Day 59 – Cookie Sharing

Math 8 – Today’s class was working on sharing a cookie problem. It turned out to be a fantastic class, perhaps the best we’ve had this year. The problem had a low entry with lots of ways to solve it. We were able to walk around the room and see the different solutions.

The above solution is one of the most intuitive.  Students realize that 1/2 the people get 1/2 the cookies (21) and since they each share this equally, they each get 10.5.  This continues for the next two people.

Below is the most common solution.  Students would turn this into a rate question as students naturally understand rates with little to no instruction. They find that 3.5 cookies cost $1 and then calculate how many cookies each person can have.

The rate thing is pretty interesting. Why are students so comfortable with rates? I think it’s because rates are usually very concrete. They explain the relationship between tangible things. Cookies per unit dollar. Kilometers per unit hour. Miles per unit gallon.

Next we had the fraction solution. This one is really neat because in our discussion the students realize that they are once again dealing with percents. 7/12 is 7 parts of the whole.

Finally I would end our tour with the primary goal for the lesson: equivalent ratios.  This wasn’t the most common solution, but every class did have it.

Once you get to the equivalent ratio solution, you can see that it is perhaps the cleanest to exhibit and explain. I didn’t see this at the time, and I may come back to it and highlight this property.

The class was full of Flow, engaged students and learning.  So awesome.

Now here is my dirty secret about the day. Many of my students were on field trips so the class size was in the range of 18 kids.  While I can totally manage a class of 30, wow does the party change when the numbers drop.  Behaviour problems were almost non-existent, and the level of dialogue was amazing.

If someone tells you that class size doesn’t matter, maybe they’re right… Unless they’re referring to a class where students are engaged in collaborative work that needs to be discussed and shared, in which case they will be dead wrong.

Day 58 – Force Diagrams

Physics 11 – Students got to practice drawing force diagrams today. They’re were lots of good questions, usually ones that I want to deal with later. They were invoking Newton’s Third Law, friction, and all sorts of things.

The above graphic is a good example of why we label our forces. Students want to draw a force pushing the skater to the right. However, no one can think of where this force comes from. What is its agent? The closest we get is skater on skater. I found this to be hard to explain. The best I could come up with was a thought experiment where a person imagines they are floating in space. Can they imagine themselves moving around and directing their motion? Most people see the need to push off of something. That something would be the agent. In the above case, since we can’t name the agent, it’s probably not a force.

Day 57 – Working on the 3D Printer

Math 8 – I kept working in the Printrbot Simple 3D printers today. It’s been hard finding the time to get them working. I had to replace one y-axis that was bent. Once I had done this, I realized that the extruder fan on the other printer had also been broken. It is difficult to find time to work on them, with all of the other tasks I have to do.

In the meantime, I have modeled a Greenland paddle in Onshape. The model has 4 variables that the students will have to measure and scale, in order to have a scaled model of a paddle. From there, the students will print out their paddle.

Day 56 – Improving the Timer

Engineering Physics – This cart launcher timer project has been really good. All students are learning a ton from it, working hard, and are engaged. Some students are really taking off with it.

One group had finished the basic task early, so they added a machine learning algorithm to their timer. They added a switch that allows the user to pass the flag/hand/obstacle over the photoresistor. From this pass they do an analogRead and determine how much light is being picked up by the photoresistor. They then use this for the rest of their timer code.

Day 55 – Solving for Variables

Math 8 – An issue that comes up periodically in math 8 is the need for students to reverse engineer a math statement like “14% of some number is 32.” For some kids they can work backwards using their number sense. Other kids can be helped along by showing them that an easier statement to solve would be “10% of some number is 30” and realize that this is a division question. Lots of other kids simply don’t know what to do.

So today I introduced the idea of “solving for a variable.” We had previously covered some properties such as the multiplicative property of equality, so we had the tools to do this bit of algebra.  My main intent was to show that such an equation can be solved using tools that we know and understand, and that tricks aren’t needed.

Of course next class I saw several kids using some sort of cross multiply strategy…

Day 54 – Whiteboarding Hooke’s Law

Physics 11 – Students presented their results on whiteboards today. In one class it is like pulling teeth to get students to talk in a whiteboard meeting. It is incredibly frustrating. I spoke with a few students after class, and they thought that maybe 1/2 the class was actually able to answer or question things that were said during the meeting, but chose not to.

Students did a good job of determining that the slope of the line on a Fs vs x graph is the stiffness of the spring, so that was pretty cool. Many groups didn’t think to find the equation of the line which was another beat my head against the wall moment. I really would like to get a modeling workshop here in Vancouver so I can improve on this aspect in my classes. Students are slowly coming around to the idea of modeling physics, but other details like having the kids take over discussions in class, along with timing on topics, continue to elude me.

Day 53 – Student Teacher

Math 8 – Today I had my student teacher preparing and giving the lessons for math.  She did a pretty job, and seems pretty comfortable in front of the class.

I really notice subtle things in language and questioning that are important.  For example, if the class is asked something like, ” did everyone get it?” with a thumbs up, sideways or down, it’s important to acknowledge students that have their thumb down. You can’t just move on because most of the thumbs are up.  Well, maybe it’s best to move on but you need to let the kids that need help know that you will give them help.

Day 52 – Hooke’s Law Lab

Physics 11 – Students conducted a lab on Hooke’s Law today.  They were prompted to model the relationship between an external force and how it affects a spring it is acting on.  Data collection went pretty well and I strongly suggested that students use Excel to produce their graphs. Several groups opted to hand graph their data, which was very surprising to me. However, after pointing out a few things that they could do to improve their graphs, most of these groups eventually realized that re-doing it in Excel would be a lot of faster and probably more accurate.

Day 51 – Discounts

Math 8 – Today the class worked on the above problem. Lots of groups had problems with it, and couldn’t move off the idea that 30% + 45% + 25% = 100%. They couldn’t think of any other thing to do with the numbers.

There was also some nasty misconceptions with adding fractions! Lots of kids did 45/100 + 25/100 + 30/100 = 100/300.

By the third class of math 8 I finally found out what I had to do as a teacher to get the students on the right track. First, I had to make sure that the problem doesn’t turn into a money issue. If students equate the discount to saving money, there will be trouble. Keep the problem centered on saving gas, because everyone agrees that you can’t have a car drive without using fuel. Secondly, I had to really listen carefully to what the students say and really jump in when they say something like “45% of 70”. A ha! What operation is associated with the word “of”? That’s right, multiplication, not addition…

The neat thing about this problem, after I’ve done the good things needed to pull it off, is how engaged the students get. They can taste how close they are to a solution and want to solve it.  It was Friday afternoon, the dismissal bell had gone, and I had several kids sticking around to finish their work.

Day 50 – Misconceptions of Gravity

Physics 11 – Today was our Misconceptions in Gravity class. We did a lot of voting and discussion centered on three themes: what things affect gravity?, do small things also have a force of gravity?, and do interacting objects have an equal force of gravity acting on each other?.

There’s too much on these subject to list here, but the above diagram is one of the more convincing arguments. Students see that as they add additional particles to the diagram (X, Y, Z, etc), each new particle has a force of gravity acting between it and A. The extension of this is that large objects, or objects with millions or billions of particles, will have the same number of force arrows as does the small object (A).

Some students were a bit too “white flag-ish” for this class.  It’s so easy to tune out and say to yourself “I don’t know.”  Those students can make this a difficult lesson to teach. But other students really like it. It’s interesting and challenging.  It’s solving a mystery or a puzzle.