allowed the students to see why some of the world's problems have not been solved due to issues that they have never made connections with before. The conversation was enjoyable and worth the period that we spent on it for sure and I would do it again. 

Here is the slide show that was used: https://drive.google.com/open?id=1QVrhWcdUsVrspBD0OUMe9Q_1XdaqrlEZBpfen01sp6o 

To get ready for their upcoming structures unit, they are doing a homework assignment that will let them build and also collapse different structures. It is called Catastrophe and the developers have done a wonderful job of applying the laws of physics to the designs. My students have already started using the terms tension and compression without having learned it in class. 

The assignment they are working on is: https://drive.google.com/open?id=1N3Q3ELicDaoT5lAhIY5IwIIWHlU4slCXvFPrDrjK3m4

Next week is the launch of the structures unit and they will be working with another class. Lots of hands on building and exploration to do as we go into the end of the year!

Math: Finding Area

I was able to participate in a Lesson Study done by the Junior School teachers this week which focused on the development of understanding of area. With a focus on conservation and additivity when finding the area of irregular shapes. During the conversation, the idea that students forget these concepts as they begin to learn the formulas of shapes. With this in mind, I wanted to teach the area of a triangle by starting back at the start of understanding area. 

To do this, I told the students that they would be erasing their brains of all past knowledge and we would be progressing together. We talked about how measurements were originally taken by using body parts, but that different sized people would have different sized hands/feet. Then standardized units of measure were created so that everyone knew what was being talked about. We then explored why they were called units squared. For some students they had not thought of this since their younger years, and only now were able to grasp the concept. It was a short review, but important to understand that it is the total number of square units. 

We when looked at the area of a rectangle and saw how it is an array. You have for example, 10 groups of 6 boxes in the rectangle, so we can use that to do it faster. Students they made the connection that this would relate to the base x height formula they had learned. 

Finally we did a paper cutting exploration to show how two triangles make one rectangle. They understood that if we know how to find the area of a rectangle, than cutting up a triangle so that it fits into a rectangle allows us to use our array understanding to find the area. This was then connected with the formula that we then developed together. 

Once all students felt confident with this task, they were put into groups with their own shape that they needed to create a similar slide show showing how to change the shape back into a rectangle and then use this to develop a formula. Groups were arranged on purpose by processing speed so that they could think through the problem together and no one would be left behind. This was because the goal of the lesson was for them to think deeply about how conservation of area can occur. 

Now, they are creating their slide shows and will present to others in small groups next Wednesday. They will have the slides shared as their own "notes" to refer back on for their homework. This will be a good launch for their individual solving of irregular shapes as well. 

Slide show used: https://drive.google.com/open?id=1AZP9F2b9kqAH7oDlLUaTZ7ARx8j5nGHvK8Xe8yv45L8 

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.