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 

Making Math More Like Science

This is my second time teaching Grade 7 Science, and once again I am blown away with the simplicity of the material but how it "blows our brains" as my students explain. As a class we have spent days talking about The Particle Theory. These 5 postulates have caused us to question everything from why does it take longer to make a cold tea than hot to the fact that we are made of the same stuff of dinosaurs. What would seem like 5 simple rules has caused all students in the class to question, explore and expand their thinking.

Having taught math for the majority of my career, I am used to parents and students feeling that the same enrichment and challenge only comes from the exploration of material beyond the curriculum. We have to leave the material of Grade 7 so that a student can become equally engrossed and inquisitive about the material as their peers. However, from observing my Science students I challenge this full heartedly. As we explore the same concepts of Science, each student is driving their thinking forward from their own questions. No new material is being presented to them, but they are using their current knowledge to ask questions and see how they can apply this thinking to the world around them. The difference I see from this and a math class is that math does not encourage student driven questions. There is a sense that an order must occur in the learning of material and that the teacher should guide it. I want to put this thinking in the garbage this year and make it so that math and science are structured in the same manner; the presentation of foundational concepts and the time for students to explore and make connections on their own.

This will be a challenge. I know from personal experience that students are taught to ask questions in science since these exhibit wonder and excitement about the material. Asking questions in math class could have a very different reaction from peers and the teacher. It could indicate an inability to grasp the concept, not able to focus on the prescribed task or "not what we are thinking of at the moment". Students, and parents, are trained to learn, practice and then perform rather than the science of learn, question, explore and perform.

To do this I have made my students first math project to be one where they need to ask their own question where proportional reasoning is the base. How far they push and go with the ideas is up to them. My last blog post goes into more details of the project. However, over this past week I am more convinced that a great exploration and student driven activities are necessary in math classes to develop the math students my high school coworkers are hoping to have come their way. They are wanting to have the thinkers, and not just the calculators.

The Time for Inquiry - Where should it be in the learning process of a math classroom

Scrolling through my google reader I saw a quick, short post from David Wees asking how do we encourage more questions and the following image:



I am a teacher that believes in inquiry learning and also the power of a student driven project or product, but usually these occur as a summary or summative of learning. However, after my recent experiment of completing the Barbie Bungee activity at the start of my unit and in a non-worksheet format, I have seen and appreciate the power of exploring ideas and concepts through the unknown. This activity had my students exploring the ideas of linear equations without knowing what a linear equation was.

They asked brilliant questions including:

• Does the height of the Barbie matter?


• Should I find out how much she weighs?


• Are all the elastics pre-stretched? How can I make sure that they are all pre-stretched the same amount?


• Can I cut my elastics up into smaller parts?

Now, only 9 classes after that activity where students didn't know what they were looking for, they are now appear to be automatically programed into trying to find a constant rate of change and a starting point (y=mx+b) in each of the problems we look at. As they have gained a greater understanding of their topic they are not asking the insightful questions from before but instead are wondering why I didn't leave the space on their table of values to include the zero starting value, or if they need to capitalize their variables in an equation. I don't know if I should be celebrating or concerned.

I also just finished being apart of a webinar by Roger Schank, author of Teaching Minds who shared his view of how he feels that Algebra's sole purpose is as a method to easily test students, and make benchmarks for university entrance exams. He feels that the multiple steps and multiple areas to have an error do not benefit a student, but only the adults and institutions who require an easy way to grade and place students by how they solve for a variable or express a pattern in the appropriate standard formula.

I know that my students participating in Barbie Bungee activity didn't need to know the point-slope form or y-intercept form in order create a table, graph the data and find a pattern but they did it anyways. I also know that they used their algebra skills to create a formula or relationship to determine how many elastics they needed to use, all with levels of success. All of this great learning happened, but was followed up with 9 in class days to ensure that they understood what slope meant, how to calculate it in the 3 ways it could be presented in a standard question and how it connects to a graph of a line.

At the end of the day, I am left questioning... do my students know more now that they have been provided the vocabulary and structure to work with linear relations, or have I put a stop on their creative application of the concepts. As a class we will be doing more STEM-like activities and I will be looking to see what my students go to first as their method to solve these new challenges. Will they begin by breaking down the big problem into smaller ones? Will they play with the materials and ask questions to determine if they can find any pattern? Or will they think in what way a linear pattern could be created and what the start and change values should be. Will their questioning level increase or have they reached a level of understanding where they have no desire to explore and think through the problems thoroughly.

 

Freestyle Barbie Bungee - No Steps Required

After completing day 1 of the infamous Barbie Bungee activity I look on my twitter to see the the following tweet from @ddmeyer:

How many different ways can a popular lesson (Barbie Bungee) go wrong? Extremely provocative post from @mathhombre. bit.ly/ULssnB

— Dan Meyer (@ddmeyer) February 2, 2013

Even though it is only Day 1 of the experience of our 3 day activity, I want to respond to @mathhombre and share what is happening in my Grade 8 class.

Goal:
In 3 math classes, you and your bungee company will take your first customer to the drop point, letting them fall over the side and experiencing the most exhilarating moment of their plastic doll life. Your job is to determine the right length of the bungee cord that will create the best fall. Good Luck!

With only the above goal, my class has started their 3 day (no worksheet) activity to get their Barbie closest to the floor. The students were given only two things to guide them. One is the outline of what is happening and the other is a graphic organizer to help them break down their large question into smaller, simpler ones that they are able to answer. Divided into groups of 3 or 4 with a barbie, ruler, meter stick and 10 rubber bands they have a day to create a plan that will help them determine how many rubber bands they will need to create the best fall for their barbie. As explained in the outline, they have no idea what that height is until the drop day and they aren't allowed to drop their barbie if they don't have a logical and well thought out explanation that includes data to support their ideas. To help those that may get stuck I created scaffolding questions that could be given depending where they were being challenged and needing support. I also created a worksheet just in case groups became too lost and frustrated that the overall goal was not being met.

The three days are broken down as follows:

Day 1:

• Collect your materials (barbie, 10 elastics, ruler, metre stick)


• Create a plan in how your group will determine the final number of rubber bands for the drop day.


• Ensure that you are thinking of how to collect DATA as evidence for your proposal.

Day 2:

• Write a proposal for your company answering the question of How do you know the approximate number of rubber bands needed to drop the barbie from a height.


• The proposal will explain why you know the number of rubber bands based on the data you have collected in the previous class.


• When given the test height, use your proposal to determine the number of rubber bands. Make the cord and test it in the secret location. You are not allowed to guess and check for the test drop day.

Day 3:

Drop Day

My students will test their ideas and are required to write a proposal on the test drop day, alter their plans accordingly and drop them next Wednesday. After this we will be sharing how each group created their plan and explain their method with the class. My hope is that each group will write out their plans/formulas/calculations/tables on chart paper and post them around the room. As a class they will do a gallery walk to find similarities and differences between their own methods and others. We will also explore which methods worked better than others and ask why that was.

From this I plan on launching into the linear relations unit by associating vocabulary with their methods . For example:

• Some students were creating a table of values but didn't know that is what it was called or various ways to create one.


• Another group was determining how much further the Barbie would drop with each added rubber band but didn't know that this is the rate of change.


• Other groups were debating which central tendency (mean,median,mode) would be the most valuable one to use in the situation for their test trials (which they determined they needed).

The students bring with them and understanding of percentages, finding patterns and creating an equation to represent a pattern but all within structured standard questions. I am hoping (fingers crossed) that this unstructured activity will give them a starting point to explore and identify what is important in a problem, how to measure it and if there is anyway that they can use their results to make a prediction. We also will be exploring what makes a prediction valid and how to question if it will work in various situations.

I have no idea if any of the groups will save their Barbie's brains or allow them to have a great fall, but already with the lack of structure of history of working through similar problems they automatically directed themselves to the steps and processes a worksheet would have done. I just feel that a structured worksheet directions would not have made them ask the following questions which were heard today:

• Should we measure the weight of the Barbie? I know that in Science we have to do that thing with gravity and weight.


• If there are 6 centimeters from the Barbie's head to the floor with one meter, will it double when we double the height and number of rubber bands or will it stay the same?


• Are all the elastics the same size and thickness and pre-stretched the same amount like my jeans?

I wasn't planning on posting until the end of the process, but after @mathhombre's comments, I wanted to share that we are testing this very idea over the next few days.

I hope that you will check in and see how things progress next week. I will also be thinking about where to take the group next and posting their created proposals to show the diversity of what they were able to come up with on their own and without coaching.